Holly, it isn't just math that this is being done to. Nor is this a recent phenomenon.
Everybody "knows" that DDT is a carcinogen. Everybody "knows" that elephants are endangered. Everybody "knows" that 3 Mile Island was an absolute nuclear disaster. The list is long, and Gell Mann amnesia is a real thing.
Thanks for enduring the distress and frustration of reading and commenting on this book in such detail. Despite the frustration regarding the harm that this book and teaching methodology are inflicting upon the current student generation and this to our country and society, you appear from my vantage point as a non reader relying on your review to have managed to treat this in an unbiased manner. As someone who received my BA in quantitative studies 63 years ago and has been grateful on innumerable occasions ( both professionally and in my many avocations) for the skills and insight as well as rigor that such an education provided me, I am appalled at the lack of mathematical understanding that the majority of current high school graduates possess . I hope that your review of this book and the danger that this methodogy presents is widely shared and restacked. 👏👏👏Happy to support your efforts as a subscriber.
Thank you for thoroughly dissecting the philosophy behind current math education. I took math classes in college up through differential equations, so I would regards myself as slightly above the mean in math ability - but when it came to understanding the methodology my public school kids' math classes used, I was utterly bereft. The textbook and the teachers were of no help.
Whew. That was one of the most cognitively dissonant things I have ever read. I concur that suffering is an appropriate description. What conjures the grandest shudder of all of it for me is the valorizing of collective reward/punishment. I remember few aspects of my primary school education less fondly than group projects. These were, without fail, a euphemism for “Johnny’s dad gave the school a lot of money, but Johnny has zero interest in doing any actual work, so we’ll saddle one of the shy nerdy kids with him, who’ll quietly do all the work for fear of a bad grade and/or Johnny and his cohort beating said shy nerdy kid up on the recess deck.” That anyone can manage to twist this dynamic into “progress” is horrifying to me.
The ONLY time I enjoyed group work was in 10th grade biology where I was at a table with one of the football players and he cut up the animals for dissection and I did the writing. All other group projects were nightmares. Even in college.
After having shepherded our son through a sixth grade mathematics "teacher" (who had been the English teacher), but they needed a switch because the regular mathematics teacher went out on medical leave, I concur wholeheartedly that many things can happen in those crucial learning years that can throw a young person off track that have nothing to do with the ability or desire to learn. He survived and thrived in spite of that disastrous decision because he had supportive parents, but not every kid has that.
Reading your review of MATH-ish helped me relive many conversations with my wife over the dinner table. She taught advanced algebra, trig, and calculus in two of the poorest schools in NC and SC for 45 years.
She routinely cursed the direction that math education was headed and accurately predicted what has now transpired.
It is gratifying for both of us to know that someone like you has taken up the banner that she proudly carried prior to retiring.
I made it to the end. I design and deliver professional development for teachers - mostly math teachers. Baoler’s work comes up A LOT. I’ve found some of it very useful. Some, not so much. I’m certain many of my colleagues will jump on this new book. In fact, I would not be at all surprised to be gifted a copy. Thanks for the review. It’s given me a heads up.
Do math teachers really do interpretive dance? I know at least one does, since she put it in the book, but is that a common thing? I always thought it was a joke, sort of like saying that someone's kid was majoring in left-handed puppeteering. I really didn't know it was an actual thing.
I honestly don’t know any teachers who do interpretive dance. I suppose it *could* be a thing. I’ve used movement to help myself and learners (kids & adults) with kinesthetic cues for memory or processing. One of my faves is doing an activity called the Algebra walk. Go outside, draw a huge coordinate plane on the pavement with sidewalk chalk and have the kids plot themselves using ordered pairs. Big fun. And you start with scatter plots to graph linear relationships and move right on through all the other kinds. 🌻
A terrific write-up, Holly. Thank you for taking the time.
My comment is just that getting out of public school isn't always the answer. We've been through a number of private schools (at the elementary and start of junior high level), and they've been worse about this than our local public school (to which we are now sending our daughter).
I worry that it may change as we move through the high-school track (not just for math), but in my area, for now, it seems that the private schools (at least the smaller ones) are doubling down harder on many aspects of the MATH-ish approach. That may be a symptom of my locality (NY state blue-county, non-NYC area).
