Stanford Math Course: What are you learning/going to do differently for math?

[Pen]

If you are taking the Stanford Math Course, what are you learning from it?  Are you making changes in what/how you will be teaching math?  What?

[Woodland Mist Academy]

I am not sure what to think of The Mathematician's Lament. I thought it started well, but by the end I was disheartened and irritated.  I suspect that is partly because I disagreed with some of his thinking. For one, I disagree with his thoughts on poetry--perhaps even with his thoughts on creativity in general. Am I the only one?

 

 

 

 

[Woodland Mist Academy]

As far as changes, none so far. AoPS offers and promotes mathematical creativity in spades. I see its effects trickling into everyday life. Just yesterday dd was contemplating a math concept and writing it out. It was not a new concept, but it was new to her, and the fact that it came out of her dreamy reveries while she was avoiding a different school subject was a bit of a shock to her--a delightful moment, for sure.

 

 

[Pen]

I am on dial up and can't get some things, but went through the first several transcripts to the videos, and as well had read a lot of Jo Boaler's book.  I haven't seem to come to the Mathematician's Lament yet, where is that?

 

I am interested in the idea that there will probably be a class for the students themselves in fall (?).  I think I want my ds to do that.

 

My ds wanted to watch The Story of Math documentary over the last couple of days instead of regular math, and I think taking the Stanford course is what made me say, "Yes."   I had the feeling maybe that would be more important than doing some problem sets.

[Woodland Mist Academy]

I am on dial up and can't get some things, but went through the first several transcripts to the videos, and as well had read a lot of Jo Boaler's book.  I haven't seem to come to the Mathematician's Lament yet, where is that?

 

It was somewhere in the first sesson--not sure which clip.  Here's a link someone else posted on a different thread.

 

http://mysite.science.uottawa.ca/mnewman/LockhartsLament.pdf

[Lucy the Valiant]

Initial thoughts: (in random order)

 

> Pen, I hadn't heard of the Story of Math - gonna look that one up.

 

> Stereotypes: Yep, I definitely heard that message, loud and clear: girls are not as good at math as boys. In fact, it never even entered my head to go into a STEM field, even though I did have straight A's in math in school (it just never even crossed my mind - I *knew* what I was good at, ya know?).

 

> So excited for my kiddos! I think this is going to be GREAT for my mathematical interaction with them - I know this is a side issue, but I am just so excited.

 

> I want to read her book! (Is it just me, or can anyone else not get away from the cc / transcripts? I can't look away! Aaagh!)

 

> Have been mulling over AOPS . . . this is going to push me over the edge. Gonna have to order it.

 

Off to read Lockhart's Lament.

 

[Woodland Mist Academy]

> I want to read her book! (Is it just me, or can anyone else not get away from the cc / transcripts? I can't look away! Aaagh!)

 

 

Me too! I think the book would be a better format for me.

[Eagle]

Ds LOVED the posters that I made for chapter 3.9. Usually if he gets anything wrong in math he has a complete meltdown. Yesterday I showed him my posters and we talked about your brain growing when you make mistakes. Today he made a few errors in math and casually commented "hey, my brain must be growing right now" before correcting his mistakes. I just about fell off my chair.

[Lucy the Valiant]

Ds LOVED the posters that I made for chapter 3.9. Usually if he gets anything wrong in math he has a complete meltdown. Yesterday I showed him my posters and we talked about your brain growing when you make mistakes. Today he made a few errors in math and casually commented "hey, my brain must be growing right now" before correcting his mistakes. I just about fell off my chair.

 

Willing to share? :) (At least the ideas?)  *grin*

[Chrysalis Academy]

So now there are at least 3 threads about this class, I will lose track of what I've posted where!

 

One thought that immediately comes to mind is that I need to ramp up the challenge for dd10.  My goal is to teach to mastery, and she easily averaged ~95% on all her chapter tests last year, no scores under 90%.  She was happy about this, and I felt like she learned a ton last year, and she has a lot of confidence in her math abilities, which I was going for.

