Pen 23,905 Report post Posted July 28, 2013 Before I bother, would a pit stop for an appendix of links shared thus far in this discussion be helpful? I can gather, give brief description and post if it would be helpful. Â ps: Tanton is a lot of fun. :) Â Yes! Â Thanks for the Tanton link! Share this post Link to post Share on other sites

Pen 23,905 Report post Posted July 28, 2013 ... Â So, I suck at math (for now).... Â I may suck at math, but I still speak five languages ... Â Â Â Â A couple more thoughts--I am glad you added the "for now" and I am wondering, from the word you used whether Danica McKellar's Math Doesn't Suck Â might help. Â And also wanted to mention that I think The Great Courses: Mastering the Fundamentals of Mathematics is pretty good. Â Â Languages are super important and helpful, I think, and can open a lot of doors. Â I don't think math should be ignored, but if you can pass languages on to your child that is a huge plus, and not to be taken lightly. Â Particularly for a child who turns out to enjoy that it would likely be as good or better to have that than a STEM direction. Â My $0.02. Share this post Link to post Share on other sites

justamouse 3,928 Report post Posted July 28, 2013 I don't think there's ANYTHING wrong with passing familial strengths down. Not at all. HOWEVER, a Liberal Arts Education would open up doors for my child that my own family might not be able to. And, the alternative is that our familial strengths may be perfect for the child, for it's his own strength, also.Â I am not saying that I'm going to every do anything other than homeschool, either. I'm just saying that there are advantages, and criticisms, and to truly do best by our children, we need to acknowledge the gaps.Â And, Regentrude is right, we have to facilitate as they get older, but unless that is a capable tutor, I still think it's not the perfect solution (which may not be found this side of heaven or without millions of dollars). I have many Teaching Company classes, but, as excellent as they are (and friends and I were just talking about the differences between the online Yale courses and TC--Though I LOVE the Yale course, TC is far more detailed and the college level we'd consider college level work-My 14 yo will be using the Yale course this year with ease) they are sill not the perfect, which is a tutoring/dialogue with a master professor.But, then, kids right now have lecture halls with hundreds plus students and do they get much more?Â Â We don't have the perfect, we all have to do with what we have, and so we do the best by them as we can. Share this post Link to post Share on other sites

Pen 23,905 Report post Posted July 29, 2013 Oh no... Â Now that I see the James Tanton site, I am wondering if his Algebra might have been a better choice than AoPS--- Â At least it looks like another good alternative! Â ETA: Â or...at least Â I like the way he was explaining things on the quadratics part...I'm not really sure which of his books would be "algebra"... Â Â I liked what he had to say here.Â Â Reminds me a bit of the Lament, but different too. Share this post Link to post Share on other sites

Chrysalis Academy 43,537 Report post Posted July 29, 2013 Oh no... Â Now that I see the James Tanton site, I am wondering if his Algebra might have been a better choice than AoPS--- Â At least it looks like another good alternative! Â ETA: Â or...at least Â I like the way he was explaining things on the quadratics part...I'm not really sure which of his books would be "algebra"... Â Â I liked what he had to say here.Â Â Reminds me a bit of the Lament, but different too. :001_wub: Â So much more encouraging than the Lament!! Share this post Link to post Share on other sites

Bang!Zoom! 608 Report post Posted July 29, 2013 Somewhere in those links I was carried into quadratic estimation and patterns and was happy as a lark the entire day. Â That was like a flipping opera! Â :drool: Share this post Link to post Share on other sites

quark 8,720 Report post Posted July 29, 2013 Oh no... Â Now that I see the James Tanton site, I am wondering if his Algebra might have been a better choice than AoPS--- Â At least it looks like another good alternative! Â ETA: Â or...at least Â I like the way he was explaining things on the quadratics part...I'm not really sure which of his books would be "algebra"... Â Â I liked what he had to say here.Â Â Reminds me a bit of the Lament, but different too. Â How we came across Tanton is that during kiddo's algebra 1 course, he became very enamored by number theory. He did some AoPS but wanted more. After he finished algebra 1, I googled around and found Tanton's site and emailed him to ask what he would suggest for my younger child who had finished algebra 1 and was thirsting for more materials on number relationships and patterns. He replied: Â As for what might be good for your son, there are two possibilities. 1. Under LEARN TO THINK I have three books (which do already come with soluitions) that I have written for middle-schoolers with some algebra under their belts. It is a review of ideas, but getting at them from the viewpoint of a mathematical thinking, rather than rote doing. I suspect your son would a) go through them quickly but B) enjoy them! (They really do represent a different way of thinking to the traditional approach.) 2. The real book that you might want to look at is THINKING MATHEMATIC! Volume 1: Arithmetic = Gateway to All. (I can send you a file of the solutions. Just let me know.) This book is surprisingly advanced for its elementary content and is quite a challenge.Â (My LEARN TO THINK series is based on this book, but toned down.) This might be a goodÂ thing to look and plan to work through together. You can find it at www.lulu.com/spotlight/jtanton.Â Of course, after this is volumes 2, 3, 4, ... After this, your son will be done with all of highschool mathematics AND thinking like a true mathematician! Â I took his advice and we worked our way very slowly through the first volume...some of it was too easy and some of it was at the other extreme! Even after he had finished a rigorous algebra course. I left it on the shelves for kiddo to work on on his own once he was ready for the harder parts. Then, I think we lost the book! lol. I can't seem to find it. Â FWIW, I would go with AoPS and use Tanton's as a supplement. Share this post Link to post Share on other sites

