# Stanford Math Course coming, anyone else interested?

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How many kids do you know that can take the reciprocal and multiply but have no idea what that means?

I would say the vast majority of people I encounter have no idea WHY that is done. Because their teacher never explained it, and in some cases did not understand herself (no disrespect to you, I am sure you are proficient in your subject; many math teachers are not and even dislike math.)

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What happens later in life is, if they ever have to take math again they wind up flipping the wrong number or doing some other thing that is close but complete nonsense. So right answers aren't really the holy grail in math.

I am not talking about just coming up with a correct number; to me, a right answer also implies a correct procedure.

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Often mathematicians will try to prove something by contradiction and discover a whole new branch of mathematics. 2+2 doesn't always equal 4.

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Agreed. But even there, there are objective criteria on what is considered clean math. A proof by contradiction has to be logically correct. Your new theory has to base on clear axioms and your theorems must be proven. Not every out-of-the-box-idea satisfies mathematicians' criteria for a logical extension of a concept. One can't just invent random stuff and call it "new math".

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I completely agree that students should not be afraid to make mistakes and that they should be encouraged to learn from them. Unfortunately, with much that I have seen about math education, "mistake-friendly culture" sounds dangerously close to the attitude that conceptual experimentation is more important than actual proficiency and that feeling good about math is more important than arriving at the correct result.

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It is simply reality that, in order to function in today's society, people need a certain set of math skills to manage their daily lives, be financially literate for example. (People might not be in so much financial trouble if they had a clearer understanding of exponential growth and compound interes)

The other aspect is that there are vastly more jobs that require a math background, starting from basic algebra and geometry needed by a carpenter or plumber to advanced calculus needed by scientists and engineers, than there are jobs that require art proficiency. For many more people art will be a source of enjoyment, creative expression and spiritual growth than a tool for their daily work. Any education needs to reflect this. So no, I do not believe one can, or should, make math education voluntary.

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I agree with that. Â And then, I think, there comes the big question, how does one make it effective, so it is not just occupying a chair in a room, or filling out workbooks which somehow do not then lead to being able to use it in life.

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And I think good use of math and science to do good research and figure that out would be helpful. Â

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As I read both Boaler's work and the Milgram criticism, I think they both have validity.

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From feeling very frustrated with the whole thing, like when I read the Lament and felt like okay, I agree with at least a lot of that (not all in my case), but it does not tell me what to do instead. Â Though I have ordered his Measurement book.

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I do think the project and group approach would be helpful, but it has to be the right sort of project. Â The bits of "look inside" on the type of project maths that seem to be getting generated by this new reform approach look like it might result in, say for exponential growth, something like drawing rabbits Â multiplying, where the time and memory of the student is going to go too much to the drawing of rabbits and too little to the point of the exponential growth. Â  Though if it did work to help memory about exponential growth, that would be something, and maybe worth it taking more time than seems needed--rather than to do things that seem more streamlined, but went in one ear and out the other. Â Or result in a series of problem sets completed, but no connection being made to life.

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A project that went straight at a problem based on finances might be a lot better. Â And if it needed graphics, maybe a dollar or euro etc. symbol that is easy and fast could show some amount of money, rather than lots of energy placed on the art and craft aspect. Â

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I think the current way is not working, but rather than an overhaul based on conjecture, I think perhaps it would take significant trials and evaluations not just of the idea of "traditional" versus "reform" but exactly what, even exactly what projects or open ended problems prove out as being helpful in the long run and in reality of the world--beyond Â the end of book tests and SATs and APs.

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I agree with that. Â And then, I think, there comes the big question, how does one make it effective, so it is not just occupying a chair in a room, or filling out workbooks which somehow do not then lead to being able to use it in life.

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To me the key would be teachers that are actually proficient in math and enthusiastic about it.

As long as math teachers in this country are frequently lacking subject expertise (if you want to teach level x of math, you need a thorough understannding of several years of material beyond that level), nothing can possibly change. New curricula and methods are bandaid solutions.

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I do think the project and group approach would be helpful, but it has to be the right sort of project.

And a competent teacher. Doing meaningful group projects requires even more insight on part of the teacher than the traditional frontal method. It is easy to spend a lot of class time on projects and feel great about it - without resulting in any meaningful learning.

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IMO, the quality of math education stands and falls with the subject expertise of the math teachers. No amount of education reserach, new methoids and gimmicks will compensate for underprepared and incompetent teachers. I would prefer teachers had to first obtain a math degree and then a teaching license; without being proficient in content, learning "how" to teach is utterly useless.

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I completely agree that students should not be afraid to make mistakes and that they should be encouraged to learn from them. Unfortunately, with much that I have seen about math education, "mistake-friendly culture" sounds dangerously close to the attitude that conceptual experimentation is more important than actual proficiency and that feeling good about math is more important than arriving at the correct result.

This is precisely the problem I have with the course. I am afraid that this will be what the teachers take from it.

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However if we are dealing with teachers that don't understand the algorithm for fraction division (and I think you are right this is often the problem). I am not sure what can be done.Â

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It is astounding how low the standards are for math teaching. But I think most of this is coming from elementary schools where the kids don't have access to a real math teacher. So maybe having specialists at the elementary level would improve things a bit. I am not sure.Â

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To me the key would be teachers that are actually proficient in math and enthusiastic about it.

As long as math teachers in this country are frequently lacking subject expertise (if you want to teach level x of math, you need a thorough understanding of several years of material beyond that level), nothing can possibly change. New curricula and methods are bandaid solutions.

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This! Absolutely. Â I would say probably worse than a bandaid, a complete waste of time money and resources and sometimes completely counter productive. Â Kind of like the connected math stuff from 10 years ago. Nobody knows how to teach that way and you send a bunch of confused kids home to confused parents.

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That said I love some of those problems. But they are to be used with great caution. Kind of like chemistry experiments in kindergarten.

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Anyhow I think you are spot on. The real elephant in the classroom (to borrow the title of her book) is that the teacher has no understanding and enthusiasm for mathematics.

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Â I would prefer teachers had to first obtain a math degree and then a teaching license; without being proficient in content, learning "how" to teach is utterly useless.

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Before I got my math credential I had a different teaching credential and a math degree. I decided I probably should have a math credential so I made a few phone calls thinking it would be pretty easy to get. You would be (or perhaps you wouldn't be) surprised at how different the requirements are. Apparently there is a math ed degree where you don't really take real math classes except the low level math that one would take at a community college. Then you take math history, math education, math knitting, math sculpture...ok I am being cheeky.

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But no real math.

