tag:blogger.com,1999:blog-53033074821589225652014-08-15T07:56:01.694-07:00Math Mama Writes...Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger499125tag:blogger.com,1999:blog-5303307482158922565.post-49694163771275792802014-08-03T12:42:00.002-07:002014-08-06T07:24:17.139-07:00Math Mama's Gazette - Issue Number OneI am creating a two-page newsletter, aimed at community college math students, which I'll be handing out to students, both at our Math Jam program these two weeks before the fall semester, and at the math lab during the semester.<br /><br />I'm happy to share it with others. I hope to have one issue for each week of the fall semester, 15 to 17 issues. If you use it, you'll have to change the bits that refer to my college. And please include this line: "Math Mama is Sue VanHattum, who blogs at mathmamawrites.blogspot.com." My copy is two-column. You can see it <a href="https://drive.google.com/file/d/0B4Lou9CsLnQxNmtsdkNDalJGdG8/edit?usp=sharing" target="_blank">here</a>. (Let me know if that link isn't enough to get you an editable copy.)<br /><br />Like it? Please let me know.<br /><br /><br /><br /><br /><br /><br /><style><!-- /* Font Definitions */ @font-face {font-family:Times; panose-1:2 0 5 0 0 0 0 0 0 0; mso-font-charset:0; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:3 0 0 0 1 0;} @font-face {font-family:Times; panose-1:2 0 5 0 0 0 0 0 0 0; mso-font-charset:0; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:3 0 0 0 1 0;} @font-face {font-family:"Engravers MT"; panose-1:2 9 7 7 8 5 5 2 3 4; mso-font-charset:0; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:3 0 0 0 1 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} p.MsoHeader, li.MsoHeader, div.MsoHeader {mso-style-unhide:no; mso-style-link:"Header Char"; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; tab-stops:center 3.0in right 6.0in; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} p.MsoTitle, li.MsoTitle, div.MsoTitle {mso-style-priority:10; mso-style-unhide:no; mso-style-qformat:yes; mso-style-link:"Title Char"; mso-style-next:Normal; margin:0in; margin-bottom:.0001pt; text-align:center; mso-pagination:widow-orphan; font-size:24.0pt; mso-bidi-font-size:12.0pt; font-family:"Engravers MT"; mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"; font-weight:bold; mso-bidi-font-weight:normal;} span.HeaderChar {mso-style-name:"Header Char"; mso-style-unhide:no; mso-style-locked:yes; mso-style-link:Header; mso-ansi-font-size:12.0pt; mso-bidi-font-size:12.0pt;} span.TitleChar {mso-style-name:"Title Char"; mso-style-priority:10; mso-style-unhide:no; mso-style-locked:yes; mso-style-link:Title; mso-ansi-font-size:24.0pt; mso-bidi-font-size:12.0pt; font-family:"Engravers MT"; mso-ascii-font-family:"Engravers MT"; mso-hansi-font-family:"Engravers MT"; font-weight:bold; mso-bidi-font-weight:normal;} .MsoChpDefault {mso-style-type:export-only; mso-default-props:yes; font-size:10.0pt; mso-ansi-font-size:10.0pt; mso-bidi-font-size:10.0pt;} @page WordSection1 {size:8.5in 11.0in; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:.5in; mso-footer-margin:.5in; mso-paper-source:0;} div.WordSection1 {page:WordSection1;} @page WordSection2 {size:8.5in 11.0in; margin:.8in .8in .8in 58.5pt; mso-header-margin:.5in; mso-footer-margin:.5in; mso-columns:2 even .5in; mso-paper-source:0;} div.WordSection2 {page:WordSection2;} </style> --> <div class="WordSection1"><div class="MsoTitle">Math Mama’s Gazette</div><div style="border-bottom: solid windowtext 1.5pt; border: none; mso-element: para-border-div; padding: 0in 0in 1.0pt 0in;"><div align="center" class="MsoNormal" style="border: none; mso-border-bottom-alt: solid windowtext 1.5pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: center;"><span style="font-family: "Engravers MT";">Issue Number 1, August 4, 2014</span></div></div><div align="center" class="MsoNormal" style="text-align: center;"><br /></div><div class="MsoNormal" style="text-align: justify;"><br /></div></div><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="mso-break-type: section-break; page-break-before: auto;" /></span></b> <br /><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 18.0pt; mso-bidi-font-size: 12.0pt;">Math</span>isn’t news, why a newspaper? </b></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;">Well, there’s lots about math that’s news to most folks, and a gazette sounded fun. I’m all about fun, so I decided to go for it. </div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;">This first issue and the next few will have lots of ideas (some surprising) about how people learn math. If you’ve never enjoyed math, or never done very well with it, try changing your perspective with some of these tips. You might like the results. </div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;">Every issue will include a not-so-traditional <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">advice</i></b> column, a <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">puzzle</i></b>, and a <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">comic</i></b>, newspaper favorites. There will also be <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">links</i></b>to cool math stuff online.</div><div style="border-bottom: solid windowtext 1.5pt; border: none; mso-element: para-border-div; padding: 0in 0in 1.0pt 0in;"><div class="MsoNormal" style="border: none; mso-border-bottom-alt: solid windowtext 1.5pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;"><br /></div></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="margin-left: 49.5pt; text-align: justify; text-indent: -49.5pt;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 18.0pt; mso-bidi-font-size: 12.0pt;">A Few</span> Math Myths </b></div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;">Myth #1:</b> Learning math is learning how to follow procedures - there's a lot to memorize.</div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;">Myth #2:</b> Some people have a 'math mind' and some don't. (A more unfortunate variant of this is: Men are better at math than women.)</div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;">Myth #3:</b> Math requires simple logic; intuition and creativity have no place. </div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;">Myth #4:</b> There is one right way to do math problems.</div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;">Myth #5:</b> I don’t need to know math - I’ve got my calculator and the Internet.</div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;">Myth #6:</b> Mathematicians do problems quickly, in their heads, by working alone until the problem is solved.</div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;">In this issue, we’ll address myth number one. (Keep coming back for more myth-busting.)</div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 18.0pt; mso-bidi-font-size: 12.0pt;">What is</span>math? Is it procedures?</b></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;">Most people think it’s adding, subtracting, multiplying, and dividing; knowing your times tables; knowing how to divide fractions; knowing how to follow the rules to find the answer. <span style="mso-spacerun: yes;"> </span>These bits are one tiny corner of the world of math. </div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;">Math is seeing patterns, solving puzzles, using logic, finding ways to connect disparate ideas, and so much more. People who do math play with infinity, shapes, map coloring, tiling, and probability; they analyze how things change over time, or how one particular change will affect a whole system. </div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;">Math is about concepts, connections, patterns. It can be a game, a language, an art form. Everything is connected, often in surprising and beautiful ways.</div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 18.0pt; mso-bidi-font-size: 12.0pt;">What</span> do you memorize?</b></div><div style="border-bottom: solid windowtext 1.5pt; border: none; mso-element: para-border-div; padding: 0in 0in 1.0pt 0in;"><div class="MsoNormal" style="border: none; mso-border-bottom-alt: solid windowtext 1.5pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify; text-indent: .25in;">I went into math because I have a bad memory. If I had trusted my memory to be up to it, I think I would have gone into science. </div><div align="right" class="MsoNormal" style="border: none; mso-border-bottom-alt: solid windowtext 1.5pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: right;"><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt;">[continued on back]</span></div><div class="MsoNormal" style="border: none; mso-border-bottom-alt: solid windowtext 1.5pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;"><br /></div></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 18.0pt; mso-bidi-font-size: 12.0pt;">Puzzle: </span>Math Without Words</b> </div><div class="MsoNormal" style="text-align: justify;">by James Tanton (jamestanton.com)</div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-J_ZfajLLl2M/U96P-ZMqsFI/AAAAAAAABZg/x79TGTxqCLU/s1600/jt+mwow%231.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-J_ZfajLLl2M/U96P-ZMqsFI/AAAAAAAABZg/x79TGTxqCLU/s1600/jt+mwow%231.png" height="320" width="258" /></a></div><div align="center" class="MsoNormal" style="text-align: center;"><br /></div><div align="center" class="MsoNormal" style="text-align: center;"><span style="mso-no-proof: yes;"></span></div><span style="font-family: "Times New Roman"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="mso-column-break-before: always;" /></span> <br /><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-size: 18.0pt; mso-bidi-font-size: 12.0pt;">Math Mama’s</span> Advice</i></b></div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">Dear Math Mama</span></b><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">, I am a math tutor at a small Los Angeles community college. The students I have who need the most help are older women who are back in college, or here for the first time, who have had unpleasant math experiences in their youth. Do you have any ideas for us?</span></div><div align="right" class="MsoNormal" style="text-align: right;"><span style="font-family: Times; font-size: 8.0pt; mso-bidi-font-size: 10.0pt;">- </span><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">Paula</span></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">Dear Paula,</span></b><span style="font-family: Times; mso-bidi-font-size: 10.0pt;"> I had quite a few older women in one class last fall, and I had them in mind as I thought about your question. </span></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">First, I think it's important to address their fears directly. I recommend <i style="mso-bidi-font-style: normal;">Managing the Mean Math Blues</i>, by Cheryl Ooten, or <i style="mso-bidi-font-style: normal;">Overcoming Math Anxiety</i>, by Sheila Tobias. You can get used copies online for $3 or $4. My favorite site for that is betterworldbooks.com.</span></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">I also recommend an audio track I created, called Math Relax. It's a guided meditation to help people overcome math anxiety. It works best if the student listens to it every night for a few weeks. (Go to mathmamawrites.blogspot. com, and look on the right-hand side for the Math Relax audio track. It’s free.)</span></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">I think helping them lead from their strengths might be even more important, though. I try to help each class become a community. Some groups take off with it, and others don't. The older students know what they want, and are ready to go with it. </span></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">This particular class became an amazing community. Most days they came in over an hour early (we were<i style="mso-bidi-font-style: normal;"> <b style="mso-bidi-font-weight: normal;">so</b></i>lucky the classroom was empty before their class!) and studied together. One of the students led the group, and even though I like getting questions in class, they felt freer to ask questions in their group. They were each determined to ‘get it’, and kept at it until they did.</span></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">I asked my students what advice I might offer you, and they said that working together was key. They said keeping each other going when it got tough was the most important thing they did for each other.</span></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">If you tutor one-on-one, you could still help this dynamic along by introducing the students to each other. Have you heard that “the one doing the most work is the one doing the most learning”? That would mean that you learn more from tutoring than they do - unless you can get them helping each other.</span></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">Perhaps if you recommend some of your favorite online resources for them to check out, they'll discover things that excite them. Many of my students really like watching math videos. Check out vihart.org, khanacademy.org, mathtv.com, or (my favorite) jamestanton.com.</span><span style="font-family: Times; font-size: 8.0pt; mso-bidi-font-size: 10.0pt;"></span></div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">Good luck, and thanks for writing.</span></div><div align="right" class="MsoNormal" style="text-align: right;"><span style="font-family: Times; mso-bidi-font-size: 10.0pt;">- Math Mama</span></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;">Have a question for <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">Math Mama</i></b>? Deliver it to Sue VanHattum, in AA-210, and Math Mama will answer it in the next issue!</div><div style="border-bottom: solid windowtext 1.5pt; border: none; mso-element: para-border-div; padding: 0in 0in 1.0pt 0in;"><div class="MsoNormal" style="border: none; mso-border-bottom-alt: solid windowtext 1.5pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;"><br /></div></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="MsoNormal" style="text-align: justify;"><b style="mso-bidi-font-weight: normal;">What do you memorize?<span style="mso-spacerun: yes;"> </span></b><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt;">[continued from front]</span></div><div class="MsoNormal" style="text-align: justify;">But I figured there was no way I could memorize all those bones and muscles, chemical reactions, and so on.<span style="mso-spacerun: yes;"> </span>So I stuck with math.</div><div class="MsoNormal" style="text-align: justify; text-indent: .25in;">You need to know your multiplication facts to be able to factor numbers and polynomials smoothly. (If you don’t know them, there are easy ways to commit them to memory now. Professor VanHattum has a handout on this.) You’ll want to know that the x-axis is horizontal, and the y-axis is vertical, for algebra. And in trigonometry you’ll need to memorize a few definitions. Most everything else is more about understanding the connections than about memorizing. </div><div style="border-bottom: solid windowtext 1.5pt; border: none; mso-element: para-border-div; padding: 0in 0in 1.0pt 0in;"><div class="MsoNormal" style="border: none; mso-border-bottom-alt: solid windowtext 1.5pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;"><br /></div></div><div class="MsoNormal" style="text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-EIXW1QUDP0Q/U96QFRRk5SI/AAAAAAAABZo/NXpLmC701s4/s1600/cooking+bacon+graph.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-EIXW1QUDP0Q/U96QFRRk5SI/AAAAAAAABZo/NXpLmC701s4/s1600/cooking+bacon+graph.png" height="276" width="320" /></a></div><br /><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-size: 18.0pt; mso-bidi-font-size: 12.0pt; mso-no-proof: yes;"></span><span style="font-size: 18.0pt; mso-bidi-font-size: 12.0pt;"></span></div><div align="right" class="MsoNormal" style="text-align: right;"><span style="font-size: 10.0pt; mso-bidi-font-size: 12.0pt;">from <a href="http://xkcd.com/418/">xkcd.com</a></span></div>Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com2tag:blogger.com,1999:blog-5303307482158922565.post-82220453600410023682014-08-01T12:51:00.000-07:002014-08-01T12:51:37.552-07:00A Sloppy Computerized TestMy college is running a program called Math Jam for two weeks before the semester begins, and it sounds fabulous. I'll be teaching it for the first time, starting on Monday. We use MyMathLab, and our director said students in prior years (who loved Math Jam) found the program helpful. So I will use it with my students next week, along with lots of other, more interesting mathematical explorations.<br /><br />I checked out the first test just now, and got below 90% in a Beginning Algebra, or perhaps pre-algebra, topic. Let's look at why. I had 3 questions at least partly wrong out of 22.