Thursday, August 30, 2012

Meet the New Bloggers (week 2)

This week I'll be introducing you to Malcolm, Sarah, Mark, Algebrainiac, Jeff, David, Nancy, MPA, Tyler, and Ian. Last week I subscribed to 2 new blogs. My blog roll is just too long. If I add any this week, I'd better go delete some...

Many of the new bloggers mentioned that this initiation is helping them to keep writing - training wheels help. Just remember to keep riding that bike after the training wheels come off!

Malcolm Eckel, blogging at Solving Problems, wrote I wish my teacher training had told me... His summary: Three pieces of advice I wish I'd gotten - your grading systems don't have to follow the traditional model, wait time for students to think is *crucial*, and one concrete strategy for making a connection with students.
Making a personal connection with your students is not a vague, ill-defined process.
(Sue here:) I am super-impressed with anyone who emails all of their students. I'm also impressed with how many bloggers are using mastery-based grading systems (SBG or otherwise).

Sarah Educating (@saraheducating), blogging at Sarah Educating, wrote This is what being a teacher looks like? Her summary: My post is about how before I started teaching, I never realized how much of the job of a teacher is the social/emotional stuff.  A lot of the best and hardest moments of my teaching career haven't been about the classwork, they've been in helping kids do the hard work of being a person.  Life is hard!
In many ways though, as hard as it can be to wade through the drama to the heart of the matter, it’s one of the very best parts of my job. 
This brought back memories. Early in my teaching career I taught middle school. I wasn't very good, but I did help one student become the person she wanted to be. (Maybe more than one...)

Mark Davis (@graphpapershirt), blogging at Graph Paper Shirt, wrote I Wish I Had Known… His summary: I wished I had learned how to continue growing professionally in an environment that offers little support or even makes fun of the desire to go above and beyond.  Furthermore, I wished I had learned that trying and succeeding in a few things is far better than being made to believe that you have to do everything at once.
I realized that I was beginning to collect a pile of underpants.
Ahh, bookmarks = underpants, I get it. Yep, usin' 'em. 

Algebrainiac (@algebrainiac1), blogging at Algebrainiac, wrote My Algebra 1 Skills List. Algebrainiac's summary: I am sharing my version of my Algebra 1 Skills List, that I have used and improved over the last 4 years.  I also shared my thoughts about incorporating Interactive notebooks in my classes this year. I LOVE the premise behind them, but it kind of feels like a lot to take on. I would love suggestions on my skills list and helpful hints on INBs!
It is kind of refreshing that 2 periods of math a day I know what I am doing and where I am going because it is Algebra 1.
I know how that feels. I'm doing so much new in my Calc I class, it makes me grateful to go to my Calc II class and know exactly what's next - I've done it so often. 

Jeff Brenneman (@brennemania), blogging at Trust Me - I'm a Math Teacher, wrote Ninjas: Undeniably Awesome. But Student Motivational Tool? His summary: I'm trying out a rather nebulous "achievement" system in my class called The Ninja Board. Students will earn ninja points and ninja rankings for various actions in class. The hope is that students will be more creative and deep with various class activities as a result.
That's what my students are inevitably going to ask me, and I'm not going to tell them. ... I'm purposely not going to tell my students what they can do to earn ninja points or ranks. I want them to discover that on their own.
Intriguing. I sure want to find out how this turns out. I'll have to follow Jeff's blog, won't I? (I don't think it's a good idea for college students, so I probably can't use it myself. But still, I'm intrigued.)

David Price (@compactspaces),  blogging at Compact Spaces, wrote XKCD and girls (part 1). His summary: Girls don't suck at math, and there are a few reasons (including luck) why I thought this from an early age! I am excited about teaching math in a school where a majority of students are girls.
However, it’s only over the past year or so I’ve become more aware of another (and perhaps) the largest advantage - I LOOK LIKE a math nerd.
I'm curious. Does a high ratio of girls in a school help the girls to be more assertive? 