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I had to talk to several math departments to figure out how to fill the state requirements using my regular math classes. The conversations were always kind of funny. I would start by explaining my situation "I have a real degree from x university (a good one)". It was like they had never seen anything like it. I am sure there are a few teachers out there with regular math degrees but not a whole lot. I was finally able to find someone to count my Geometry of Surfaces to count for "geometry" and who would look the other way that I had only taken Calc 3 in college (and not Calc 1 and 2 because I passed out of them in HS and there were no records of this). I did have to take stats and computer programming. Which felt a little silly but whatever. He let me write a paper for the history requirement. He waived the math knitting and basket weaving.

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That said I worked with some teachers who in spite of having a pretty light math background were pretty enthusiastic an knowledgeable about their content. You know in LiPing Ma's book she talks about Chinese teachers who have very little advanced math but still do a pretty good job teaching. Still for upper level high school classes I do think that a more solid math background is necessary.Â

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But OK, so say you have a bunch of real mathematicians teaching public school math. I am not sure this is a recipe for success either. I mean they have a kind of a "different" perspective on the world. Â I am sure that there are a few of them that could pull it off. But many are really far out there and have no relationship to high school mathematics. They would probably change the entire curriculum. I am not sure this would be a bad thing. It might be quite good. But I think the content would have to change. 9th grade Logic. 10th grade Elementary Number Theory 11th grade Probability 12th Grade ? Â Mathematicians write things like "Elements of Mathematics" a very cool curriculum but I wouldn't give it to your average kid.

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I am a bit disturbed that the math ed departments and the math departments can't seem to work together. I'd like see them put down their weapons and learn a bit from each other. I see a few interesting ideas that they seem to have but they (the math ed folks) tend to get all evangelical about things. "We have this great new method of teaching that no one has ever thought about before...it's called encouraging critical thinking." Goodness really? I find this kind of thing very sad.

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I thought the professor teaching this course was from the mathematics dept. (ie she IS a mathematician) rather than the math ed. dept.? I realize the course is coming out of the ed dept but I thought that was just the way it was listed. Did I get that wrong?

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https://ed.stanford.edu/faculty/joboaler

• PhD (Mathematics Education) King's College, London University. (1996)
• MA (Mathematics Education) King's College, London University (1991)
• BSc (Psychology) Liverpool University (1985)
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I thought the professor teaching this course was from the mathematics dept. (ie she IS a mathematician) rather than the math ed. dept.? I realize the course is coming out of the ed dept but I thought that was just the way it was listed. Did I get that wrong?

That's what I thought, but in viewing the intro lesson again I see she says she is a professor of mathematics education. So she is from the education department. Which explains the more psychology-based feel to the course.

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But OK, so say you have a bunch of real mathematicians teaching public school math. I am not sure this is a recipe for success either. I mean they have a kind of a "different" perspective on the world. Â I am sure that there are a few of them that could pull it off. But many are really far out there and have no relationship to high school mathematics. They would probably change the entire curriculum. I am not sure this would be a bad thing. It might be quite good. But I think the content would have to change. 9th grade Logic. 10th grade Elementary Number Theory 11th grade Probability 12th Grade ? Â Mathematicians write things like "Elements of Mathematics" a very cool curriculum but I wouldn't give it to your average kid.

Oh, I don't mean sending mathematicians into the schools. They should also have some training in pedagogy, in developmental psychology, whatever a teacher needs. My point was simply that this has to come *on top* of subject knowledge, not *instead of*.

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https://ed.stanford.edu/faculty/joboaler

• PhD (Mathematics Education) King's College, London University. (1996)
• MA (Mathematics Education) King's College, London University (1991)
• BSc (Psychology) Liverpool University (1985)

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This explains a lot.

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(I knew that she was a professor of mathematics education, but somehow I thought she had a real math background, like a bachelor's degree in math or something.)

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Add me to the list of those originally confused.

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This explains a lot.

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(I knew that she was a professor of mathematics education, but somehow I thought she had a real math background, like a bachelor's degree in math or something.)

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I know, right?

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I didn't realize that you could get a PhD in Math Ed without a degree in math. No wonder they don't get along. She is trying to speak martian to a Komodo Dragon.Â

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IMO Music Ed is way more together. You have to, you know, like play an instrument and play it pretty well to get a credential. You also have to demonstrate proficiency in conducting, multiple other instruments(Tuba, Viola, Oboe...), piano, guitar, singing, sight singing, theory. The expectations are way higher for music teachers. I can't imagine a Music ed professor having an undergraduate degree in Psychology. It just wouldn't happen. Most have PhDs in music and then you have a few Music Ed professors who have more experience working in a classroom. But everyone is expected to be highly skilled on an instrument.Â

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:confused1:

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I didn't realize that you could get a PhD in Math Ed without a degree in math.

This is precisely the root of much that is bad in math education: the people who design curricula and tell teachers how to teach are not the ones who have actually every USED mathematics on a daily basis.

They have no idea what skills are necessary *for people who will actually be using math*, and the result are programs like Connected Math (which were never intended for broad classroom use by the mathematicians involved in the development)

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*None* of the people in the Stanford department of education who are listed as having a research interest in mathematics education have a degree in math.Â  The closest one is a guy with an engineering degree.

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So then I went to look up the same thing for Cornell and found this:

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"Effective December 2008, the Mathematics Department suspended its involvement in the Cornell Teacher Education Program."

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Nice.

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I guess I am wondering if I should continue with the course. I've read quite a few mathematics education books on my own, nothing new really has been presented during the sessions I've watched, and time is not exactly unlimited. I thought this course might be a fresh take on an old problem from a female mathematician but now that I know she isn't working in math but math ed., I don't know if I want to spend my time reading/watching more of the same.

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I guess I am wondering if I should continue with the course. I've read quite a few mathematics education books on my own, nothing new really has been presented during the sessions I've watched, and time is not exactly unlimited. I thought this course might be a fresh take on an old problem from a female mathematician but now that I know she isn't working in math but math ed., I don't know if I want to spend my time reading/watching more of the same.

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It depends on your goals. I've decided not to; it's not what I expected it to be, nor is it anything I need.

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My time would be better spend doing as mathwonk suggested earlier--consulting books by the best possible mathematicians, like Euclid, Euler, Hilbert, Lagrange....

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ETA: Just reading the posts of many of those contributing to this thread would be a better use of my time.

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To me the key would be teachers that are actually proficient in math and enthusiastic about it.

As long as math teachers in this country are frequently lacking subject expertise (if you want to teach level x of math, you need a thorough understannding of several years of material beyond that level), nothing can possibly change. New curricula and methods are bandaid solutions.

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And a competent teacher. Doing meaningful group projects requires even more insight on part of the teacher than the traditional frontal method. It is easy to spend a lot of class time on projects and feel great about it - without resulting in any meaningful learning.