<br /><br /><b><span style="font-size: large;">#1</span></b><br />On an equilateral triangle, they asked for the height. I found it, rounded to tenths as requested, and got that right. Then they wanted me to find the area using the rounded answer. I did not do that. I did what I teach my students to do: Use the exact answer in your calculations, and only round at the end. My answer did not match theirs.<br /><br />I can't get back to their problem now, so I will make one that's similar. Suppose the sides are length 6in. Then the height is 6*√3, or 10.3923.... If they are asking us to round to hundredths, we'd report 10.39in for the height. Now they want area, and they ask me to use my 10.39 as the height. But the proper area (in sq.in.) is 62.3538... and by their method we'd get 62.34 sq.in. I put the proper answer of 10.35 sq.in. and got it wrong.<br /><br /><br /><span style="font-size: large;"><b>#2</b></span><br />I got 0.55 as an answer, which they asked me to round to tenths. Both 0.5 and 0.6 should be right, as 0.55 is exactly in the middle of these. But only 0.6 counts as right on this test, and I had (randomly) chosen 0.5.<br /><br /><br /><span style="font-size: large;"><b>#3</b></span><br />This one is the most interesting. They gave the diagram below, which looks a bit badly done to me. The right angle mark toward the left does not seem to coincide with the line below it, making it seem like the angle isn't really a right angle. Not a big problem, I can still assume a right angle there. But they have only marked two right angles. I do not believe I have enough information to determine the area of this figure unless I know more about the angles. I believe the one unmarked line segment has an unknown length. I think they meant to show two attached parallelograms (or a parallelogram attached to a rectangle), but that's not a given from this diagram.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-UAwsBGd2s0A/U9vs4XrjIPI/AAAAAAAABZQ/4aA8ZlrxZLg/s1600/geometry+and+Measure+R1-A+weird+question.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-UAwsBGd2s0A/U9vs4XrjIPI/AAAAAAAABZQ/4aA8ZlrxZLg/s1600/geometry+and+Measure+R1-A+weird+question.png" /></a></div><br />What do you think?<br /><br />I think they need to learn more about rounding, and more about what one can read from a figure. Hmm... I wonder if all their tests will be this sloppy. <br /><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com10tag:blogger.com,1999:blog-5303307482158922565.post-39420194727036924582014-07-19T14:56:00.001-07:002014-07-19T14:56:39.993-07:00Playing With Math: Crowd-funding Campaign Has 9 Hours Left...... and we need almost $1000 to meet our stretch goal. I am hoping we estimated a little bit high so that the Spanish translation can still be done quickly. It would be great if Vi Hart saw my message on her Facebook page, and decided to check us out. But it doesn't look like that's going to happen.<br /><br />We've raised $10,569 so far, and may raise a few hundred more by the end of the day. We surpassed our original goal by $3000. And more importantly, contributors have reserved almost 300 copies of the book. We are eager to know what they all think once they've had a chance to read it.<br /><br />If you haven't contributed yet, you still have a few hours left. <a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank">$25 will reserve you a copy of Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers</a>. I think you'll be very happy to have this book in your home.<br /><br /><br /><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com2tag:blogger.com,1999:blog-5303307482158922565.post-5924775416674767482014-07-16T22:26:00.001-07:002014-07-16T22:26:40.482-07:00Playing With Math: Crowd-funding Campaign Ends on SaturdayI hope to post soon about my lovely adventures in math at the <a href="http://themathcircle.org/" target="_blank">Math Circle Teacher Training Institute</a>. But that post will have to wait until <a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank">the crowd-funding campaign for <i>Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers</i></a> is over. We reached our original goal of $7500 on Sunday, July 6, after only 17 days, giving us the funds we need to publish this fabulous book. Our stretch goal is $4000 more, for the Spanish translation. We are about halfway there, but we only have 3 days left. Can we make it?<br /><br />If you haven't reserved your copy yet, please <a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank">do it now</a>! <br /><br />While I was visiting family and friends in Michigan, I spent some time this past weekend with my friend Chris (who has helped with the book from the very beginning). While our kids played in the pool, we discussed index entries, and which terms might need cross-referencing. For example, Jamylle Carter had students build their own <i>inclinometers</i>, and wrote about it in her chapter on the Oakland Math Circle. If you had read about them, forgotten the word, and wanted to re-read her description a year later, you might think of them as angle-measuring devices, and look up angle. So we’ll cross-reference her inclinometer description under <i>angles, measurement</i>.<br /><br />Here's a picture of an inclinometer. (The boy was drawn with a photo of my son as the model. He's older now.)<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-wBZfHToR1DU/U8dddjex18I/AAAAAAAABXk/zrdNauBpwnw/s1600/2+boy+w+inclinometer+lp+gv.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-wBZfHToR1DU/U8dddjex18I/AAAAAAAABXk/zrdNauBpwnw/s1600/2+boy+w+inclinometer+lp+gv.jpg" height="320" width="315" /></a></div><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank"><br /></a></div><div class="separator" style="clear: both; text-align: left;"><a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank">Don't forget to get your copy of this fabulous book.</a></div>Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-56946150018285384702014-07-05T18:00:00.000-07:002014-07-05T18:00:01.069-07:00How I'm Playing With Math Today: GeometryIn between sessions of trying to prep the manuscript for page layout, I've been playing with <a href="http://euclidthegame.com/" target="_blank">Euclid: The Game</a>. I am loving it. It may be just the same constructions kids learn to do in geometry class. But geometry is my weakness in math, and I love trying to figure out how to do these constructions. Exactly a year ago, I posted about <a href="http://mathmamawrites.blogspot.com/2013/07/euclidean-construction-science-vs-magic.html" target="_blank">another construction game</a>. The two are different enough that you might enjoy doing both. I'd love to hear what you think of them.<br /><br /><br />Here are a few links to other geometry construction tasks:<br /><ul><li><a href="http://mr-stadel.blogspot.com/2014/06/fun-with-name-tent.html" target="_blank">Andrew Stadel's Name Tent Challenge</a></li><li><a href="http://www.dr-mikes-math-games-for-kids.com/blog/2014/06/heptagons-and-the-politics-of-19th-century-france/" target="_blank">Constructing a Heptagon (Is it possible?)</a></li><li><a href="http://letsplaymath.net/2007/06/05/puzzle-patty-paper-trisection/" target="_blank">Trisecting the angle</a> (impossible with Euclidean axioms, possible with origami axioms)</li></ul><br />More geometry links:<br /><ul><li>James Tanton worked with Great Courses on <a href="http://www.thegreatcourses.com/tgc/courses/course_detail.aspx?cid=1033" target="_blank">a geometry video series</a>. Cool!</li><li><a href="http://untilnextstop.blogspot.com/2014/06/one-resource-weekday-1-geometry-tasks.html" target="_blank">Geometry Tasks</a></li></ul><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com2tag:blogger.com,1999:blog-5303307482158922565.post-46334026558424053662014-07-04T07:38:00.000-07:002014-07-04T07:38:56.361-07:00Playing With Math: Almost to the Finish Line!<b>Campaign Update</b><br />I would love to be able to see what's causing our good days. I have no idea what made July 1<sup>st</sup> our best day for number of contributors since the beginning of the campaign, with 23 contributors, including ... a $1000 contribution from Nancy Blachman, founder of the <a href="http://juliarobinsonmathfestival.org/" target="_blank">Julia Robinson Mathematics Festival</a>. Thank you, Nancy! We are now at 93% of our goal, with $6960 coming in from 212 contributors. Our thanks go out to each one of the 212. Every contribution makes a difference.<br /><br />Yesterday was our lowest number of contributors yet, just 3. And today may be low, too, with everyone out having fun on the 4<sup>th</sup>. So if you know someone who you think would like<i> Playing With Math</i>, please let them know about it.<br /><br /><br /><br /><b>The Book Reviews </b><br />Recently, <a href="http://samjshah.com/2014/07/01/playing-with-math/" target="_blank">Sam Shah</a> and <a href="http://beverleyabaird.wordpress.com/2014/06/30/its-monday-what-are-you-reading-7/" target="_blank">Beverly Baird</a> have posted lovely reviews. And I began to be aware of something very cool. Each reviewer notices different things about the book, and uses different chapters when they mention their favorite parts of it.<br /><br />Every chapter is special to me in one way or another, or it wouldn't have made it into the book. But of course other people don't always love the same things I do. So it's great to hear the love coming in about so many different chapters.<br /><br />I started the process of compiling the stories in this book as a story-lover and a math-lover, with very little interest in illustrations. I knew the book needed them to break up the text, but I didn't have much sense about what that would involve, what sorts of illustrations would be helpful, or even how to manage them on my computer. (I was saving lots of low-resolution images until half a year ago, which caused lots of trouble that I've finally taken care of.) I have come to love the illustrations we've pulled together.<br /><br />Sam quotes Rodi Steinig's chapter, On Noticing and Fairness:<br /><blockquote class="tr_bq">We began today’s math circle, the first of six sessions, sitting in an “ogre.” Not a circle, not an oval, but an ogre, the kids’ way of precisely describing the shape we made.</blockquote>The kids were voting on the animals to be included in Zooman's private zoo, and an ogre sounds right at home in that discussion. Their first vote led to the tamandua (ant-eater) winning. Here's our tamandua...<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-y1Ll6AZ_VF0/U7LY3horlsI/AAAAAAAABWc/ykR62UnBIIk/s1600/1+tamandua+lp.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-y1Ll6AZ_VF0/U7LY3horlsI/AAAAAAAABWc/ykR62UnBIIk/s1600/1+tamandua+lp.png" height="320" width="187" /> </a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Beverly mentions Julia Brodsky's interest in encouraging the children “to make mistakes and enjoy it.” As it turns out, that theme is repeated throughout the book. Here's an illustration that warms my heart, from Mary O'Keeffe's chapter, Agents of Math Circles.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-XvKcEKgpDSM/U7La-UAC1kI/AAAAAAAABWo/NIUkcvMbZGA/s1600/2+einstein+md.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-XvKcEKgpDSM/U7La-UAC1kI/AAAAAAAABWo/NIUkcvMbZGA/s1600/2+einstein+md.png" height="320" width="179" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div>I don't think anyone will buy the book for the illustrations, but if you find yourself reading it over and over, as I have, the illustrations will be one of the special graces of this heart-warming collection.<br /><br /><br /><br /><b>A Puzzle</b><br />There hasn't been enough math on this blog of late. So here's a puzzle-problem from <a href="https://twitter.com/jamestanton/status/485041619113369600" target="_blank">James Tanton</a>:<br /><blockquote class="tr_bq">Give an example of a cubic polynomial and a quadratic whose three points of intersection form an equilateral triangle.</blockquote>Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-63745561672684700172014-07-01T05:08:00.002-07:002014-07-04T07:23:03.649-07:00Playing With Math: Crowd-Funding Campaign Enters its Second Week<div><div><div><div><div><div><div><div><div><div><div><div><div><b>The Book</b></div>Did you know that that there are over 50 people working on <i>Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers</i>?! We are authors, puzzle & game-makers, artists, and editors. The most recent additions to the group are mathematical artists who agreed to share a piece of their work - the opening page of each section now features an amazing, thought-provoking work of art.</div>To see some of their work, you can visit these websites:</div><ul><li>The Math Circle Section piece comes from Paul Salomon (already in our group for his wonderful imbalance puzzles). Here's more: <a href="http://lostinrecursion.wordpress.com/art/stars-of-the-minds-sky">lostinrecursion.wordpress.com/art/stars-of-the-minds-sky</a> </li><li> The Homeschoolers section piece comes from Erik and Martin Demaine. Here's more: <span style="color: black; font-family: "Times New Roman"; font-size: 12pt;"><a href="http://erikdemaine.org/curved">erikdemaine.org/curved</a> </span></li><li><span style="color: black; font-family: "Times New Roman"; font-size: 12pt;"></span> The Passionate Teacher section piece comes from Tom Banchoff and Davide Cervone. Here's more: <a href="https://mail.google.com/">http://www.math.brown.edu/TFBCON2003/art/welcome.html <span id="goog_1695154010"></span></a> and <a href="http://www.math.union.edu/%7Edpvc/professional/art/welcome.html">http://www.math.union.edu/~dpvc/professional/art/welcome.html</a></li><li>The Resource section piece comes from Henry Segerman. Here's more: <span style="font-family: Times; font-size: 10pt;"><a href="http://www.shapeways.com/shops/henryseg"><span style="color: blue;">www.shapeways.com/shops/henryseg</span></a></span></li></ul></div></div></div>Here's the last illustration that was made for our book. It was a community effort with original concept by me - inspired by Melanie Hayes' chapter (At the Eye of the Hurricane), drawing by Linda Palter, caption by a reader from this blog who I know only as Teach for Life, and lettering by Maria Droujkova. I love it, and I hope it goes viral some day...<br /><br /><div style="text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-GiTKJwExX6A/U7a4uGk2muI/AAAAAAAABXA/DBiMmbvUqkE/s1600/4+hurricane+learning+lp+md.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-GiTKJwExX6A/U7a4uGk2muI/AAAAAAAABXA/DBiMmbvUqkE/s1600/4+hurricane+learning+lp+md.png" height="320" width="156" /></a></div></div><div><br /></div><div>The book is now ready to go to page layout. What a thrill! I am so proud of all of us.</div><div><br /><br /></div><a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank"><b>The Campaign</b></a></div>Sol Lederman interviewed me last week, and posted the interview as part of his <a href="http://wildaboutmath.com/2014/06/23/sue-vanhattum-inspired-by-math-38/">Inspired by Math</a> series. Just before he posted it, Adrian Pumphrey, of <a href="http://mathedout.wordpress.com/2014/06/26/book-review-playing-with-math-feat-editor-sue-vanhattum/">MathEd Out</a>, offered to interview me too. That happened on Wednesday, and is now posted <a href="http://mathedout.wordpress.com/2014/06/26/book-review-playing-with-math-feat-editor-sue-vanhattum/">on his site</a>. If you like podcasts, listen to the interviews and let me know what you think. The two conversations definitely went in different directions.</div></div>As of this writing, we have over $5000 in contributions pledged, 67% of our $7500 goal, with 177 supporters. With your help, we can keep the momentum up. Maybe we'll be lucky enough to talk about our stretch goals toward the end of the month. Getting translations out quickly would be lovely. </div><div>Are you inspired enough to head over to <a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank">the campaign site</a> right now and make a $25 contribution (or more) to reserve yourself a copy? I hope so. </div></div></div>Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-21129435775317375252014-06-25T22:34:00.000-07:002014-06-25T22:34:08.403-07:00Playing WIth Math: Can We Keep the Campaign's Momentum Up?<a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank">Our crowd-funding campaign</a> has been going very well - we are delighted and grateful. We are 48% of the way to our $7500 goal, on day 6. Our first three days brought us 95 contributors, and our next three days have so far only brought us 31 contributors. I'll need to figure out who else would like to know about the book, so that doesn't slow down to a drizzle. If you'd like to send a note to a friend or two who might like the book, we would be quite grateful. (<a href="https://docs.google.com/document/d/18mRPEiU5bw67wBMpaqxujm8BEhZfSfa88sRXRE7Yxjg/edit" target="_blank">My own appeal letter is here.