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<div dir="ltr" data-setdir="false"><div><div>Deirdre,</div><div><br></div><div>Thank you for detailed posting about teaching math.</div><div><br></div><div>When my children needed help with their homework, I could almost always think of a solution that was mathematically valid, but was not what the text book used. </div><div><br></div><div>I was a bit annoyed with the implication that there was only one acceptable method. There are very few, if any, math problems that can be solved by exactly one method. In fact, important discoveries have been made when two methods give answers that looked to be different, but upon further work can be shown to be equivalent.</div><div><br></div><div>In my math classes, it was about the math, with very limited references to the people. There must have been people named Euclid, Euler or Fourier because those names are on equations or methods. None of my text books had a picture or any biographical info.</div><div><br></div><div>I watched enough of the Vedic multiplication, to agree that it is correct. Since I don’t often need to multiply large numbers by hand, it isn’t obvious that it will be an efficient use of my time to learn that technique.</div><div><br></div><div>Once I read a book about calculating. It suggested doing addition starting with the most significant digit. </div><div><br></div><div>My wife went to an all girls high school. She could not read as fast as most people, but she did have 100% comprehension of what she did read. When she took one of the standard college application tests her reading score was lower then her math score. She got called into the counselors office because “girls are supposed to be better at reading than math.” </div><div><br></div><div>This was before it was common to have any instruction in test taking. So the naïve method was to read the whole section and then go to the questions on the next page and try to remember what you had read. Now everyone is taught that the questions are in the order of the reading section. Start with the first question and then read into the assignment until you find the answer. Then look at the next question.</div></div><br></div><div dir="ltr" data-setdir="false">I suspect the elephant in the room is that many people choose to teach math, not because they love math, but because they love counting their own coins.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Paul</div><div><br></div>
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On Sunday, July 11, 2021, 12:59:30 PM PDT, Deirdre Saoirse Moen <deirdre@deirdre.net> wrote:
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<div><div id="ydp6fcf0c66yiv0879048183"><div>First, I know a fair amount about the current sad state of pedagogy in the US because of grad school, as most of the people I went to grad school with (for both degrees) were teachers going so they’d get more coin. Thus, many of the lunch conversations were about the current state of things.<div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">These days, there’s an unfortunate focus on “teaching to the test,” meaning focusing on the correct answer rather than the concepts behind the answer.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">This post calls that “item teaching” as opposed to “curriculum teaching.” <a shape="rect" class="ydp6fcf0c66yiv0879048183" href="http://www.ascd.org/publications/educational-leadership/mar01/vol58/num06/Teaching-to-the-Test%C2%A2.aspx" rel="nofollow" target="_blank">http://www.ascd.org/publications/educational-leadership/mar01/vol58/num06/Teaching-to-the-Test¢.aspx</a></div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">That’s what the paper Paul linked is referring to, but with a framing that’s uncomfortable to hear.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">Second, because most math problems (in K-12) *have* a right answer, we tend to focus on “right” vs. “wrong” without realizing that there’s mastery involved to get to the point where you are right. And THAT is not what’s taught. If you were learning to hand-cut dovetail joints, you might have a first effort that looked like this:</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183"><a shape="rect" class="ydp6fcf0c66yiv0879048183" href="https://www.reddit.com/r/woodworking/comments/abyrja/my_first_attempt_at_handcut_dovetails_the_horror/" rel="nofollow" target="_blank">https://www.reddit.com/r/woodworking/comments/abyrja/my_first_attempt_at_handcut_dovetails_the_horror/</a></div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">There’s a recognition in that trade that it’s going to take you multiple attempts to get there, but basically anyone *can* cut good dovetails, it just takes practice.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">Someone else’s first effort might look like this:</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183"><a shape="rect" class="ydp6fcf0c66yiv0879048183" href="https://www.reddit.com/r/woodworking/comments/ohnzzk/first_dovetail_made_a_bunch_of_mistakes_and/" rel="nofollow" target="_blank">https://www.reddit.com/r/woodworking/comments/ohnzzk/first_dovetail_made_a_bunch_of_mistakes_and/</a></div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">In current math pedagogy, they’d be tracked into genius classes without regard to the thought *that they both may wind up with the same level of skill*.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">Instead, students are often tracked into slow learning classes because of a failure of pedagogy, not their future mathematical potential, but then their future mathematical potential is nerfed because they’re now put in a class where the district just has to do their best, and that already wasn’t good enough. :P</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">Unfortunately, lifelong earning potential in the US correlates highly with math ability (if you exclude outliers such as sports and entertainment, but even those have their math). You probably can’t get into med school without p-chem. You can’t get into law school without significant math. CompSci typically requires 1-2 years of calculus even if you never use it. We use math skills as gatekeeping.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">Also, it’s far more likely that women and people of color are tracked into those lesser classes (as, yes, I have been, though I’ve also been tracked into genius classes too). Despite that, I managed to wind up getting code in space before I was 18.