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IMO, the quality of math education stands and falls with the subject expertise of the math teachers. No amount of education reserach, new methoids and gimmicks will compensate for underprepared and incompetent teachers. I would prefer teachers had to first obtain a math degree and then a teaching license; without being proficient in content, learning "how" to teach is utterly useless.

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Yes. Â And a competent teacher. Â Agreed. Â Whether that necessarily means a math degree I am not sure, some of what went into math degree work seems to me far removed from elementary and most middle and upper school education needs in math, but certainly some significant content knowledge is needed. Â

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That said I worked with some teachers who in spite of having a pretty light math background were pretty enthusiastic an knowledgeable about their content. You know in LiPing Ma's book she talks about Chinese teachers who have very little advanced math but still do a pretty good job teaching. Still for upper level high school classes I do think that a more solid math background is necessary.Â

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Good point.

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But OK, so say you have a bunch of real mathematicians teaching public school math. I am not sure this is a recipe for success either. I mean they have a kind of a "different" perspective on the world. Â I am sure that there are a few of them that could pull it off. But many are really far out there and have no relationship to high school mathematics. They would probably change the entire curriculum. I am not sure this would be a bad thing. It might be quite good. But I think the content would have to change. 9th grade Logic. 10th grade Elementary Number Theory 11th grade Probability 12th Grade ? Â Mathematicians write things like "Elements of Mathematics" a very cool curriculum but I wouldn't give it to your average kid.

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Yes. Â I think that too is an issue. Â I went to a university with a very strong maths and sciences dept and there were a lot of jokes about people who could send spaceships to other planets, but could not change a battery in a flashlight...or balance a checkbook, or with less exaggeration, could not make a simple repair to an engine or manage their own finances. Â  Â  Though I also know a couple of math major graduates--from less esoteric based universities-- who are currently working in totally different areas, and might make wonderful math teachers. Â One has been my son's music teacher, and I know her to be good at teaching, even though she does not have a credential. Â Another does do tutoring to earn some cash, but again, no credential to be able to do teaching in schools.

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I am a bit disturbed that the math ed departments and the math departments can't seem to work together. I'd like see them put down their weapons and learn a bit from each other. I see a few interesting ideas that they seem to have but they (the math ed folks) tend to get all evangelical about things. "We have this great new method of teaching that no one has ever thought about before...it's called encouraging critical thinking." Goodness really? I find this kind of thing very sad.

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On the bolded--I am not just a bit disturbed by it. Â I am extremely disturbed and disheartened by that. Â I think both sides have a point and that by coming together they might actually get somewhere meaningful and that would truly be a big improvement.

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I think that math education (and all formal education) should be voluntary beyond a *solid* 8th grade level (prealgebra level in the case of math).

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That might be a good idea. Â It is certainly up to the prealgebra level (and some easy algebra and geometry) that gets used a great deal in life.

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Â I think I would also include some basic statistics as necessary these days. Â So much decision making depends on it, even if one's career does not use it. Â For example, I had a friend going through cancer treatment options who could not understand any statistical thinking, and it was a great impairment to her not to have that knowledge as she tried to decide what to do.

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I completely agree that mistakes need to be fixed and that students need to be evaluated but you need to get students to feel comfortable so that they can show you what they are thinking. Not just correcting the answer but correcting the wrong thinking.Â

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How many kids do you know that can take the reciprocal and multiply but have no idea what that means? What happens later in life is, if they ever have to take math again they wind up flipping the wrong number or doing some other thing that is close but complete nonsense. So right answers aren't really the holy grail in math. Often mathematicians will try to prove something by contradiction and discover a whole new branch of mathematics. 2+2 doesn't always equal 4. Of course you probably don't want your first graders to be answering that 2+2=1 but this is something that my son would have probably done if he was put in a mixed group class. He'd be so bored he'd answer everything mod3. But that's another topic entirely.

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Anyhow I am pretty sure what is meant by a "mistake friendly culture" is not encouraging a test with only 40% correct. Â I think the idea is to encourage kids to look critically at eachother's mistakes so that they understand what they are doing (and perhaps what they were doing wrong).

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One of my big qualms with this course is that I am afraid much of this will be misunderstood by the teachers and that their take away will be to lower standards. I really don't think this is the intent, but I could easily see someone getting confused.

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I understood the "mistake friendly" idea the same way as you. Â I hope it does not result in lower standards because of being misunderstood.

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One thing I got as a big help already from the course was to start asking my ds to tell me his thinking on problems he gets right. Â Â

For him it is hard to articulate that at all since he often seems to work in some intuitive way (the idea that males apparently process math in brain area like the amygdala, while females apparently do it in the frontal cortex was intriguing), where he himself is not sure of the steps he did in his head.

And then, since I tended to ask only when it was a wrong answer, that made the question get associated with doing something wrong, and thus stressful to be asked about that.

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Just that one thing has made a positive difference here in the past few days.

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I also think from what I have gotten from the course so far that I have decided on a course of action for Algebra 1, which I was in a dilemma about as of a week or two ago.

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Â I thought this course might be a fresh take on an old problem from a female mathematician but now that I know she isn't working in math but math ed., I don't know if I want to spend my time reading/watching more of the same.

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Agreed.

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Slightly off topic, but I thought some might find this series of graphs very interesting.

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Note the lonely EdD folks in the waaaay bottom left of the third graph- by far the lowest on every measure of ability. Also note that education is in the third quadrant of all four of these, with very little company! Here's the study it's from:Â https://my.vanderbilt.edu/smpy/files/2013/02/Wai2009SpatialAbility1.pdf

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Thank you onaclairadeluna for posting those links. If I do watch any more of the lectures, I'll certainly do so with a more critical eye.

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Agreed.

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Slightly off topic, but I thought some might find this series of graphs very interesting.

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Note the lonely EdD folks in the waaaay bottom left of the third graph- by far the lowest on every measure of ability. Also note that education is in the third quadrant of all four of these, with very little company! Here's the study it's from:Â https://my.vanderbilt.edu/smpy/files/2013/02/Wai2009SpatialAbility1.pdf

Thank you onaclairadeluna for posting those links. If I do watch any more of the lectures, I'll certainly do so with a more critical eye.

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Not sure I am understanding the graph--are the x and y supposed to be graphed on the usual x-axis and y axis? Â Â

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I am not surprised to see my own field (JD) apparently low on this chart for math ability, but am very surprised to see it apparently ranked quite low for verbal ability, which is contrary to my own experience and observations. Â

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I am not surprised to see my own field (JD) apparently low on this chart for math ability, but am very surprised to see it apparently ranked quite low for verbal ability, which is contrary to my own experience and observations. Â

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I agree.Â  I always thought that law was the equivalent of medical school for humanities types.