</a>)<br /><br />Sol Lederman <a href="http://wildaboutmath.com/2014/06/23/sue-vanhattum-inspired-by-math-38/" target="_blank">posted his interview with me</a>, at Wild About Math. It's part of his Inspired by Math podcast series. It was fun to do. I think it will be fun to listen to.<br /><br />While we are visibly posting and tweeting, we are also putting some finishing touches on the book behind the scenes. Today Erik and Martin Demaine agreed to share their beautiful artwork with our readers. We will be including <a href="http://erikdemaine.org/curved/Kentucky/thumbs/E0352-003_medium.html" target="_blank">this piece</a> in the book.<br /><br />Here's another review. I like how each review reflects different facets of the book. This is from Melissa Greene, and was posted at her blog, <a href="http://reflectionsfromdrywoodcreek.blogspot.com/2014/06/playing-with-math.html" target="_blank">Reflections from Drywood Creek</a>.<br /><br /><blockquote class="tr_bq">I was recently sent a manuscript copy of <i>Playing with Math: Stories from Math Circles, Homeschoolers & Passionate Teachers </i>edited by Sue VanHattum. <i>Playing with Math</i> is definitely not a math textbook. It's a conglomeration of helpful stories and examples of how people who love math are sharing that love with others.<br /><br />The book is divided into four sections: 1. Math Circles and More: Celebrating Math; 2. Homeschoolers Do Math; 3. Passionate Teachers: In The Classroom; and 4. Resources. Each section starts with a brief introduction followed by stories from a variety of authors. Each story is followed by an example of various math games, puzzles and problems for you to try. <br /><br />In <i>Math Circles and More</i>, I learned that groups of people gather to work on math problems together. There are math circles, math clubs, and math festivals. Math lovers even put together math trails where they map out an area and provide math questions that can be answered by observing that surrounding area. Go figure! (...no pun intended :) I had no idea that people actually gather to solve math problems for fun. <i>Math Circles and More</i> provides unique stories by people who have started or participated in these groups. I was inspired at the possibility of gathering in a math club.<br /><br /><i>Homeschoolers Do Math</i> starts off with stories from bloggers you may recognize, Julie Brennan of <a href="http://livingmath.net/"><i>Living Math!</i> </a>and Jimmie Lanley from <a href="http://jimmiescollage.com/"><i>Jimmie's Collage</i></a> and the <a href="http://notebookingfairy.com/"><i>Notebooking Fairy</i></a>. Both ladies, among others, share anecdotes about doing math while homeschooling. Each mom shares her journey on helping her child become successful with math, from overcoming personal fears, to turning math haters into math lovers.<br /><br />The stories of <i>Passionate Teachers</i> are shared in section three. These teachers rise above standardized tests, government mandates, and miscellaneous grading policies to help children succeed with math both in the classroom and for life. The introduction states, "<i>Good teachers have always worked valiantly to provide a rich learning environment for the children in their care, and to overcome the limitations imposed by the structure of schooling. In this section, you’ll get a peek at a few teachers who discuss their work and their struggles online. One of the themes is how textbooks get in the way. We’ve ceded much of our power to textbook publishers, and finding ways to move beyond the textbook can be very powerful.</i>" As a homeschooler, I can personally say that I've let textbooks rule my way for teaching math because of insecurity. I think homeschoolers and classroom teachers alike can glean from the wisdom here.<br /><br />Finally, the Resource section is packed with a plethora of ideas to support you whether you are a novice or math aficionado. There are online resources and living math book lists. I enjoyed perusing the Meet the Author section.<br /><br />You can <a href="https://www.incited.org/en/projects/4992-Playing-With-Math">click here</a> to learn more about <i>Playing with Math</i>. There is a brief video by VanHattum and information for purchasing the book. I can see <i>Playing with Math</i> being very popular amongst math lovers and not so much math lovers looking for a survival resource. It appears to have something for everyone. </blockquote>Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-61910864697805792472014-06-22T21:58:00.002-07:002014-06-22T21:59:07.958-07:00Playing With Math: Another Review<b>Preview</b>: Today I was interviewed by Sol Lederman for his <a href="http://wildaboutmath.com/" target="_blank">Inspired by Math</a> podcast series. He'll post it tomorrow. We had lots of fun talking about math and the book. He asked me what math is, and I got scared for a moment that I wouldn't have anything much to say. I got over that hump.<br /><br /><br /><br /><b>Review</b>: Holly Brown heard about <i>Playing With Math</i> on the Living Math Forum email list. Her review of the book follows:<br /><div class="gmail_default" style="color: #0b5394; font-family: georgia,serif;">"Playing With Math" came along at a very fortuitous moment for me. I'm a homeschooling mom (teaching my 11yo, 9yo & 5yo, boys) who also happens to be a certified math teacher with classroom & tutoring experience. I've just moved to a new town and was thinking about starting up math circles in my home as a way to jump-start math learning for my boys. When I began homeschooling years ago, I thought I had to find the "best, right curriculum" for my son to achieve math mastery. I've been moving away from that idea slowly but surely over the years (with help from the Living Math group and especially Julie Brennan's posts). I have taken a lot from the Charlotte Mason methodology as I've implemented my boys' education, and feel like a "Playing With Math" or Living Math approach is the right way to go. Now, to unlearn my "teacherly" ways, and relearn how to let the kids and math lead the learning! This book is the ideal place to start. </div><div class="gmail_default" style="color: #0b5394; font-family: georgia,serif;"><br /></div><div class="gmail_default" style="color: #0b5394; font-family: georgia,serif;">I would highly recommend the book <i>Playing With Math</i> to any parent, teacher, or homeschooler, as it offers a new way to look at math and how your child/student would benefit from a completely different approach to math. This book is filled with inspirational stories from parents, teachers, and homeschoolers, all of which are unique, but convey the same message: we must release our fear that children can't/won't learn math unless it's drilled into them in the "right" order, with the right "curriculum," and embrace exploring math in a totally new way, with the excitement of seeing the beauty in and having FUN with math. <i>Playing With Math</i> also provides a number of math problems, activities and games to get you started right away. Want more? There's also an abundance of references to a variety of other inspiring books as resources. One suggestion might be to add an appendix to the book, listing these amazing resources, categorized by age/grade appropriateness.</div><div class="gmail_default" style="color: #0b5394; font-family: georgia,serif;"><br /></div><div class="gmail_default" style="color: #0b5394; font-family: georgia,serif;">As a homeschooling mom, this book gives me the comfort of knowing that I DO have the freedom to take my time with math, and allow my kids to learn it at their own pace, and from any level of interest (even if that means talking infinity with my 9yo!). Even though I've been homeschooling for a long time now, it does take a while to learn to trust in your kids' ability to learn, and your ability to teach as a mentor or guide, not a "teller" or "explainer." </div><div class="gmail_default" style="color: #0b5394; font-family: georgia,serif;"><br /></div><div class="gmail_default" style="color: #0b5394; font-family: georgia,serif;">As a teacher who is not currently in a classroom, but is still tutoring in math, one quote in particular really struck me, from Maria Droujkova: "Adults often strive very hard to get rid of any and all possible traces of confusion for kids, making things dreadfully boring. That prevents kids from developing problem solving skills and other tools for mathematical decision-making." I saw myself in this quote, and quite agree with it. Taking it one step further, I would say that, for myself, this can be an aspect of teacher ego rearing its head. I feel like, if I haven't completely, "correctly" explained a concept until the student confirms they "get" my way, then I haven't really done my job. This puts the onus and reward on the teacher, when really, the student is the one doing the learning. The more a student discovers or explores on their own, the more permanent that learning experience will be. To be fair, as a tutor, I'm often working within time and goal restraints, usually within the context of a system that does not allow for math fun and exploration. (For example, finishing a course so the student can "move on" or "finish up" high school math, or prepping for the SAT which has so much at stake for these kids.) Without quite understanding why, I have been dissatisfied for a while with the limitations of hourly tutoring, which I think is why I have been pondering the idea of doing Math Circles. What fun to be able to explore math with students in an open environment, having no requirements or limitations other than our interest and potential! </div><div class="gmail_default" style="color: #0b5394; font-family: georgia,serif;"><br /></div><div class="gmail_default" style="color: #0b5394; font-family: georgia,serif;">One final note. This book is all about math, but the fundamental ideas underpinning it are applicable to learning in any subject, and for students of all ages. If looked at from this perspective, you can take away so much more, especially if you are interested in ideas about learning and education. I hope this book accomplishes all the goals the authors have for it, and more: to inspire people everywhere to see the beauty and joy inherent in math and in playing and puzzling with math ideas by starting their own groups, supplementing their child's education, or even taking their students'/children's whole math experience in a completely new direction. </div>Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-16854213785883708792014-06-21T03:30:00.000-07:002014-06-21T08:36:15.266-07:00Playing With Math: More reviews coming in...<a href="http://www.aplayfulpath.com/playing-math/" target="_blank">Bernie</a>, <a href="http://fawnnguyen.com/2014/06/20/20140618.aspx" target="_blank">Fawn</a>, <a href="http://researchinpractice.wordpress.com/2014/06/20/sues-book-is-ready-for-press-and-needs-crowdfunding/" target="_blank">Ben</a>, <a href="http://mathprojects.com/2014/06/21/playing-with-math-stories-from-math-circles-homeschoolers-and-passionate-teachers/" target="_blank">Chris</a>, <a href="http://mathhombre.blogspot.com/2014/06/playing-with-math.html" target="_blank">John</a>, <a href="http://mathteachermambo.blogspot.com/2014/06/playing-with-math.html" target="_blank">Shireen</a>, and <a href="http://geekmom.com/2014/06/playing-math-stories-math-circles-homeschoolers-passionate-teachers/" target="_blank">Laura</a> (geekmom extraordinaire) have all written lovely posts about the book. Here's one more. Debbie McDuffee is one of the 5,000-plus members of Living Math Forum. She wrote this to share there, and with a number of other homeshool groups. I asked if I could share it here.<br /><br /><br />Hi Everyone,<br /> <br /> I want to thank Sue for making her manuscript of <i>Playing with Math</i> available, and I cannot tell you how much I enjoyed this book. As someone who has my Master's in education, I've read my share of education books, both assigned and because I am completely passionate about the subject. I can say without hesitation that this book is truly special. Sue, you've really got something great here!<br /> <br /> What a lovely, comfortable book, a relaxing conversation between people from all math backgrounds, that you can read and let sink in. Or, you can follow the sparks it ignites. Or, you can wonder, research and continue to spark. Or you can compile what works for you and your kids from all of the anecdotes in the book and reinvigorate or even, dare I say, redefine, math in your household or classroom. This book has so many purposes and I truly wanted to start reading it again as soon as I was finished (and I will ... many times!). And it's the kind of book you will get more from every time you read it.<br /> <br /> Sue's writing style sets a comfortable dialogue between the author and the reader right away. It's not preachy, judgy or really particularly instructive. Instead, it's a party of anecdotes that got this reader excited about not just doing math with kids, but playing with math myself, just for the fun of it. They say that the best education is when you focus on yourself instead of your child, so you can be the example, and this book inspires me to do just that.<br /> <br /> <i>Playing with Math</i> also helped me understand math circles like no other. I've looked at various writings on math circles and none have spoken to me the way <i>Playing with Math</i> has. The balance of accessibility without talking down just works for me. It's not trying to be didactic, but the mix of many experiences allows me to construct my own ideas of what math circles can mean in my own life with kids.<br /> <br /> Oh, and I literally had web searches open as I was reading this, searching for things like "Waldorf coloring math facts" and "math olympiad problems" so as I read, I amassed a bunch of resources to get started at the same time. T<i>he Moscow Puzzles</i> book is available on Amazon for $3.99 prime!<br /> <br /> The other thing that strikes me is that the different examples within a topic, while all demonstrating the main theme of "playing with math," have varied enough approaches that there really is something for everyone to glean. For example, in the math circles section, two of them definitely resonated more for me than the others, even though there was valuable information in all of them, and I'm sure I will pick and choose different elements from all of them that work for me. The Homeschooling section's wonderful blend of anecdotes, advice and examples did the same.<br /> <br /> I love that there are example problems and math games and activities sprinkled throughout the book. What a perfect idea, since everything about the book is so inspirational ... you can start learning right away! <br /> <br /> The "Passionate Teachers" section literally made me respect teachers more. I love knowing that there are still teachers willing to step out of the box and do what is right for the kids. Reading this section reinforces that creativity is alive and well in the classrooms ... I hope more and more teachers can be inspired by this book. <br /> <br /> As if all of this wasn't enough, the "Resources" and "Conclusion" sections are filled with more places to find ideas, both online and in books, tips for mentoring, how to support girls, and so much more. This books is truly one of the most well-rounded I have read. While it still sticks to the theme and doesn't try to be everything mathematics, it thoroughly explores "playing with math" and what it can mean to the reader on many different levels.<br /> <br /> It is evident how much work and passion went into the making of this book. What an amazing collaboration! Thanks again Sue, and everyone who contributed.<br /> <br /> Debbie McDuffee<br />M.Ed. and Founder of <a href="http://www.lacihomeschool.org/" target="_blank">LACI Homeschoolers' Association </a><br /><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-90356108283809484492014-06-20T06:36:00.002-07:002014-06-20T10:21:45.978-07:00Playing With Math Crowd-Funding Campaign<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-JiXDB2Tu9JU/U6Rti6KwQMI/AAAAAAAABVs/zx4mlIwkqco/s1600/Book+cover+for+upload.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-JiXDB2Tu9JU/U6Rti6KwQMI/AAAAAAAABVs/zx4mlIwkqco/s1600/Book+cover+for+upload.jpg" height="320" width="224" /></a></div><br /><blockquote class="tr_bq"><i>Sue VanHattum has assembled a marvelously useful and inspiring book. It is filled with stories by people who don't just love math, they share that love with others through innovative math activities. Playing With Math is perfect for anyone eager to make math absorbing, entertaining, and fun. </i></blockquote><blockquote class="tr_bq"><br /><div style="text-align: right;"><a href="http://lauragraceweldon.com/blog-2/">Laura Grace Weldon</a>, author of <i>Free Range Learning</i></div></blockquote><br />Our crowd-funding campaign is at <a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank">incited.org</a>. Check us out!