Nancy,  blogging at Infinitelymanysolutions, wrote Venn diagrams. Her summary: This post is about using Venn diagrams to make connections between related concepts in math.
We’ve become so focused on our own grade level standards that we block out everything else and forget the big picture of how it all fits together.
I like her idea of having students use Venn diagrams to compare mathematical procedures. A student example shows the differences and similarities between addition and multiplication of fractions.

Making Paper Airplanes (@makingairplanes), blogging at Making Paper Airplanes, wrote What I Only Wish I Had Learned... MPA's summary: After a somewhat crazy and chaotic first year of teaching, I am thrilled to be starting the new year with a full-time, full-year job and my own classroom!  Looking back at last year, it is important to me to keep my eye on the big picture this year, starting with not freaking out too much about the first day!
Everything doesn’t need to be perfect on day one.
I don't know. After 25 years, I still obsess over my first day. And I really like how that turned out this semester. But yeah, big picture comes first.

Tyler Borek (@tybo9188), blogging at Real Problems, wrote The Applied Problems Shortage. His summary: This is a post about the hierarchy of problem-writing difficulty (procedural, conceptual, and applied), the resulting shortage of conceptual and applied problems, and the impact on students.
Then, last year, as a tutor, I found myself facing the same situation that my teachers faced– a surplus of educational ambition, but a shortage of applied problems.    
Applied problems are harder to make up than conceptual; both are harder to create than simple procedural problems. And that's why our Internet problem-sharing is so important. If I give one to everyone and get dozens, we're all richer.

Ian Frame (@mrframemath), blogging at Igniting Inquiry, wrote 10 Years From Now... His summary: My thoughts about what I want my students to say a decade from now. Surprisingly for a math teacher, it's not how to solve equations or add fractions.
There is so much more to life than knowing how to find the roots of polynomials.
“In Mr. Frame’s class, I always have the chance to succeed." Yeah.

The round up of week two responses is at these blogs: Julie, Fawn, Anne, Megan, Bowman, Sam, Lisa, John, @druinok, Tina, and Kate.

Saturday, August 25, 2012

Meet the New Bloggers (week 1)

With so many new bloggers, it's hard to imagine reading all their posts. I get to read just 8 of them carefully, and introduce them to you. Without further ado, meet Carey, Janet, Amy, Dan, Nolan, NB, Jeff, and Michelle.

Carey Lehner (@careylehner), blogging at  I am a Teacher.  This is my Journey., wrote Learning Logs. Here's how Carey sums it up: I am going to try and incorporate learning logs as my closer to the class.  I am hoping they will help students become more reflective learners.  I am also hoping that by reading their reflections I will become a better teacher.
I also think it will help me improve my skills as a teacher by reading what works well and what doesn't for the students.
(Sue here...) I'd like to get my students writing more. After all the other changes I've implemented have become more routine, perhaps I can use the writing prompts Carey suggests.

Janet Villani (, blogging at jvillani, wrote My endless search for iPad apps. Here's how she sums it up: I'm implementing iPads into my classroom.  My post talks about different apps to use.   
I was looking for apps that allowed for collaboration, communication and exploration.
No iPads in my life (yet), so I can't use these suggestions.What's your favorite?

Amy Zimmer,  blogging at Ms. Z Teaches in Mathland, wrote Week 1 of the blogging initiative. Here's how she sums it up: Sorting out your activities by days of the week, and, oh, an introduction.
To those of you, like me, can get overwhelmed by all the deliciousness of curricula and how to deliver it, I offer you this one bit of advice...
Amy has students make up their own word problems. She gave an example for systems of equations using cafeteria food. Cool.

Dan Bowdoin (@danbowdoin), blogging at Technology Integration for Math Engagement, wrote It's All About TIME! Here's how he sums it up: This post is all about how TIME was started. Through the inspiration of writing tech grants for my classroom, I took to the blogosphere to look for more information. This journey has led me to discover so many new tools and ideas, and I now enjoy taking the time to share my TIME ideas with you.
I recognized the need to lead by example.
It looks like Dan has some good ideas about writing grant proposals.