Chrysalis Academy 43,537 Report post Posted July 29, 2013 I find this site really confusing. Â Is "Learn to Think" above contained in the Mathematical Thinking books? And that's the pre-high school thing, to be followed by Thinking Mathematics? Â And is there actually a course, like that he teaches, or you just buy the books and work through them? Â They look really cool, like a great preAlgebra supplement, and then you'd do Tinking Mathematics in High School (or at that level of math)? Or as a supplement to AoPS Algebra? Â Am I grocking this correctly? Share this post Link to post Share on other sites

quark 8,720 Report post Posted July 29, 2013 Yes Rose, I do think you are grocking it correctly lol. Tanton's is not your standard curriculum teaching method--AoPS isn't either but at least there's a familiar math progression in the textbooks and there are solution books--and I agree it can be confusing (Note: You might want to google for his youtube lectures for more hand-holding). Â That's why I think of it as a supplement and am saving the rest for later. DS is already busy enough as it is with his many math trails. We'll get to Tanton when we get to Tanton lol. But I don't see Tanton mentioned much here so I thought I'll suggest his materials for future bookmarking or for kids ready and willing to work at that level or kids who think Tanton is THE bunny trail they want to take atm. :) Share this post Link to post Share on other sites

Chrysalis Academy 43,537 Report post Posted July 29, 2013 Cool, thanks Quark! I'm watching the powerpoints now. Â Yeah, last thing we need is yet another supplement, but I do like the looks of it! Share this post Link to post Share on other sites

Pen 23,905 Report post Posted July 30, 2013 Tanton's Solve This puzzles, btw, was in the Jo Boaler resources section (of her book--don't know if on the Stanford course too), but was so expensive compared to things like Martin Gardner, that I bypassed it. Â Has anyone seen "Solve This"? Â Or the also quite expensive Math Encyclopedia? Â I do not know about my ds--I suspect that if he sees the videos Â at all, he may well like the way Ruszcyk does his--a bit reminds me of Bill Nye the Science Guy in feel, but for myself, I definitely prefer Tanton's calmer more straightforward (to me) style. Â And I loved what I went through of Tanton's Quadratics. Â If anyone has the books, especially the first of the 10 volume series, is it similar in approach to the way his quadratics sections on GDay math seem? Share this post Link to post Share on other sites

Pen 23,905 Report post Posted July 30, 2013 If Mathwonk is still reading this thread-- Â I am wondering about the issue of interest in the "whys" of math. Â Do you notice any difference in your epsilon students between the boys and girls in the degree to which they are interested in "why" (versus perhaps "how") questions about math? Share this post Link to post Share on other sites

Kathy in Richmond 2,860 Report post Posted July 30, 2013 Tanton's Solve This puzzles, btw, was in the Jo Boaler resources section (of her book--don't know if on the Stanford course too), but was so expensive compared to things like Martin Gardner, that I bypassed it. Â Has anyone seen "Solve This"? Â I own Tanton's Solve This & find it very useful & fun for planning math club activities. Many of the activities and games in this book require a group of students. While it's still fun to read through, I'm not sure how much you'd get for your money with a single student. Â If Mathwonk is still reading this thread-- Â I am wondering about the issue of interest in the "whys" of math. Â Do you notice any difference in your epsilon students between the boys and girls in the degree to which they are interested in "why" (versus perhaps "how") questions about math? Â I'm the former academic director of Epsilon camp. There have been very few female campers so far, so comparisons may not be valid. Not many girls apply, and those who do apply & attend Epsilon are some of the very brightest & smartest kids we have. And altogether, campers as a whole at Epsilon are very much interested in why mathematics works. But, no, there wasn't any apparent difference to me between boys & girls. It was more of an individual thing depending on what subject each kid was most interested in. For example, in geometry, we had a couple of boys who stayed after each class wanting to know why, why, why...and literally had to be chased out to the next activity. Share this post Link to post Share on other sites

mathwonk 709 Report post Posted July 30, 2013 I agree with Kathy, in that I have not noticed this difference, but i tend not to always notice whether my students are boys or girls. In general I tend to have more boys than girls, so in a sense all my girls are more special cases, hence harder to generalize about. This summer I just finished a 2 month online algebra course which had participation from about 10 students, one of whom had a girlish codename, and most of the others I assumed were boys. Â When I have 9 boys and one girl, it probably isn't too meaningful to draw conclusions from the girl's pattern of participation. Â Thinking back to college classes, some girls may sometimes be more open and willing to make mistakes, which would be a plus in doing math problems. I really didn't think about it much at the time, and often had trouble answering the question of how many girls were in the class as opposed to how many boys. Â I tend to remember the interested students more, and I can better remember how many of those were girls or boys. Almost always the most interested students include girls, even if the total number of girls is small. Â Â In general the question of "why" is overlooked so much in traditional math classes that all the students are somewhat new to these matters. Even my super bright epsilon campers this summer were accustomed to just taking formulas for granted and only using them to compute answers ti problems. Â But when I pressed them to answer why, they took to it well, and seemed to enjoy it. Â Â I have a 43 page set with 65 problems, with some hints and explanations, from my epsilon experience as a pdf file, but don't know if it has interest for anyone here. If so, I could email it I guess but the limits on this browser do not allow posting such large files to my knowledge. Maybe better, I could also post it on my UGA webpage and let interested persons download it for themselves. Of course they are not polished, and were personalized to the responses of a specific set of kids whose responses are not included, but I would be curious to know if they might interest someone who wants to see what topics interest a mathematician (at least this one), rather than an elementary textbook writer. Â In 2 months, I may have said, we covered quite a lot, some perhaps not commonly met in a traditional course or at least from a different perspective: re - expanding a polynomial in X as a polynomial in (X-a), application to completing the square and eliminating the X^2 term of a cubic as well as finding tangent lines, quadratic and cubic formulas, Descartes rule of signs (including the proof), rational root theorem, factor theorem, the connection between the factor theorem and "casting out 3's", criteria for divisibility by 3,7,11; multiplicities of roots, inductive approach to finding formulas for the sum of the kth powers of the first n positive integers (e.g. 1^2 + 2^2 + ...+n^2 = ?, for k=2), slope and area formulas (differential and integral calculus), tangent lines as viewed by Euclid, Descartes, Newton, applied problems in optimization, areas, volumes, fundamental theorem of calculus, appreciation and application of properties stated in intermediate value theorem and Rolle's theorem. Â One peculiarity of my course was that I appreciate and try to validate and encourage any degree of participation at all. Mastery is not at all required, although it may be desired in the back of my mind. I.e. I take whatever partially correct answer I get, and try to move on from there upwards. I accept that the kids are learning at least part of the story, whatever they are ready for now. Â As usual every course I teach contains at least one topic I am learning myself for the first time, this summer it was Descartes rule of signs. Â (Do these topics pop up in the sources being considered here?) Share this post Link to post Share on other sites