<br /><br /><br /><br />Dear Readers,<br /><br /><i><b>Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers</b></i> has <a href="http://mathmamawrites.blogspot.com/2014/05/playing-with-math-authors-and-artists.html">over 30 authors</a>, who each tell their delightful stories of sharing their enthusiasm for math with others. Over the past 5 1/2 years I've been compiling and editing <a href="http://mathmamawrites.blogspot.com/2014/05/playing-with-math-table-of-contents.html">the chapters</a> with love and care, creating this amazing 328-page book. It's ready to head to the printers now, and can soon be in your hands. Whether you enjoy math and want materials that will help you share some math-love with your kids, or you fear and loathe math and need help getting over that hurdle so you won’t pass it on, <i>Playing With Math</i> will give you inspiration and lots of new ideas.<br /><br />Today is the first day of <a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank">our crowd-funding campaign</a>. For a contribution of $25, we’ll send you a book as soon as it’s printed. In case the idea of crowd-funding is new to you, here’s how it works: You can contribute anything from $1 to $5000 (with rewards at each contribution level) to help us pay for our illustrators, editors, page layout person, and printing. This is our way of asking for community support for this book as part of the production process. We hope to build lots of energy around the ideas in the book through this campaign. You can see more details at <a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank">incited.org</a>. <br /><br />Besides contributing, here’s another way you can help. Think of five friends who would enjoy this book. Do you have friends who get frustrated helping their kids with math homework, or teach young kids but don’t feel real comfortable with math themselves? Do you have friends who enjoy math, and want more materials to share with the kids in their lives? Do you know someone who might want to start a math circle? Can you send this appeal along to them? <br /><br />I’m hoping for the power of exponential growth with this. Our outrageous goal is to change the way people all over this country, and maybe even the world, think about math. I think this book is a good start – <i>if</i> it gets into people’s hands. If you each send this to five friends who might enjoy the book, and each of them sends it to five friends, and each of them … Well, pretty soon we cover the world, right? ;^) (In fact, if we kept it going through eleven steps, that would make 5 to the 11<sup>th</sup> power, or over 40 million people. Does Sue dream big? Yep.) <br /><br />So I’m asking you for two things:<br /><ol><li>Go to <a href="https://www.incited.org/en/projects/4992-Playing-With-Math---the-Book" target="_blank">incited.org</a> and contribute. (A $25 contribution gets you a book.) If you do it right now, you won’t forget. </li><li>Email five friends who might like to read <i>Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers</i>, and ask them to read this. </li></ol><br />Thanks! <br /><br /><br />Warmly,<br />Sue VanHattum<br />Richmond, CA<br />mathanthologyeditor@gmail.com<br /><br /><br /><br /><br /><blockquote class="tr_bq"><i>Mathematics is a creative activity, like music. It requires some technique, and the technique has to be taught, but the main point is elsewhere - it is all about creativity, a sense of enjoyment, and higher purpose. This book goes a long way in that direction. </i><br /><br /><div style="text-align: right;">Ivar Ekeland, author of <i>The Cat in Numberland </i></div></blockquote><br /><br /><blockquote class="tr_bq"><i>The Internet is presently bursting with vibrant writing about mathematics learning; yet it can be difficult to navigate this wealth of resources. Sue VanHattum has carefully collected and arranged some of the best of this writing. Imagine having a cheerful, knowledgeable, caring, and patient native interpreter accompany you on a tour of a foreign land. That's Sue in the land of math. She and the authors collected here care deeply about welcoming everyone to the world of mathematics. Whether you play with math every day, or are struggling to believe that one can play with math, Playing With Math will provide inspiration, ideas and joy. </i><br /><a href="http://christopherdanielson.wordpress.com/">Christopher Danielson</a>, author of <i>Talking Math with Your Kids</i> </blockquote><br /><br /><blockquote class="tr_bq"><i>As a homeschool mom who grew up hating math, I didn’t want to pass that attitude on to my children. I thought if I bought a textbook and relearned it, I would somehow learn to enjoy it. That didn’t seem to help. Then I read Playing With Math and discovered that math isn’t what you find in a textbook at all. It’s all around us, it’s beautiful, and most of all, it’s exciting! This book is a gem that I turn to again and again for fun and inspiration.</i><br /><br /><div style="text-align: right;">Shalynn Wilson </div></blockquote>Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-28327660151472844702014-06-19T11:04:00.000-07:002014-06-19T11:04:19.862-07:00Math Circles, Salons, and PartiesOn Twitter, Sam Shah just said I was an expert on Math Circles. Funny, I still don't feel like an expert at all. My teacher responses, built over decades, seem to interfere. For me, it's easier to host a math party or a math salon.<br /><br />Thinking about all that, I googled Math Salon and Math Party. I saw lots of cool posts under Math Salon, but the livelier Math Party was mostly stuff I wouldn't go near - corporate and very traditional (dry, memory-based) notion of math learning. Interesting...<br /><br />So much is coming together today... I have finally made progress on getting <a href="http://www.playingwithmath.org/">the Playing With Math website</a> to look the way I want it to. Looking over the history, I was reminded that a colleague had pointed to the site a while back, when it looked just silly. I thought I'd reply to her post, and got wandering around on her blog.<br /><br />Holly Graff wrote the chapter One and a Quarter Pizzas for the homeshooling section of <i>Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers</i>. On her blog, Unschooling Days, she posted last year about a math salon she was running at her home. Lovely post, which includes a delightful video I wanted to share here.<br /><br />Holly writes:<br /><blockquote class="tr_bq">Here is a time-lapse video one of the kids made, inspired by an experiment we did in math salon about the mathematics involved in Tchokwe art from southwestern Africa:</blockquote><br /><iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/HHJZPMWc5KM" width="560"></iframe> Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-39923908001261572352014-06-06T18:04:00.000-07:002014-06-06T18:04:02.059-07:00Want to write a review of Playing With Math? Contact me!<div dir="ltr" id="docs-internal-guid-e4ac3284-73d8-060a-e77c-ffca5accb3d0" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: italic; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers</span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"> is finally going to press. After 5 1/2 years of work, I am ready to send it out into the world. We expect to publish this fall.</span></div><br /><div dir="ltr" style="line-height: 1.15; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">In a recent series of posts, I shared the <a href="http://mathmamawrites.blogspot.com/2014/05/playing-with-math-authors-and-artists.html">short bios our authors and artists have put together</a> so you can see what an exciting group of authors we have, then I shared the <a href="http://mathmamawrites.blogspot.com/2014/05/playing-with-math-table-of-contents.html">Table of Contents</a> so you can get a small taste of what's to come, and finally I shared <a href="http://mathmamawrites.blogspot.com/2014/05/playing-with-math-rave-reviews-from.html">the short reviews a few people wrote</a> that will appear on the back cover of the book.</span></div><br /><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Now we need some longer, meatier reviews. If you would like a copy of the manuscript to review, just email me at mathanthologyeditor@gmail.com. I will send you a pdf. If you can post your review on June 20 or close to it, I would be delighted. That's when our crowd-funding campaign at incited.org will begin. </span>Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-52103729633040576552014-05-26T20:44:00.000-07:002014-06-18T14:29:38.006-07:00Playing With Math - Rave Reviews from Early ReadersMathematics is a creative activity, like music. It requires some technique, and the technique has to be taught, but the main point is elsewhere - it is all about creativity, a sense of enjoyment, and higher purpose. This book goes a long way in that direction. <br /><div style="text-align: right;">Ivar Ekeland, author of <i>The Cat in Numberland </i></div><br /><br />Sue VanHattum has assembled a marvelously useful and inspiring book. It is filled with stories by people who don't just love math, they share that love with others through innovative math activities. <i>Playing With Math</i> is perfect for anyone eager to make math absorbing, entertaining, and fun. <br /><div style="text-align: right;"><a href="http://lauragraceweldon.com/blog-2/">Laura Grace Weldon</a>, author of <i>Free Range Learning </i></div><br /><br />The Internet is presently bursting with vibrant writing about mathematics learning; yet it can be difficult to navigate this wealth of resources. Sue VanHattum has carefully collected and arranged some of the best of this writing. Imagine having a cheerful, knowledgeable, caring, and patient native interpreter accompany you on a tour of a foreign land. That's Sue in the land of math. She and the authors collected here care deeply about welcoming everyone to the world of mathematics. Whether you play with math every day, or are struggling to believe that one can play with math, <i>Playing With Math</i> will provide inspiration, ideas and joy.<br /><div style="text-align: right;"><a href="http://christopherdanielson.wordpress.com/">Christopher Danielson</a>, author of <i>Talking Math with Your Kids</i> and <a href="http://talkingmathwithkids.com/">talkingmathwithkids.com</a></div><br /><br />As a homeschool mom who grew up hating math, I didn’t want to pass that attitude on to my children. I thought if I bought a textbook and relearned it, I would somehow learn to enjoy it. That didn’t seem to help. Then I read <i>Playing With Math</i> and discovered that math isn’t what you find in a textbook at all. It’s all around us, it’s beautiful, and most of all, it’s exciting! This book is a gem that I turn to again and again for fun and inspiration.<br /><div style="text-align: right;">Shalynn Wilson<br /><br /><br /><br /><br /><br /><div style="text-align: left;"><span style="font-size: x-small;">[These reviews will eventually show up at <a href="http://playingwithmath.org/">playingwithmath.org</a>, which I'm still getting ready for prime time.] </span></div></div>Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com1tag:blogger.com,1999:blog-5303307482158922565.post-20272049198541964922014-05-26T20:38:00.000-07:002014-05-26T20:38:00.297-07:00Playing With Math - Table of ContentsPreface 9 <br />Introduction 13 <br /><br /><br /><span style="font-size: large;"><b>Math Circles and More: Celebrating Math </b></span><br /><br />Section Introduction 19 <br /><br />The Art of Inquiry: A Very Young Math Circle, Julia Brodsky 23 <br /> Puzzle: Imbalance Abundance, Paul Salomon 29 <br /><br />Rejoicing in Confusion, Maria Droujkova 31 <br /> Game: Parent Bingo, Maria Droujkova 35 <br /><br />Parents and Kids Together, Sue VanHattum 37 <br /> Puzzle: Foxes and Rabbits, Sue VanHattum 45 <br /><br />On Noticing and Fairness: A Mindful Math Circle, Rodi Steinig 47 <br /> Puzzle: Is this for real? Avery Pickford 52 <br /><br />Bionic Algebra Adventures, Colleen King 53 <br /> Story: Alexandria Jones in Egypt, Denise Gaskins 58 <br /><br />The Oakland Math Circle: A First Iteration, Jamylle Carter 63 <br /> Game: Fantastic Four, Exploratorium Staff 69 <br /><br />A Culture of Enthusiasm for Math, Amanda Serenevy 71 <br /> Activity: Vertices, Edges, and Faces, Amanda Serenevy 74 <br /><br />Seized by a Good Idea, Stephen Kennedy 75 <br /> Puzzle: Math Without Words #1, James Tanton 81 <br /><br />A Prison Math Circle, Bob and Ellen Kaplan 83 <br /> Puzzle: Math Without Words #2, James Tanton 86 <br /><br />Agents of Math Circles, Mary O’Keeffe 89 <br /> Puzzle: Food for Thought, Jan Nordgreen 94 <br /><br />The Julia Robinson Mathematics Festival, Nancy Blachman 95 <br /> Saint Mary’s Math Contest Sampler, Br. Alfred Brousseau 97 <br /> Exploration: Candy Conundrum, Joshua Zucker 97 <br /><br />A Young Voice: Consider the Circle, Elisa Vanett 99 <br /><br /> <br /><span style="font-size: large;"><b>Homeschoolers Do Math </b></span><br /><br />Section Introduction 103 <br /><br />Tying It All Together, Julie Brennan 105 <br /> Game: Place Value Risk, Sue VanHattum 112 <br /><br />Advice from Living Math Forum, Julie Brennan 113 <br /> Puzzles: Deep Arithmetic, Sue VanHattum 119 <br /><br />Transitioning to Living Math, Jimmie Lanley 121 <br /> Game: Math Card War, Denise Gaskin 126 <br /><br />At the Eye of the Hurricane, Melanie Hayes 129 <br /> Puzzle: Self-Referential Number Square, Jack Webster 142 <br /><br />One and a Quarter Pizzas, Holly Graff 143 <br /> Game: Function Machine, Sue VanHattum 148 <br /><br />The Math Haters Come Around, Tiffani Bearup 149 <br /> Puzzle: Magic Hexagon, Michael Hartley 155 <br /><br />Mapping the Familiar, Malke Rosenfeld 157 <br /> Game: Racetrack, Sue VanHattum 159 <br /><br />Radically Sensible Ideas, Pam Sorooshian 161 <br /> Game: Dotsy, Leonard Pitt, Cinda Heeren, Tom Magliery 168 <br /><br />A Young Voice: An Unschooler at College, Lavinia Karl 169 <br /><br /><br /><span style="font-size: large;"><b>Passionate Teachers: In the Classroom </b></span><br /><br />Section Introduction 173 <br /><br />Teach Less, Learn More, Sue VanHattum 177 <br /> Game: Modular Skirmish, John Golden 181 <br /><br />Trust, Montessori Style, Pilar Bewley 185 <br /> Puzzle: Measuring With Paper, by B. Zolkower, D. Abrahamson 190 <br /><br />Math In Your Feet, Malke Rosenfeld 191 <br /> Game: Fizz Buzz, by Michael Hartley 197 <br /><br />Dinosaur Math, Michelle Martin 199 <br /> Puzzle: Alien Math, Amanda Serenevy 201 <br /><br />Better Teaching Through Blogging, Kate Nowak 203 <br /> Activity: Candy Launcher, Sean Sweeney 208 <br /> Background:Using Math to Describe Gravity, Sue VanHattum 213 <br /><br />Putting Myself in My Students’ Shoes, Allison Cuttler 217 <br /> Puzzle: What Number Am I? Jonathan Halabi 220 <br /><br />An Argument Against the Real World, Friedrich Knauss 221 <br /> Puzzle: Octopus Logic, Tanya Khovanova 223 <br /><br />Area of a Circle, Fawn Nguyen 225 <br /> Exploration: Coloring Cubes, Joshua Zucker 227 <br /><br />Textbook Free: Kicking the Habit, Chris Shore 229 <br /> Activity: Guess My Dice, Kaleb Allinson 231 <br /><br />Math Is Not Linear, Alison Forster 233 <br /> Puzzle: A Little Math Magic, Jonathan Halabi 239 <br /><br />A young voice: Geometric Delights, Luyi Zhang 241 <br /><br /><br /><b><span style="font-size: large;">Resources</span></b> <br /><br />Introduction and Internet Resources 247 <br /><br />Math and the Electronic Commons, Maria Droujkova 252 <br /><br />Creating Math Teachers at Play, Denise Gaskins 255 <br /><br />Math Playground: Designing Games for Real Learning, Colleen King 260 <br /><br />Supporting Girls, Sue VanHattum 266 <br /><br />How to Become Invisible, Bob Kaplan 280 <br /><br />Starting a Math Club, Maria Droujkova, Sue VanHattum 282 <br /><br /><b>Conclusion</b> 285 <br /><br />Sue’s Book Picks 297 <br /><br />Hints for Puzzles 306 <br /><br />Meet the Authors 311 <br /><br />Acknowledgements 320 <br /><br />Index 322 Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-51747909562060114222014-05-26T18:28:00.001-07:002014-06-06T15:50:35.651-07:00Playing With Math - the Authors and Artists<div style="text-align: left;"><span style="font-family: inherit;"><span style="font-size: small;">The book is almost here! We are preparing for a publicity and fund-raising campaign</span></span>, and now seemed like a good time to introduce the wonderful people who came together to create this book. So, without further ado...