 

But now instead of feeling good about this, I'm feeling like it means things are too easy!   So I'm looking to add a lot more long, struggly, problem-solving sessions, rather than just letting her fly through another year of MM.  (she says, laughing evilly, rubbing her hands together)

 

I'm still grappling with the whole assessments issue - how often to assess, what to assess, etc.  I don't see not assessing at all, I don't feel confident enough to know that she knows what she needs to know without doing some end-of-chapter assessments, but I want to keep it low key/diagnostic (which is basically how I handled it last year) and not have it feel high-stakes at all.  She is upset when she misses things on the tests, I definitely need to do more work on making it clear that mistakes are a good thing, a learning opportunity, not something to be avoided.

 

Yeah, I think I've been a little too helpful, and it's been a little too easy.  I'm not exactly sure what to do differently yet, but I'm hoping some more ideas will bubble up.

[Eagle]

Willing to share? :) (At least the ideas?) *grin*

http://tinypic.com/r/98t4sg/5

http://tinypic.com/r/2e36cye/5

 

 

Ds is 5, so he likes my attempt at cartoon characters. :)

[Chrysalis Academy]

One thing I've been mulling over, that I think I need to change, is the output expectation, as I ramp up to more challenging problem-solving.  With MM, the goal for a day is to finish a lesson, with LOF it's to do 2-3 chapters, etc.  But I can see that there will be a need to have days where we might just do one or two problems - challenging problems that you have to really set up and think through and discuss, like the examples given in the class.  That will require a shift in thinking in my part, as well as a significant shift in what it means to "progress" or "stay on track".  That's something I embrace theoretically, but knowing myself I know it will make me uncomfortable, as well, so I'll have to stay vigilant to not fall back into "finish already and move on" mode.

[Woodland Mist Academy]

One thing I've been mulling over, that I think I need to change, is the output expectation, as I ramp up to more challenging problem-solving.  With MM, the goal for a day is to finish a lesson, with LOF it's to do 2-3 chapters, etc.  But I can see that there will be a need to have days where we might just do one or two problems - challenging problems that you have to really set up and think through and discuss, like the examples given in the class.  That will require a shift in thinking in my part, as well as a significant shift in what it means to "progress" or "stay on track".  That's something I embrace theoretically, but knowing myself I know it will make me uncomfortable, as well, so I'll have to stay vigilant to not fall back into "finish already and move on" mode.

 

This is what I am dealing with right now. Part of me is starting to panic because we didn't finish a math book in a 12 month span. The other part remembers not only were we doing multiple programs, but there was more than one day when only one problem got done. (With a lot of---DON'T GIVE ME ANY HINTS! --going on.)

 

In full disclosure: I readily admit to looking longingly at books with pages of fill in the formula problems on some of those days. ;)

[EKS]

I am not sure what to think of The Mathematician's Lament. I thought it started well, but by the end I was disheartened and irritated.  I suspect that is partly because I disagreed with some of his thinking. For one, I disagree with his thoughts on poetry--perhaps even with his thoughts on creativity in general. Am I the only one?

 

You are not the only one.

[Mrs. A]

Subbing to this thread so I can come back and discuss. I'm only part way through the first session.  I'm hoping to get through a lot tonight.  I am so excited to be able to approach math without fear of being found incompetent.  

[Bang!Zoom!]

I actually dreamed about The Lament last night. Not like that had any impact on me, right? lol

[Pen]

I am not sure what to think of The Mathematician's Lament. I thought it started well, but by the end I was disheartened and irritated.  I suspect that is partly because I disagreed with some of his thinking. For one, I disagree with his thoughts on poetry--perhaps even with his thoughts on creativity in general. Am I the only one?

 

 

I thought the end where he summarized the stages of math education in USA as it is now was very funny, and with some important truth to it.  I also thought the parts where he wrote about Geometry proofs was very interesting.  It makes me wonder if, for example, something like AOPS does it more the way Lockhart thinks it should be being done...or if any program does that.  It makes me feel good about our Jousting with Armadillos choice, since that fits a lot of what I think he and Boaler in her book think should be different--although it would be better if we had a way to do that with a group of kids working together.  

 

I guess that unlike Lockhart I think poetry can be appreciated by hearing it--not necessarily writing it.  I think that people need to be able to be competent at writing even if they do not write poetry.  And I think they need to be competent at arithmetic and math even if they do not do the sort of mathematics as poetry he is talking about.  I agree that the dream idea it starts with where music gets taught from the start as manipulating written music on paper would be ridiculous.  And I see the analogy to math.  But I do not see the analogous solution.  