Nolan (@ncd5y), blogging at Classroom Rationalizations, wrote Shopping at Lowe's (and New Year, New Challenges - he couldn't stop at just 1). Here's how he sums it up: My post talks about using 2 coupons for Lowe's to learn about systems of equations.
Ultimately, I think the students will be able to make connections with all the different representations in a natural and intuitive way.
I can use this to help my pre-calc students review linear equations. I'll tell them about the coupons my buddy Nolan got at Lowes, and ask which they'd prefer $10 off of 10% off. I may use this on Monday! Thanks, Nolan.

Nutter Buttersmith (@reminoodle), blogging at The MathSmith, wrote Why I am Nutter Buttersmith/The MathSmith. Here's how she sums it up: My blogpost is a story of how I became Nutter Buttersmith and The MathSmith.  This includes how I started blogging and how I discovered the math blogging community.
So, that, in a nutshell is how I became both Nutter Buttersmith and The MathSmith!
Looks like NB enjoys her puns. Following.

Jeff de Varona (@devaron3), blogging at The Problem Bank, wrote Eight (yes 8!) Goals for This School Year. Here's how he sums it up: Every year I make a few teaching goals, but this year I've got EIGHT.  This post is the result of the past year I've spent on Twitter, since every one of these goals has Twitter-influence written all over it.  SBAR, whiteboarding, passions, videos...I'll need help, but I can't wait to get started.
I try to create an environment where it’s understood that we are all learning together, and that mistakes are another tool to help us learn.
My favorites are #2, improved questioning and mathematical discourse, and #6, continue to celebrate mistakes.

Michelle Riley,  blogging at A Year of Growth, wrote Why "A Year of Growth"? Here's how she sums it up: This post provides insight into the title of my blog and the importance of growth in teaching.  It also reflects on why I have been trying to blog.
I titled this blog "A Year of Growth" because I wanted to remind myself that each and every year is an opportunity to grow; to grow as an instructor, to grow as a mentor, to grow as an individual.
Michelle also wrote, "I ... believe that this is the best professional development I have had over the last 3 years." Yep, me too. And what a good way to close. May we all enjoy our teaching and our guerrilla professional  development this year.

Update: Posts featuring all the other bloggers participating in the first week of the Math Blogging Initiation: Julie, Fawn, Anne, Megan, Bowman, Sam, Lisa, John, @druinok, Tina, and Kate.

Friday, August 24, 2012

Happy Math Mama: Teaching is Glorious

Wow! What a week! I'm enjoying all three of my classes - pre-calculus, calculus I, and calculus II. I started each of them with a project at the heart of the course. More engaging than hearing me talk about my teaching philosophy, but a little scary for many of the students. (And my pre-calculus project was not well enough thought out.) We've been working from handouts all week, and many of the students will be relieved as we move toward the textbook in pre-cal and calc II. In calc I it will take a little longer to get in sync with the text, because I did not want to start with limits.

Calculus is a beautiful and powerful story, with historical necessity driving it. Starting with limits (a supremely technical and possibly alienating topic) seems guaranteed to turn droves of students away from what could be their favorite math class ever. About a year ago, I read the first 6 pages of Morris Kline's Calculus: An Intuitive and Physical Approach, and was entranced. (The link goes to the Google book, which allows you to read all of those first 6 pages. The rest of the book didn't work quite so well for me, but it may for you.) That, along with a bit of a mini-history in Matt Boelkins' book, helped me set the stage during the first week. I assigned those 6 pages for students to read as homework this weekend in both calc I and II. (And I wish I had made a handout asking them a few questions about it. It's done now - I'll assign it on Monday.)

Here's the mini-history from Boelkins' preface (page v):

Several fundamental ideas in calculus are more than 2000 years old. As a formal subdiscipline of mathematics, calculus was first introduced and developed in the late 1600s, with key independent contributions from Sir Isaac Newton and Gottfried Wilhelm Leibniz. Mathematicians agree that the subject has been understood rigorously since the work of Augustin Louis Cauchy and Karl Weierstrass in the mid 1800s when the field of modern analysis was developed, in part to make sense of the infinitely small quantities on which calculus rests.