<br /><br /></div><div style="text-align: left;"></div><div style="text-align: center;"></div><div style="text-align: center;"> <span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="color: red;">Meet</span> <span style="color: #6aa84f;">the</span> <span style="color: purple;"><span style="background-color: white;">Authors</span></span> <span style="color: orange;">and</span> <span style="color: blue;">Artists</span>!</span></span></div><br /><br /><b>Alison Forster</b> is currently a high school math teacher at the Doane Stuart School in Albany, NY where she teaches algebra, geometry, precalculus, and an elective of her own design called "Foundations of Mathematics." She got her start having fun with math with homeschoolers at the age of sixteen and never looked back. <br /><br /><b>Allison Cuttler</b> is originally from New Jersey and fell in love with math at Haverford College, a small liberal arts school outside of Philadelphia. After completing her Masters in Applied Mathematics at the University of California, San Diego, she discovered her true passion for teaching math and programming at High Tech High Chula Vista, a project-based charter school serving San Diego’s South Bay community. In the fall of 2011, she moved back to NJ and has been teaching at North Star Academy College Preparatory High School in Newark, New Jersey ever since. In her free time she enjoys ultimate frisbee and running, exploring local cuisine, and blogging at <a href="http://infinigons.blogspot.com/">infinigons.blogspot.com</a>. <br /><b><br /></b><b>Amanda Serenevy</b> is the executive director of the <a href="http://riverbendmath.org/" target="_blank">Riverbend Community Math Center</a>, an organization that promotes access to high-quality math education for people of all ages in north-central Indiana. In that capacity, Amanda presents hands-on math activities, leads workshops for teachers, and mentors elementary, high school, and undergraduate students. After teaching in Bob and Ellen Kaplan's Math Circle program in Boston, Amanda became active in the Math Circle movement, connecting mathematicians with young students interested in mathematics. In 2007, Amanda earned a Ph.D. from Boston University with a dissertation on the dynamics of networks of inhibitory neurons. She has published research on mathematical neuroscience and iterated matrix maps, and has additional research interests in geometric topology and mathematical origami. <br /><br /><a href="http://www.withoutgeometry.com/" target="_blank"><b>Avery Pickford</b></a> is currently a fifth and sixth grade math teacher in the San Francisco Bay Area, and the way he teaches math does not equal the way he was taught math. In his fifteen years of teaching he has had the pleasure of teaching math and science to students from third grade to graduate school. He is always eager to discuss progressive teaching, and is especially interested in student-posed problems. In addition to his love of math, he is also an amateur photographer. <br /><br /><b>Betina Zolkower</b> is an associate professor at Brooklyn College (City University of New York) where she teaches methods and research courses for pre- and in-service middle and high school mathematics teachers and conducts research on the functional grammar of whole-group conversations in mathematics classrooms. Betina is the founding co-director of the Grupo Patagónico de Didáctica de la Matemática (<a href="http://gpdmatematica.org.ar/">gpdmatematica.org.ar</a>), a lesson study/instructional design collective of teachers and teacher educators in Southern Argentina whose work is inspired by Hans Freudenthal's realistic mathematics education. Betina is also a <a href="https://www.flickr.com/photos/27519060@N05/" target="_blank">photographe</a>. <br /><br /><b>Bob Kaplan</b> has worked on mathematics with people from four up, most recently at Harvard University. In 1994, with his wife Ellen, he founded <a href="http://themathcircle.org/" target="_blank">The Math Circle,</a> a program open to all comers, for the enjoyment of pure mathematics. He has also taught philosophy, Greek, German, Sanskrit, and “Inspired Guessing.” He is the author (as Robert Kaplan) of <i>The Nothing That Is: A Natural History of Zero</i> (Oxford 2000), and with his wife, <i>The Art of the Infinite: The Pleasures of Mathematics</i> (Oxford 2003), <i>Out of the Labyrinth: Setting Mathematics Free</i> (Oxford 2007), and <i>Hidden Harmonies: The Lives and Times of the Pythagorean Theorem</i> (Bloomsbury Press 2010). In the past year the Kaplans have opened over a thousand Math Circles in Brazil, each aimed at the poorest sections of the country. The program is planned to expand over the next five years. Bob lives with his wife in Massachusetts, but plays cricket for the Grange Club in Scotland, where he first became acquainted with naught. <br /><br /><b>Chris Shore</b> teaches high school algebra, geometry, and an International Baccalaureate math course, effectively engaging adolescents in the mathematics classroom. Chris is the editor and publisher of <a href="http://mathprojects.com/" target="_blank">The Math Projects Journal</a>, a professional newsletter offering innovative math lessons, most of which are published as the book, <i>MPJ’s Ultimate Math Lessons</i>. As a leader in implementing instructional change, Chris has made presentations nationwide to teachers and administrators on improving math instruction and raising standardized test scores. He is the department chair at his high school and has led his team to being the highest-performing school in the county. Chris is the 2001 California recipient of the Presidential Award for Excellence in Mathematics and Science Teaching. <br /><br /><b>Colleen King</b> is the co-founder of a mathematics learning center where she teaches K-12 students the art of problem solving. Colleen's unique approach to math instruction includes computer programming, robotics, science projects, and role-playing games. Each class is an adventure and students enjoy the unpredictable learning experiences. Colleen is probably best known for her work on <a href="http://www.mathplayground.com/" target="_blank">MathPlayground.com,</a> a popular educational site for elementary and middle school students. Colleen's goal is to one day design a game that captures the collaborative problem solving and "hard fun" that takes place at her math center. <br /><br /><b>Denise Gaskins</b> says, "Math is not just rules and rote memory. It's like ice cream, with more flavors than you can imagine. And if all your children ever do is textbook math, that’s like feeding them broccoli-flavored ice cream.” As a veteran homeschooling mother of five who loves math, she wants to help other homeschoolers see the variety and richness of the subject. Denise writes the <a href="http://letsplaymath.net/" target="_blank">Let's Play Math! blog</a> and started the Math Teachers at Play blog carnival to share creative ideas for learning, teaching, and understanding math. She’s also taught physics, which was just one story problem after another. What fun! <br /><br /><b>Dor Abrahamson </b>is a professor of education at the University of California, Berkeley. He does research on how students learn mathematical concepts and invents systems for learning mathematics. These two strands of Dor's work come together in an approach called "design-based research", by which researchers can make contributions to both practice and theory. Dor is particularly interested in finding ways of helping children build on their intuition when they learn mathematics. When kids seem to get things "wrong," Dor looks for the grain of "right" in their intuition, and he creates systems that help kids connect these intuitions with formal mathematical ways of describing the world. Most of Dor's work has been on the concepts of proportionality and probability. Recently he has put out a free iPad app called the <a href="https://itunes.apple.com/us/app/mathematical-imagery-trainer/id563185943?mt=8" target="_blank">Mathematics Imagery Trainer for Proportion</a>. <br /><br /><b>Elisa R. Vanett</b> is currently a senior at John Adams high school. She plans on attending Indiana University South Bend and enrolling in the nursing program, pursuing research as an undergraduate, and minoring in creative writing. <br /><br /><b>Ellen Kaplan</b> was a classical archaeologist through graduate school at Harvard and in Germany, and has also taught biology, Greek, Latin, and the history of many places and times. She began teaching mathematics to integrate an all-male department, but was so delighted by the breadth and depth of the field that she ended up co-founding the Math Circle with her husband, illustrating his book, <i>The Nothing That Is</i> (Oxford 2000), and writing <i>The Art of the Infinite </i>(Oxford 2003), <i>Out of the Labyrinth: Setting Mathematics Free</i> (Oxfod 2007), and <i>Hidden Harmonies: The Lives and Times of the Pythagorean Theorem</i> (Bloomsbury Press 2010) with him. With their son, Michael, she has written <i>Chances Are ... Adventures in Probability</i> (Viking 2006), and <i>Bozo Sapiens: Why to Err Is Human</i> (Bloomsbury). They are at work on their third book. In the past year Ellen and Bob Kaplan have opened over a thousand Math Circles in Brazil, each aimed at the poorest sections of the country. The program is planned to expand over the next five years. <br /><br /><b>Ever Salazar</b> has been teaching math and physics in Ciudad Guayana, Venezuela for four years. He has always been interested in math, and loves to solve puzzles from math competitions, which were his only source of real math in high school. When he turned nineteen, he discovered Martin Gardner's books, and since then his passion for math has been entangled with the need to show this awesomeness to other people. And when he discovered ViHart, MinutePhysics, CGPGrey, Veritasium and other educational channels on Youtube, he knew that was his place. He is currently teaching Calculus at Universidad Católica Andrés Bello and illustrating for the Youtube channel MinuteEarth. <br /><br /><b>Fawn Nguyen</b> has been teaching geometry, algebra 1, and sixth-grade math for the last ten years at Mesa Union Junior High in Somis, CA. Prior to teaching math, she was a middle school science teacher for fourteen years. Inspired by her father, who taught math for over thirty years, Fawn has always had a deep love for mathematics, especially problem solving. She is passionate about making math accessible, relevant, and fun for students. She blogs about teaching at <a href="http://fawnnguyen.com/">fawnnguyen.com</a>. Fawn currently is a presenter of the University of California, Santa Barbara’s Mathematics Project and is also helping to lead the <a href="http://www.mathteacherscircleto.org/" target="_blank">Thousand Oaks Math Teachers' Circle</a>. <br /><br /><b>Friedrich Knauss</b> worked for close to two decades as a software engineer, and then decided to reboot his career, switching tracks to the teaching profession. Like most new teachers, he assumed that teaching was mostly a matter of presenting information in a clear and logical fashion, and the eager and hungry young minds would eat it up. It took one year at an inner city Los Angeles school to realize that subject knowledge was the least part of teaching; he has been using his skills as an engineer and scientist to improve his craft ever since. He blogs at <a href="http://blog.mathpl.us/">blog.mathpl.us</a>. <br /><br /><b>Holly Rebekah Graff </b>is an unschooling mom and former public school science teacher. She believes that every child deserves the freedom, time, and support necessary to pursue her passions and construct her own rich understanding of the world. She has worked with a diverse group of students, urban and rural, pre-kindergarten through high school, in a variety of settings from crowded urban classrooms to intimate groups of homeschoolers. She currently teaches science classes for homeschoolers at her home in the Catskills of New York. She blogs at <a href="http://unschoolgirls.blogspot.com/" target="_blank">Unschool Days</a> about the school-free lifestyle. Her interests include writing, theater, creating collage, swing dancing, snowboarding, baking, and gardening. <br /><br /><b>Jack Webster</b> did his undergraduate degree in mathematics at Cambridge University, and is particularly interested in set theory and formal logic. He works in radio communications now as a programmer and mathematician. Jack blogs at <a href="http://jaxwebster.wordpress.com/">jaxwebster.wordpress.com</a>, where he has posted a number of other puzzles he has created. <br /><br /><b>James Tanton</b> has been doing puzzles all his life. He's created <i>Math Without Words</i>, a lovely book of puzzles, along with a number of other books and videos taking a playful approach to math. You can find links to all of this and more at <a href="http://jamestanton.com/">jamestanton.com</a>. <br /><br /><b>Jamylle Carter </b>is a mathematician and a musician. In 2009 she joined the full-time mathematics faculty at Diablo Valley College in Pleasant Hill, California. Before then, she trekked all over the country for mathematics: bachelor’s degree from Harvard University; Ph.D. from University of California, Los Angeles; and postdoctoral positions at a large public research university, a science museum, and two National Science Foundation mathematics institutes. She has published research on applied mathematics for image processing. Jamylle has also played piano since the age of five. A finalist in a Los Angeles songwriting competition, she has been a director, arranger, and pianist for choirs nationwide. Jamylle is currently a pianist and choir director for the East Bay Church of Religious Science in Oakland, California. <br /><br /><b>Jan Nordgreen</b> started writing his blog, <a href="http://easyquestion.net/thinkagain/" target="_blank">think again</a>, in Santa Cruz, Bolivia. Through moves to France, the Cayman Islands, and back to Bolivia, and through hurricane Ivan, France Télécom, and satellite-only connections, he kept the blog going. During his two-year stay in Thailand he renamed the blog ”thnik again” and it shot to the number one Google result for ”thnik.” He currently resides in Lanzarote, Spain. <br /><br /><b>Jimmie Lanley</b> is the mom of one creative daughter. After seven years of teaching in public schools, she became a stay-at-home mom when Mel was three years old and the whole family moved to China. She has taught Mel at home ever since. Her research into curricula and homeschooling philosophies led her to a Charlotte Mason style, which she finds very satisfying. Jimmie likes sewing, writing, traveling, and cooking from scratch. She blogs at <a href="http://jimmiescollage.com/">jimmiescollage.com</a> and <a href="http://notebookingfairy.com/">notebookingfairy.com</a>. <br /><br /><b>John Golden</b> is a math teacher educator, elementary and secondary, at Grand Valley State University in West Michigan. He is interested in how people learn math and how to support teachers in the classroom, with particular interest in learning-math-game connections and dynamic geometry. He blogs at <a href="http://mathhombre.blogspot.com/">mathhombre.blogspot.com</a>, tumbls at <a href="http://mathhombre.tumblr.com/">mathhombre.tumblr.com</a> and tweets from @mathhombre. <br /><br /><a href="http://jd2718.org/" target="_blank"><b>Jonathan Halabi</b></a> lives in the Bronx, where he teaches high school math. He is the founding mathematics teacher at the High School of American Studies at Lehman College (2002) and designed and planned much of that school's curriculum. Jonathan has also taught college math, middle school enrichment, and methods and content to preservice math teachers. He is a union activist, and is interested in problem solving, numbers, and social justice. He often speaks on mathematical problem solving. <br /><br /><b>Joshua Zucker</b> is the founding director of the Julia Robinson Mathematics Festivals, which bring deep, collaborative problem solving to a wide range of students. He discovered his love for number theory at Dr. Arnold Ross's summer program at Ohio State University over twenty years ago. Joshua taught at Stanford’s Education Program for Gifted Youth, community colleges, and public and private high schools, before becoming a freelance math teacher. In 2006, he helped begin the Math Teachers' Circle project at the American Institute of Mathematics. He currently is a part-time instructor for the Art of Problem Solving, as well as a leader at several math circles in the San Francisco area. <br /><br /><b>Julia Brodsky</b> is a homeschooling mom with three naughty and curious kids. When she is not with her family, she works as a rocket scientist for NASA Goddard, runs a weekly <a href="http://www.artofinquiry.net/testimonials/">Art of Inquiry</a> math circle for elementary school