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A physicist, an engineer, and a statistician were out game hunting. The engineer spied a bear in the distance, so they got a little closer. "Let me take the first shot!" said the engineer, who missed the bear by three meters to the left. "You're incompetent! Let me try" insisted the physicist, who then proceeded to miss by three meters to the right. "Ooh, we *got* him!!" said the statistician.

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I agree.Â  I always thought that law was the equivalent of medical school for humanities types.

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Yes. Â And some areas of law like patent law require a science background--usually a bachelors in a science field or the equivalent. Â Others use a fair bit of math and or science -- more than one might think--in the business law areas, if one is a lawyer working with companies that also tend to have MBA's in them--at least sometimes . Â  And statistics gets used a lot in court situations. Â But nearly all law areas use a lot of oral and written expression and tons of reading.

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I went to Ivy league schools so my thinking on it may be skewed, but I would guess that most of my law school classmates had close to perfect scores on the verbal parts of SAT, and generally fairly high on math too, but not as high.

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Just throwing this out there from the graphs origins.

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Not intended to derail or whatever. Carry on...

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an engineer, theoretical physicist, and mathematician were in the same hotel in different rooms, when small fires broke out in each room. The engineer grabbed the fire extinguisher and put out the fire. The physicist sat down with pad and pencil and calculated the trajectory the water would take if he held the extinguisher at various angles, then aimed the device accordingly and also put out the fire. The mathematician wandered into the bathroom, turned on a faucet, said "a solution exists" and went back to bed.

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So, are some of you sticking with the class?Â

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... Â that feeling good about math is more important than arriving at the correct result.

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But if someone is so math wounded that it causes PTSD type symptoms to even think about it, then she or he is unlikely to be able to work at it and get to the correct results point.

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Or if someone is in class but totally tuned out, she or he is unlikely to learn much of anything. Â Or ditto for if not in class and wandering the halls or streets causing chaos instead.

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In some cases--a calculation of the correct amount of anaesthetic for surgery, or the engineering on a structure, the correct result is far more important than feeling good about it. Â

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But a 100% score on a school math test along with feeling lousy about math? Â I suppose a 100% and feeling good about it too would be best--but failing that, I think a lower grade, but feeling good about it--in a school, learning environment (not a life and death use of it) , would be better because one would be more likely to persist and thus improve. Â

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Also, I think one needs to have the experience of it being okay to make a mistake as one learns for reasons brought out in some of the Mindset materials. Â That was something that would have been hugely important in my own life. Â I was a 100% correct math type student through high school without much effort, and then was totally not prepared to actually have to work hard at it come university level. Â I remember getting a B, but feeling like I was absolutely failing, feeling like I was completely lost, leading, not to increased effort, but withdrawal, and thence to finally a C... Â which convinced me that I could not go into a math or science field, because I had been convinced by upbringing and messages around me that to have to put effort into something meant one was no good at it. Â My much younger sister on the other hand, who got different messages, was to my knowledge a sometimes A's sometimes Bs student through high school, continued to get Bs in university level math, felt fine about that so far as I know, and went on to become a doctor--a field very suited to her excellent hand/eye coordination for a surgical subspecialty.

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Which is a reason that taking the Stanford Course has helped decide me on a present plan to get AoPS for my son. Â I think he needs the experience of something challenging that he will make mistakes in, and to learn that that is fine, and to keep working on it. Â Now I just have to decide whether to start it with pre-algebra or with algebra.

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Though I have also found the Stanford Course leading me to find some math puzzles, and to try to find some other kids for my ds to have some group math time with to do some collaborative work on figuring out problems or perhaps puzzles, though not probably for "projects" -- at least not the sort where the project itself seems more involved than the learning it gives. Â  Though I am also thinking of getting something like Family Math for middle school level to see if that might help bring in some learning that is more project related and more fun. Â I am also wondering about things like Marilyn Burns books and whether they might still be worthwhile at this stage.

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It has also made me think a lot about exact words that I use with him and what impact they may have.

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Also, I think one needs to have the experience of it being okay to make a mistake as one learns for reasons brought out in some of the Mindset materials. Â That was something that would have been hugely important in my own life. Â I was a 100% correct math type student through high school without much effort, and then was totally not prepared to actually have to work hard at it come university level. Â I remember getting a B, but feeling like I was absolutely failing, feeling like I was completely lost, leading, not to increased effort, but withdrawal, and thence to finally a C... Â which convinced me that I could not go into a math or science field, because I had been convinced by upbringing and messages around me that to have to put effort into something meant one was no good at it.

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I absolutely agree and can relate to your experience. This is one of the main reasons I homeschool.

I would, however, not call what is needed a "mistake friendly culture", but rather an appropriately challenging school education that is NOT geared towards the low performing end of the class, that does NOT hand out easy As for no effort, and that teaches students to work hard if they want a good grade.

You might find Richard Rusczyk's article interesting where he talks about the "tyranny of the 100%". (I don't have the link, please google). A student who always gets 100% correct is not using appropriately challenging curriculum. If THAT is what is meant by "mistake friendly", I wholeheartedly agree; hearing this statement come from a math *educator*, however, I am deeply suspicious that this is just another touchy-feely "we-all-feel-good-about-math" thing.

I believe students who learn in an atmosphere that *requires and rewards* effort and hard work for *every* student will feel better about their accomplishments, in math and other subjects.

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But if someone is so math wounded that it causes PTSD type symptoms to even think about it, then she or he is unlikely to be able to work at it and get to the correct results point.

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Or if someone is in class but totally tuned out, she or he is unlikely to learn much of anything. Â Or ditto for if not in class and wandering the halls or streets causing chaos instead.

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In some cases--a calculation of the correct amount of anaesthetic for surgery, or the engineering on a structure, the correct result is far more important than feeling good about it. Â

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But a 100% score on a school math test along with feeling lousy about math? Â I suppose a 100% and feeling good about it too would be best--but failing that, I think a lower grade, but feeling good about it--in a school, learning environment (not a life and death use of it) , would be better because one would be more likely to persist and thus improve. Â

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Also, I think one needs to have the experience of it being okay to make a mistake as one learns for reasons brought out in some of the Mindset materials. Â That was something that would have been hugely important in my own life. Â I was a 100% correct math type student through high school without much effort, and then was totally not prepared to actually have to work hard at it come university level. Â I remember getting a B, but feeling like I was absolutely failing, feeling like I was completely lost, leading, not to increased effort, but withdrawal, and thence to finally a C... Â which convinced me that I could not go into a math or science field, because I had been convinced by upbringing and messages around me that to have to put effort into something meant one was no good at it. Â My much younger sister on the other hand, who got different messages, was to my knowledge a sometimes A's sometimes Bs student through high school, continued to get Bs in university level math, felt fine about that so far as I know, and went on to become a doctor--a field very suited to her excellent hand/eye coordination for a surgical subspecialty.