In both calc classes, I talked about the 3 phases of this history:
  • ancient history, in which Archimedes (and probably many others) figured out areas of simple curved shapes like the circle,
  • the 1600's, in which Newton and Leibniz developed the calculus, and fought over it, and
  • the 1800's, in which Cauchy and Weierstrass built a logical foundation for the parts that Newton and Leibniz had left pretty fuzzy. (I told them this was where the textbook treatment of limits belonged, and that we'd build up to it after playing with the deep ideas developed by Newton and Leibniz.)

In Calc I, I also described the two main problems calculus was invented to solve - finding slopes of curvy lines, which is the same as finding rates of change and instantaneous velocity, and finding areas. I had them graph  y=x2,  draw in a tangent line at x=2, and estimate the slope. I heard lots of good conversations. Toward the end I asked them what definitions they already knew for tangent. They don't know the definition of tangent we use for calculus yet, but that definition just makes precise our intuition. (Unlike limits, which do not really connect with any prior intuitions.) They gave me the circle and trig definitions, and we discussed how to define tangent in this new situation. We did not arrive at anything momentous, but the issue is in their heads now, hopefully simmering.

I loved starting this way. In the calc II class I had planned for them to find the area of a circle on the first day, but left out the best part - cutting up a circle. So their project extended to day 2, and I also used it in calc I on day 2. Fawn Nguyen's work on this with middle school students was my inspiration. Although my students know much more mathematical content, I think this is a tremendously valuable lesson in mathematical thinking. How many people notice this important difference between the two circle formulas they've memorized, C= 2πr  and A=πr2?  C= 2πr is a simple algebraic revision of the definition of π (since π is defined as the ratio of circumference to diameter), and A=πr2 is a provable theorem. Here's my handout (after revisions):

Circumference and Area of a Circle
Thinking about Definitions and Proofs

You probably know the ‘formulas’ for circumference and area of a circle. (Do you have any tricks for remembering them?)

But where did they come from?

Part I.
The number pi is defined as the ratio of circumference to diameter: π=C/D
Regardless of the size of the circle, and of the units of measure used, the circumference will always be pi times the diameter. (Why?)  From this definition, we get the more usual form: C= 2πr

Part II.
Now let’s try to find the area of a circle. We’ll pretend we don’t know any ‘formulas’.
1.     Start by drawing a circle as carefully as possible on the centimeter graph paper on back.  What is its radius?
2.     Make a guess, just by looking, for the area of your circle. Guess: _________
3.     Now come up with the best estimate you can for the area of your circle. Describe how you did it:

Part III. Once you’ve gotten to this point, get a (coffee filter) circle from me and fold it through the center as many times as you can. Cut on the folds. Arrange the pieces in a way that helps you re-think area. Are you seeing anything interesting?

Part IV. Can we turn any of our estimates into a proof?

I saw some eyes lighting up as students saw the circle turning into a lumpy rectangle, and came up with area = height (radius) times width (half the circumference), on their own! Then we got to discuss whether we had a proof yet. (No, it's not a rectangle. We'll need something like limits to turn this into a proper proof.)

On Wednesday and Thursday, we worked through the first projects in the Boelkins text. My students need lots more detailed instructions than he provides. I'm going to modify this quite a bit for my next class. But I do like it.


There are always a few students in Calc I who have taken the course before. I was talking to two of them in my office, and discussing the need for limits. We've been taking the slope of secant lines, where the two points are very close. We want to bring them crashing together. So we're looking at the limit as the distance between them (h) goes to 0 of the slope. As I explained, I realized that all the pictures with limit questions use x instead of h, and never have the hole in the function at 0. I drew my own picture, and helped them see the connection of limits to the slopes we're trying to find. When I address this in class next week, I hope to have a good drawing of this. I can't believe I never noticed this lack before.