students, organizes the annual <a href="http://rockville.patch.com/groups/schools/p/math-olympiad-celebrates-problem-solving">Math Kangaroo Olympiad for Montgomery County kids</a> - and still keeps some sanity. She is constantly fascinated by the way children learn and solve problems. Julia grew up in Russia, where she was a mediocre student in one of the best math magnet schools of St. Petersburg. Later, she had a lot of fun working as an International Space Station astronauts' instructor at Johnson Space Center. Julia also enjoys writing poetry, hiking, and watching somebody else working instead of her. <br /><b><br /></b><b>Julie Brennan</b> hosts the Living Math Forum, a five thousand-member Yahoo group engaged in discussion and sharing of math education experience and resources. Her website, <a href="http://livingmath.net/">livingmath.net</a>, is full of information on teaching and learning math in non-traditional ways. Julie’s homeschooling experience is reflected in the site’s content and articles, but many parents of schooled children and teachers also benefit from the information. Julie sells Living Math History lesson plans on the site, a fascinating approach to learning math through the study of the masters who discovered it. Julie worked professionally as a CPA and financial consultant prior to staying home with her four children. She currently teaches classes for homeschoolers. <br /><br /><b>Kaleb Allinson</b> is a high school math teacher and the department head at Lake Stevens High School in Lake Stevens, WA. He taught middle school during his first four years of teaching and has taught at the high school for eleven years. He currently teaches Geometry, Advanced Algebra and AP Calculus. Kaleb has always enjoyed attempting to solve problems that he has never seen before. When he’s not teaching he's quite busy with his six energetic kids. <br /><b><br /></b><b>Kate Nowak</b> teaches mathematics at Charlottesville High School in Charlottesville, Virginia. She has loved puzzles, logic, and origami from an early age. In addition to teaching for eight years, Kate has also written real-world lessons at Mathalicious, completed an engineering degree, and fixed airplanes for the U.S. Navy. She is passionate about showing kids that mathematics is fun and fascinating, and improving her craft in collaboration with colleagues around the globe. She has written the popular blog f(t) since 2007. <br /><br /><b>Lavinia Karl</b> was unschooled. She earned a B.A. in math from Knox College. Now she's in her twenties, exploring life's possibilities. <br /><br /><b><a href="http://blog.drlindapalter.com/" target="_blank">Linda Palter</a> </b>is a chiropractor in West Michigan. She can also be found square dancing, crafting, and playing fetch and frisbee with a very high-energy dog. <br /><br /><b>Luyi Zhang</b> is presently an undergraduate math major at the Massachusetts Institute of Technology and an instructor of online math courses at Art of Problem Solving. In middle and high school she participated in numerous math contests, placing in the top ten statewide in MATHCOUNTS and qualifying for the USA Math Olympiad. She has taught middle school students through Breakthrough Collaborative and has worked with gifted students at the math camps MathPath and Epsilon. She blogs about her original geometric creations such as Sierpinski triangle brownies and beaded teddy bears on her website, <a href="http://geometricdelights.wordpress.com/" target="_blank">Geometric Delights</a>. <br /><b><br /></b><b>Malke Rosenfeld</b> is a percussive dance teaching artist, math explorer, curriculum designer, editor, and writer. Her interdisciplinary inquiry focuses on the intersections between percussive dance and mathematics and how to best illustrate these connections for students. In her Math in Your Feet program, percussive dance becomes the platform for a robust choreographic inquiry into mathematical thinking, practices and topics. You can find out more about Malke’s many collaborative math and making projects at <a href="http://malkerosenfeld.com/">malkerosenfeld.com</a>. <br /><br /><a href="http://www.moebiusnoodles.com/" target="_blank"><b>Dr. Maria Droujkova</b></a> is a curriculum developer and mathematics education consultant. She organizes meetings with project and community leaders in the Math 2.0 interest group, an online collaboration of hundreds of researchers and educators interested in modeling software, computational tools, and social media in mathematics education. The group has held more than one hundred events since 2009, and has given rise to several ongoing research and development projects. Natural Math, the company Maria founded in 2001, provides a unique forum where researchers and developers join parents and teachers for discussions of family mathematics, early algebra, individualized instruction, and math clubs. <br /><br /><b>Mary O'Keeffe</b> is a founding advisor of <a href="http://albanyareamathcircle.blogspot.com/" target="_blank">Albany Area Math Circle</a>, a wonderful community of problem solvers with whom she has been happily making mistakes since 2001. She is also a public policy economist, specializing in public finance and mathematical economics. She teaches economics at Union College in Schenectady, New York, where her students run a free Volunteer Income Tax Assistance (VITA) site for low-income working families, people with disabilities, and senior citizens. She is also the Associate Director of the Math Prize for Girls, which brings together hundreds of young women from across the U.S. and Canada for a celebration of extreme problem solving each year. Her latest initiative is launching the Guerrilla Math Circles movement. <br /><b><br /></b><b>Melanie Hayes</b> has made it her life’s work to help gifted children find their niche and achieve their goals. She is passionate about creating a world where all children are encouraged to wonder, explore, and think. Melanie holds a M.Ed. with an emphasis in the intellectual, social, and emotional needs of gifted and talented children. She is also a credentialed teacher and educational consultant with experience in evaluation, assessment, intervention, professional development, teaching, and mentoring. Melanie has gifted twins, so she experiences life with gifted children on a personal level as well, both the joys and the hardships. She writes about her work and family on her blog, <a href="http://mjhayes.wordpress.com/" target="_blank">Life Among the Gifted</a>. Melanie homeschools her children and enjoys watching them learn and grow through their daily activities. She loves to travel, paint, sculpt, garden, write, and hike in the wilds. <br /><b><br /></b><b>Michael Hartley</b>, creator of <a href="http://dr-mikes-math-games-for-kids.com/" target="_blank">Dr. Mike's Math Games for Kids</a>, was raised in Perth, Western Australia. He's loved math since he was a child, so it was natural for him to do a Ph.D. in mathematics, in a branch of geometry. After a ten-year stint teaching in colleges and universities in Malaysia, he returned to Perth to work as a mathematician in the oil and gas industry. <br /><br /><b>Michelle Martin</b> is a public school teacher at Prairie Creek Community School in Northfield, Minnesota, where she works with a class of fourth and fifth graders. She loves having the opportunity to weave math and other subjects together. Her favorite moments are those when students glimpse the wonder and awe of mathematics. She writes about the work of her class at <a href="http://prairiecreek.typepad.com/herons" target="_blank">The Rookery</a>. <br /><b><br /></b><b>Nancy Blachman</b> strives to make math cool, fun, and engaging, finding her inspiration in the work of Vi Hart and Martin Gardner. Nancy is co-founder of the Nueva Math Circle, founder of <a href="http://mathdelights.org/">MathDelights.org</a> and the Julia Robinson Mathematics Festival, and is a member of the organizing committee for the Gathering for Gardner. Nancy has taught after-school math classes and math camp for four years and Mathematica classes for ten years. Nancy earned a B.Sc. in Mathematics from the University of Birmingham, UK, a Masters in Operations Research from the University of California at Berkeley, and a Masters in Computer Science from Stanford University. <br /><b><br /></b><b>Pam Sorooshian</b> has been teaching college-level economics and statistics since 1976. She's also been a homeschooling mom to three now-grown children. Pam is a proponent of unschooling, in which there are no lessons, assignments, tests, or grades, and children learn naturally while following their own interests with the encouragement and strong support of their parents. Pam has been a speaker at many homeschooling conferences and an American Educational Research Association conference, and is on the Board of Directors of the National Home Education Network and the HomeSchool Association of California. <br /><b><br /></b><b>Paul Salomon</b> is a math nerd.teacher.artist living in Saint Louis. He designed his imbalance problems during his time at Saint Ann’s School in Brooklyn, where he taught math to grades 5 through 12 and helped develop a mathematical art program. Paul shares his own mathematical art through Twitter (@lostinrecursion) and his blog, <a href="http://lostinrecursion.wordpress.com/" target="_blank">Lost in Recursion</a>. Paul also coauthors <a href="http://mathmunch.org/" target="_blank">Math Munch</a>, a weekly math blog written with middle schoolers in mind, aimed at helping them dig in to the mathematical world that exists outside of math class. <br /><b><br /></b><b>Pilar Bewley</b> holds two AMI Montessori certifications (ages 3 to 6 and 6 to 12), as well as a M.Ed. in Montessori Education. A self-professed "math hater" from childhood, she discovered the beauty of mathematics and geometry during her Montessori training courses. She lives with her math geek husband and Montessori baby in San Diego, CA. <br /><br /><b>Rodi Steinig</b> is the founder, director, and leader of the Talking Stick Math Circle. Her goal is to awaken the inner mathematician and to shepherd the unfolding of abstract reasoning in every child. Her formal training is in economics and education. Rodi continues to hone her craft of math circle leadership under the gentle guidance of Bob and Ellen Kaplan. Her mathematical interests are logic, history, hydrodynamics, sacred geometry, the misapplication of statistics, and the expression of mathematical concepts via multiple modalities. Rodi blogs at <a href="http://talkingsticklearningcenter.org/category/math-circle-blog">talkingsticklearningcenter.org/category/math-circle-blog</a>. <br /><br /><b>Sean Sweeney</b> currently teaches high school Algebra and Calculus just outside of Philadelphia at Woodlynde School, a college prep school for students with learning disabilities. He constantly looks for exciting ways to engage students in math who have often had bad experiences with it in the past. More activities, ideas and songs from Sean can be found at <a href="http://sweeneymath.blogspot.com/">sweeneymath.blogspot.com</a>. <br /><br /><b>Stephen Kennedy</b> first learned the pleasures of mathematics at Stonehill College in Massachusetts and ever since has wondered why nobody told him earlier. He teaches mathematics at Carleton College in Northfield, Minnesota. He co-directs the Carleton College Summer Mathematics Program for Women and served a five-year stint as co-editor of the Mathematical Association of America’s magazine for undergraduates, Math Horizons. <br /><br /><b>Sue VanHattum</b> has been teaching math at the community college level for over twenty years, and recently branched out to teach math at her son’s freeschool. She created the Richmond Math Salon, a monthly event she hosted at her home, gathering kids and their parents together to play with math. She blogs about math and math education at <a href="http://mathmamawrites.blogspot.com/" target="_blank">Math Mama Writes</a>. Sue appreciates both the community-building possibilities inherent in public schools, and the freedom to learn naturally available through homeschooling. Outside of math, teaching, and writing, her interests include gardening, living simply, activism for the rights of all, and children’s books. Sue is a single parent, raising one son. <br /><br /><b>Tanya Khovanova</b> received her Ph.D. in Mathematics from Moscow State University in 1988. At that time her research interests were in representation theory, integrable systems, super-string theory, and quantum groups. Her research was interrupted by a period of employment in industry, where she became interested in algorithms, complexity theory, cryptography, and networks. Several years ago she resigned from industry to return to research. Her current interests lie in combinatorics, number theory, probability theory, and recreational mathematics. Her website is located at <a href="http://tanyakhovanova.com/">tanyakhovanova.com</a>. She also writes a highly popular <a href="http://blog.tanyakhovanova.com/" target="_blank">math blog</a>, and produces the <a href="http://numbergossip.com/" target="_blank">Number Gossip website</a>. <br /><b><br /></b><b>Tiffani Bearup</b> used to be a pretty average, run-of-the-mill, standard-issue mom trying to figure out life in suburbia and her place in it. Then she started unschooling, and things got a little crazy! Crazy good! As this book went to press she and her three kids were all traveling through South America. She blogs at <a href="http://freeplaylife.com/">freeplaylife.com</a>. <br /><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-31045408419642716752014-05-18T10:05:00.000-07:002014-05-18T10:05:47.237-07:00Using Math to Describe Gravity (from Playing With Math)We are nearing completion of the book, <i>Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers</i>. Our copy edit process was really a deeper editing process, and took over a year, with us working through a few chapters a week at first, getting everything just right. We finished it on May 9, Mother's Day. (My son was born on Mother's Day. I didn't realize until this moment how much I like it that our copy edit finished on Mother's Day too!)<br /><br />One of the last pieces to go through copy edit was <a href="http://sweeneymath.blogspot.com/2009/08/m-catapult-project-pt-1-catapult-plans.html" target="_blank">Sean's catapult activity</a> that goes with Kate Nowak's chapter, Better Teaching Through Blogging. I had to build a catapult to test out the instructions Sean gave. I am not a crafts sort of person, so that had to wait until I had plenty of time to deal with it. Last fall, after I finally made my catapult, made my small adjustments to Sean's piece, and sent it to our copy editor, she asked a lot of questions about the math. I began to realize that we needed an explanation of the math behind the catapult project.<br /><br />So I wrote one last piece for the book, Using Math to Describe Gravity. I had fun writing this one. Most of what I wrote for the book took me a long time (and lots of agonizing) to write. This one was easy and quick. I finally realized that I really enjoy writing explanations. (I think I know my next book project...) I thought this might be useful to have online, so I'm including a modified version here. Enjoy! <br /><br /><br /><span style="font-size: large;"><b><br /></b></span><span style="font-size: large;"><b>Using Math to Describe Gravity</b></span><br /><br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-KCMHiCCibAo/U3jW2nr1ALI/AAAAAAAAA_0/oScK5dvOow4/s1600/c3+fountain.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-KCMHiCCibAo/U3jW2nr1ALI/AAAAAAAAA_0/oScK5dvOow4/s1600/c3+fountain.jpg" height="133" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">flickr.com/photos/joemacjr/189254474</td></tr></tbody></table><br />In the picture above, we see water shooting upward. Whenever you squirt water from a hose pointed up at an angle, it follows a similar path. Have you ever wondered why? Math is helpful whenever we want to think about how something is changing.<br /><br />For example, the idea of velocity tells us how position is changing with respect to time. (Unlike speed, which is just a positive number, velocity has direction, and can be negative to indicate a downward direction.) If you are driving at 70 miles per hour, in one hour you will have driven 70 miles. In two hours, 140 miles. Mathematicians generalize this idea by writing distance = rate * time.