 

I think that is in part why I said yes to the movie watching in place of doing math for the last couple of days...it allows an appreciation of math, perhaps, a little like being able to listen to a symphony even when one cannot write one or play an instrument in one.  What is the math equivalent of learning to play an instrument well?  I am not sure.  

 

I do like the puzzles and games idea.  But does it actually translate into math ability?  I do not know.  Does playing chess from a young age actually translate into math skills?  And, if it does, would that be a cause or just a correlation?   My ds was at Waldorf and started academics late, but did play chess and games like that...is that why he now is caught up to typical grade level or ahead in math?  Hard to say.  Maybe someone has statistics on this instead of it being just an idea from Lockhart that it might be so.  That he is a mathematician does not necessarily mean that his ideas of how to teach math would be successful.

 

I am not sure that going to math appreciation is the way to achieve math competence, nor that going to child versions of what mathematicians do is actually it either.  I was part of the "new math" experiment, and I don't think it was very successful.  One got a lot of theory, and very little computation.  For most of us most of the time it is the computation that is actually used.  OTOH, I do not think the traditional method is working well either.   

 

Lockhart wrote that he thinks people do not use much practical math they learned.  The last time I dealt with a carpenter and an electrician I was impressed by how very much math they were using.  No, not perhaps trigonometry as Lockhart said carpenters do not.  But, yes, a lot of quick mental math as to basic calculations, and geometry in the carpenter's case.  I think it is true that most adults do not remember how to solve a quadratic equation--when would we usefully do that?  Maybe I am missing daily opportunities when it would help me and I do not even realize that.

 

Boaler, in her book that I was reading, has an example of someone on a diet told they can have, as I recall it, 3/4 of 2/3 of a cup of cottage cheese.  (Really?  Why on earth would someone be told that in that way?)  Anyway, she says the person solves the problem not by recalling how to do the fraction computation, but by putting the cottage cheese out on a cutting board and flattening it into a circle and then dividing it into quadrants and taking away one of them.  I am not sure if that was supposed to be an example of a positive way of adults dealing with math in real life or not.  I thought it was a very messy approach, dirtying a cutting board in addition to bowl and measurer and leaving the remaining cottage cheese that presumably gets returned to the container more vulnerable to going bad from contamination, compared to just getting out 1/2 cup and serving it....or 8 tablespoons.  Maybe if one learned that math is important because it helps reduce the number of dirty dishes it would  help.  Does Kitchen Table math do that?  It is below my ds's level now, but the name sounds so intriguing.

 

I don't know how best to teach math so that  people in general--or even just my ds in particular -- can learn and remember and be able to apply such knowledge to real life as adults so that they can do a problem like this.  I think in my case that did come from the traditional approach of learn to multiply the numerators and the denominators and reduce.   I recall learning fractions from a "programmed" math workbook where one did problems mentally and moved a strip of paper down to uncover the answers on the side, which sometimes said to go somewhere else if it were wrong or right.  And I recall there were many such books that year and a class competition to get through them fastest.  My recollection is that it was fun, and that it was used for fractions, decimals, percents, and ratios for 5th grade--and it seems to have lasted in my memory.   I have not seen anything like that available these days.  It was not, I am sure, what Lockhart would like in terms of creativity and so on.  I'm not in contact with others from that school anymore to know if they too recall it as being fun and still can remember  and use those parts of math.  But I have the feeling that one other problem with math teaching is that when something good is found, it gets dumped for some reason, along with the not so good parts.

 

When I used to tutor math, the method was also what I think Lockhart would not like as being traditional...  and yet, it did seem to work in some way... and seemed to help get past phobias because of understanding and being able to do it, not because of love of it.  If it could be fun and loved too, that would be better.

 

Boaler gives another example of nurses not using a formula for calculating amounts of medicine, that made a little more sense to me, of why not to use that and use other approaches instead--for example, perhaps to use up  whole vials of a medicine in smaller units that equal the total needed, rather than to use parts of larger units, if perhaps it is something that does not keep well, or if it is something where one is not sure of uniform distribution of an active substance.    But there still seemed to be an avoidance of a straightforward calculation, perhaps because it looks complex, and was never taught in a way that it could become easy.  Or maybe because most nurses are female and have math phobia from being traumatized.    ????