I'd like for this woman to meet with all her fellow professionals, tell everyone to put their debts and paychecks on the table and use her money to pay off the most disadvantaged people first. Savings? Nope. Let's bring her down a notch. And, while we're at it, let's not figure her pay based on her hours or her educational attainment. Let's just guess at it and get close enough. So grateful my kids are grown. If I ever get grandchildren, I'll have to have study sessions.
I renewed my subscription so that I could read this to the end. It specifically touched a nerve because the other morning my 2nd grade daughter was working on her math homework and asked for some help with 13-7 (which apparently requires a specific algorithm involving “making a 10”). After trying to help her, she said, “I just don’t think you are smart enough. You aren’t saying it the way my teacher does.” (Note the Marxist enthusiasts everywhere cheering for this victory of teacher over mother) I hope someone will relay my deficiency to the United States Naval Academy which must have awarded me a degree in Mechanical Engineering in error.
Fascinating. Your review led me to the realization that I don’t think I was taught much number sense in elementary school (this would have been in the 90s). I only remember rote memorization, touch dots, and pages of traditional practice problems. I think math would have made more sense with some of the methods you discussed. I’ve learned some of those things over time by experience, but most of them were never taught.
The obsession with group work and keeping everyone on the same playing field is maddening. I remember having to be in groups to take turns reading aloud in 2nd grade. When you’re a kid reading well above grade level, it’s grating to listen to a kid who has to sound out the word “the.” I can’t imagine it was a good experience for her either. Somehow, I doubt group work in math is any better.
Unfortunately, the concept of people not being an “x person” applies to more than just math. Maybe it’s not as glaring, but it’s there. I can’t tell you how many math and science majors I went to college with who were terrified of writing because they believed they were just bad at it. Hell, I thought I was bad at it until I realized that, outside of English/literature class, there was way less emphasis on minimum word counts and descriptive language. Not everyone is going to be a novelist, but most people just haven’t had spelling, grammar, or any kind of skills for clear, concise written communication reinforced after the sixth grade or so. It’s all essentially just “write a rough draft about an idea about this book” or “write a rough draft of a personal essay,” which does not help you refine writing skills generally, nor does it prepare most people for the type of writing they will do in real life.
Thanks for the review. I was oblivious to the apparently standard, rather rigid, process for advancing in mathematics. For something so susceptible to clericalized testing (i.e., where a test can be graded by a clerk who merely compares test answers with the answer table) a boxed-in progress path is chilling. So it is good that you give credit for worldviews that would allow for different learning paths. The encouragement of group activities as the primary method of learning math is also chilling: based on my (admittedly limited) personal experience, what is more likely to happen is that in most groups, one or two people will understand and the rest will rely on that understanding. The idea may be that since study groups can work well for some, even most, students, then study groups can be formalized and standardized. But what makes study groups work, when they do, is that the groups are largely chosen by the participants, so they are likely to be socially compatible, and they function mostly as a reminder of things already learned, with only a few participants learning substantial amounts for the first time. Sadly, study groups never worked well for me, so I stopped interfering with them: I didn’t participate. Of course, not having read the book, I may have misunderstood both the author’s recommendations about group learning and your comments on it. Lastly, I wanted to mention a bit of amusing confusion. One of your screen shots shows ‘11 minutes reading time left in the book’ and also shows ‘16%’ of the book read (I am citing these figures from memory, so as not to lose my train of thought and maybe my long comment by checking precisely). That struck me as really impressive reading speed, or a really short book, or both, until I realized that the screenshot would have been from the third or fourth time you had paged through.
Also: 1. The interpretive dancer stands upright, legs together, arms extended in the same plane as the torso, stage right, facing the audience (forming a ‘t’). 2. Next, a step by the left leg to the left, as the arms are lowered. 3. Then, the head and torso begin to bend toward the stage as the dancer pivots to the left, the right leg swinging through a quarter of a circle, so the dancer is no longer facing the audience: they (the dancer) are/is at 90 degrees to them (the audience). 4. Another step, either left or right leg as the dancer chooses, since this is interpretive dance, and the dancer begins to crouch. 5. The dancer moves to hands and knees. 6. The dancer sprawls full length on the stage, head facing away from the audience. Dancer may vocalize a sob, if desired. 7. Advance further left while coming back to hands and knees, head toward stage left. 8. Rise to a crouch, arms half raised, head tilted upward. 9. Another step to the left, rising to full height, arms raised above head. Dancer may assume a facial expression of ‘JOY!’ and glance toward the audience. 10. Dancer runs off stage.