Next Week:
  • More practice with finding tangents through numeric approximation and algebraic work,
  • Starting to define the idea of limit,
  • Defining the derivative,
  • Sketching graphs based on function and derivative values, and
  • Sketching the graph of the derivative of a graphed function.

Saturday, August 18, 2012

Start. Continue. Stop.

I saw it at Tina's blog (Drawing on Math), and it's been in my head since then. Seems like weeks ago. It's only been two days. That's how much my mind's been whirring. (Writing this at 2am, because I just couldn't sleep.) What I want to start doing in my classes, what I want to continue doing, and what I want to stop doing.

  1. Using the techniques I learned at that WAYK workshop, at least some of the signs.
  2. Bringing food. This might not pan out. I'd like to have tea and healthy munchies available in the back of the room. (This comes from WAYK. It's the 'meadow' you might want to head to when you're 'full' (of learning).) I'm considering bananas, popcorn, apples, essene bread, nuts, maybe sweets.
  3. Doing more math (less rules of the course, syllabus, blah blah) on day one, picking a problem that's at the heart of the course. This is part of starting my planning by reflecting on my goals.

  1. Designing the course from what I know it to be about, rather than following the textbook. I might use the textbook daily (or I might not). But I design the course. Designing my calculus course is the main thing keeping me awake nights - I can't stop thinking about it.
  2. Letting students retest. My linear algebra students really came through in the end because of this. They earned the highest grades I've ever been able to give (about 8 A's, 4 B's, 1 C, and 1 D). I think all my students can do this if they're willing to make the commitment.
  3. Having the students work in groups of 4 much of the time, and in pairs when I'm doing anything close to lecture (so they can check in with a partner on what I just presented).
  4. Searching for cool projects that go well with the courses I teach.
  5. Offering one mastery test on problem solving, which will appear as a subtest of each test I give. I'll be doing this in pre-calc, and probably in calc I. I don't think I can do it in calc II. The students only have to solve one problem to master this.
  6. Offering donut points: When a student catches me in a mistake, it's a donut point. When the class has gotten 30 donut points, I bring in donuts. Two functions: 1. Get those mistakes cleared up. 2. More importantly, get the students questioning what I'm saying.
  7. Doing much of what I mentioned in this First Day post 3 years ago, including index cards to learn their names and call on them,  making a phone list, and stamping homework.
  8. Blogging. Aka reflecting on my teaching.

  1. I might stop putting grades on tests. I've used percents on tests. (Quizzes get x.x/2, which may work well, actually.) I might switch to just putting  'Mastered', 'Getting close', 'Needs more work', or something similar, and still putting the percent in my gradebook. (Mastered=90% to 100%, Getting close=65% to 89%.) Or, I might think about it this semester, and try to implement it later. I feel like I'm trying to do a lot new already, and I don't want to overload myself.
  2. I'd like to move away from the expensive textbooks put out by conventional publishers (and toward open source textbooks). I don't get to choose this alone, really. My department picks the required textbook together. I'm hoping to be able to influence them on the next calculus text. The Guichard looks the most conventional (and therefore the most likely to appeal to the whole department), but it doesn't have as many exercises as I'd like.
  3. I'll stop doing 'thumbs up-down-sideways' (mentioned in that First Day post), because I'd like to replace it with 'show your level', where students hold one hand sideways with 4 fingers spread to show the levels (1. not there, 2. getting some, 3. getting it, 4. could explain to others and extend), and point with the other hand to their level.

What's changing and what's staying the same for you?

Wednesday, August 15, 2012

Math Blogger Initiation: May I help you?

Sam Shah is providing an amazing community service. He's offered to help new bloggers get started with a 4-week-long initiation: each week the new blogger gets a prompt to write about, and gets featured on the blog of a more established blogger. I have the honor of being one of the volunteer "established bloggers".

Sam expected maybe 20 or 30 participants. He got almost 200. There are about ten volunteers, so we'll each get almost 20 new bloggers to feature.