Â

Which is a reason that taking the Stanford Course has helped decide me on a present plan to get AoPS for my son. Â I think he needs the experience of something challenging that he will make mistakes in, and to learn that that is fine, and to keep working on it. Â Now I just have to decide whether to start it with pre-algebra or with algebra.

Â

Though I have also found the Stanford Course leading me to find some math puzzles, and to try to find some other kids for my ds to have some group math time with to do some collaborative work on figuring out problems or perhaps puzzles, though not probably for "projects" -- at least not the sort where the project itself seems more involved than the learning it gives. Â  Though I am also thinking of getting something like Family Math for middle school level to see if that might help bring in some learning that is more project related and more fun. Â I am also wondering about things like Marilyn Burns books and whether they might still be worthwhile at this stage.

Â

It has also made me think a lot about exact words that I use with him and what impact they may have.

Â

You bring up some interesting thoughts that reflect my own experience as a student and also in upbringing. Ironically, it was this very upbringing that convinced me as a teen that I didn't want the same for my future child(ren). I knew I could have been good at math if it was approached differently in my school and if my parents could have accepted that I simply learn differently from my extremely studious, more linear sibs. I was more than willing to put in effort but was lost because I didn't have the resources to learn math the way that would have stuck best in my head. And I think it was this whole knowledge, knowing math education can be addressed in a non linear, play-based fashion that helped me feel at home teaching math to my young child despite my own bad experiences in school. I was willing to take the risk and be out of the box with him because I experienced first-hand what in-the-box teaching does to certain learners.

Â

I feel it's a serious disservice that more homeschoolers are not made aware of livingmath.net and the efforts Julie Brennan has put into making math more accessible and real to every child. I also wanted to suggest that Family Math, though wonderful, might be a little young for your son (I think he's the same age or perhaps older than mine?)...or maybe not, just that it strikes me that he might really enjoy and prefer puzzle books by Martin Gardner instead (some are available as inexpensive Dover titles on Amazon and elsewhere). I have some titles linked in my siggy that could be helpful.

Â

FWIW, I didn't sign up for this course because from the description it didn't feel like they were going to tell me anything critical that was new kwim? At least not in my homeschool setting. But like a pp said I am learning so much from this discussion alone...I am confident it is much more than what I would have learned from the course.

Â

ETA:

It has also made me think a lot about exact words that I use with him and what impact they may have.

Â

This! It's hard to be careful about everything we say and not very realistic imho to watch each word...but being aware at certain times and having the right body language too...it can make a big difference.

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But if someone is so math wounded that it causes PTSD type symptoms to even think about it, then she or he is unlikely to be able to work at it and get to the correct results point.

Â

Or if someone is in class but totally tuned out, she or he is unlikely to learn much of anything. Â Or ditto for if not in class and wandering the halls or streets causing chaos instead.

Â

In some cases--a calculation of the correct amount of anaesthetic for surgery, or the engineering on a structure, the correct result is far more important than feeling good about it. Â

Â

But a 100% score on a school math test along with feeling lousy about math? Â I suppose a 100% and feeling good about it too would be best--but failing that, I think a lower grade, but feeling good about it--in a school, learning environment (not a life and death use of it) , would be better because one would be more likely to persist and thus improve. Â

Â

Also, I think one needs to have the experience of it being okay to make a mistake as one learns for reasons brought out in some of the Mindset materials. Â That was something that would have been hugely important in my own life. Â I was a 100% correct math type student through high school without much effort, and then was totally not prepared to actually have to work hard at it come university level. Â I remember getting a B, but feeling like I was absolutely failing, feeling like I was completely lost, leading, not to increased effort, but withdrawal, and thence to finally a C... Â which convinced me that I could not go into a math or science field, because I had been convinced by upbringing and messages around me that to have to put effort into something meant one was no good at it. Â My much younger sister on the other hand, who got different messages, was to my knowledge a sometimes A's sometimes Bs student through high school, continued to get Bs in university level math, felt fine about that so far as I know, and went on to become a doctor--a field very suited to her excellent hand/eye coordination for a surgical subspecialty.

Â

Which is a reason that taking the Stanford Course has helped decide me on a present plan to get AoPS for my son. Â I think he needs the experience of something challenging that he will make mistakes in, and to learn that that is fine, and to keep working on it. Â Now I just have to decide whether to start it with pre-algebra or with algebra.

Â

Though I have also found the Stanford Course leading me to find some math puzzles, and to try to find some other kids for my ds to have some group math time with to do some collaborative work on figuring out problems or perhaps puzzles, though not probably for "projects" -- at least not the sort where the project itself seems more involved than the learning it gives. Â  Though I am also thinking of getting something like Family Math for middle school level to see if that might help bring in some learning that is more project related and more fun. Â I am also wondering about things like Marilyn Burns books and whether they might still be worthwhile at this stage.

Â

It has also made me think a lot about exact words that I use with him and what impact they may have.

Â

Â

You bring up some interesting thoughts that reflect my own experience as a student and also in upbringing. Ironically, it was this very upbringing that convinced me as a teen that I didn't want the same for my future child(ren). I knew I could have been good at math if it was approached differently in my school and if my parents could have accepted that I simply learn differently from my extremely studious, more linear sibs. I was more than willing to put in effort but was lost because I didn't have the resources to learn math the way that would have stuck best in my head. And I think it was this whole knowledge, knowing math education can be addressed in a non linear, play-based fashion that helped me feel at home teaching math to my young child despite my own bad experiences in school. I was willing to take the risk and be out of the box with him because I experienced first-hand what in-the-box teaching does to certain learners.

Â

I feel it's a serious disservice that more homeschoolers are not made aware of livingmath.net and the efforts Julie Brennan has put into making math more accessible and real to every child. I also wanted to suggest that Family Math, though wonderful, might be a little young for your son (I think he's the same age or perhaps older than mine?)...or maybe not, just that it strikes me that he might really enjoy and prefer puzzle books by Martin Gardner instead (some are available as inexpensive Dover titles on Amazon and elsewhere). I have some titles linked in my siggy that could be helpful.

Â

FWIW, I didn't sign up for this course because from the description it didn't feel like they were going to tell me anything critical that was new kwim? At least not in my homeschool setting. But like a pp said I am learning so much from this discussion alone...I am confident it is much more than what I would have learned from the course.