Notes:
a. Arm and leg movements are indicated to clarify the more fluid and expressive movements of Dancers in wheelchairs, or with assistive facilitators;
b. A commentator may be used to sing the various mathematical elements: 10 steps, signifying base 10; the angles and arcs on display; the proportion of stage traversed, etc.
***********
I look forward to seeing other Pit of Progress choreography, though I quite understand if I turn out to be an audience of one.
This was different than I expected. In some ways, it doesn't sound as bad (there are real and useful things that Boaler is advocating for) but in some ways it's worse--because the terrible ideas are being laundered by presenting them with some useful ideas.
A couple of specific examples:
1. Her idea about area. "Instead of finding the are of 2x12, you ask how many ways you can find an area of 24." That's batshit insane. And it's all in that word INSTEAD. No, you don't do it INSTEAD of finding the area. You do it ALSO. It's a great way to extend the basic formula into higher-level thinking. Plus, how the hell are students supposed to find all the ways of getting an area of 24 if they don't know how to calculate area in the first place? It's the whole idea of replacing what works with the new idea. No. Add new ideas and ways that are good. Don't replace what works.
2. The idea that kids can come up with an -ish answer without learning and memorizing the basics -- basics of addition and subtraction and times tables. This is easily one of my biggest frustrations with modern ideas about teaching science and math: expecting kids to be able to figure stuff out without having the requisite background knowledge. How on earth can a kid come up with an -ish answer if she hasn't memorized times tables? It's crazy.
3. Procedural vs. conceptual understanding. I'm in elementary school, so that affects how I see this a lot. But early elementary kids have very little abstract reasoning skills. Late elementary (like my 5th grade) they are starting to be able to. It takes a lot of abstract reasoning to be able to understand how the concrete and procedural relate. The lack of abstract reasoning is why advocates say focus on conceptual and hands-on understanding, but my experience is the real problem is the kids struggle to make that connect with the algorithms. THAT's where the abstract reasoning lay--in the connections. And thus instead of helping it make sense, it ends up confusing the kids even more. My 5th graders are just beginning to be able to see how the conceptual understanding and procedural stuff connect. I find so much greater success teaching the procedurally first, and THEN showing how they connect to the concrete and conceptual.
In fact, I did this today: teaching multiplication with decimals. First I taught the how, and then we went into the concepts--the why (especially why we don't bother lining up the decimal like we did when adding). Over and over, when I use this --how, then why-- it works better.
4. The way she advocates using groups is simply crazy. Deliberately pairing kids who are getting it with those who struggle, then randomly picking one assignment to make the group's grade--just insane. The purpose of a grade is to show what a kid can and can't do. The end.
Yes. You see why it was so frustrating? I remember related rates problems in calculus, which drove me insane for a long time. (Things like if a ladder is leaned against a building, and thus forming the hypotenuse of a right triangle, calculating the rate at which it falls if it takes X seconds to hit the ground or whatever.) My Calc 1 professor was 9,000 years old and when asked questions could only repeat the same thing in the same words. In the tutoring office, the minute my tutor drew the problem out, just a simple little sketch, I got 90% of the way there. If he had done that — two approaches instead of one — I’d have had my light bulb moment on the second one. So multiple approaches? Yes, please. But dear God, some of the rest of it was soooooooo frustrating.
I wrote this as a note, but notes disappear. I should add it here. After graduating a 4-year college, I went to a local college to try to get a web design degree. I had to take a lot of general education classes.
In one of those classes, we were split into groups. We were given a piece of paper with a scenario on it. It stated something like “If your boat crashed and you landed on an island what would you do first, then next?” And we had to order the tasks in whichever way made the most sense.
We did this individually. Then we were to discuss it in the group and come up (through discussion) what we thought the best answers would be. So we each had one list of personal choices and one list that everyone in the group “agreed” about.