I wanted to offer something else. I know I needed lots of hand-holding when I was starting up my blog. I'm not sure I could have done it without Kate's help. Sam will be away this week, so I'm adding my own layer here. If you're one of the group of 200, and have questions, comment on this post. I'll take on the first 5 people with questions. You can email me at mathanthologyeditor on gmail after being one of the first 5 to comment here.

To all of you, have fun!

Sunday, August 12, 2012

Getting Ready for Day One

A few years ago, I stopped going over my syllabus in class on the first day. For the lower level classes, I created a Syllabus Quiz, asking them when my office hours were (and addressing all the most important points on my syllabus), due on the 2nd day of class. Both semesters last year I began with the Put Your Group on the Axes exercise. I like that, but I want to think more about my first day.

Chris Shore just posted about his first day plans. What I liked most was this idea:
... an American martial artist who toured fighting schools in China ... said that for all the good teachers, he learned everything they were going to teach him in the first lesson, and the rest of his time with them was spent mastering those first-day lessons.
Reading that made me want to clarify for myself what my goals are for my classes, and to plan my Day One activities to point students toward those goals.

My goals for each class:
  • help students form a learning community, where they feel safe taking risks
  • provide tasks that are deeply engaging
  • help students learn to problem-solve
  • help students become more persistent (teach them about how useful a flexible mindset is)
  • help students learn the 'material' of the course, along with a broader understanding of what math is
My first question to myself, then, is whether my axes activity helps build a community. It definitely helps students bond in their groups of 4, and they use math in an unusual way. But I have noticed that they struggle with it. (And many give up the struggle too quickly.) If I have a group of 4 of us up front model it, then they'll have a better sense of how to do it (and maybe I can get a student to model persistence, even). I'll be working for a few minutes with the whole class; I think that might be a better way to start this activity. In Pre-calculus, we'll begin with this. In both my calculus classes, I'm starting with an activity that gets at the heart of the course. I've figured that out below for Pre-calculus, too. So the axes activity will come after the more course-specific activity.

In Calculus, we'll be starting with graphing y=x2, and drawing a tangent line at x=2, freehand. They'll do that in their groups of 4, and estimate the slope of their tangent line. Together, we'll talk about the various meanings of the word 'tangent'.  This task is at the heart of the course. Then they'll do the axes exercise.

In Calculus II, they'll start with finding the area of a circle. I want them to begin to address the difference between definitions (pi is defined to be the ratio of circumference to diameter) and proved theorems (area can be shown, by ancient methods that lead toward calculus, to be half the circumference times the radius). They'll also do the axes exercise.

I'm working now on creating a task for the Pre-Calculus class. It won't be as deep as the other two, unless I come up with something better in the next week. I like to think the students' job in that course is to learn to identify families of functions. So I'm writing up some dialogues that should go with some graphs. One each for linear, quadratic, exponential, and periodic.


Here's what I've got for now:

Stories and Graphs

Alicia: “The days are getting shorter now. The sun’s still up until past 8pm, but I’ve noticed that it’s a bit earlier each week.”
Bo: “I wonder what the longest and shortest days are.”

Cristina: “If you go back in my family, I have my two parents, 4 grandparents, 8 great-grandparents – did you know my great-grandma lives with us?”
Diego: “Whoa, mine too! No wait, she’s my great, great. She’s 93.”
Cristina: “We’d have 16 of those. I wonder how far back until everyone’s related.”
Diego: “Hmm, there’s 7 billion people on Earth but it would be less the further you go back…”

Erlino: “I pay $30 a month for this phone, plus 1 cent a minute. Sure glad I don’t pay for data too.”
Foday: “I use about an hour a day. My plan is $40 a month with no per-minute charges.”

Greta: “We visited the Grand Canyon this summer. At one of the view points, I stood at the edge of an incredible cliff. My brother dropped a little rock, and we heard it hit 3 seconds later.”
Hazel: “I wonder how far that is.”

Please draw a graph (with axes labeled) to go with each story. Identify each one as linear, quadratic, exponential, or periodic.