Plum 13,636 Report post Posted July 30, 2013 I watched this TedTalk again and thought of this thread. I have to look at hisÂ blog again. Dan Meyer: Math Class Needs a Makeover Â DY/Dan Dan Meyer Algebra Lesson Plans- with videos Share this post Link to post Share on other sites

Pen 23,905 Report post Posted July 31, 2013 I agree with Kathy, in that I have not noticed this difference, but i tend not to always notice whether my students are boys or girls. In general I tend to have more boys than girls, so in a sense all my girls are more special cases, hence harder to generalize about. This summer I just finished a 2 month online algebra course which had participation from about 10 students, one of whom had a girlish codename, and most of the others I assumed were boys. Â When I have 9 boys and one girl, it probably isn't too meaningful to draw conclusions from the girl's pattern of participation. Â Thinking back to college classes, some girls may sometimes be more open and willing to make mistakes, which would be a plus in doing math problems. I really didn't think about it much at the time, and often had trouble answering the question of how many girls were in the class as opposed to how many boys. Â I tend to remember the interested students more, and I can better remember how many of those were girls or boys. Almost always the most interested students include girls, even if the total number of girls is small. Â Â In general the question of "why" is overlooked so much in traditional math classes that all the students are somewhat new to these matters. Even my super bright epsilon campers this summer were accustomed to just taking formulas for granted and only using them to compute answers ti problems. Â But when I pressed them to answer why, they took to it well, and seemed to enjoy it. Â Â I have a 43 page set with 65 problems, with some hints and explanations, from my epsilon experience as a pdf file, but don't know if it has interest for anyone here. If so, I could email it I guess but the limits on this browser do not allow posting such large files to my knowledge. Maybe better, I could also post it on my UGA webpage and let interested persons download it for themselves. Of course they are not polished, and were personalized to the responses of a specific set of kids whose responses are not included, but I would be curious to know if they might interest someone who wants to see what topics interest a mathematician (at least this one), rather than an elementary textbook writer. Â In 2 months, I may have said, we covered quite a lot, some perhaps not commonly met in a traditional course or at least from a different perspective: re - expanding a polynomial in X as a polynomial in (X-a), application to completing the square and eliminating the X^2 term of a cubic as well as finding tangent lines, quadratic and cubic formulas, Descartes rule of signs (including the proof), rational root theorem, factor theorem, the connection between the factor theorem and "casting out 3's", criteria for divisibility by 3,7,11; multiplicities of roots, inductive approach to finding formulas for the sum of the kth powers of the first n positive integers (e.g. 1^2 + 2^2 + ...+n^2 = ?, for k=2), slope and area formulas (differential and integral calculus), tangent lines as viewed by Euclid, Descartes, Newton, applied problems in optimization, areas, volumes, fundamental theorem of calculus, appreciation and application of properties stated in intermediate value theorem and Rolle's theorem. Â One peculiarity of my course was that I appreciate and try to validate and encourage any degree of participation at all. Mastery is not at all required, although it may be desired in the back of my mind. I.e. I take whatever partially correct answer I get, and try to move on from there upwards. I accept that the kids are learning at least part of the story, whatever they are ready for now. Â As usual every course I teach contains at least one topic I am learning myself for the first time, this summer it was Descartes rule of signs. Â (Do these topics pop up in the sources being considered here?) Â I noticed much on quadratics and possibly some on cubics for Tanton materials as I was looking at contents and so on. Â Finding sums of series of numbers I've seen in several places, but how it is covered I do not know since I've only seen contents previews not the materials themselves. Â But I've Â not seen any of this in material intended for elementary students. Â I would say those topics are way beyond anything I've seen intended for elementary students--which is, as I understand it, the whole point of the epsilon program, isn't it? Â When I asked about the interest in "why" it was not so much to try to understand Â about girls pattern of participation as to understand whether the boys who are very advanced in math are interested in the "why" of math. Â Apparently, according to Boaler, 2/3 aprox. of boys more often do not care about that, but I thought maybe the 1/3 who do include the top end math students. Â Â Â That even in the under 12 year old group there are many more boys than girls in special math camp is interesting too. Share this post Link to post Share on other sites

Pen 23,905 Report post Posted August 1, 2013 I was one of those kids who simply didn't "get" math. Some of my earliest memories are me sitting at a school desk with sheets upon sheets of basic addition, subtraction, multiplication and division before me. I do not remember receiving any explanation as to how do to these problems, and I distinctly remember not understanding what the numbers meant. By the time we got to long division, I simply gave up.Â Â ... Â Â The more I look at the James Tanton stuff, it makes me wonder if maybe either his book for middle schoolers or his first volume (which seems to cover everything from adding into part of algebra) of the 10 volume set could be helpful for you. Â I find the way he explains things to be helpful in areas that I found awful in school (like quadratics, for which he takes an understanding rather than memorizing formulas approach) and guess that it might also be true for how he handles things like division. Â I saw a Tanton excerpt on long division which he shows by "exploding dots" (dots in boxes that show the different place value positions) Â which at least to me was a new way to show it and I thought could be helpful. Â Share this post Link to post Share on other sites

EKS 13,675 Report post Posted August 1, 2013 Going back to the Stanford math course--has anyone looked at lessons 5 and 6?Â They're much better, though what's funny is that every single thing she talks about being so revolutionary math-wise is a standard part of the Singapore math program. Share this post Link to post Share on other sites

Pen 23,905 Report post Posted August 1, 2013 For example: Â Â http://www.jamestanton.com/wp-content/uploads/2009/11/book_4_division_teaser.pdfÂ Â on division. Â Â Or maybe Sal Khan Khanacademy videos? Share this post Link to post Share on other sites

