tag:blogger.com,1999:blog-5303307482158922565.post782910641147694231..comments2017-08-14T21:34:20.641-07:00Comments on Math Mama Writes...: Sue's Top Ten Issues in Math EducationSue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger32125tag:blogger.com,1999:blog-5303307482158922565.post-70143366094154463302014-03-29T09:57:50.743-07:002014-03-29T09:57:50.743-07:00Nice article highlighting the reasons for math pho...Nice article highlighting the reasons for math phobia and the solutions to end it. I totally agree with you on this. People (both children and grown-ups) need to understand that math is not boring, it is recreational. This will make learning math a happy and positive experience. (http://myblogxpedition.blogspot.com/2014/03/math-can-be-recreational.html)sbloggerhttps://www.blogger.com/profile/00943520777853669818noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-84585335612161849682012-04-04T13:18:18.890-07:002012-04-04T13:18:18.890-07:00Duh. Right up there. I'll edit now. Thanks.Duh. Right up there. I'll edit now. Thanks.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-83290341260883552652012-04-03T13:29:33.292-07:002012-04-03T13:29:33.292-07:00Here you are:
"Why does a quadratic (y=x2), w...Here you are:<br />"Why does a quadratic (y=x2), which gives a U-shaped parabola as its graph, have the same sort of U-shaped graph after you add a straight line equation (y=2x+1) to it? (This was a recent blog post somewhere. I can't find it, though. Can someone point me to it?)"JJhttps://www.blogger.com/profile/16829561981417320165noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-18120492528239174552012-04-03T10:41:57.664-07:002012-04-03T10:41:57.664-07:00Umm, where did I ask for a reference? I'm sure...Umm, where did I ask for a reference? I'm sure I did, but I'm not remembering...Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-15966369069208470242012-04-02T04:58:43.113-07:002012-04-02T04:58:43.113-07:00Hi, Sue, as I dig deeper in your blog I keep findi...Hi, Sue, as I dig deeper in your blog I keep finding worthwhile posts. <br />I think I've found the reference you'd asked for:<br />this video by James Tanton explains the U-shape of the general quadratic:<br /><a href="http://www.youtube.com/watch?v=SA61hmwUD8I" rel="nofollow">All Quadratic Graphs are U-shaped</a>JJhttps://www.blogger.com/profile/16829561981417320165noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-81062444197002186622012-01-31T05:53:07.228-08:002012-01-31T05:53:07.228-08:00I wish I had some advice to offer you, but I don&#...I wish I had some advice to offer you, but I don't know anything about how life works there, and wouldn't be able to say anything useful to you.<br /><br />Good luck.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-6364961745794370672012-01-30T22:03:08.571-08:002012-01-30T22:03:08.571-08:00We're from Singapore and as you know there is ...We're from Singapore and as you know there is much talk about the country's success in Math Olympaid and the like.<br /><br />However, I would like to share that the way math is taught here is darn boring. Typical scenario is:<br />Teacher teaches concept, show method to solve problem and after that it's just lots and lots of drills and practice to ensure you get your A's for exams.<br /><br />I see so many interesting ways that you guys make math fun for the kids and I wish this can be done here.<br /><br />The problem with the way math learning is done here is that they pile up so much in the syllabus at the primary level. Only the smart ones can cope well, the rest just work like hell. Also, there is so much emphasis on mathematical heuristics which I feel, some kids are not quite ready for it at a young age. So in the end, they just get as much exposure as they can from practicing and memorise all the diff methods. That is not learning to think, it's just learning how to be a robot and react to a problem as quickly as possible so you can finish the exam paper in time.<br /><br />My daughter is 11 and a gifted child. Many times she discovers ambiguity in the questions in the teacher's worksheets. I told her this is a good learning situation and she can discuss with your teacher. I'm dismayed that the teacher just tell her to use a particular interpretation because that fits the answer. She refuse to admit that the question has a problem. That is ridiculous. I feel all learning should be interactive between kids and teachers and I"m so so disappointed the teacher just kill a kids curiousity like that.