[Woodland Mist Academy]

Yikes! I don't get it. :confused1: 

 

I need to look up math in the dictionary again. . .

 

Maybe it doesn't mean what I think it means.

 

 

[Chrysalis Academy]

Yikes! I don't get it. :confused1:

 

I need to look up math in the dictionary again. . .

 

Maybe it doesn't mean what I think it means.

 

:lol: I feel this way about a lot of things lately . . . but remembering Inigo Montoya always makes me gigle!

[Chrysalis Academy]

Ack! Stupid captcha is eating my posts.  Pen, I really liked what you wrote and had some deep thoughts about it, but just lost them.  We're leaving for a camping trip, so I'll have to wait till next week to try and recreate.

[taffnus]

I watched lesson 1 yesterday and I'm remembering a discussion in a thread from last year on classical education where people talked about the beauty of mathematics. I don't understand that yet but I'm motivated to try. I've always felt like I should be able to understand math because I'm very logical and organized in my thinking. I have always blamed my teachers, especially my algebra teacher WAY back in the 8th grade. I had a bad experience and have always felt like that determined my failure in math. I'm determined not to let that happen to my girls but, as my dd almost 10 is approaching middle school and algebra, I'm starting to panic. I don't know that I'll be able to teach like this and honestly, I don't know where I'd turn to find someone who could. I've looked at local schools that allow homeschoolers and they ALL teach Saxon. I couldn't do that to my dd who has a belly full of Singapore. Anyway...my thoughts are shooting in millions of directions and will hopefully converge into some coherent thoughts by the end of the class. 

[Pen]

taffnus,

 

Maybe you would enjoy teaching yourself Algebra and beyond now?   You might find materials that would work for you well and that you enjoy it now outside of the school setting.  It would also maybe allow your children to see you doing and enjoying math--sort of like it is supposed to be helpful for kids to see their parents reading.

[mathwonk]

I have not seen Lockhart's book, Measurement, but the reviews for it here claim it contains

 

the sort of positive examples of how to teach math that he advocates. I believe there is a short video

 

of him making a presentation. There is also a positive review by a well known mathematician I know and respect,

 

Barry Mazur.

 

http://www.hup.harvard.edu/catalog.php?isbn=9780674057555&content

 

http://www.hup.harvard.edu/catalog.php?isbn=9780674057555&content=reviews

 

The following review is by someone called "Math mama"

 

"Book Review: Measurement, by Paul Lockhart

In 2002, Paul Lockhart wrote A Mathematican's Lament, a 25-page exploration of much that is wrong with math education. I liked it, but I'd rather explore how to do math education right. Last year he came out with Measurement, a 398-page exploration of mathematics itself. It is delightful, and I want to recommend it to all my students in pre-calculus, calc I, and calc II. I think anyone who has some experience with geometric and algebraic reasoning can enjoy this book.

 

His publisher, Harvard University Press, put out a short video of Lockhart explaining the difference between math and science questions and why he thinks of math as one of the arts, with the help of a nice geometry problem. The video will give you a small taste of what's in store for you in the book."

 

her page:

 

http://mathmamawrites.blogspot.com/2013/05/book-review-measurement-by-paul-lockhart.html

 

 

I noticed again that some of his examples come straight out of the most classic sources. E.g. the fact that a cone inscribed in a hemisphere has half the volume was due to Archimedes, and is beautifully explained in Harold Jacobs' Geometry, where in fact I learned it the first time. The result of Archimedes, was that the volume of cone and a hemisphere add up to that of a cylinder, and that the cone has 1/3 the volume of the cylinder, hence the hemisphere has 2/3 of it.

 

This result, as is well known, was what Archimedes wished to have adorn his tombstone.

[Pen]

Mathwonk, Thank you for those links!  I didn't think to see if Lockhart might have offered something up that he thought better, rather than just a complaint with what is wrong.

[Lucy the Valiant]

http://tinypic.com/r/98t4sg/5

http://tinypic.com/r/2e36cye/5

 

 

Ds is 5, so he likes my attempt at cartoon characters. :)

 

Eagle, thank you! You inspired me to make a couple of my own (but I'm going to save them for my big hoopla on the "First Day of School". :) )

 

Pen, I agree with a lot of what you're saying - I *will* say that this course has gotten me thinking and re-thinking some things, so I'm glad about that, for sure.