Chrysalis Academy 43,537 Report post Posted August 1, 2013 Going back to the Stanford math course--has anyone looked at lessons 5 and 6?Â They're much better, though what's funny is that every single thing she talks about being so revolutionary math-wise is a standard part of the Singapore math program. Â I didn't realize they'd posted the next lessons yet, thanks! off to check it out Â :auto: Share this post Link to post Share on other sites

Chrysalis Academy 43,537 Report post Posted August 1, 2013 Going back to the Stanford math course--has anyone looked at lessons 5 and 6?Â They're much better, though what's funny is that every single thing she talks about being so revolutionary math-wise is a standard part of the Singapore math program. Â Â Right, it's kind of disturbing, isn't it? I mean, that teaching number sense is revolutionary. Â But not all that surprising to those of us who pulled our kids from ps because of frustration in how math was taught, and then spent hours searching for a math program that would actually teach number sense and conceptual understanding . . .Â Â I do feel better, though, now that it's getting into the actual recommended techniques and procedures. Â Yep, we work on number sense, mental math, number bonds. Â Yep, we talk about math, about the many different ways to solve a problem - dd and I often compare how we did it and talk about the differences. Â We kind of make a game of looking for "elegant" solutions, kind of for fun but you see how important it is to pick an efficient strategy when you get harder problems (like AoPS/Alcumus). Â MM does an excellent job teaching number sense & mental math. Â So I'm not feeling like I'm completely missing the boat in terms of what & how I ought to be teaching. Â The biggest thing I gleaned from Lesson 5 is to make sure to keep talking about math - have an oral session every day, don't feel like the goal is to get her to the point where she can go off and do math by herself, as if that somehow is superior (oh look, she's working independently!) because there is so much value in the math discussions we are having. Share this post Link to post Share on other sites

mathwonk 709 Report post Posted August 1, 2013 Yes Pen, one goal of the epsilon program as announced there is to present material they will not encounter in standard courses, but since I am not an expert on what is out there I sometimes worry if I am living up thst claim in what I do for them. Â I don't actually know the content of many of the courses discussed here, so I worry I may be repeating standard stuff without realizing it sometimes. Â Â What I actually do is not consciously avoid standard stuff, but rather I just present my take on things and let it go where it leads me. I also let the level rise higher than usual, guided by my own opinion of what can be attempted, and also guided by what I get back from the kids. This tends to work and so far apparently what I do is pretty different from what they get elsewhere and more advanced. Sometimes though, especially when I steal problems from the internet or even famous books, the kids have already seen them. Â Â It is pretty common for me to encounter bright youngsters who know more about some aspects of elementary math than I do, since my advantage is more in advanced math. But I have spent my life trying to understand math at all levels, so I tend to have different perspectives on most topics I present than they have seen before. Â I always thought through every subject I taught in college every time i taught it, to try to understand it better and in a more elementary and natural way. eventually I began to see fundamental things from a perspective that was partly new even to some of my colleagues, who may have taught it the same every year as the way they were taught. Â It also helps that I have consulted historical sources more than some people, as those old forgotten great books make things clear in a unique way. Â A person interested in number theory can really not do better than read Gauss, but even mathematicians are reluctant to do this. We are all afraid either that we won't understand the old great books, or that they will be outdated. Â Here is a discussion of that topic I contributed to on mathoverflow: Â http://mathoverflow.net/questions/28268/do-you-read-the-masters/51868#51868 Share this post Link to post Share on other sites

Arcadia 22,693 Report post Posted August 1, 2013 The biggest thing I gleaned from Lesson 5 is to make sure to keep talking about math - have an oral session every day, don't feel like the goal is to get her to the point where she can go off and do math by herself, as if that somehow is superior (oh look, she's working independently!) because there is so much value in the math discussions we are having. My favorite word growing up was "Why". Drove everyone nuts :lol: my kids take after me and hubby is luckily amused rather than annoyed. Share this post Link to post Share on other sites

mathwonk 709 Report post Posted August 2, 2013 my epsilon algebra notes are now online at my website at roy@math.uga.edu specifically: Â http://www.math.uga.edu/~roy/epsilon13.pdf Â Â these may not be useful, but if your child can do these problems, then he/she has a very bright future as a math student/ mathematician. Â Â and i am glad to respond to any questions, because that was the way these were used, with constant interaction. Â Â i.e. these are probably too hard to complete alone, even for the very gifted, but maybe you yourself can perform the tutor function. that would be fun. I may not be here every day, but please take advantage of me as suits you and as I am available for. Share this post Link to post Share on other sites

tessellate 2 Report post Posted August 2, 2013 I am new to this forum.Â My child attends school, but is highly capable so we also provide a great deal of supplementation at home. Â I have completed the Stanford class through lesson 6 (lessons 7 and 8 are not yet available) and have learned much that explains some of the issues my child is having with rote memorization of math facts and timed tests. Â http://joboaler.com/timed-tests-and-the-development-of-math-anxiety/ Â I did not understand how an advanced learner could be years ahead of age group in conceptual understanding and performance in most subjects, yet balk at rote memorization of math facts and timed tests. Boaler's article, which also cites studies of others, explains how advanced learners tend to be the ones most impacted by math anxiety affecting their performance.Â I am now reading Boaler's book.Â Â Regarding the academic dispute at Stanford between Boaler and Milgram, Jo Boaler has all of that linked on her website www.joboaler.comÂ What she says in her book makes a lot of sense as to how and why children do or do not learn to be fluent with numbers.Â As to the academic "scandal", she left Stanford, then they asked her to return.Â It's fascinating how academic ideas about education become entrenched and politicized.Â Â Other academics have written about the math wars at length, here's an interesting contributionÂ http://www.math.cornell.edu/~henderson/courses/EdMath-F04/MathWars.pdf Â Hope this is helpful/interesting.Â I have enjoyed reading the various comments here.Â Â Â Â Â Share this post Link to post Share on other sites