Â

That's my current experience with my oldest. I know he can do it. He's getting a B in Pre-algebra. There has been a lot of hard work and frustration on his part. There were portions that came super easy to him. He loves statistics and probability. And he struggled immensely on volume and surface area of solids. The curriculum was quite rigorous for him. There were some things that worked and some things where I really needed to intervene and explain step by step. He's extremely hard on himself. Before this course, I was already planning on taking a semester in 8th to just review and let all that information sink in before we move onto Algebra. My hope was that it would give him the time to regain some confidence and begin Algebra with a much better mindset. We were going to work on some of the basics up to practicing the multi-step problems that seemed to give him the most trouble. I had also planned on adding in some math puzzles and other games like Dragonbox to change it up a bit.Â

Â

For my dd, who loves school, loves to read, but was already struggling with math, I started using Arithmetic Village with her and she just LOVES it! She has her Little People King and Queen with her kit. I have found her playing on her own; counting and adding. She was really struggling with MM1A. She's normally a very workbooky type of girl, but has a serious aversion to being wrong. She's a perfectionist and will shut down when she starts getting things wrong, not good for math. So we've been going slow in math. Too slow for me, but I'm trying to be very gentle about it.Â

Â

I have 2 of the Family Math books that I really need to go through for more ideas.Â

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And he struggled immensely on volume and surface area of solids.

Printing out geometric nets and making his own models. Pouring sand/salt into his models and than pouring out to compare volumes may help. For example when I was in school, we had to pour sand from a cone to a cylinder of the same base area. It was fun and help us remember.

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I absolutely agree and can relate to your experience. This is one of the main reasons I homeschool.

I would, however, not call what is needed a "mistake friendly culture", but rather an appropriately challenging school education that is NOT geared towards the low performing end of the class, that does NOT hand out easy As for no effort, and that teaches students to work hard if they want a good grade.

You might find Richard Rusczyk's article interesting where he talks about the "tyranny of the 100%". (I don't have the link, please google). A student who always gets 100% correct is not using appropriately challenging curriculum. If THAT is what is meant by "mistake friendly", I wholeheartedly agree; hearing this statement come from a math *educator*, however, I am deeply suspicious that this is just another touchy-feely "we-all-feel-good-about-math" thing.

I believe students who learn in an atmosphere that *requires and rewards* effort and hard work for *every* student will feel better about their accomplishments, in math and other subjects.

Â

I have not yet found that one, but in looking for it, I found some others and his blog.

Â

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I absolutely agree and can relate to your experience. This is one of the main reasons I homeschool.

I would, however, not call what is needed a "mistake friendly culture", but rather an appropriately challenging school education that is NOT geared towards the low performing end of the class, that does NOT hand out easy As for no effort, and that teaches students to work hard if they want a good grade.

Actually, she advocates giving lower end students harder work. But it seems that in order to do that she winds up simplifying the curriculum that the very top students get. I could see how this might improve average performance (not sure if I believe it does but I am willing to entertain the notion) but I have a very hard time believing that it would be suitable for the top 1% and perhaps not even the top 5% of students who are going to need not just harder and more accelerated math but different math.

Â

Â

The lesson is at the 6 minute mark.

Â

It is a clip of a model teacher. I think the teacher actually does a pretty good job of introducing fraction division and at the end of the class she introduces the algorithm. So there is some direct instruction going on. More than I even do with my own kids. I stay further away from standard algorithms with them but this is mostly because both kids are dyslexic and I need to adjust for the way they learn. I think your average kid would do just about right learning the standard algorithm after a 20-30 minute class discussion like the one presented.

Â

Later in the lesson there is a girl who starts to talk about inverses but she can't quite get it into words or at least not enough to convince anyone in the class. I think the teacher should have helped out more here. The pictures and the abstraction are completely connected and the teacher lost an opportunity for teaching.Â

Â

OK I have to back track. At first I thought she wasn't dumbing the curriculum down but on second thought the kids in the video are a little older than I thought. I was going to initially say that Â she is failing to differentiate for the top 1% maybe the top 5%. Upon rewatching I would say that this lesson doesn't meet the needs of the top 20% at least. But I think it is a pretty good lesson nevertheless. I certainly think she is making the majority of the kids in her class work. It doesn't seem fluffy or feel good at all. It seems pretty mathematically sound. When kids give her faulty reasoning she gently calls them to the mat on it (she encourages them to try to convince her but of course their reasoning is faulty and they can't). It's a lesson on how to check to see if your math is sound or if you are applying some weird magical thinking to your homework. I actually kind of liked it. But in no way would this work for GT kids. Â (Well I actually borrowed this to use with my 8 year old but gosh those kids are way older). By the time she is that age she will definitely have moved on.Â

Â

So I have mixed feelings. The methods she is advocating are not bad but she is completely dismissing the needs of GT kids. She claims that gt kids are served in these types of classrooms and says that the evidence backs her up. But I still don't believe her.

Â

Doing hard problems, making mistakes, and having a growth mindset are all things that gt kids can benefit from. I follow her that far but putting a gt kid in the classroom example that she gives would be a disaster.

Â

FYI I think Pen asked this. I will probably stick around to see what she has to say for the second half of the course. I am giving up on the assignments but I find it kind of interesting (even when I disagree with what she is saying).

Â

I went to go look for the article on the Tyranny of the 100% but instead found this...http://www.artofproblemsolving.com/Resources/articles.php?page=mistakes

Â

So, OK maybe some mistakes are better than others. There is of course a difference between doing math that is hard enough so that you are challenged and make mistakes because you are learning and making mistakes because you are just being dingy. We certainly don't want to encourage sloppiness or carelessness in math.

Â

Here it is (Tyranny of the 100%)...

http://mathprize.atfoundation.org/archive/2009/Rusczyk_Problem_Solving_Presentation_at_Math_Prize_for_Girls_2009.pdf

Â

and the video

Â

http://mathprize.atfoundation.org/archive/2009/rusczyk

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So I have mixed feelings. The methods she is advocating are not bad but she is completely dismissing the needs of GT kids. She claims that gt kids are served in these types of classrooms and says that the evidence backs her up. But I still don't believe her.

Â

Â

These are my thoughts too. She doesn't specifically address gifted students, but I don't believe her plan is in their best interests. Possibly the average of the group as a whole will be better in this all-inclusive group format, but I think the individual data for the gifted students would show a problem. Something that concerns me is that the discussion forum has teachers saying how great it is that they can tell their principals that they won't need to divide students into ability groups anymore. Several of them mentioned having to tell parents about their "so-called gifted" students not getting separated from the main group anymore. I feel sad for the students who would have benefitted from a gifted class which will no longer be offered thanks to the advice of this course.

Â

I do plan to see the course through to the end. I have finished the first four chapters and do feel that I got something from the course. I just don't believe some of the research results are as universal as they state.