[taffnus]

taffnus,

 

Maybe you would enjoy teaching yourself Algebra and beyond now?   You might find materials that would work for you well and that you enjoy it now outside of the school setting.  It would also maybe allow your children to see you doing and enjoying math--sort of like it is supposed to be helpful for kids to see their parents reading.

 

Thanks, Pen. I actually have been thinking that for a while and began talking with my dh about it this weekend. He wants to join me (although he remembers more than I do). I think we just may tackle an algebra course together this year. If you had told me 5 years ago I'd be re-learning algebra, I'd have told you to jump in a lake!!!!

[taffnus]

Eagle, thank you! You inspired me to make a couple of my own (but I'm going to save them for my big hoopla on the "First Day of School". :) )

 

Pen, I agree with a lot of what you're saying - I *will* say that this course has gotten me thinking and re-thinking some things, so I'm glad about that, for sure.

 

Love them!! Great job. I'm headed to bed wondering if my creative juices will begin to flow....

[Lucy the Valiant]

In addition to some of Pen's thoughts, I'm also not sure that I agree with the total dismissal of speed as it relates to math facts; her focus in that section then subtly slipped to saying that TEACHING math quickly was not a goal, but that is different to me than student recall. I'm thinking she would not be a fan of xtramath.com, for example, but for my students who have been through a few years of Singapore and completely understand the concepts of addition and subtraction, xtramath was a fun way for them to improve their speed. And - yes - as something that I expect them to have memorized cold, speed *does* indicate solid memory (a critical foundation in the grammar stage). I wish she would have distinguished between [speed in recall] and [speed in problem solving]. (I'm not suggesting that speed should be forced on all kids, but for those that it *does* help, it shouldn't be summarily dismissed, either. All 3 of my children currently doing xtramath have commented to me that they feel more confident and happy because of their increased speed; it takes work, and - yes, persistence. :) )

 

One other "gripe" I have about the course (besides her completely off-based comments on Common Core's "content processing" which is replacing the study of literature, and a subject that I had better not even start on) is that this is most definitely a PSYCH course, and not a math course. I have 2 education degrees, so that shouldn't come as any surprise to me at all, but one of my primary reasons for taking this class was to connect with and better understand my child who simply *ADORES* math. And the heavy focus on kids who found math traumatic (a bit of a strong word, IMO) seems to obscure a focus on kids who *do* seem to intrinsically "get" math and would (I believe) respond quite well to guided questions.

 

I'm still actually waiting to get to any math.

[Mom-ninja.]

I haven't read Lament yet.

 

I'll be back

[Lucy the Valiant]

I'm switching to this thread, as the links there are just confirmation to me that this professor and I are coming from a completely different mindset (to use the phrase :) ).

 

http://forums.welltrainedmind.com/topic/477667-stanford-math-course-coming-anyone-else-interested/page-4?do=findComment&comment=5091163

[Pen]

Thanks, Pen. I actually have been thinking that for a while and began talking with my dh about it this weekend. He wants to join me (although he remembers more than I do). I think we just may tackle an algebra course together this year. If you had told me 5 years ago I'd be re-learning algebra, I'd have told you to jump in a lake!!!!

 

What materials do you think you will use?  And on your own or enroll in something?  It could be an interesting way to pretest (an already have) materials for your children when they are ready--though I think there may also now be things intended for adult use.

[taffnus]

What materials do you think you will use?  And on your own or enroll in something?  It could be an interesting way to pretest (an already have) materials for your children when they are ready--though I think there may also now be things intended for adult use.

 

I have another post asking about curriculum. Right now, I'm really considering AoPS pre-algebra (I couldn't pass the post-test on their website for pre-algebra or their pre-test for algebra). I've had some other good recommendations from that post too. I guess my main interest in AoPS is to preview it for my dd who is just starting SM5. I would possibly choose a different course if I didn't have that motive as well. I'm still considering though.