What are you planning for your first day?

Saturday, August 11, 2012

Open Source Textbooks for Calculus and Pre-Calculus

I believe all of the textbooks I've mentioned below are licensed either as Creative Commons or with GNU licensing.

It looks like the best site for finding textbooks that are Calculus-level and above is the American Institute of Mathematics' Open Textbook Initiative. I found the Strang and Guichard there, though I knew of the Strang already. Boelkins is hoping to make it onto their approved list when his text is more complete. They also have two Linear Algebra texts, which I may look at for the Spring, although I really like the text we're using.

For Calculus, I've found:
  • Active Calculus, Matt Boelkins (523 pages, single variable, project-oriented)
  • Contemporary Calculus, Dale Hoffman (split into 3 books, most Calc I course will need the first two)
  • Calculus, David Guichard (single variable, 318 pages, multi-variable available too)  
  • Calculus, Benjamin Crowell (single-variable, 205 pages, infinitesimal approach, very readable)
  • Calculus, Gilbert Strang (multi-variable, 671 pages, MIT, somewhat poor quality pdf - looks like it went through a copy machine)
I think I may use material from all of these, plus the dozens of things I've found on blogs (collected in this draft google doc for now). I really like the Active Calculus, and hope to use it extensively. But I'll be playing things by ear somewhat, as I find out over time what works with my students.

And for Pre-Calculus, I've found:
Neither of the first two has a separate chapter for triangle trigonometry, which I like to do first. (I think we often learn best in the same order the topics were first discovered.) Lucky me, this trigonometry text starts with triangle trig.

Many of my students have very limited budgets. I'm so happy to be able to find what look like good texts that they'll be able to print for under $15. (For the longer texts, I may suggest printing only the relevant chapters to keep the cost down. I think the 1092 pages would cost around $30.)

Eventually I hope to convince my department to use these, or others like them, as the official texts for the courses. (Then maybe we could require a reading device, which would allow the students to have that paid for through student aid.) Many of my linear algebra students had the text on an ipad or similar device. I think they were able to mark it up. Backpacks are going to get lighter, and wallets are going to suffer less.

For both courses, I'll be adding in activities and problems from Exeter (Glenn Waddell's posts on Exeter's problems are very convincing) and this Rich Problems collection. And here's a fun-looking book a few students might be willing to look at,  Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving, Sanjoy Mahajan. I am now making a flyer to post at my office door.

Here's another long list of free textbooks.

[For anyone local to Berkeley, Copy Grafik has good prices. You can print over 300 pages, and get it bound with plastic and vinyl covers for $12.]

Thursday, August 2, 2012

Book Progress: Playing With Math

(This is a preliminary sketch...)
I got new copies of my manuscript printed yesterday. Every time I do that, I'm so excited. I love holding the book in my hands.

Here's our table of contents. There are still a few minor changes expected, but as you can see, it's pretty complete at this point. (The most glaring absence in the manuscript now is the lack of artwork. That's coming.)

   Playing With Math: 
      Stories from Math Circles, Homeschoolers, 
      and Passionate Teachers


Preface                                                                                          9
Introduction                                                                               13

Section 1. Math Circles and More: Celebrating Math
Section Introduction                                                                    19
The Art of Inquiry: A Very Young Math Circle, Julia Brodsky  23
   Game: Dotsy, Leonard Pitt, Cinda Heeren, & Tom Magliery  30
Rejoicing in Confusion, Maria Droujkova                                   31
   Game: Parent Bingo, Maria Droujkova                                    35
Parents and Kids Together, Sue VanHattum                                37
   Puzzle: Alien Math, Amanda Serenevy                                    45
Bionic Algebra Adventures, Colleen King                                   47
   Story: Alexandria Jones in Egypt, Denise Gaskins                        53
The Oakland Math Circle: A First Iteration, Jamylle Carter       59
   Game: Fantastic Four, Exploratorium Staff                              64
A Culture of Enthusiasm for Math, Amanda Serenevy               65
   Puzzle: Vertices, Edges, and Faces, Amanda Sernevy              67
Seized By a Good Idea, Stephen Kennedy                                  69
   Puzzle: Math Without Words #1, James Tanton                        75
A Prison Math Circle, Bob and Ellen Kaplan                             77
   Puzzle: Math Without Words #2, James Tanton                       80
Agents of Math Circles, Mary O’Keeffe                                    83
   Puzzle: Food for Thought, Jan Nordgreen                               88
The Julia Robinson Mathematics Festival, Nancy Blachman     89
   Saint Mary’s Math Contest Sampler, Br. Alfred Brousseau    91
   Exploration: Candy Conundrum, Joshua Zucker                     91
A Young Voice: Consider the Circle, Elisa Vanett                       93