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Something that concerns me is that the discussion forum has teachers saying how great it is that they can tell their principals that they won't need to divide students into ability groups anymore. Several of them mentioned having to tell parents about their "so-called gifted" students not getting separated from the main group anymore. I feel sad for the students who would have benefited from a gifted class which will no longer be offered thanks to the advice of this course.

Â

Oh dear. I hadn't seen that. That is terrible. That was my fear, that it would propagate a negative attitude toward gt students. They get enough negativity by teachers as it is we don't need to give them any more ammunition.

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The beauty of mathematics is that there is no room for debate whether something is correct. It does not depend on the personal preferences or political views of the evaluator - a solution either is correct or wrong. In that respect, a "mistake friendly culture" is the last thing I would want for my child's math education.

Yes, making mistakes happens and is a way to learn, and a student should be encouraged to make different attempts and play around with the problems - but IMO math education is not supposed to be "mistake friendly": it is supposed to teach creative problem solving that arrives at a *correct* solution.

Â

It needs to be specified what the author considers as "regular" and what qualifies as "testing". Having a student do math problems is only useful if the results are evaluated on a continuing basis: EVERY problem is checked EVERY day. To me it makes no sense to have the student work on math and NOT verify that he is doing the problems correctly (this can be self-checking by the student). Now, what distinguishes "testing" from daily "checking"? The author needs to be precise.

Daily checking is absolutely essential. Timed tests under pressure can be done infrequently, but must be done, in sufficiently large intervals. Since an evaluation of math mastery only makes sense if *long term* mastery is evaluated, comprehensive examinations at semester/year end are much more valuable than weekly quizzes that test only the concept currently studied, but not whether last months' material can still be applied.

Â

Speed: speed can be overrated, but speed is not obsolete. A student who lacks a quick recall of math facts will struggle in higher math when he is distracted from the actual problem by being hindered in numerical computations. Math is not *about* speed, but an automatic recall of facts frees the student's mind to ponder the actual problem and not be mired in arithmetic. Of course, quick rcall does not guarantee a ggood mathematical understanding and thus speed drills should not be emphasized over probelm solving. However, I am cringing again at the word "mistake friendly": math should be precise, not fuzzy.

Â

When I hear statements like this, I am glad I am staying away from courses presented by math *educators*. Much of what is problematic in math education comes from the education departments. I'd rather listen to a real mathematician like Lockhardt, with whose "Lament" I agree ecompletely.

Â

Regentrude, I loved this whole post but in particular the bolded. Â Thank you!

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This reminds me of a teacher who teaches the advanced math class at a local middle school. She lectured the students one day on the math projects they had recently presented.

Â

"I want more glitter!"

Â

She meant that literally. She was happy that there was more glitter on the posters for the next class presentation. She considered it a success--these were, after all, the advanced kids. (and thus more capable with glitter?)

Â

:confused:

That sh&%\$! makes me crazy!

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Several of them mentioned having to tell parents about their "so-called gifted" students not getting separated from the main group anymore. I feel sad for the students who would have benefitted from a gifted class which will no longer be offered thanks to the advice of this course.

Gifted or not, there is suppose to be differentiation in math and language arts instruction in every classroom. Pull-out options however tends to be subjected to school politics, district politics and PTA politics as well as budget constraints. My older's former school have aides for language arts pull outs and none for math pull outs. Language Arts needed much more "firefighting" resources from the district budget.Â  I just feel it is an excuse if the teachers use this course to scrap differentiation.

Â

Â They get enough negativity by teachers as it is we don't need to give them any more ammunition.

Unfortunately that is the luck of the draw kind of situation.Â  My boys teachers from Kindergarten until now have been supportive.

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I just feel it is an excuse if the teachers use this course to scrap differentiation.

Â

I agree. Unfortunately, some made it sound like they were looking for an excuse.

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But if someone is so math wounded that it causes PTSD type symptoms to even think about it, then she or he is unlikely to be able to work at it and get to the correct results point.

Â

Or if someone is in class but totally tuned out, she or he is unlikely to learn much of anything. Â Or ditto for if not in class and wandering the halls or streets causing chaos instead.

Â

In some cases--a calculation of the correct amount of anaesthetic for surgery, or the engineering on a structure, the correct result is far more important than feeling good about it. Â

Â

But a 100% score on a school math test along with feeling lousy about math? Â I suppose a 100% and feeling good about it too would be best--but failing that, I think a lower grade, but feeling good about it--in a school, learning environment (not a life and death use of it) , would be better because one would be more likely to persist and thus improve. Â

Â

Also, I think one needs to have the experience of it being okay to make a mistake as one learns for reasons brought out in some of the Mindset materials. Â That was something that would have been hugely important in my own life. Â I was a 100% correct math type student through high school without much effort, and then was totally not prepared to actually have to work hard at it come university level. Â I remember getting a B, but feeling like I was absolutely failing, feeling like I was completely lost, leading, not to increased effort, but withdrawal, and thence to finally a C... Â which convinced me that I could not go into a math or science field, because I had been convinced by upbringing and messages around me that to have to put effort into something meant one was no good at it. Â My much younger sister on the other hand, who got different messages, was to my knowledge a sometimes A's sometimes Bs student through high school, continued to get Bs in university level math, felt fine about that so far as I know, and went on to become a doctor--a field very suited to her excellent hand/eye coordination for a surgical subspecialty.

Â

Which is a reason that taking the Stanford Course has helped decide me on a present plan to get AoPS for my son. Â I think he needs the experience of something challenging that he will make mistakes in, and to learn that that is fine, and to keep working on it. Â Now I just have to decide whether to start it with pre-algebra or with algebra.

Â

Though I have also found the Stanford Course leading me to find some math puzzles, and to try to find some other kids for my ds to have some group math time with to do some collaborative work on figuring out problems or perhaps puzzles, though not probably for "projects" -- at least not the sort where the project itself seems more involved than the learning it gives. Â  Though I am also thinking of getting something like Family Math for middle school level to see if that might help bring in some learning that is more project related and more fun. Â I am also wondering about things like Marilyn Burns books and whether they might still be worthwhile at this stage.

Â

It has also made me think a lot about exact words that I use with him and what impact they may have.

Yes to all this - I've gleaned the same insights as well. Â That's been worth it.

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I absolutely agree and can relate to your experience. This is one of the main reasons I homeschool.

I would, however, not call what is needed a "mistake friendly culture", but rather an appropriately challenging school education that is NOT geared towards the low performing end of the class, that does NOT hand out easy As for no effort, and that teaches students to work hard if they want a good grade.

You might find Richard Rusczyk's article interesting where he talks about the "tyranny of the 100%". (I don't have the link, please google). A student who always gets 100% correct is not using appropriately challenging curriculum. If THAT is what is meant by "mistake friendly", I wholeheartedly agree; hearing this statement come from a math *educator*, however, I am deeply suspicious that this is just another touchy-feely "we-all-feel-good-about-math" thing.