Then we were given the answers and if your personal answers were worse than the groups, you learned that you work better in a group. If your personal answers were better than the group’s, it meant that you should learn to be more vocal about your good ideas because the group talked you out of them or overrode your good answers.
I was one of the people who did better personally. It was probably a lack of confidence. But I learned that groups suck. I do better alone. I may do better in groups nowadays with confidence, but this article is talking about children.
The idea of journaling about my thoughts when thinking of math makes me feel less confident than I would be just simply doing math. My mind might have confused a lack of confidence in meta-cognition with a lack of being good at math.
From the book: "Another strategy the Railside teachers used was giving group quizzes, in which they collected the work of just one group member (randomly chosen) and everyone in the group would get that person's grade for that piece of work."
From Holly: “I cannot imagine anything worse for the kind of smart, often introverted kids — especially boys, who are frequently years behind their female peers in social skills — who excel in traditional mathematical settings than making them responsible for everyone else’s learning, lest their own grades suffer.”
That’s terrifying. In this case, it’s not even that the group is discussing and turning in one compiled piece of work, but that it could be the lazy or stupid kid’s work that you solely get judged by!
No, it is not that smart kid’s responsibility to teach all the rest of the children in the group. That’s the teacher’s responsibility. It seems the teachers (who go along with this) want to abdicate their responsibility to the students!
I really hope Boaler reads this review, though I doubt she will. As far as her book goes the phrase "curate's egg" comes to mind. She appears to have good ideas and then combines them with something else to make it bad.
"Ish" is a good example.
Estimation is a critical skill that everyone should have. It can save you from all sorts of expensive mistakes because you can tell the sum was wrong so you need to go back and check. (Or sometimes that the sum is right and someone is scamming you).
But it's a first step not an answer. So giving someone full credit for almost the right answer is flat out wrong and is, in itself, dangerous. 10% off is fine for estimating. 10% off can be disastrous if you rely on that number to give you (say) the fuel required to drive to the next town in a remote area.
Holly, it isn't just math that this is being done to. Nor is this a recent phenomenon.
Everybody "knows" that DDT is a carcinogen. Everybody "knows" that elephants are endangered. Everybody "knows" that 3 Mile Island was an absolute nuclear disaster. The list is long, and Gell Mann amnesia is a real thing.
Thanks for enduring the distress and frustration of reading and commenting on this book in such detail. Despite the frustration regarding the harm that this book and teaching methodology are inflicting upon the current student generation and this to our country and society, you appear from my vantage point as a non reader relying on your review to have managed to treat this in an unbiased manner. As someone who received my BA in quantitative studies 63 years ago and has been grateful on innumerable occasions ( both professionally and in my many avocations) for the skills and insight as well as rigor that such an education provided me, I am appalled at the lack of mathematical understanding that the majority of current high school graduates possess . I hope that your review of this book and the danger that this methodogy presents is widely shared and restacked. 👏👏👏Happy to support your efforts as a subscriber.
Thank you for thoroughly dissecting the philosophy behind current math education. I took math classes in college up through differential equations, so I would regards myself as slightly above the mean in math ability - but when it came to understanding the methodology my public school kids' math classes used, I was utterly bereft. The textbook and the teachers were of no help.
Whew. That was one of the most cognitively dissonant things I have ever read. I concur that suffering is an appropriate description. What conjures the grandest shudder of all of it for me is the valorizing of collective reward/punishment. I remember few aspects of my primary school education less fondly than group projects. These were, without fail, a euphemism for “Johnny’s dad gave the school a lot of money, but Johnny has zero interest in doing any actual work, so we’ll saddle one of the shy nerdy kids with him, who’ll quietly do all the work for fear of a bad grade and/or Johnny and his cohort beating said shy nerdy kid up on the recess deck.” That anyone can manage to twist this dynamic into “progress” is horrifying to me.
The ONLY time I enjoyed group work was in 10th grade biology where I was at a table with one of the football players and he cut up the animals for dissection and I did the writing. All other group projects were nightmares. Even in college.
After having shepherded our son through a sixth grade mathematics "teacher" (who had been the English teacher), but they needed a switch because the regular mathematics teacher went out on medical leave, I concur wholeheartedly that many things can happen in those crucial learning years that can throw a young person off track that have nothing to do with the ability or desire to learn. He survived and thrived in spite of that disastrous decision because he had supportive parents, but not every kid has that.