Section 2. Homeschoolers Do Math
Section Introduction                                                                    97
Tying It All Together, Julie Brennan                                           99
   Puzzle: Pigeons Everywhere, Jan Nordgreen                         107
A Few Questions Answered, Julie Brennan                              109
   Puzzles: Fun With Basic Arithmetic                                      116
Transitioning to Living Math, Jimmie Lanley                           117
   Game: Math Card War, Denise Gaskin                                  123
Learning From My Kids, Melanie Hayes                                 125
   Puzzle: Self-Referential Puzzle #1, Jack Webster                  140
One and a Quarter Pizzas, Holly Graff                                      141
   Game:                [this one needs written permission]             146
The Math Haters Come Around, Tiffani Bearup                       147
   Puzzle: Magic Hexagon, Michael Hartley                              154
Mapping the Familiar, Malke Rosenfeld                                   155
   Puzzle: Function Machine                                                      157
Radically Sensible Ideas, Pam Sorooshian                                 159
   Game: Place Value Risk                                                          168
A Young Voice: An Unschooler at College, Lavinia Karl          169

Section 3. Bringing Our Passion Into the Classroom
Section Introduction                                                                  173
Trust, Montessori Style, Pilar Bewley                                      181
   Puzzle: Foxes and Rabbits, Sue VanHattum                          187
Math In Your Feet, Malke Rosenfeld                                       189
   Puzzle: Is This for Real? Photo by Avery Pickford               197
Dinosaur Math, Michelle Martin                                              199
   Story: The Imaginary Carousel, Levshin and Alexandrova    201
Blogging Towards Better Teaching, Kate Nowak                     207
   Puzzle: Will 2010 Be Another 1989? Jan Nordgreen             211
Putting Myself in My Students’ Shoes, Allison Cuttler            213
   Puzzle: A Little Math Magic, Jonathan Halabi                      216
An Argument Against the Real World, Friedrich Knauss         217
   Puzzle: Octopus Logic, Tanya Khovanova                            219
Area of a Circle, Fawn Nguyen                                                 221
   Exploration: Coloring Cubes, Joshua Zucker                         223
Textbook Free: Kicking the Habit, Chris Shore                         225
   Puzzle: What Number Am I? Jonathan Halabi                       228
Math Is Not Linear, Alison Forster                                            229
A young voice: Geometric Delights, Luyi Zhang                      237

Section 4. Resources                                                                245
Part 1. The Wealth Online
Introduction                                                                               247
Maria Droujkova, Electronic Commons                                   253
The Game of Math Goes Online, Colleen King                        257

Part 2. Who’s Doing Math? Making Change
Introduction                                                                               263
Debunking Math Myths, Sue VanHattum                                 259
Supporting Girls, Sue VanHattum                                             265
How to Become Invisible, Bob Kaplan                                             273

Part 3. Finding & Doing More
Sue’s Book Picks                                                                       275
Starting a Math Club, Circle, or Other Math Alternative         281
A Note on Online Sites (and a few more links)                        284
Hints for Puzzles                                                                       285

Conclusion of the Book                                                          287

References                                                                                  300
Meet the Authors                                                                        301
Acknowledgements                                                                    309
Index [coming]                                                                           310

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