Pen 23,905 Report post Posted August 3, 2013 ... Â Other academics have written about the math wars at length, here's an interesting contributionÂ http://www.math.cornell.edu/~henderson/courses/EdMath-F04/MathWars.pdf Â Â Â A lot to read in that article, but I think an excellent perspective there and understanding of the reform vs. traditional issue can be deepened. Â Thank you for sharing it. Â And I highly recommend it to others reading this thread. Share this post Link to post Share on other sites

Plum 13,636 Report post Posted August 7, 2013 I was just at the Oak Meadow site and they had a little blurb on the home page about their teachers taking this course. I wonder what they think....... Share this post Link to post Share on other sites

Eagle 3,059 Report post Posted August 9, 2013 I'm curious how many people are still actively taking this course? I took a break after the first four segments while I was out of town and it was difficult to motivate myself to pick it back up. But I am so glad I did! I am really getting a lot from this class and have lots of ideas floating around my head about what I want our math schooling to look like this coming year. I want to encourage those who stopped partway through to consider starting up again. Things get quite interesting in chapter 5. Share this post Link to post Share on other sites

Chrysalis Academy 43,537 Report post Posted August 9, 2013 I am. Â I've done through Lesson 7. Â I agree, I liked lessons 5-7 very much. Share this post Link to post Share on other sites

onaclairadeluna 115 Report post Posted August 10, 2013 I am not online much (summer) but I just had a chance to watch lesson 5. Glad to see this course is getting better.Â Share this post Link to post Share on other sites

Pen 23,905 Report post Posted August 10, 2013 I have a question about an earlier part--cannot recall lesson number. Â Where it showed an image of a synapse with brightness and said that making mistakes causes more neural activity ... I do not recall exactly what it said...but anyway I have been thinking about that and wondering if anyone knows where one might find more information about that. Â Â The implication was that making errors actually strengthens the brain. Â How do they know what the activity they might see on brain imaging is from--that is, if it goes along with making mistakes, might it be that the increase in whatever was seen comes from increased emotion related to making a mistake, rather than from something leading to improvement in thinking or something like that? Â Also, when I took music lessons at one point, my teacher was very adamant about going slowly when starting a new piece because mistakes made get learned and are very hard to get unlearned, compared to going slow at first and getting it right and then speeding up to a normal playing speed. Â So if the something is showing up on a brain scan that indicates high activity, could it not mean that yes, a new connection is being made at that moment, but it is not the correct connection? Â This may have been answered in the course itself somewhere, butÂ I am sort of limited in my access to the Course due to my dial-up connection speed. Â I am happy that I can get it at all, but cannot access certain parts like the Discussion area where perhaps this got answered. Â Â Share this post Link to post Share on other sites

Chrysalis Academy 43,537 Report post Posted August 10, 2013 I have a question about an earlier part--cannot recall lesson number. Â Where it showed an image of a synapse with brightness and said that making mistakes causes more neural activity ... I do not recall exactly what it said...but anyway I have been thinking about that and wondering if anyone knows where one might find more information about that. Â Â The implication was that making errors actually strengthens the brain. Â How do they know what the activity they might see on brain imaging is from--that is, if it goes along with making mistakes, might it be that the increase in whatever was seen comes from increased emotion related to making a mistake, rather than from something leading to improvement in thinking or something like that? Â Also, when I took music lessons at one point, my teacher was very adamant about going slowly when starting a new piece because mistakes made get learned and are very hard to get unlearned, compared to going slow at first and getting it right and then speeding up to a normal playing speed. Â So if the something is showing up on a brain scan that indicates high activity, could it not mean that yes, a new connection is being made at that moment, but it is not the correct connection? Â This may have been answered in the course itself somewhere, butÂ I am sort of limited in my access to the Course due to my dial-up connection speed. Â I am happy that I can get it at all, but cannot access certain parts like the Discussion area where perhaps this got answered. Â Â Â Pen, these are great questions. Â As a (former) neuroscientist myself, these kinds of statements and the implication that you can go from "more neural activity" to increased learning in a direct linear way makes me crazy. Â Â You are absolutely right, brain scans like fMRI measure nothing but increased blood flow, and EEGs measure increased electrical activity. Â These measurements don't tell us why it is occuring, or even what exactly is occurring - in fact, in many cases, learning is accomplished by strengthening some connections and pruning others, and you can't tell from a crude measure like blood flow what is actually going on at the neural level, so this is a really sloppy way of talking about the benefits of working on hard problems and making mistakes you can learn from. Â Strong emotion often inhibits learning - so anxiety and stress around making mistakes, if mistakes are not acceptable, can definitely inhibit learning. Â Making mistakes in a supportive context can focus your attention on what you need to learn, or what you don't understand, and this attention focusing can enhance learning, but to go from that to saying "mistakes strengthen connections between neurons" or "mistakes increase neural activity = enhanced learning" is stretching it, to say the least. Â I think that people find talking about the brain sexy, and they feel like if they can say "well, actual brain studies have shown X" it makes their case stronger, which ain't necessarily so . . .Â Â Again, I found the course presentations weakest when it attempted to make points like this, and strongest when it talked about how to teach math conceptually & effectively. Share this post Link to post Share on other sites