Reading your review of MATH-ish helped me relive many conversations with my wife over the dinner table. She taught advanced algebra, trig, and calculus in two of the poorest schools in NC and SC for 45 years.
She routinely cursed the direction that math education was headed and accurately predicted what has now transpired.
It is gratifying for both of us to know that someone like you has taken up the banner that she proudly carried prior to retiring.
Thanks for what you're doing, Holly!
Please tell Mrs. McGirt I said "Thank you for your service, ma'am!"
I made it to the end. I design and deliver professional development for teachers - mostly math teachers. Baoler’s work comes up A LOT. I’ve found some of it very useful. Some, not so much. I’m certain many of my colleagues will jump on this new book. In fact, I would not be at all surprised to be gifted a copy. Thanks for the review. It’s given me a heads up.
Do math teachers really do interpretive dance? I know at least one does, since she put it in the book, but is that a common thing? I always thought it was a joke, sort of like saying that someone's kid was majoring in left-handed puppeteering. I really didn't know it was an actual thing.
I honestly don’t know any teachers who do interpretive dance. I suppose it *could* be a thing. I’ve used movement to help myself and learners (kids & adults) with kinesthetic cues for memory or processing. One of my faves is doing an activity called the Algebra walk. Go outside, draw a huge coordinate plane on the pavement with sidewalk chalk and have the kids plot themselves using ordered pairs. Big fun. And you start with scatter plots to graph linear relationships and move right on through all the other kinds. 🌻
Well, there's this (which I have to say is phenomenally beautiful and enigmatic):
https://youtu.be/MASNukczu5A?si=-F1kmjwlfUQQar2-
Well, dog bite my big toe. That’s one of the coolest things I’ve ever seen. Thanks for sharing! 🌻
A terrific write-up, Holly. Thank you for taking the time.
My comment is just that getting out of public school isn't always the answer. We've been through a number of private schools (at the elementary and start of junior high level), and they've been worse about this than our local public school (to which we are now sending our daughter).
I worry that it may change as we move through the high-school track (not just for math), but in my area, for now, it seems that the private schools (at least the smaller ones) are doubling down harder on many aspects of the MATH-ish approach. That may be a symptom of my locality (NY state blue-county, non-NYC area).
I'd like for this woman to meet with all her fellow professionals, tell everyone to put their debts and paychecks on the table and use her money to pay off the most disadvantaged people first. Savings? Nope. Let's bring her down a notch. And, while we're at it, let's not figure her pay based on her hours or her educational attainment. Let's just guess at it and get close enough. So grateful my kids are grown. If I ever get grandchildren, I'll have to have study sessions.
I renewed my subscription so that I could read this to the end. It specifically touched a nerve because the other morning my 2nd grade daughter was working on her math homework and asked for some help with 13-7 (which apparently requires a specific algorithm involving “making a 10”). After trying to help her, she said, “I just don’t think you are smart enough. You aren’t saying it the way my teacher does.” (Note the Marxist enthusiasts everywhere cheering for this victory of teacher over mother) I hope someone will relay my deficiency to the United States Naval Academy which must have awarded me a degree in Mechanical Engineering in error.
Fascinating. Your review led me to the realization that I don’t think I was taught much number sense in elementary school (this would have been in the 90s). I only remember rote memorization, touch dots, and pages of traditional practice problems. I think math would have made more sense with some of the methods you discussed. I’ve learned some of those things over time by experience, but most of them were never taught.
The obsession with group work and keeping everyone on the same playing field is maddening. I remember having to be in groups to take turns reading aloud in 2nd grade. When you’re a kid reading well above grade level, it’s grating to listen to a kid who has to sound out the word “the.” I can’t imagine it was a good experience for her either. Somehow, I doubt group work in math is any better.
Unfortunately, the concept of people not being an “x person” applies to more than just math. Maybe it’s not as glaring, but it’s there. I can’t tell you how many math and science majors I went to college with who were terrified of writing because they believed they were just bad at it. Hell, I thought I was bad at it until I realized that, outside of English/literature class, there was way less emphasis on minimum word counts and descriptive language. Not everyone is going to be a novelist, but most people just haven’t had spelling, grammar, or any kind of skills for clear, concise written communication reinforced after the sixth grade or so. It’s all essentially just “write a rough draft about an idea about this book” or “write a rough draft of a personal essay,” which does not help you refine writing skills generally, nor does it prepare most people for the type of writing they will do in real life.