 

http://forums.welltrainedmind.com/topic/481178-self-educate-algebra/

[Woodland Mist Academy]

 Right now, I'm really considering AoPS pre-algebra (I couldn't pass the post-test on their website for pre-algebra or their pre-test for algebra). I've had some other good recommendations from that post too. I guess my main interest in AoPS is to preview it for my dd who is just starting SM5.

 

This is what I'm doing (working through AoPS Pre-A) . For the first couple weeks, Dd and I sat side-by-side working together as she adjusted to the format. Then we worked independently, but still side-by-side. After the start of the Math Revolution which began with the Pre-A Argument Heard 'Round the World, we are no longer allowed to work anywhere near each other. :tongue_smilie:

 

We are, however, enjoying working on it completely separately while having a bit of a friendly race getting through the book. Well, usually friendly. ;)

 

I wanted to add my support to those thinking of working through AoPS themselves--with or without their children.

 

Also, I want to encourage giving AoPS (or any challenging program) a fair chance with different approaches before deciding it's not a good fit. (Of course, some things just aren't and that's OK too--just make sure it's not how you are using the book that's the problem.)

 

One a side note--My dh thinks it would be great fun to have the three of us take an ACT practice math test with the loser paying for dinner. I can't understand why they both started laughing, then looked at me and said, "Better start saving some money!" . . :001_huh:    

 

;)

[Chrysalis Academy]

This is what I'm doing (working through AoPS Pre-A) . For the first couple weeks, Dd and I sat side-by-side working together as she adjusted to the format. Then we worked independently, but still side-by-side. After the start of the Math Revolution which began with the Pre-A Argument Heard 'Round the World, we are no longer allowed to work anywhere near each other. :tongue_smilie:

 

We are, however, enjoying working on it completely separately while having a bit of a friendly race getting through the book. Well, usually friendly. ;)

 

I wanted to add my support to those thinking of working through AoPS themselves--with or without their children.

 

Also, I want to encourage giving AoPS (or any challenging program) a fair chance with different approaches before deciding it's not a good fit. (Of course, some things just aren't and that's OK too--just make sure it's not how you are using the book that's the problem.)

 

One a side note--My dh thinks it would be great fun to have the three of us take an ACT practice math test with the loser paying for dinner. I can't understand why they both started laughing, then looked at me and said, "Better start saving some money!" . . :001_huh:    

 

;)

 

 

Your whole post cracked me up! 

 

I'm working through AoPS PreA too, and I agree, I highly recommend it whether you have your dc use this book or not.  It explains stuff I had no idea about.  I mean, I did it in high school and college math classes (including calculus), I guess, but I had NO CLUE what I was doing or why.  Now I do, and it's such an amazing epiphany!

 

Not to mention, it's making me a much better teacher.  And doing Alcumus is giving me a taste of what it is like to grapple with a hard problem - the frustration, then that "yes!" sense of excitement when you get it right, or how good it feels when you look at a problem and just know, without even working it out, what the answer must be . . . having these experiences as a learner makes me a more effective, as well as a more empathetic, teacher.

[taffnus]

Your whole post cracked me up! 

 

I'm working through AoPS PreA too, and I agree, I highly recommend it whether you have your dc use this book or not.  It explains stuff I had no idea about.  I mean, I did it in high school and college math classes (including calculus), I guess, but I had NO CLUE what I was doing or why.  Now I do, and it's such an amazing epiphany!

 

Not to mention, it's making me a much better teacher.  And doing Alcumus is giving me a taste of what it is like to grapple with a hard problem - the frustration, then that "yes!" sense of excitement when you get it right, or how good it feels when you look at a problem and just know, without even working it out, what the answer must be . . . having these experiences as a learner makes me a more effective, as well as a more empathetic, teacher.

 

 

This is what I'm doing (working through AoPS Pre-A) . For the first couple weeks, Dd and I sat side-by-side working together as she adjusted to the format. Then we worked independently, but still side-by-side. After the start of the Math Revolution which began with the Pre-A Argument Heard 'Round the World, we are no longer allowed to work anywhere near each other. :tongue_smilie:

 

We are, however, enjoying working on it completely separately while having a bit of a friendly race getting through the book. Well, usually friendly. ;)

 

I wanted to add my support to those thinking of working through AoPS themselves--with or without their children.