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-57727505081033184462011-08-29T12:32:12.672-07:002011-08-29T12:32:12.672-07:00Sue, I understand why Dr. Marty directed me to you...Sue, I understand why Dr. Marty directed me to your blog!! I'll need to come back to this post and leave comments... Wow! Say it Loud and Proud....POWEROrgMathhttps://www.blogger.com/profile/12495180918850995961noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-74375728621806203772011-04-21T08:42:37.591-07:002011-04-21T08:42:37.591-07:00"most of this is done wrong in most classroom..."most of this is done wrong in most classrooms" Agree! If you really want to teach kids math you need to be creative enough and not just stick to standard kind of teaching. Make it more interactive and challenging through different activities and games.. Thanks for the lists.Math Software For Kidshttp://www.mathsoftwareforkids.comnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-78645757150811451442010-03-11T06:13:33.182-08:002010-03-11T06:13:33.182-08:00it sounds like one-right-answer is part of what dr...it sounds like one-right-answer is part of what drew you to math in the beginning. for me, i was less one-right-answer than "the teacher can't tell me i'm wrong, and i can tell her she's wrong (if she is)." heady power for a kid. <br /><i>this looks like, not only the same</i><br />ballpark, <i>but the same</i> foul line.<br /><i>(our answers match almost exactly;<br />here again is "math is the authority".<br />it looks to me... and it may just be<br />another kid-with-a-hammer<br />obsession-of-the-day... like<br />to the extent that we differ at all<br />in discussions around "can there<br />really be foundations?", one big<br />issue is *context dependence*.<br />"is it *always* such-and-such"<br />asks the student.<br />and we have an opportunity to<br />do *philosophy* of math:<br />"hold on... there is no 'always'...<br />what type of object *is*<br />blahblahblah?"<br />[student stares dumbfaced as if<br />you have betrayed them: you're<br />"getting all mathy" on them].<br />now you've gotta make a decision.<br />go back to plain english and confusion<br />(usually this is the *right* option, <br />so don't get me wrong here)<br />or remind them once again...<br />and make it stick a little better...<br />that by "always" one means something<br />like<br />"every monic trinomial"<br />or<br />"every continuous function"<br />or<br />"all the equations in the exercise set"<br />or<br />some particular thing<br />with<br />dammit, a *name*.<br />and that we can't mean what we say<br />until we can say what we mean and<br />that this occurs much less often than<br />people think but it's easily remedied<br />if you'll just take some bloody care<br />once in a while like a math geek<br />and that one of our best tricks is <br />specifying the universe of discourse.</i><br /><br />3*4=13 isn't wrong if you're in base 9. i love finding what's right in a wrong answer. it's a good use i've put my arguing skills (lawyer for a daddy) to as a teacher. i can say "it sounds like you're thinking about this other sort of problem." i can show a student the right thing they did among the wrong thing(s).<br /><i>a great trick indeed.<br />so i'll put my mojo on it.<br />"your answer would be marked 'wrong' <br />*in the context*<br />of a [graded] base-ten calculation"<br />("... but *we* know... even if your<br />silly dont-blame-me-those-are-the-rules<br />*grader* doesn't know or care... that<br />we're clever enough, not only to <br />understand what's wrong<br />*in base ten context*<br />can be made right by <br />*changing* the context to base 9...")<br /></i><br /><br />programming would be a draw for some kids. papert saw it that way, too. i don't think it's "the answer" for all kids. and can you imagine a teacher saying "your program is wrong" because it doesn't match the model 'right answer'? yikes!<br /><i>only for the ones who want to know how computers work (loops and logic); right. the "authority" here typically comes from "what happens when you run the code" (and not from the teacher's pet peeves as happens all too often in elementary math); this is a Good Thing.