Thanks for the review. I was oblivious to the apparently standard, rather rigid, process for advancing in mathematics. For something so susceptible to clericalized testing (i.e., where a test can be graded by a clerk who merely compares test answers with the answer table) a boxed-in progress path is chilling. So it is good that you give credit for worldviews that would allow for different learning paths. The encouragement of group activities as the primary method of learning math is also chilling: based on my (admittedly limited) personal experience, what is more likely to happen is that in most groups, one or two people will understand and the rest will rely on that understanding. The idea may be that since study groups can work well for some, even most, students, then study groups can be formalized and standardized. But what makes study groups work, when they do, is that the groups are largely chosen by the participants, so they are likely to be socially compatible, and they function mostly as a reminder of things already learned, with only a few participants learning substantial amounts for the first time. Sadly, study groups never worked well for me, so I stopped interfering with them: I didn’t participate. Of course, not having read the book, I may have misunderstood both the author’s recommendations about group learning and your comments on it. Lastly, I wanted to mention a bit of amusing confusion. One of your screen shots shows ‘11 minutes reading time left in the book’ and also shows ‘16%’ of the book read (I am citing these figures from memory, so as not to lose my train of thought and maybe my long comment by checking precisely). That struck me as really impressive reading speed, or a really short book, or both, until I realized that the screenshot would have been from the third or fourth time you had paged through.
Also: 1. The interpretive dancer stands upright, legs together, arms extended in the same plane as the torso, stage right, facing the audience (forming a ‘t’). 2. Next, a step by the left leg to the left, as the arms are lowered. 3. Then, the head and torso begin to bend toward the stage as the dancer pivots to the left, the right leg swinging through a quarter of a circle, so the dancer is no longer facing the audience: they (the dancer) are/is at 90 degrees to them (the audience). 4. Another step, either left or right leg as the dancer chooses, since this is interpretive dance, and the dancer begins to crouch. 5. The dancer moves to hands and knees. 6. The dancer sprawls full length on the stage, head facing away from the audience. Dancer may vocalize a sob, if desired. 7. Advance further left while coming back to hands and knees, head toward stage left. 8. Rise to a crouch, arms half raised, head tilted upward. 9. Another step to the left, rising to full height, arms raised above head. Dancer may assume a facial expression of ‘JOY!’ and glance toward the audience. 10. Dancer runs off stage.
Notes:
a. Arm and leg movements are indicated to clarify the more fluid and expressive movements of Dancers in wheelchairs, or with assistive facilitators;
b. A commentator may be used to sing the various mathematical elements: 10 steps, signifying base 10; the angles and arcs on display; the proportion of stage traversed, etc.
***********
I look forward to seeing other Pit of Progress choreography, though I quite understand if I turn out to be an audience of one.
🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣
This was different than I expected. In some ways, it doesn't sound as bad (there are real and useful things that Boaler is advocating for) but in some ways it's worse--because the terrible ideas are being laundered by presenting them with some useful ideas.
A couple of specific examples:
1. Her idea about area. "Instead of finding the are of 2x12, you ask how many ways you can find an area of 24." That's batshit insane. And it's all in that word INSTEAD. No, you don't do it INSTEAD of finding the area. You do it ALSO. It's a great way to extend the basic formula into higher-level thinking. Plus, how the hell are students supposed to find all the ways of getting an area of 24 if they don't know how to calculate area in the first place? It's the whole idea of replacing what works with the new idea. No. Add new ideas and ways that are good. Don't replace what works.
2. The idea that kids can come up with an -ish answer without learning and memorizing the basics -- basics of addition and subtraction and times tables. This is easily one of my biggest frustrations with modern ideas about teaching science and math: expecting kids to be able to figure stuff out without having the requisite background knowledge. How on earth can a kid come up with an -ish answer if she hasn't memorized times tables? It's crazy.