 

Also, I want to encourage giving AoPS (or any challenging program) a fair chance with different approaches before deciding it's not a good fit. (Of course, some things just aren't and that's OK too--just make sure it's not how you are using the book that's the problem.)

 

One a side note--My dh thinks it would be great fun to have the three of us take an ACT practice math test with the loser paying for dinner. I can't understand why they both started laughing, then looked at me and said, "Better start saving some money!" . . :001_huh:    

 

;)

I must say, you two have tipped the scale strongly in favor of AoPS. Thank you! I must say there's a part of me that's a little concerned I'll get into it and not be able to do it and my dd will whiz by me. :huh:  At least I'll have a year on her. That's gotta help in some measure.

[Chrysalis Academy]

I must say, you two have tipped the scale strongly in favor of AoPS. Thank you! I must say there's a part of me that's a little concerned I'll get into it and not be able to do it and my dd will whiz by me. :huh:  At least I'll have a year on her. That's gotta help in some measure.

 

Yeah, nothing is quite so motivating to brush up on your skills as the prospect of having a 10 year old pass you by . . .  ;)

[Woodland Mist Academy]

I have not seen Lockhart's book, Measurement, but the reviews for it here claim it contains

 

the sort of positive examples of how to teach math that he advocates. I believe there is a short video

 

of him making a presentation. There is also a positive review by a well known mathematician I know and respect,

 

Barry Mazur.

 

http://www.hup.harvard.edu/catalog.php?isbn=9780674057555&content

 

http://www.hup.harvard.edu/catalog.php?isbn=9780674057555&content=reviews

 

The following review is by someone called "Math mama"

 

"Book Review: Measurement, by Paul Lockhart

In 2002, Paul Lockhart wrote A Mathematican's Lament, a 25-page exploration of much that is wrong with math education. I liked it, but I'd rather explore how to do math education right. Last year he came out with Measurement, a 398-page exploration of mathematics itself. It is delightful, and I want to recommend it to all my students in pre-calculus, calc I, and calc II. I think anyone who has some experience with geometric and algebraic reasoning can enjoy this book.

 

His publisher, Harvard University Press, put out a short video of Lockhart explaining the difference between math and science questions and why he thinks of math as one of the arts, with the help of a nice geometry problem. The video will give you a small taste of what's in store for you in the book."

 

her page:

 

http://mathmamawrites.blogspot.com/2013/05/book-review-measurement-by-paul-lockhart.html

 

 

I noticed again that some of his examples come straight out of the most classic sources. E.g. the fact that a cone inscribed in a hemisphere has half the volume was due to Archimedes, and is beautifully explained in Harold Jacobs' Geometry, where in fact I learned it the first time. The result of Archimedes, was that the volume of cone and a hemisphere add up to that of a cylinder, and that the cone has 1/3 the volume of the cylinder, hence the hemisphere has 2/3 of it.

 

This result, as is well known, was what Archimedes wished to have adorn his tombstone.

 

I think I missed this post.  I'm glad I found it because the book looks good.

 

Thanks!

 

 

[Pen]

...--just make sure it's not how you are using the book that's the problem.)

 

...

 

 

Could you speak to this more?  About how you've found it good to use the book, and also what signs would suggest to you that it actually was not a good fit for a particular person--adult or child as case may be?

[Chrysalis Academy]

Could you speak to this more?  About how you've found it good to use the book, and also what signs would suggest to you that it actually was not a good fit for a particular person--adult or child as case may be?

 

I'm interested in hearing about this too.  I started a thread on the logic board asking how people are using the different components of AoPS, and it was really interesting, because the answers were all over the map.  It gave me some good ideas to try, though, before giving up and assuming that it's a bad fit.  

 

Here's the thread, in case you want to check it out:

 

http://forums.welltrainedmind.com/topic/476133-aops-prea-users-talk-me-through-how-you-use-it/

[Woodland Mist Academy]

Could you speak to this more?  About how you've found it good to use the book, and also what signs would suggest to you that it actually was not a good fit for a particular person--adult or child as case may be?

 

I don't think there is one right way to use AoPS. My daughter uses it independently, but I don't think that using it together or adapting means AoPS is not a good fit. There is some middle ground between strictly used AoPS and a more traditional program.