</i>owenhttps://www.blogger.com/profile/09249915192605437832noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-77281524890347849962010-03-08T19:51:52.316-08:002010-03-08T19:51:52.316-08:00it sounds like one-right-answer is part of what dr...it sounds like one-right-answer is part of what drew you to math in the beginning. for me, i was less one-right-answer than "the teacher can't tell me i'm wrong, and i can tell her she's wrong (if she is)." heady power for a kid. <br /><br />3*4=13 isn't wrong if you're in base 9. i love finding what's right in a wrong answer. it's a good use i've put my arguing skills (lawyer for a daddy) to as a teacher. i can say "it sounds like you're thinking about this other sort of problem." i can show a student the right thing they did among the wrong thing(s).<br /><br />programming would be a draw for some kids. papert saw it that way, too. i don't think it's "the answer" for all kids. and can you imagine a teacher saying "your program is wrong" because it doesn't match the model 'right answer'? yikes!Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-62002139460571997332010-03-08T18:57:49.481-08:002010-03-08T18:57:49.481-08:00My son is thinking so much about what I'd call...My son is thinking so much about what I'd call place value these days. "60 and 60 is 120, right?" "Yep." No writing - at home, anyway. Lots of mathematical thought.<br /><br />I've long been puzzled by your emphasis on "the code". Maybe someday I'll get it... :^)<br />---sue v.<br /><br />maybe today!<br /><br />the "places" of "place value" are<br />places *in* certain symbol strings!<br />it sure doesn't matter that you<br />*speak* of such strings without<br />having actual *written* code<br />in front of your actual eyes...<br />that's not what i'm always <br />going on about at all...<br /><br />60+60=120<br />presumably gets its interest<br />from 6+6=12,<br />together with, right,<br />the "place value" concept...<br />*as it manifests in base ten*.<br /><br />now of course you and your kid<br />don't have to have spoken of<br />bases-other-than-ten for <br />the essential *role* of "ten"<br />in discussions of place value<br />to have become quite clear<br />all around.<br /><br />"what's so special about ten?"<br />i can now imagine asking <br />some kid of the same age<br />if i were lucky enough to<br />know any...<br />and i'd sure enough expect<br />(maybe with a *little*<br />stack-the-deck prompting<br />from me) pretty soon to<br />start hearing about the<br />role of *zero* (in, again,<br />certain symbol-strings).<br /><br />and when our conversations<br />*without* written work begin<br />to break down... and if we<br />still *care*... why then,<br />we'll break out some *pencils*<br />and take a look:<br />"what do you mean, *precisely*?".<br /><br />we've been talking about code all along.<br /><br />tangent.<br />calculating with numbers<br />is the very *model* of<br />one-right-answer-ism:<br />3*4=13<br />is just flat-out wrong.<br />and this is our greatest strength.<br /><br />in principle, anything worth <br />talking about passionately<br />in a math class should have<br />the *same* character:<br />there *is* a right answer<br />if we could only find it.<br /><br />in order to have this happen,<br />we have to agree on things.<br />we *can't* agree... and be<br />*sure* we agree... and be *right*...<br />without certain so-called "rigorous<br />definitions": marks on paper<br />(generally; otherwise<br />*verbatim verbal formulas*<br />memorized syllable-for-syllable<br />[mostly... i don't seek a <br />"rigorous" definition of "rigor"...<br />"one is *this* many"<br />and its ilk (so-called "ostensive <br />definitions") are all the rigor <br />we can *get* sometimes]).<br /><br />generally the "rigor" one speaks of<br />is... i think... pretty *close* to the<br />being-able-to-calculate-it-out-like-a-computer<br />thing i spoke of (with reference to<br />elementary arithmetic) a moment ago.<br />and this comes from "code".<br /><br />again. our power in mathematics<br />comes to an amazing extent from<br />being-able-in-principle to emulate<br />some doesn't-know-anything-*but*-code<br />*machine*.<br /><br />now i'm as much of a luddite as the next<br />guy, if the next guy figures the wrong turn<br />was somewhere around "domesticated animals".