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">It was this experiment: <a shape="rect" class="ydp6fcf0c66yiv0879048183" href="https://agupubs.onlinelibrary.wiley.com/doi/10.1029/JA083iA12p05685" rel="nofollow" target="_blank">https://agupubs.onlinelibrary.wiley.com/doi/10.1029/JA083iA12p05685</a></div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">So next, another of the issues is that math is taught so that you have to solve the problem in *one specific way*. That’s not math, that’s pedagogy.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">Like this example in Vedic math of how to multiply 32 x 11 from this video at 0:50:</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183"><a shape="rect" class="ydp6fcf0c66yiv0879048183" href="https://www.youtube.com/watch?v=grkWGeqW99c" rel="nofollow" target="_blank">https://www.youtube.com/watch?v=grkWGeqW99c</a></div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">(BTW, there are a *bunch* of other math shortcut tips and tricks from a variety of cultures on YouTube, and I find them fascinating.)</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">If you used that technique to get an answer in a US (public K-12) classroom, you’d be marked down even though it is absolutely a valid way to solve that problem.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">Different cultures have different approaches to teaching math, so a student from India who’d learned Vedic math would suddenly be getting the right answer the wrong way if they moved to the US. This is where you get into the “our approach to teaching math is racist” issue. In other subjects, we do take other cultures’ learning concepts into account where possible. But not math, reportedly.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">Third, I want to talk for a minute about the concept of teaching people about people who look like them. The only women in math or science I was taught about were the Curies. Granted, things are better now, but it absolutely meant something to me that there were people like Grace Hopper in my field. (For those who don’t know, the annual conference for women in computing is Grace Hopper, started by Anita Borg.)</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">For example, a friend of ours, his mother is Rosalyn Yalow, who won a Nobel Prize in Medicine. <a shape="rect" class="ydp6fcf0c66yiv0879048183" href="https://www.nobelprize.org/prizes/medicine/1977/yalow/biographical/" rel="nofollow" target="_blank">https://www.nobelprize.org/prizes/medicine/1977/yalow/biographical/</a></div><div class="ydp6fcf0c66yiv0879048183">Her work was fundamental to developing things like blood sugar testing. The only reason I happen to know about her is because I know her son. (Also, we largely only teach about Nobel winners, but, as an example, cryptography’s an amazing field that underlies everything we do in daily digital life, but there’s never been a Nobel awarded for cryptography.)</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">I think we *should* teach about women and minorities (and queer people, etc.) in math-related fields, which we still largely don’t.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">As an example of the struggles some faced, let’s look at Alicia Boole Stott, daughter of George (Mr. Boolean) Boole.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183"><a shape="rect" class="ydp6fcf0c66yiv0879048183" href="https://www.sciencedirect.com/science/article/pii/S0315086007000973" rel="nofollow" target="_blank">https://www.sciencedirect.com/science/article/pii/S0315086007000973</a></div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">"As a woman born in the middle of the 19th century, Alicia had little educational opportunity. In England, colleges did not offer degrees to women and the study of science or mathematics was not encouraged. Alicia was only four years old when her father died so she had little opportunity to be influenced by him, and as a child, her acquaintance with formal mathematics consisted only of the first two books of Euclid.”</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">Yet she did amazing work in four-dimensional geometry, and she might have been better recognized for it were she not a woman.</div><div class="ydp6fcf0c66yiv0879048183"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183">Deirdre<br clear="none" class="ydp6fcf0c66yiv0879048183"><div class="ydp6fcf0c66yiv0879048183"><div><br clear="none" class="ydp6fcf0c66yiv0879048183"><blockquote class="ydp6fcf0c66yiv0879048183" type="cite"><div class="ydp6fcf0c66yiv0879048183yqt1478651457" id="ydp6fcf0c66yiv0879048183yqt66063"><div class="ydp6fcf0c66yiv0879048183">On Jul 11, 2021, at 07:51, <a shape="rect" class="ydp6fcf0c66yiv0879048183" href="mailto:paulz@ieee.org" rel="nofollow" target="_blank">paulz@ieee.org</a> wrote:</div><br clear="none" class="ydp6fcf0c66yiv0879048183Apple-interchange-newline"><div class="ydp6fcf0c66yiv0879048183"><div class="ydp6fcf0c66yiv0879048183"><div class="ydp6fcf0c66yiv0879048183yahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:13px;"><div class="ydp6fcf0c66yiv0879048183" dir="ltr">There is a group that wants to change math instruction in CA. They say that it is a white supremist attitude to focus on getting the right answer:</div><div class="ydp6fcf0c66yiv0879048183" dir="ltr"><br clear="none" class="ydp6fcf0c66yiv0879048183"></div><div class="ydp6fcf0c66yiv0879048183" dir="ltr"><a shape="rect" class="ydp6fcf0c66yiv0879048183" href="https://equitablemath.org/wp-content/uploads/sites/2/2020/11/1_STRIDE1.pdf" rel="nofollow" target="_blank">https://equitablemath.org/wp-content/uploads/sites/2/2020/11/1_STRIDE1.pdf</a><br clear="none" class="ydp6fcf0c66yiv0879048183"></div></div></div>_______________________________________________<br clear="none" class="ydp6fcf0c66yiv0879048183">conspire mailing list<br clear="none" class="ydp6fcf0c66yiv0879048183"><a shape="rect" class="ydp6fcf0c66yiv0879048183" href="mailto:conspire@linuxmafia.com" rel="nofollow" target="_blank">conspire@linuxmafia.com</a><br clear="none" class="ydp6fcf0c66yiv0879048183">http://linuxmafia.com/mailman/listinfo/conspire<br clear="none" class="ydp6fcf0c66yiv0879048183"></div></div></blockquote></div><br clear="none" class="ydp6fcf0c66yiv0879048183"></div></div></div></div><div class="ydp6fcf0c66yqt1478651457" id="ydp6fcf0c66yqt57032">_______________________________________________<br clear="none">conspire mailing list<br clear="none"><a shape="rect" href="mailto:conspire@linuxmafia.com" rel="nofollow" target="_blank">conspire@linuxmafia.com</a><br clear="none"><a shape="rect" href="http://linuxmafia.com/mailman/listinfo/conspire" rel="nofollow" target="_blank">http://linuxmafia.com/mailman/listinfo/conspire</a><br clear="none"></div></div>
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