WishboneDawn 3,816 Report post Posted August 10, 2013 Well the same thing applies to us college professors. On arriving for my first college teaching job I was told on Friday my first class was a formal logic class starting on Monday. This was a subject I had not studied since Freshman year 10 years before, and never used or thought about since. There went my weekend, and I was panicked for most of it, but it worked out, i.e. disaster was avoided. Â The same thing applies to every course I have taught, from algebra to calculus on up. I was taught calculus by a high powered professional functional analyst at an elite school where the professors experimented on us stronger math majors by throwing graduate level material at Freshmen. They pretty much blew me away, but eventually I survived by memorizing a lot and specializing in professors who tested for regurgitating well. Â Then I arrive as professor in a non honors calculus class in a middle level state school, with students who are pretty weak compared to any I have seen, and am given a cookbook calculus book to use that I have never seen before. I either have to read it every night and follow along, or follow my own high powered training and do my own version, which then blows my own class away. Â Â It has taken me over 40 years of teaching to arrive at the more informal, laid back, let's try whatever works, seems fun, and makes sense approach I can use now. (Moreoevr I am retired and not subject to grade scales.) And I still need lots of work on intangibles that may be natural to you, like encouragement, diplomacy, support, reasonable sense of pacing, even good handwriting, sympathy with struggles and mistakes, discipline to spend time correcting homework. Â But that's the way things work. I think you should give yourself more credit. You are doing the same thing we did, i.e. you are teaching passionately and well everything you do know. Its not what you know but how much curiosity and interest and delight you convey in those areas you do know. And you are learning and studying continually and always broadening the scope of what you can teach. Â Congratulations! (and thanks for the kind words). This was really encouraging to hear. :) Â I know this comment is a bit older but I've got one more thing to add. Before homeschooling I thought of myself as bad at math. After junior high I never did well in it so the label seemed to fit. When I started homeschooling I was an unschooler so there was a lot of play around math. When we became more formal we used Singapore.Â Â But through all that, even though I know there were things I did wrong because of my lack of knowledge there were also things I did really, really well because I was a blank slate in some respects. I had no proconceived notions of how it was all supposed to go, I soaked in Singapore and Liping Ma, when my daughter had issues I could often see them and help her because I was making the same journey.Â Â Sometimes knowing little (as long as you realize it) can be an advantage too.Â Â Even now, as she studies Algebra and geometry mostly on her own she still brings me questions that are beyond me at first but we can work them out together, making mistakes but also piecing them together and then off she goes, confident that these things can be solved on one's own (at least for the meantime). It's not ideal but again, it's a way that's worked well and resulted in a girl that enjoys the challenge of math and doesn't think it's something you have to be cautious of or afraid to approach. She's pretty fearless. Â Ironically, the one thing I am really good at, drawing, is the area that I find most difficult to teach and where she, despite having talent, is the most insecure about. Â Â A mathematician teaching my kids would have been ideal but a curious noob doing the teacher has turned out well. Of course, we have yet to tackle Algebra II. :D Share this post Link to post Share on other sites

WishboneDawn 3,816 Report post Posted August 10, 2013 Well the same thing applies to us college professors. On arriving for my first college teaching job I was told on Friday my first class was a formal logic class starting on Monday. This was a subject I had not studied since Freshman year 10 years before, and never used or thought about since. There went my weekend, and I was panicked for most of it, but it worked out, i.e. disaster was avoided. Â The same thing applies to every course I have taught, from algebra to calculus on up. I was taught calculus by a high powered professional functional analyst at an elite school where the professors experimented on us stronger math majors by throwing graduate level material at Freshmen. They pretty much blew me away, but eventually I survived by memorizing a lot and specializing in professors who tested for regurgitating well. Â Then I arrive as professor in a non honors calculus class in a middle level state school, with students who are pretty weak compared to any I have seen, and am given a cookbook calculus book to use that I have never seen before. I either have to read it every night and follow along, or follow my own high powered training and do my own version, which then blows my own class away. Â Â It has taken me over 40 years of teaching to arrive at the more informal, laid back, let's try whatever works, seems fun, and makes sense approach I can use now. (Moreoevr I am retired and not subject to grade scales.) And I still need lots of work on intangibles that may be natural to you, like encouragement, diplomacy, support, reasonable sense of pacing, even good handwriting, sympathy with struggles and mistakes, discipline to spend time correcting homework. Â But that's the way things work. I think you should give yourself more credit. You are doing the same thing we did, i.e. you are teaching passionately and well everything you do know. Its not what you know but how much curiosity and interest and delight you convey in those areas you do know. And you are learning and studying continually and always broadening the scope of what you can teach. Â Congratulations! (and thanks for the kind words). This was really encouraging to hear. :) Â I know this comment is a bit older but I've got one more thing to add. Before homeschooling I thought of myself as bad at math. After junior high I never did well in it so the label seemed to fit. When I started homeschooling I was an unschooler so there was a lot of play around math. When we became more formal we used Singapore.Â Â But through all that, even though I know there were things I did wrong because of my lack of knowledge there were also things I did really, really well because I was a blank slate in some respects. I had no proconceived notions of how it was all supposed to go, I soaked in Singapore and Liping Ma, when my daughter had issues I could often see them and help her because I was making the same journey.Â Â Sometimes knowing little (as long as you realize it) can be an advantage too.Â Â Even now, as she studies Algebra and geometry mostly on her own she still brings me questions that are beyond me at first but we can work them out together, making mistakes but also piecing them together and then off she goes, confident that these things can be solved on one's own (at least for the meantime). It's not ideal but again, it's a way that's worked well and resulted in a girl that enjoys the challenge of math and doesn't think it's something you have to be cautious of or afraid to approach. She's pretty fearless. Â Ironically, the one thing I am really good at, drawing, is the area that I find most difficult to teach and where she, despite having talent, is the most insecure about. Â Â A mathematician teaching my kids would have been ideal but a curious noob doing the teacher has turned out well. Of course, we have yet to tackle Algebra II. :D Share this post Link to post Share on other sites

Chrysalis Academy 43,537 Report post Posted August 11, 2013 Wishbone, well put and such a great reminder that our kids learn as much from us being willing to learn with them, to struggle with things we find hard, and to model persistence and grit! Â Â Â It's funny, because writing, which I have always done well and intuitively without really being taught is something I've found hard to teach, whereas math, where I too am learning a lot of conceptual stuff for the first time is actually easier to teach. Â I guess I'm more in that "beginner's mind" with math than I am with writing. Â That reminds me again of the book Why Don't Students Like School, where he talks about the fact that learners and experts do things in a fundamentally different way, and it's a mistake to expect students to solve problems "like mathemeticians" or "like scientists" or other experts, because experts have automatized a lot of the steps that need to be made explicit for learners. Share this post Link to post Share on other sites