<br />but one *glaring* benefit of computers<br />in math ed is that students will work<br />for *hours* on getting code letter-perfect<br />(if they know no human being can see<br />their failures happening), that wouldn't put<br />in five *minutes* of homework on paper<br />without getting so frantic about each <br />"move" that they fall apart before even<br />getting started. it's that "interactivity".<br />this used to break my heart but it's true.<br /><br />if schools were for clarity,<br />command-line programming<br />would begin in about first grade.<br />it's much *easier* than almost<br />any other thing you can do <br />with a computer (which is why<br />it emerged much *earlier*<br />than the hugely-user-unfriendly<br />[from a "code" point of view]<br />*graphical* interfaces that<br />erased it from the national<br />consciousness in around 1984).<br /><br />(somebody mention "logo".)<br /><br />math *is* hard.<br />but it's much easier than anything else.<br />because we've got *all* the certainty.<br />(programming on this model<br />is of course a subset of math).<br /><br />otAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-11662238046992255072010-03-07T19:08:02.334-08:002010-03-07T19:08:02.334-08:00Maria, I loved your list.
Owen wrote:
>"...Maria, I loved your list. <br /><br />Owen wrote:<br />>"the student learns essentially<br />nothing until the student's<br />pencil makes marks on the page"<br /><br />Maybe for higher math, but not at all for young kids. The mathematical issues they're working on don't usually require pen(cil) and paper.<br /><br />My son is thinking so much about what I'd call place value these days. "60 and 60 is 120, right?" "Yep." No writing - at home, anyway. Lots of mathematical thought.<br /><br />I've long been puzzled by your emphasis on "the code". Maybe someday I'll get it... :^)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-8134388260339448252010-03-07T18:20:41.904-08:002010-03-07T18:20:41.904-08:00ten for maria.
1 - There isn't enough user-ge...ten for maria.<br /><br /><b>1 - There isn't enough user-generated content or "making your own math artifacts." </b><br /><br />equations, most likely, first.<br /><br />but wait. zero-th.<br />by-hand copies of the *symbols*<br />for the material at hand.<br />"the student learns essentially<br />nothing until the student's <br />pencil makes marks on the page"<br />is a pretty good first approximation<br />a lot of the time... or anyhow,<br />i'm far from the only teacher<br />given to *saying* stuff like this.<br /><br />i've got plenty to say, too, *about*<br />this but i'm hoping for a list of ten<br />in under 2^12 characters (for a little<br />longer; i've begun to despair already<br />at least a little though if you want<br />to know the truth). <br />"unions" should look different from "u" 's<br />as an example more or less at random.<br /><br />*our medium is handwriting.*<br /><br />first-and-a-half.<br />out-loud discussion of and...<br /><br />second.<br />...written sentences *about*<br />those equations. written<br />at leisure without the <br />instructor (or fellow student).<br /><br />third.<br />similar or exact versions of such equations,<br />repeated, or, much better of course,<br />improvised, in a "public" setting<br />with small or, slightly better i<br />suppose, large *groups* of fellow<br />students. oral presentation of<br />the sentences themselves is not<br />only okay here but much to be <br />preferred (the board should not<br />be littered with sentences). <br />the "correctness" of the sentences<br />should nonetheless be at issue<br />throughout the presentation.<br />said "correctness" is to refer<br />explicitly to "code"...<br />utilizing (hey! ed jargon!)<br />the symbols from our step zero.<br /><br />it does not escape my attention<br />that the "artifacts" created by<br />the student presentations i here<br />imagine are scribbles of chalk<br />on a board, soon erased. so be it.<br /><br />...<br />leaving some out...<br /><br />sixth<br />yick, computer code.<br /><br />seventh<br />student-designed exercises,<br />exam templates, lesson plans...<br /><br />eighth<br />songs and other verse, games,<br />comics and other graphics,<br />something to astonish even me.<br /><br />ninth<br />blogs.