I believe students who learn in an atmosphere that *requires and rewards* effort and hard work for *every* student will feel better about their accomplishments, in math and other subjects.

Â

So maybe the issue is not having a mistake-friendly culture, but a mistake-inducing culture? Â Meaning that the work is challenging enough that struggling/grappling with a hard problem, and making mistakes you can learn from, is even possible. Â I think this is where I see the need to step it up - instead of thinking that if she's getting all 95% and up that's a good thing, maybe it means that she needs more challenging material.

Â

Or maybe it just means she's mastered that and is ready to move on? Â How to tell the difference (with a kid who isn't genetically predisposed to ask for harder workÂ  ;)Â  :rolleyes: )

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Â How to tell the difference (with a kid who isn't genetically predisposed to ask for harder workÂ  ;)Â  :rolleyes: )

Â

My older boy's facial expressions tells a story, while my younger gives a running commentary of how easy/tricky/hard a math question is.

Their amount of careless mistakes is negatively correlated to how challenging/entertaining the math problems are.

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WOW. The links to the "disagreement" between math and math ed at Stanford are very eye-opening (and unfortunately underscore my skepticism toward this course).Â

Â

She keeps mentioning Common Core . . . is Common Core going to adopt Reform Math? (Praying I'm wrong.)

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Actually, she advocates giving lower end students harder work. But it seems that in order to do that she winds up simplifying the curriculum that the very top students get. I could see how this might improve average performance (not sure if I believe it does but I am willing to entertain the notion) but I have a very hard time believing that it would be suitable for the top 1% and perhaps not even the top 5% of students who are going to need not just harder and more accelerated math but different math.

Â

Â

The lesson is at the 6 minute mark.

Â

It is a clip of a model teacher. I think the teacher actually does a pretty good job of introducing fraction division and at the end of the class she introduces the algorithm. So there is some direct instruction going on. More than I even do with my own kids. I stay further away from standard algorithms with them but this is mostly because both kids are dyslexic and I need to adjust for the way they learn. I think your average kid would do just about right learning the standard algorithm after a 20-30 minute class discussion like the one presented.

Â

Later in the lesson there is a girl who starts to talk about inverses but she can't quite get it into words or at least not enough to convince anyone in the class. I think the teacher should have helped out more here. The pictures and the abstraction are completely connected and the teacher lost an opportunity for teaching.Â

Â

OK I have to back track. At first I thought she wasn't dumbing the curriculum down but on second thought the kids in the video are a little older than I thought. I was going to initially say that Â she is failing to differentiate for the top 1% maybe the top 5%. Upon rewatching I would say that this lesson doesn't meet the needs of the top 20% at least. But I think it is a pretty good lesson nevertheless. I certainly think she is making the majority of the kids in her class work. It doesn't seem fluffy or feel good at all. It seems pretty mathematically sound. When kids give her faulty reasoning she gently calls them to the mat on it (she encourages them to try to convince her but of course their reasoning is faulty and they can't). It's a lesson on how to check to see if your math is sound or if you are applying some weird magical thinking to your homework. I actually kind of liked it. But in no way would this work for GT kids. Â (Well I actually borrowed this to use with my 8 year old but gosh those kids are way older). By the time she is that age she will definitely have moved on.Â

Â

So I have mixed feelings. The methods she is advocating are not bad but she is completely dismissing the needs of GT kids. She claims that gt kids are served in these types of classrooms and says that the evidence backs her up. But I still don't believe her.

Â

Doing hard problems, making mistakes, and having a growth mindset are all things that gt kids can benefit from. I follow her that far but putting a gt kid in the classroom example that she gives would be a disaster.

Â

FYI I think Pen asked this. I will probably stick around to see what she has to say for the second half of the course. I am giving up on the assignments but I find it kind of interesting (even when I disagree with what she is saying).

Â

I went to go look for the article on the Tyranny of the 100% but instead found this...http://www.artofproblemsolving.com/Resources/articles.php?page=mistakes

Â

So, OK maybe some mistakes are better than others. There is of course a difference between doing math that is hard enough so that you are challenged and make mistakes because you are learning and making mistakes because you are just being dingy. We certainly don't want to encourage sloppiness or carelessness in math.

Â

Here it is (Tyranny of the 100%)...

http://mathprize.atfoundation.org/archive/2009/Rusczyk_Problem_Solving_Presentation_at_Math_Prize_for_Girls_2009.pdf

Â

and the video

Â

http://mathprize.atfoundation.org/archive/2009/rusczyk

Â

Â

Â

Is it now the case that schools are doing a good job with the top 1% or top 5%? Â It was not the case when I was in school even with tracked groups, but maybe it has changed.

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Regentrude, your wonderful post reminds me of one of my proudest moments as a student. I had failed out of college and been required to work a year in a factory to earn tuition money. Upon returning I was faced with the challenge of taking the course following the one I had gotten a D in, (repetition was not allowed, you had to start back exactly where you left off).

Â

I worked hard, got a D on the first test, but by the final, which had 10 questions and said "answer any 7", I did them all, and initially wrote "grade any 7". I quickly and prudently reconsidered this smart alecky response, and chose 7 sure bets. But one of those included a complete proof of a theorem the prof had omitted from the course, but which I had looked up and learned in the library.

Â

I got 100% and the remark from the prof that "there were several 100's,but yours was head and shoulders above the rest."

Â

I celebrated for a week, and then concluded that the reason I had received such a high score, was not that I was so smart, but that I was in the wrong course. I petitioned the honors prof for re- admittance to the honors sequence, read the materials he told me would be prerequisite, and proudly got a B+ in the honors sequence the next semester, followed by an A- after that.

Â

So my proud moment was not the 100% in regular calc 2, but a lower grade in the better course.

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on a side note on glitter--when my ds was at brick and mortar school he had a project involving glitter that got glitter all over the floor, down into the floorboard cracks and so on... it was horrible, and there is probably some still there years later. Â  The next time he had a glitter project we dealt with it at the school, leaving the mess for the teachers to deal with. Â  Â

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Glitter in middle school? Â For math? Â  Sad!!!.

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Am I the only one who feels depressed rather than entertained by the petty fight between those few people in the various academic departments at Stanford? I have some wonderful friends there who are going about their business adding to the sum of human knowledge instead of attacking each other.

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Here is a link to someone I know and respect, who to me represents the best Stanford has to offer, and I think it's pretty wonderful:

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http://math.stanford.edu/~vakil/

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Notice he also advises high school student math circles. If you are in the Palo Alto area, and have an advanced math student, I think you will be extremely pleased if you can make contact with a math circle taught by this extraordinary man. And there are others.

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