<br /><br />The path of the water in the fountain makes the shape of a parabola. The physics of gravity explains why the water follows that path. As the force of gravity pulls us toward the center of the Earth, it creates an acceleration – a change in velocity. When we are near the surface of the Earth, that acceleration is always 32 feet per second squared (downward). That’s a weird unit, isn’t it? It means that if you are headed straight down, your velocity will increase by 32 feet per second each second. So when you drop something, one second later it has already gone from a speed of 0 feet per second to a speed of 32 feet per second. Over 20 miles per hour! In metric units, that would be 9.8 meters per second squared. (We’ll mostly stick with metric from here on out.)<br /><br />This acceleration affects the relationship between distance and time because the speed, or rate, is changing. In the driving example, if your speed goes from 55 miles per hour to 60 miles per hour to 70 miles per hour, it makes it harder to calculate how far you have driven. (Calculus is great for understanding situations where your rate of change is changing, but I've written this for people who aren't familiar with the concepts of calculus, sticking to algebraic ideas.)<br /><br />When considering the physics of situations like the fountain, we can analyze the vertical and horizontal motion separately. Gravity isn’t affecting the horizontal motion, so that stays constant. (If you were moving very fast, air resistance would slow you down. But at these speeds, we can ignore the effect of air resistance.) When you throw something upward at an angle, gravity pulls straight down, changing the vertical component of the velocity. Since the horizontal part of the motion is constant, this gradually changes the direction the object is headed, making the parabolic path you see above.<br /><br />But how do we know that it’s in exactly the shape of a parabola? To see why it is, we’ll start with a simpler experiment, throwing a ball directly up. Now the path is no longer a parabola, because the horizontal position is not changing. But, amazingly, if we were to draw a graph of height versus time, that graph would still be a parabola. To describe parabolas algebraically, we use equations like y = at<sup>2</sup>+bt+c. In this case, y is the height and t is the time.<br /><br />[Note: Depending on the flavor we want, we say the same thing in lots of different ways. rate * time = distance, R*T=D, velocity * time = height, h=v*.]<br /><br />We can figure out a lot about a, b, and c by using what we know about the physical situation. When t=0, y = a*0<sup>2</sup>+b*0+c = c, so c can be filled in by knowing your initial height. If we had no gravity (and no air resistance), what we threw upward would keep going up with a constant speed. So its height would be given by rate (velocity) times time plus initial height. Do you see why b is the initial velocity the ball has as it leaves your hand?<br /><br />That leaves a. The value of a will always be half the value of the gravitational constant - hmm, why half? In one second, the acceleration of gravity would increase velocity from 0 to 9.8 meters per second. So the average velocity during that second is 4.9 meters per second. In t seconds, we would increase from 0 to 9.8t meters per second, with an average of 4.9t meters per second times t seconds, for a height change of 4.9t<sup>2</sup> meters.<br /><br />Now we can see the effects of initial height, initial velocity, and gravity combining to make an equation of the form y = at<sup>2</sup>+bt+c for height versus time. Gravity will actually affect an object in this way no matter which direction it’s pointed. And since the horizontal motion is constant, this same sort of relationship holds when we look at height versus horizontal position, although the values for a, b, and c will change.<br /><br />When an object is launched at an angle, the value for a is determined by both gravity and the launch angle, b is determined by both the initial speed of launch and the launch angle, and c is still the initial height. To find the values for a and b, we can use the symmetry of parabolas across their vertex. If we can find the coordinates for the position of the vertex, we can use that to help use find the values for a and b.<br /><br />All this thinking can help us understand the catapult activity better:<br /><ul><li>When launching from the floor, where beginning and ending heights are the same, the x-coordinate of the vertex is just half the distance. So the vertex will be reached halfway through the time in the air.</li><li>From the time the projectile reaches the vertex until the time it hits the floor, its height is decreasing at the same rate as an object that has been dropped, so you just use 4.9t<sup>2</sup> to find how far it dropped, which tells you how high it was.</li><li>The vertex form for the equation of a parabola is y = a(x - h)<sup>2</sup> + k, where (h,k) represents the vertex, which we just found. If we assume that we launched from the origin, plugging zero in for x and y allows us to find the value for a.</li><li>With the values for a, h, and k filled in, we have an equation in x and y. We can simplify it (change it to the form y = ax<sup>2</sup>+bx+c), and then modify it for raised launches by simply changing the value of c from 0 to the height of the launch surface. </li><li>We can use the new equation to figure out where to put a target we want to hit! The target will be on the ground, where the height is 0, so we can plug in y=0, and find x. In real life, the numbers that show up are almost never simple enough for factoring to work, so we’d need the quadratic formula. Measuring the horizontal distance from the floor right below the catapult, to the positive x-value from the quadratic formula, and centering the target there, we should be able to hit it. Candy bombing, here we come! </li></ul><br /><br /><br />__________<br />My thanks to John Golden for his help improving this. Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-220715410832828922014-05-02T10:01:00.000-07:002014-05-02T10:01:18.269-07:00Linkfest for Friday, May 2Sometime in the past week, I added <a href="http://mathblogging.org/">mathblogging.org</a> to my feedly feed. They compile posts from all the math blogs they know of, with an interesting mechanism that takes you right to the original blog, instead of just linking to it. Yikes! I was already following hundreds of math blogs, and suddenly my feed doubled or tripled. I'll have to let it go eventually, it's just too much. But I found lots of interesting posts on blogs I'd never seen before, so today's linkfest will be more diverse than usual.<br /><br /><ul><li><a href="http://maaminutemath.blogspot.com/2014/04/april-28-2014.html" target="_blank">MAA Minute Math</a> (which has a new problem each weekday) had this problem on Monday: The volume (V), surface area (S), and total edge length (L) for a cube are consecutive terms in an arithmetic sequence. The largest possible side length is a+sqrt b (a,b integers). Find a+b. </li><li><a href="http://wordplay.blogs.nytimes.com/2014/04/28/num/" target="_blank">NUM+BER=PLAY</a>, quite a bit harder than the ones that repeat letters/digits.</li><li><a href="http://im-possible.info/english/library/grey/grey93.html" target="_blank">930 impossible figures</a>.</li><li><a href="http://exit10a.blogspot.com/2014/04/37-lbs-of-garbage.html" target="_blank">37 pounds of garbage</a> (kindergarten math)</li><li>Rebecka's students loved their <a href="http://www.epsilon-delta.org/2014/04/decoding-with-matricesa-scavenger-hunt.html" target="_blank">matrix-encoded scavenger hunt</a>.</li><li>Ashli is reading lots of <a href="http://the policy of requiring a passing score on an Algebra II exam for high school graduation simply cannot be justified." target="_blank">interesting research</a>. "The policy of requiring a passing score on an Algebra II exam for high school graduation simply cannot be justified." </li><li><a href="http://www.mathforgrownups.com/dont-miss-this/" target="_blank"><i>Math for Writers</i></a> is free for download, today and tomorrow. </li><li><a href="http://www.yofx.org/?p=2824" target="_blank">The tides of the quadratic formula.</a> (What can you do with this?)</li><li><a href="http://mathhombre.blogspot.com/2014/05/truchet.html" target="_blank">Math and quilting</a>, geogebra fun with John Golden.</li><li>The current issue of Nautilus (an amazing online journal) is on symmetry. This issue includes a chapter a week for five weeks. This week's chapter is called 'In Theory', and includes articles on <a href="http://nautil.us/issue/13/symmetry/impossible-cookware-and-other-triumphs-of-the-penrose-tile" target="_blank">Penrose tiles</a> and <a href="http://nautil.us/issue/13/symmetry/math-shall-set-you-freefrom-envy" target="_blank">fair sharing</a>.</li><li><a href="http://www.science4all.org/le-nguyen-hoang/newtons-laws/" target="_blank">A primer on Newton's Laws</a>, that starts out by emphasizing how counter-intuitive they are. (Physics, not math, but physics is the reason for calculus, right?)</li><li>Megan Schmidt loved how engaged her students were with <a href="http://mathybeagle.com/2014/05/02/nrichs-digit-doozy/" target="_blank">Nrich's Digit Doozy problem</a>. I also like their <a href="http://nrich.maths.org/8010" target="_blank">largest product</a> problem. I think I'll put a bunch of their posters up in the math lab in August.</li><li>Bon Crowder says <a href="http://mathfour.com/commentary/summer-slide-the-big-myth" target="_blank">the "summer slide" is a myth</a>. I concur. Let's <i>play</i> with math this summer.</li><li><a href="http://www.thusspakeak.com/baron_m/2014/05/01-FourHouses.html" target="_blank">A puzzle posed as a card game</a>.</li><li><a href="http://www.newscientist.com/article/mg22229674.500-the-mirror-crackd-why-physics-is-lopsided.html" target="_blank">Tantalizing intro</a> to 'The mirror crack'd: why physics is lopsided'. I'd like to read this, but I don't have a subscription. Bummer. </li><li><a href="http://mathhombre.blogspot.com/2014/05/four-corners.html" target="_blank">Graphing game</a> from John Golden.</li><li><a href="http://www.whydomath.org/index.html" target="_blank">Why do math?</a> from Siam, describes how math solves problems. Includes a description of google page rank (though it's not very in-depth).</li><li><a href="http://prairiecreek.typepad.com/herons/2014/04/the-answer-is-a-and-a-half.html" target="_blank">A and a half</a>. How an Oregon Trail simulation demonstrates the problems with standardized tests.</li><li><a href="http://crewtonramoneshouseofmath.blogspot.com/2014/04/moving-on-with-manipulative.html" target="_blank">Engaging students</a> in learning the multiplication facts, up to 20 times.</li></ul><br />Crazy, how much good stuff there is to read. How can anyone absorb all this?<br /><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-85590851725716257282014-04-30T17:34:00.000-07:002014-04-30T17:34:00.488-07:00Caption Contest - Sometimes Learning Math Is Like Reaching Into a HurricaneThe book I've been putting together for the past 5 1/2 years, <i>Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers</i>, is almost done. We have chapters from over 30 authors, each chapter followed by a game, puzzle, or activity. It's looking great.<br /><br />We are finishing up the illustrations now, and I need your help with one illustration. It illustrates the idea which informs the title of a chapter - At the Eye of the Hurricane, by Melanie Hayes. The illustration has two panels, sort of like a comic strip. And it reminds me of those collections of photos, with captions saying what different groups think you do. (Like this homeschooling one: <a href="http://www.lisaoutloud.net/Websites/lisaoutloud/images/homeschool.jpg" rel="nofollow" target="_blank">http://www.lisaoutloud.net/Websites/lisaoutloud/images/homeschool.jpg</a>)<br /><br /><br />Here's the text it illustrates:<br /> <style>@font-face { font-family: "Cambria Math"; }@font-face { font-family: "ヒラギノ角ゴ Pro W3"; }p.MsoNormal, li.MsoNormal, div.MsoNormal { margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: "Times New Roman"; color: black; }span.footnotereference { color: black; vertical-align: super; }p.footnotetext, li.footnotetext, div.footnotetext { margin: 0in 0in 0.0001pt; font-size: 12pt; font-family: "Times New Roman"; color: black; }.MsoChpDefault { font-size: 10pt; }div.WordSection1 { page: WordSection1; }</style> <br /><blockquote class="tr_bq"><div class="MsoNormal" style="margin-right: 1.5in; text-align: justify;"><span style="font-size: 11.0pt;">We usually think of mathematics as a series of steps, starting with the foundational building blocks and eventually building a stairway to higher mathematics. We don’t move students up the stairway until they have mastered each previous step. We feel compelled to make sure they thoroughly understand algebra before we allow them to try trigonometry or calculus. For mathematically-gifted children, this lock-step method can kill their creativity and their desire to fit the pieces of the overall mathematical puzzle together. </span></div><div class="MsoNormal" style="margin-right: 1.5in; text-align: justify;"><br /></div><div class="MsoNormal" style="margin-right: 1.5in; text-align: justify;"><span style="font-size: 11.0pt;">The learning style of some mathematically-gifted children*<span class="footnotereference"><span style="mso-ansi-font-size: 11.0pt;"><span style="mso-special-character: footnote;"><span class="footnotereference"><span style="font-family: "Times New Roman"; font-size: 11.0pt; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: "ヒラギノ角ゴ Pro W3"; mso-fareast-language: EN-US;"></span></span></span></span></span> is more akin to a hurricane; they stand at the eye and watch all the information swirling around them. Their curiosity urges them to reach into the hurricane and pull out bits and pieces of mathematical data. They ponder and experiment until they fit those bits and pieces into their prior knowledge and come up with the whole picture. To the casual observer or bewildered teacher it often seems disjointed and messy, but wonderful things are happening within the eye of the hurricane. These children are making deep connections, internalizing knowledge, and building concepts that will allow them to experiment and try out their own theories. Teaching mathematically-gifted children requires an open mind and a willingness to throw out most accepted notions of how to teach math.</span></div></blockquote><br /><br />And here's what we have so far... (Thank you, Linda Palter!)<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-KmqRWUkZC3E/U2GUgpU-xGI/AAAAAAAAA-8/yYyKs7tYV8k/s1600/tornado+&+steps.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-KmqRWUkZC3E/U2GUgpU-xGI/AAAAAAAAA-8/yYyKs7tYV8k/s1600/tornado+&+steps.png" height="400" width="202" /> </a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /><div class="mbs _5pbx userContent" data-ft="{"tn":"K"}"> It needs a title and two captions. I think the title is just 'learning math', but maybe you have a better idea. The top panel could be 'what people think' and the bottom one, 'reality'. But that doesn't quite work. What do you think?<br /><br /><br />Prize: A signed copy of the book.<br /><br /><br /><br />_______<br /><span style="font-size: x-small;">* Although the author identifies this as a trait of gifted children, I think it is likely to be a good description for anyone who loves math. (The captions do not have to refer to gifted kids.</span>)</div>Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com6tag:blogger.com,1999:blog-5303307482158922565.post-34065020558344066602014-04-26T21:31:00.003-07:002014-04-26T21:31:58.107-07:00Linkfest for Saturday, April 26Partly I'm compiling these links for my own benefit, but some of this week's posts were pretty exciting. I hope you're out there enjoying them. Please let me know. Thanks.<br /><br /><ul><li><a href="http://www.salon.com/2014/04/20/ditch_the_10000_hour_rule_why_malcolm_gladwells_famous_advice_falls_short/" target="_blank">Varied, interleaved learning</a> feels less effective, but is shown to be significantly more effective.</li><li><a href="http://www.concentric.net/~pvb/ALG/rightpaths.html" target="_blank">Visualizing solutions to n-th degree algebraic equations using right-angle geometric paths</a>. (I want to try to read this when I have more time and mental energy.)</li><li>Mr. K describes how <a href="http://blog.mathpl.us/?p=1050" target="_blank">substitute teaching has made him a better teacher</a>.</li><li><a href="http://us4.campaign-archive2.com/?u=6ae8427d1f6f3b8d6da57d629&id=66a1ac3450&e=c9eed1d024" target="_blank">Yakov Sinai models motion</a> on a square pool table with a round cushion in the middle. He's proved that the ball will eventually hit every point on the table. This helps physicists understand gasses.</li><li><a href="http://fawnnguyen.com/2014/04/21/20140408.aspx?ref=rss" target="_blank">Fawn's shopping contest</a> - a way to practice percents (for discounts and tax) in a more challenging context.