<br /><br />tenth<br />fanzines.r. r. vlorbikhttps://www.blogger.com/profile/02746118913980983815noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-32261524529378926722010-03-04T15:58:56.591-08:002010-03-04T15:58:56.591-08:00My top ten: of the day, and in no particular order...My top ten: of the day, and in no particular order.<br /><br />1 - There isn't enough user-generated content or "making your own math artifacts." In other words, severe dis-balance between giving and taking, especially for children.<br /><br />2 - The general tendency is to have an extremely impoverished list of topics for young kids. If I had a penny for every list consisting of counting and shapes entirely...<br /><br />3 - Speaking of age, tying content level to kids' ages is an unbelievably silly idea. Just say "No!"<br /><br />4 - Kids are barred from adult tasks, in all forms. Even seeing a professional at work, up close, is a rarity, let along long-term apprenticeships or short-term internships. The younger the kids, the harder it is for them to work. Wrong, wrong, WRONG!<br /><br />5 - Impoverished example spaces are prevalent throughout. Say, many curricula are using one positional system (decimal) and only two positions in it (tens and hundreds) to teach the idea initially. As a result, each example is taking an inordinately long time to learn, with shallow understanding.<br /><br />6 - Forgetting we still live in meatspace bites. Kids need to move every 10-15 minutes, and eat every half an hour or so while doing math. Also, tactile comfort objects, smells, and sounds make a difference. Oh, and while we are discussing this, learn to teach every major topic through whole-body movement.<br /><br />7 - Lack of group design is widespread. If you work in a space containing more than one kid, pretty please do tasks that work better in groups vs. individually. If you can't design such tasks, don't work in such spaces. Hint: worksheets usually work better individually. And by "individually" I mean "one person in a room with one teacher."<br /><br />8 - Math 2.0 where art thou?<br /><br />9 - Modern literacies are often nonexistent: programming, gaming, visual, social media, computational.<br /><br />10 - Stop ignoring research. Those in any way related to education, especially policymakers, who don't know first year undergraduate math methods course terminology will thereby be made into my literature review assistants for scholarly article writing. Database training included.MariaDhttps://www.blogger.com/profile/00769513929584082597noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-2341602802010242912010-03-04T11:42:52.151-08:002010-03-04T11:42:52.151-08:00Owen neglected to point to his own post, written i...Owen neglected to point to <a href="http://vlorbik.wordpress.com/2010/03/04/more-than-4k-characters-for-sue-v/" rel="nofollow">his own post</a>, written in response to this, which was too long to fit in a comment. (You'll want two windows open.)<br /><br />"4) is outright false or i’d've never<br />finished my thesis…" got me chuckling.<br /><br />Thanks, Owen! :^)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-23992702355385096302010-03-03T12:05:37.954-08:002010-03-03T12:05:37.954-08:00pat b (of this very thread)
has also worked extens...pat b (of this very thread)<br />has also worked extensively<br />on vocabulary (follow his link).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-12994972267088268722010-03-03T11:57:02.858-08:002010-03-03T11:57:02.858-08:00on (5)... specifically on
"the language of ma...on (5)... specifically on<br />"the language of math"...<br /><a href="http://www.case.edu/artsci/math/wells/pub/abouthbk.html" rel="nofollow">the handbook of math'l discourse</a><br />by charles wells is terrific.<br />(bonus point: it cites me.)<br />its author (charles wells)<br />does <a href="http://sixwingedseraph.wordpress.com/" rel="nofollow">a blog</a>. ot.