EKS 13,675 Report post Posted August 11, 2013 That statement about every time you make a mistake, a synapse is born, or whatever she said, drove me nuts. I suspect that the take home message should be, neuroscience aside, that students should encounter problems that make them think and that are difficult enough that they will make mistakes when trying to solve them. Correct placement in a good math program with a teacher who understands about balance between conceptual learning and fluency development should do the trick. Of course, correct placement does not necessarily mean with age peers. Share this post Link to post Share on other sites

mathwonk 709 Report post Posted August 14, 2013 I feel the same about the different areas of math. I.e. there are many different types and flavors of math, and sometimes I feel I do a better job at teaching the ones i don't understand as well, precisely because I am myself learning them as i teach. After I know something more or less cold, I may lose interest and excitement over it, and may also forget where the trouble spots are. Â Once when i taught algebra, one of my specialties, i also threw in some topology, which i love but in which i am more of an amateur, and one student commented that i did a better job teaching the topology. Of course i disagreed and almost took offense, thinking he just appreciated the more laissez faire approach i took in the sketch of topology as opposed to the in depth treatment of the algebra, but that's what he said, and he is more objective. Share this post Link to post Share on other sites

Chrysalis Academy 43,537 Report post Posted August 23, 2013 Ok, I finished week 8. Â I have some really mixed feelings about it. Â She addresses the fact that she's been personally attacked for advocating reform to math education very bluntly. Â But I don't really care about that - what I worry about is the data. Â I think I can draw my own conclusions about the data, provided the data is sound - the criticism that bothers me is the one I read on the Kitchen table Math site - people I respect, mathematically - that says the data has been misreported or only partially/selectively reported.Â Â There was a discussion of integrated math for high school, which I've always thought makes more sense philosophically than segregating the math into Alg 1- Geo - Alg 2 with ample time to forget. Â She recommends IMP, and I went to the website and couldn't really find anything tangible, no samples or anything, then I come here and see it's been sharply criticized as "fuzzy math" along the lines of EM - by people whose math opinions I trust. Â And mathwonk says he doesn't know of a good integrated math text, is that right Mathwonk? Â It's all kinda confusing. Â I know many people here deal with this by running Geo & Alg 2 concurrently using texts they like. Â Integrated math is definitely included in common core, and it's not clear exactly how that's being handled - it looks like CA is going to have two tracks, traditional and integrated? Â Though nothing CA does is something I automatically want to emulate! Â At the end of the course, there were some surveys about what people think should be included in a version of this course for kids. Â I've been thinking, and although i find the whole issue of gender bias/stereotyping interesting and important - it resonates with my own experience - I don't know if I really want to expose my kids to it at this point. Â I mean, they are homeschooled, they love math, their mom is the smartest person they know . . . it doesn't even cross their minds that they aren't supposed to be as good at math! Â I don't know if I want to put it in there . . .Â Â Anyway, it's been interesting, I'm glad I watched the videos, and I did glean some useful information, but when it comes to practical application -what materials, curricula etc. are good, I'm disappointed. Â I don't think I'm just jumping on the bandwagon to say that the examples seem, well, fuzzy to me. Â Hard for a non-mathemetician to pull off. Â Designed to be used in groups in a classroom. Â Not that relevant to our situation . . . and the fact that they don't recommend Art of Problem Solving, Beast Academy, or anything in that ilk makes me kinda suspicious, at best, that the general approach is not what I'm looking for. Â Anyway, random musings. I haven't had coffee yet, so it may be incoherent. Share this post Link to post Share on other sites

EKS 13,675 Report post Posted August 23, 2013 I just finished the course as well and also have mixed feelings about it.Â I completely agree that students need to develop good problem solving skills, flexible thinking (which tends to emerge from deep understanding), and persistence.Â But I am concerned that the message that many teachers will get from the course is that procedures don't matter, that quick retrieval of math facts is unimportant, and that ability grouping is bad for all students. Â I found Sebastian Thrun's comments about pacing to be particularly interesting.Â He made a point of saying that we shouldn't assume that all students need to learn math at the same speed.Â But the message for the entire course up until that point was that kids should proceed in lock step with age peers via mixed ability grouping.Â It seems to me that you can't have it both ways and I'd be interested to know Boaler's thoughts on this. Share this post Link to post Share on other sites

Chrysalis Academy 43,537 Report post Posted August 23, 2013 Great question, Kai. Â I guess it's obvious that as homeschoolers, we *don't* believe that the only way to learn math is via group discussion with mixed-ability groups . . . I'm curious how Boaler would respond to this as well. Â Â I think that in order to make this "groupthink" thing work, you have to have an incredibly skilled teacher with very appropriate problem types. Â I'd be willing to bet that this isn't the case in most classrooms across the country. Â I think there are other paths to the same destination - problem-solving skills, flexible thinking, and persistence - and that any alternative to the groupwork/classroom model got very short shrift in these presentations. Share this post Link to post Share on other sites

EKS 13,675 Report post Posted August 23, 2013 I know that the video of the group session on the border of the square made me realize how inappropriate that sort of instruction would be for my own children.Â The excruciatingly slow pace would drive them totally crazy. Share this post Link to post Share on other sites

Tress 2,921 Report post Posted August 23, 2013 I know that the video of the group session on the border of the square made me realize how inappropriate that sort of instruction would be for my own children.Â The excruciatingly slow pace would drive them totally crazy. Â That has been my thought with all the class video's, I would have been bored out of my mind with those slow class discussions. Boaler can talk all she wants about the benefits of mixed ability classes and of group discussions, I'm not buying it. Â I haven't yet finished the course, I watched several parts of session 6 this afternoon. If I start something I usually want to finish it, but those interviews (the female doctor who was 'doing math' ...ohhhhh, ahhhhh.....when she measured a desk and then ordered a replacement......aaargh :willy_nilly: ) are getting me more and more irritated. Imagine interviewing engineers who will wax eloquently about 'doing Language Arts/ Humanities' when they are reading from the box the name of the brand of cereal they are eating for breakfast....really!?! This kind of thing annoys me to no end. Share this post Link to post Share on other sites