3. Procedural vs. conceptual understanding. I'm in elementary school, so that affects how I see this a lot. But early elementary kids have very little abstract reasoning skills. Late elementary (like my 5th grade) they are starting to be able to. It takes a lot of abstract reasoning to be able to understand how the concrete and procedural relate. The lack of abstract reasoning is why advocates say focus on conceptual and hands-on understanding, but my experience is the real problem is the kids struggle to make that connect with the algorithms. THAT's where the abstract reasoning lay--in the connections. And thus instead of helping it make sense, it ends up confusing the kids even more. My 5th graders are just beginning to be able to see how the conceptual understanding and procedural stuff connect. I find so much greater success teaching the procedurally first, and THEN showing how they connect to the concrete and conceptual.
In fact, I did this today: teaching multiplication with decimals. First I taught the how, and then we went into the concepts--the why (especially why we don't bother lining up the decimal like we did when adding). Over and over, when I use this --how, then why-- it works better.
4. The way she advocates using groups is simply crazy. Deliberately pairing kids who are getting it with those who struggle, then randomly picking one assignment to make the group's grade--just insane. The purpose of a grade is to show what a kid can and can't do. The end.
Yes. You see why it was so frustrating? I remember related rates problems in calculus, which drove me insane for a long time. (Things like if a ladder is leaned against a building, and thus forming the hypotenuse of a right triangle, calculating the rate at which it falls if it takes X seconds to hit the ground or whatever.) My Calc 1 professor was 9,000 years old and when asked questions could only repeat the same thing in the same words. In the tutoring office, the minute my tutor drew the problem out, just a simple little sketch, I got 90% of the way there. If he had done that — two approaches instead of one — I’d have had my light bulb moment on the second one. So multiple approaches? Yes, please. But dear God, some of the rest of it was soooooooo frustrating.
I wrote this as a note, but notes disappear. I should add it here. After graduating a 4-year college, I went to a local college to try to get a web design degree. I had to take a lot of general education classes.
In one of those classes, we were split into groups. We were given a piece of paper with a scenario on it. It stated something like “If your boat crashed and you landed on an island what would you do first, then next?” And we had to order the tasks in whichever way made the most sense.
We did this individually. Then we were to discuss it in the group and come up (through discussion) what we thought the best answers would be. So we each had one list of personal choices and one list that everyone in the group “agreed” about.
Then we were given the answers and if your personal answers were worse than the groups, you learned that you work better in a group. If your personal answers were better than the group’s, it meant that you should learn to be more vocal about your good ideas because the group talked you out of them or overrode your good answers.
I was one of the people who did better personally. It was probably a lack of confidence. But I learned that groups suck. I do better alone. I may do better in groups nowadays with confidence, but this article is talking about children.
The idea of journaling about my thoughts when thinking of math makes me feel less confident than I would be just simply doing math. My mind might have confused a lack of confidence in meta-cognition with a lack of being good at math.
From the book: "Another strategy the Railside teachers used was giving group quizzes, in which they collected the work of just one group member (randomly chosen) and everyone in the group would get that person's grade for that piece of work."
From Holly: “I cannot imagine anything worse for the kind of smart, often introverted kids — especially boys, who are frequently years behind their female peers in social skills — who excel in traditional mathematical settings than making them responsible for everyone else’s learning, lest their own grades suffer.”
That’s terrifying. In this case, it’s not even that the group is discussing and turning in one compiled piece of work, but that it could be the lazy or stupid kid’s work that you solely get judged by!
No, it is not that smart kid’s responsibility to teach all the rest of the children in the group. That’s the teacher’s responsibility. It seems the teachers (who go along with this) want to abdicate their responsibility to the students!
I really hope Boaler reads this review, though I doubt she will. As far as her book goes the phrase "curate's egg" comes to mind. She appears to have good ideas and then combines them with something else to make it bad.
"Ish" is a good example.
Estimation is a critical skill that everyone should have. It can save you from all sorts of expensive mistakes because you can tell the sum was wrong so you need to go back and check. (Or sometimes that the sum is right and someone is scamming you).
But it's a first step not an answer. So giving someone full credit for almost the right answer is flat out wrong and is, in itself, dangerous. 10% off is fine for estimating. 10% off can be disastrous if you rely on that number to give you (say) the fuel required to drive to the next town in a remote area.