</li><li><a href="http://nixthetricks.com/" target="_blank"><i>Nix the Tricks</i></a> is a free ebook created by Tina Cardone with the help of dozens of math teachers online. Which 'tricks' are you attached to? Which make you cringe when your students mention them?</li><li>A number of bloggers are answering <a href="http://grantwiggins.wordpress.com/2014/04/23/conceptual-understanding-in-mathematics/" target="_blank">some questions Grant Wiggins posed</a>. Number one, why is division by zero undefined?</li><li><a href="http://mathbabe.org/2014/04/23/interview-with-a-high-school-math-teacher-on-the-common-core/" target="_blank">Cathy O'Neill interviewed Fawn Nguyen</a> on the math Common Core standards. Fawn is an optimist. I fear that the goodness she describes in the standards may be overpowered by the harm done with the endless testing, money for testing (instead of for teaching and learning), evaluations of schools and teachers determined by testing, etc.</li><li>A game. <a href="http://jacquerie.github.io/hh/" target="_blank">Make a graph</a> with the given number of edges at each node.</li><li>Geoff's series of posts (especially <a href="http://emergentmath.com/2014/04/23/nctmnola-processing-session-3-summer-school-is-dead-long-live-summer-school/" target="_blank">number three on summer school with Jo Boaler</a>, <a href="http://emergentmath.com/2014/04/23/nctmnola-processing-session-4-i-may-have-missed-my-calling/" target="_blank">and number four on Chirstopher Danielson's hexagons</a>) about the workshops he attended at the NCTM conference in New Orleans made me wish I could have been there. </li><li><a href="http://talkingsticklearningcenter.org/proving-stuff-mathematical-thinking-with-five-year-olds-3-0/" target="_blank">What do proofs with 5-year-olds look like?</a> Rodi tells them, <i>“I hear with my eyes and see with my ears.”</i> And they work very hard to prove her wrong.</li><li>I am dedicating <i>Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers</i> to Seymour Papert. You can get some nuggets of his by following <a href="http://dailypapert.com/?p=1303" target="_blank">The Daily Papert</a>. From Wednesday: “You learn in the deepest way when something happens that makes you fall in love with a particular piece of knowledge. “ </li><li><a href="http://www.doingmathematics.com/2/post/2014/04/knowing-alongside.html" target="_blank">When students make their own definitions</a>... </li><li>Mr, Honner, <a href="http://mrhonner.com/archives/11847" target="_blank">Solving Pallet Equations</a>.</li><li>I have not managed to solve the <a href="http://numberwarrior.wordpress.com/2014/04/25/robot-maze-puzzle/" target="_blank">Robot Maze Puzzle</a>. Can you?</li><li><a href="http://infinitesums.com/commentary/2014/riemann-sums-and-hand-turkeys" target="_blank">Leading into calculus, estimating areas</a>.</li><li><a href="http://mathnotations.blogspot.com/2014/04/parametricprojectile-motion-simulated.html" target="_blank">Parametric projectile motion simulated in Desmos</a>.</li><li>Are you required to have the standard you are teaching on the board? <a href="http://blog.mathpl.us/?p=1020" target="_blank">Mr. K describes </a>why that sucks. Spoilers, anyone? And then Brooke Powers describes how helpful it is to <a href="http://powersfulmath.wordpress.com/2014/04/14/why-i-always-lead-with-the-punchline/" target="_blank">share your bigger goals</a> at the beginning of a unit. (I don't think my way of doing that would satisfy the folks hovering over high school teachers. Thank goodness I teach college.)</li></ul><br />This one's not math, but it's too good not to mention: <a href="http://nautil.us/issue/12/feedback/ants-swarm-like-brains-think" target="_blank">Researchers are analyzing similarities between the behavoir of ants and neuron</a>s. Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com2tag:blogger.com,1999:blog-5303307482158922565.post-24254683727400450472014-04-20T15:58:00.000-07:002014-04-20T15:58:00.029-07:00Linkfest for Sunday, April 20 (a small one)<ul><li>Nat Banting on <a href="http://musingmathematically.blogspot.com/2014/04/conceptualizing-drills.html" target="_blank">making practice more conceptual</a> - ask students to do the last step in posing the problem. Nice!</li><li>Andrew Knauft descrbies why he thinks <a href="http://blog.amathknauft.com/2014/04/geogebra-quadratics-desmos.html" target="_blank">Geogebra > Desmos</a>. </li><li>A site for finding, building, and storing formulas online, <a href="http://formulasheet.com/#h" target="_blank">Formula Sheet</a>. (hat tip to <a href="http://blog.mrwaddell.net/" target="_blank">Glenn Waddell</a>, whose diigo account may have inspired me to get one - which I don't use. Maybe I should ask him to teach me how to make it useful. I love his real posts, but his Diigo Links (Weekly) are often full of useful ideas too.)</li><li><a href="http://mathinyourfeet.blogspot.com/2014/04/learning-math-without-body.html" target="_blank">Malke wonders</a> whether lack of recess (and the movement it encourages) is taking away children's ability to make sense with their bodies.</li></ul><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-26612187449274775232014-04-18T10:17:00.004-07:002014-04-18T10:17:47.909-07:00Linkfest for Friday, April 18<ul><li>Jen Orr's first graders <a href="http://jenorr.com/?p=251" target="_blank">tell number stories and make a video of it</a>.</li><li>David Cox's post,<a href="http://coxmath.blogspot.com/2014/04/fostering-hypothesis-wrecking-mindset.html" target="_blank"> Fostering the Hypothesis Wrecking Mindset,</a> includes a list of a dozen good problems.</li><li>Dan Finkel has been enjoying how much thinking goes on when people play his <a href="http://mathforlove.com/2014/04/horseshoes-and-hand-grenades/" target="_blank">Horseshoes game</a>, a variation on a classic number game. (Winner is the one who gets <i>closest</i> to the target number, using 4 given numbers.)</li><li>Got some interesting data in a pdf file, and want to put it into a spreadsheet? Flowing Data points to <a href="http://flowingdata.com/2014/04/08/extract-csv-data-from-pdf-files-with-tabula-2/" target="_blank">a nice program to help with that</a>.</li><li>The <a href="http://tonysmaths.blogspot.co.uk/2014/04/109th-carnival-of-mathematics.html" target="_blank">109th Carnival of Mathematics</a> points to a game the author seems to like as well as 2048. I'll try it - <a href="http://www.johnrausch.com/puzzleworld/app/lunar_lockout/lunar_lockout.htm" target="_blank">Lunar Lockout</a>.</li><li>Toomai made a video - <a href="http://toomai.wordpress.com/2014/04/07/parabolas-iii/" target="_blank">All Parabolas are the Same Shape</a>.</li><li>Mimi's <a href="http://untilnextstop.blogspot.com/2014/04/parametric-equations-project.html" target="_blank">Parametric Equations Animation Project</a></li><li>Mr. K is <a href="http://blog.mathpl.us/?p=1029" target="_blank">introducing exponent properties with geometric series</a>. I think I'm going to try to involve series in as many pre-calc topics as possible next semester.</li><li>Jonathan Claydon wrote <a href="http://infinitesums.com/commentary/2014/3/23/a-year-with-desmos" target="_blank">A Year with Desmos</a>.</li></ul><br /><br /><br /><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-16697761776984873832014-04-05T08:38:00.001-07:002014-04-05T08:38:44.778-07:00Linkfest for Saturday, April 5<ul><li>This video shows <a href="http://toomai.wordpress.com/2014/03/31/parabolas-ii/" target="_blank">multiplying by using a parabola</a>. Completely impractical, but I was curious why it worked. I figured it out and then wondered if my pre-calculus students could figure it out too. I wanted a demo instead of a video, so I <a href="https://www.desmos.com/calculator/f8auuzhllk" target="_blank">built something in Desmos</a>. (Hide the equations, and click on the three dots. The middle dot will always multiply the absolute values of the other two.) It's not perfect, but it might be good enough to impress my students.</li><li>I've seen <a href="http://blog.mathedpage.org/2014/03/the-function-dance.html" target="_blank">this cute list of functions, with the person's arms illustrating the graph</a>, on a number of blogs lately. I see two that are wrong. Henri sees one wrong, and has quibbles with four of them. What do you see?</li><li>Common Core for math... I keep hearing that the math standards are pretty good. But if the tests ignore the most important standards (the process standards, which describe mathematical thinking), then they're being used badly. <a href="http://dianeravitch.net/2014/04/02/jonathan-katz-on-some-problems-of-common-core-mathematics/" target="_blank">This post by Jonathan Katz</a> goes into some detail.</li><li><a href="http://studyofchange.wordpress.com/2011/09/17/week-1-practicing-engagement/" target="_blank">Nice exercise. </a>One person looks at the board, and describes the graph drawn there. Their partner must draw it from the verbal description.</li><li>Quintic polynomials. There is no formula for the roots. <a href="http://www.johndcook.com/blog/2014/04/03/quintic-root/" target="_blank">But there is this.</a> I want to learn more!</li><li><a href="http://fawnnguyen.com/2014/04/02/prices-proportions-percents.aspx?ref=rss" target="_blank">Fawn's lesson for proportional thinking.</a></li><li><a href="http://dailypapert.com/?p=1286" target="_blank">Papert on "hard fun."</a></li><li>I like <a href="http://www.geogebratube.org/student/m1992" target="_blank">this diagonal problem</a>, but when I tried it in class my students were not persistent enough to succeed with it. David Cox's post on <a href="http://coxmath.blogspot.com/2014/04/hypothesis-wrecking-and-diagonal-problem.html" target="_blank">how he used it with his students</a> makes me want to try it again. </li><li>In whatif?, xkcd's creator, Randall Munroe, takes a silly question and analyzes it with math and physics to come up with an answer. <a href="http://what-if.xkcd.com/90/" target="_blank">In this episode</a>, he figure how how big a splash you'd get from a tree as big as all trees on earth falling into an ocean with the water of all the ocean's on earth.</li><li><a href="http://www.moebiusnoodles.com/2014/04/inspired-by-calculus-math-circle-week-3/" target="_blank">In this post from her calculus for kids series</a>, I like Maria's thoughts on how we help kids learn problem-solving.</li></ul><br /><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-5670481874953571122014-03-30T09:21:00.001-07:002014-03-30T09:21:11.552-07:00Linkfest for Sunday, March 30<ul><li>Michael Pershan asks some good questions about <a href="http://rationalexpressions.blogspot.com/2014/03/stealing-tricks-from-teaching-fractions.html" target="_blank">how to approach the teaching of complex numbers</a>.</li><li>Fawn Nguyen has another <a href="http://mathtalks.fawnnguyen.com/2014/03/29/week-14.aspx" target="_blank">Math Talk</a> with her students. (I'm wondering if students think about which sorts of visual patterns will give a quadratic function and which will give a linear function.)</li><li><a href="http://www.openmathbook.org/" target="_blank">OpenMathBook</a>, a blog <span>"to promote, discuss, and develop free and open source mathematics textbooks".</span></li><li>Ihor describes a high school class <a href="http://climeconnections.blogspot.com/2014/03/noon-day-adventure-at-panther-academy.html" target="_blank">recreating the experiment Eratosthenes conducted 2200 years ago</a>. (Some day I want to try it...)</li><li>Maria is <a href="http://www.moebiusnoodles.com/2014/03/inspired-by-calculus-math-circle-week-2/" target="_blank">conducting calculus math circles with 7 to 11 year olds</a>. I am fascinated. My understanding of calculus is so steeped in algebraic thinking, it was hard for me to imagine at first. I love what she's doing.</li></ul><br /><br /><br />Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0tag:blogger.com,1999:blog-5303307482158922565.post-13618694149682725502014-03-28T08:50:00.000-07:002014-03-28T08:50:53.585-07:00Guest Post: John Spencer Addresses "Frustrated Parent"<i>John's was the first post I saw about the silly complaint going around from "Frustrated Parent". (Now I've seen about three more. They all have good things to say.) John has graciously allowed me to share his whole post here. (But <a href="http://www.educationrethink.com/2014/03/in-defense-of-new-math.html#gpluscomments" target="_blank">the comments over at his place are an interesting mix</a>, so go on over there too.) Here's John:</i><br /><br />There are many things I hate about the Common Core standards. I hate the way teachers were pushed out of the creation and adoption phase and how we have little voice in the implementation. I hate the fact that the standards will continue to be assessed with standardized, multiple choice tests and that these scores will be used with Value Added Measures in both teacher salary and teacher evaluation. However, I think it's important that in our criticism of bad policy we are careful to avoid blasting good pedagogy.<br /><br /><br />I'm seeing many of these posts making their rounds on Facebook.<br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-hLgGn-k8GrQ/UzT5dgS59lI/AAAAAAAAA9I/x3tzrDfTDqw/s1600/frustrated+parent+complaint.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-hLgGn-k8GrQ/UzT5dgS59lI/AAAAAAAAA9I/x3tzrDfTDqw/s1600/frustrated+parent+complaint.jpg" /></a></div><br /><br /><br />I'm seeing statements like, "What the hell is a number line and why do kids need it?" Or, "just teach them the basics." The notion of using a manipulative, playing with numbers, breaking them them apart and comparing processes is somehow viewed as non-mathematical.<br /><br />The truth is that number lines are powerful tools for understanding integers. True, when subtraction is something simple that requires no "borrowing" it feels like a joke. However, the goal is to build up number sense. It's to help them understand math conceptually. If you flip the numbers and end with a negative number as an answer, suddenly a number line helps make the negative-positive relationship more powerful.<br /><br />This parent's snarky answer about "the process used would get you terminated" is based on a faulty assumption that a first grader needs the same approach as an engineer. And yet . . . this "new math" approach that people mock is something we use constantly in real-world, mental math. <br /><br />Consider it this way: You have fifty-three dollars and you need to give someone twenty-seven dollars. What are you going to do to figure it out? If you find yourself breaking by tens and going backward, chances are you are using a mental number line.<br /><br />Oh, you could pull out a piece of paper and do that math that way, but chances is are that as an engineer, you'd be fired . . . or at least laughed at.<br /><br />I remember someone posting an angry rant about doing multiplication by breaking it up into different pieces. "Just teach the algorithm!" the parent posted.<br /><br />I posted a response. "If the bill is 27.42 and you want to leave a twenty percent tip, what's the answer? How did you find it?"<br /><br />Some people divided by five. Others multiplied by .2. Still others moved one decimal over and doubled it. Some rounded up to thirty. In other words, there were multiple processes that worked and each of them involved understanding the properties of numbers. In other words, most people used a process mentally that they were openly mocking on Facebook.<br /><br /><br /><div style="text-align: center;">* * *</div><br />Oddly enough, many of these same people who are mocking "new math" in their posts are also lamenting the fact that Singapore is kicking our butts in math. What they fail to realize is that the places where math is working are the places where they are building number sense.<br /><br />I've seen what happens when students lack number sense. They learn a lockstep process and think that math is the same as baking a cake. They follow the recipe without understanding why they are doing what they are doing. However, when they get into something as simple as linear equations, they struggle to know what to "do first," when there are often two or three options.<br /><br />When students lack number sense and they get the wrong answer, they fail to understand why an answer is illogical. You end up with a student who misplaces a decimal number and never finds his or her mistake. Asking students to think conceptually and engage in diagnostic problem-solving isn't superfluous. It's actually part of "the basics."<br /><br />I know that the "new" math looks different, but instead of criticizing it for being hard or being complicated, try thinking about the theories behind it. There's a reason we're using manipulatives, breaking things apart, using number lines and comparing processes. This is how math works.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.com0