Tiberia 921 Report post Posted August 23, 2013 I finished the class too, and have mixed feelings. The two main things I learned, which have totally changed the way I teach math are: Â 1.The mindset teaching. My dd has/had a fixed mindset about math. I gave her a short, simple summary of the mindset teaching, and she totally got it. Now that's in our vocabulary, and she understands what I mean when I tell her to learn from a mistake, not feel like a failure. It's a process, but we're moving in the right direction.Â Â 2. The "more than one way" approach to problem solving. I take simple examples and we look at them from different ways. Eg. How many different ways can we make 25. Can you make it two different ways each using addition, subtraction, multiplication, and division? This may seem simplistic to some, but it's freeing us to explore math and enjoy it more.Â Â Other than those two things (which are huge!), I don't know that I'll make changes in curriculum or expectations. Yes, she still has to memorize math facts, learn long division, fractions, etc. But, this class will make me a better teacher and engage dd's curiosity much more. I can present the same material, but in a more interesting and useful way, tailored to dd's strengths and needs. Â Overall, it was a good class for me. I applaud Jo Boaler for attempting to identify and change the problems in US math education, and I hope this can help. But, I don't think sweeping changes or common core standards are going to necessarily solve the problem in our schools. I understand both sides of the Math Wars, and won't pick a side. I will try to understand and use the best ideas from both sides, and my kiddo will hopefully get the benefits. Share this post Link to post Share on other sites

EKS 13,675 Report post Posted August 23, 2013 Â Â I haven't yet finished the course, I watched several parts of session 6 this afternoon. If I start something I usually want to finish it, but those interviews (the female doctor who was 'doing math' ...ohhhhh, ahhhhh.....when she measured a desk and then ordered a replacement......aaargh :willy_nilly: ) are getting me more and more irritated. Imagine interviewing engineers who will wax eloquently about 'doing Language Arts/ Humanities' when they are reading from the box the name of the brand of cereal they are eating for breakfast....really!?! This kind of thing annoys me to no end. Â :iagree: Â It completely annoyed me that most of the examples those people were giving of "using math" in real life were really just examples of them using simple arithmetic that was on something like a 4th or 5th grade level.Â Share this post Link to post Share on other sites

Pen 23,905 Report post Posted August 25, 2013 Ok, I finished week 8. Â I have some really mixed feelings about it. Â She addresses the fact that she's been personally attacked for advocating reform to math education very bluntly. Â But I don't really care about that - what I worry about is the data. Â I think I can draw my own conclusions about the data, provided the data is sound - the criticism that bothers me is the one I read on the Kitchen table Math site - people I respect, mathematically - that says the data has been misreported or only partially/selectively reported.Â Â There was a discussion of integrated math for high school, which I've always thought makes more sense philosophically than segregating the math into Alg 1- Geo - Alg 2 with ample time to forget. Â She recommends IMP, and I went to the website and couldn't really find anything tangible, no samples or anything, then I come here and see it's been sharply criticized as "fuzzy math" along the lines of EM - by people whose math opinions I trust. Â And mathwonk says he doesn't know of a good integrated math text, is that right Mathwonk? Â It's all kinda confusing. Â I know many people here deal with this by running Geo & Alg 2 concurrently using texts they like. Â Integrated math is definitely included in common core, and it's not clear exactly how that's being handled - it looks like CA is going to have two tracks, traditional and integrated? Â Though nothing CA does is something I automatically want to emulate! Â At the end of the course, there were some surveys about what people think should be included in a version of this course for kids. Â I've been thinking, and although i find the whole issue of gender bias/stereotyping interesting and important - it resonates with my own experience - I don't know if I really want to expose my kids to it at this point. Â I mean, they are homeschooled, they love math, their mom is the smartest person they know . . . it doesn't even cross their minds that they aren't supposed to be as good at math! Â I don't know if I want to put it in there . . .Â Â Anyway, it's been interesting, I'm glad I watched the videos, and I did glean some useful information, but when it comes to practical application -what materials, curricula etc. are good, I'm disappointed. Â I don't think I'm just jumping on the bandwagon to say that the examples seem, well, fuzzy to me. Â Hard for a non-mathemetician to pull off. Â Designed to be used in groups in a classroom. Â Not that relevant to our situation . . . and the fact that they don't recommend Art of Problem Solving, Beast Academy, or anything in that ilk makes me kinda suspicious, at best, that the general approach is not what I'm looking for. Â Anyway, random musings. I haven't had coffee yet, so it may be incoherent. Â Â I haven't gotten anywhere near that far, hope to do so, and to have more to say at that point. Â On "IMP"--I was curious and got a used IMP book labeled Year 1 for High School. Â The I seems to be for "Interactive", not Integrated. Â Though it also seems to be both integrated and discovery in approach. Â I actually think the book looks excellent, and wish I did have a group of kids to be able to do it interactively. Â However, I think it looks suitable, at least as it begins and at several spots I flipped open to along the way, for about the age/stage my ds is at now--which is to say 11 and just started AoPS algebra with concurrent review of basic math--or, hence, also possibly for the age/stage your older dd is. Â It might make school even for an accelerated high school student more fun to get one of these problems each week, but I think he/she would likely be bored with just something like this, and for a highly gifted math student like the epsilons at the math camp Mathwonk had told us about, I think it would not be a good fit at 9th at all probably--unless that child had not been lucky enough to have a situation like the camp or any interesting math and this course would kindle a latent interest and love for math. Â Still, bottom line, I think the sort of kid who likes Beast Academy or AoPS would very likely Â like this too--only at a younger age. Â I cannot compare to EM having never seen that. Â I would share your concerns that if your girls do not have any sense that math is supposed to be a problem for girls one might not want to introduce that. Â That would be a hard call. Â Â Share this post Link to post Share on other sites