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-91254596883988313082010-03-02T12:00:10.038-08:002010-03-02T12:00:10.038-08:00love it. thanks for the nod. for multiplying with...love it. thanks for the nod. for multiplying with compass & straightedge one need only construct certain similar triangles. right triangles at that so it's even easier. bust out a couple compasses and an interlocuter; i guarantee you'll find out *something* interesting. nothing says spring like repeated addition. yours in the struggle. owen thomas (MathEdZine). http://vlorbik.wordpress.com/Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-71660395614588883302010-02-28T15:49:50.865-08:002010-02-28T15:49:50.865-08:00I'm not sure what my top 10 would be, but let ...I'm not sure what my top 10 would be, but let me point out some of yours that I especially like:<br /><br />9. Earlier is not better. I wish there were more discussion of this! It's a constant battle to slow things down, to dig deeper, to give kids time to play with the math, to gain understanding. Which leads me to <br /><br />3. Games are to math as books are to reading. Playing with math really means playing with math. I would pair this with problem solving (in the sense of working on unusual, longer, problems)<br /><br />2. To teach math you need to know it deeply. <br /><br />And then I think we diverge, or maybe I would phrase things differently.<br /><br />Arithmetic is rich. I think that doesn't match you exactly. But that might be on my list.<br /><br />Jonathan<br /><a href="http://jd2718.wordpress.com" rel="nofollow">jd2718</a>jd2718http://jd2718.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-63715019126576871592010-02-28T14:15:16.722-08:002010-02-28T14:15:16.722-08:00>I think it's much like AP classes here: th...>I think it's much like AP classes here: the grading dynamic really changes when it's teacher + students vs external exam...<br /><br />Great point! I wouldn't go so far as to call it a positive aspect of the testing, but I can see what you're saying there...<br /><br /><br />I do think there's a cultural difference, too.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-23234148942137943262010-02-28T10:28:49.638-08:002010-02-28T10:28:49.638-08:00(blushing)(blushing)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-54166240825160980992010-02-28T10:11:38.247-08:002010-02-28T10:11:38.247-08:00You are a woman after my own heart and mind, Sue. ...You are a woman after my own heart and mind, Sue. I've known that from my first read of your blog. You say the things that need saying, and that I have said many times before in various settings. <br /><br />Preach it, Sister!Mary DYhttps://www.blogger.com/profile/16327760791419830509noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-38474067175543025532010-02-28T09:33:00.026-08:002010-02-28T09:33:00.026-08:00Yes, Kate, I agree with you totally. (I was being ...Yes, Kate, I agree with you totally. (I was being flippant before. Sorry if it felt like I was ignoring your real concern.)<br /><br />>I just wish I knew how to convince the people who decide what we teach (and when and how.)<br /><br />There's no easy answer to that. If it were one person, maybe you could go in and get them to see all this. But it's not; it's a huge bureaucracy. So the question is, how do we change the huge institution we know as school? And that's a hard one. <br /><br />For me, it seems like a first step is getting math teachers who understand how big the change needs to be, and then all together we can organize and pressure the system. I'm not at all clear on how to do something like that successfully. <br /><br />And maybe even that language (organize and pressure) is wrong. Maybe the change will be more organic. <br /><br />I think our 'revolution' posts may point to ways the internet can effect huge change. It's not just about how teachers teach, it's about how students interact with the system (school). <br /><br />But you <i>are</i> stuck in a rotten system. When they require you to teach too much, you cannot do right by the students. <br /><br />At my college, I have more flexibility, but there are still very rotten aspects: Why does a math course need to have intermediate algebra (alg II) as a prerequisite to count as college level? I say it's because we're using math as a filter, in a way that's not necessary, and that's ugly.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-16048201344306514382010-02-28T07:58:36.168-08:002010-02-28T07:58:36.168-08:00Well, there's a difference between doing the b...Well, there's a difference between doing the best we possibly can with the crappy standards we've been handed, and getting to work with quality curricula in the first place. Don't you think? There's only so much pushing back and revolting I can do when I'm held accountable to a test of an unreasonable amount of age- and math-sophistication-inappropriate material.Kate Nowakhttps://www.blogger.com/profile/14229054922453438248noreply@blogger.com