 

Presuming a child is strong in math, I would think possible signs that AoPS might not be a good fit are if a child doesn't enjoy the exploration approach of trying to puzzle out the concept first. If this is just a frustrating waste of time, I might look elsewhere. If the explanations confuse the child, I would rethink my plans about using AoPS at this moment. If your child needs frequent explicit review as opposed to elegantly scaffolded concepts, maybe something else would work better.  Blank stares not followed by light bulb moments usually aren't good ;) . Frustration and tears can go either way at my house. That can be a clue to switch gears or that we're on the right path. YMMV.

 

Keep in mind my vast experience with AoPS consists of one child for about a year. :tongue_smilie:

 

 

For us part of the beauty of AoPS is the focus on why something works, as opposed to relying on memorization of formulas.  Flying through pages of straightforward math would just send her searching for something else. She could have worked more quickly through regular programs to find challenge, but I'm not convinced that's the right path for her. The discovery and depth are enriching.

[Woodland Mist Academy]

I'm interested in hearing about this too.  I started a thread on the logic board asking how people are using the different components of AoPS, and it was really interesting, because the answers were all over the map.  It gave me some good ideas to try, though, before giving up and assuming that it's a bad fit.  

 

Here's the thread, in case you want to check it out:

 

http://forums.welltrainedmind.com/topic/476133-aops-prea-users-talk-me-through-how-you-use-it/

 

I don't remember if I saw this thread or not. I'll look.

[Chrysalis Academy]

Ok, I'm halfway through What's Math Got to do with it.  Although it's kind of hard to read about the Railside School study because of the KTM website's criticisms ringing in my ears, I am gleaning some gems from this book.  Here are the changes I'm planning based on it and the class, and the discussions here:

 

1) 6th grade will be The Year of Problem Solving.  I had been planning to start informal logic, but I've decided to push that back in favor of a second math session each day that will focus on problem solving - both grappling with tough problems, and learning about problem-solving techniques, and meta-study about what math and science are all about.  So our math hour will continue pretty much as planned, but we'll have this special time really devoted to working on problem-solving.  

 

2) Prelection + Assessment for learning.  I realized in reading the A for L chapter that while I do prelection in other subjects, I don't really do it for math.  I mean, I teach the lesson, but I don't take the time at the beginning of a chapter or topic to say, "Ok, here's what we'll be working on for the next x weeks, and here is why it's important and how it fits in to the big picture, and here is what you will know by the end."  So I have decided to do this, explicitly: to create a written set of goals, learning objectives, whatever you call them, at the beginning of each chapter, to explicitly discuss them.  Then at the end of the chapter, ask dd to read through them again and rate whether she feel that she can do/knows all of those things.  Again, kind of a meta-analysis of her math understanding - so she really has to think about what she's learned, and ask herself if she feels like she has mastered it.

 

 We will still do chapter tests so that we can objectively assess mastery, but I am not going to write scores on the tests, she gets really hung up and discouraged if her score is "low" - anything below 90% is low to her.  Instead I'm thinking that I'll highlight mistakes (rather than x-ing them out) and give the paper back to her to correct, with assistance/discussion as needed.

 

I think these things will help us take the next step in shaking off the whole obsession with getting 100% and focus on scores that she and I both  probably do too much, and hopefully create time and space for thinking about math learning and thinking, and developing problem solving skills and focus. They are as much for me to stop and think about my teaching as for her to stop and think about her learning.

 

Anyway, that's what I'm thinking right now.  We start Monday, so we'll see how it goes!

 

Anybody else doing anything different?

[Pen]

Ok, I'm halfway through What's Math Got to do with it.  Although it's kind of hard to read about the Railside School study because of the KTM website's criticisms ringing in my ears, I am gleaning some gems from this book.  Here are the changes I'm planning based on it and the class, and the discussions here:

 

1) 6th grade will be The Year of Problem Solving.  I had been planning to start informal logic, but I've decided to push that back in favor of a second math session each day that will focus on problem solving - both grappling with tough problems, and learning about problem-solving techniques, and meta-study about what math and science are all about.  So our math hour will continue pretty much as planned, but we'll have this special time really devoted to working on problem-solving.  

 

2) Prelection + Assessment for learning.  I realized in reading the A for L chapter that while I do prelection in other subjects, I don't really do it for math.  I mean, I teach the lesson, but I don't take the time at the beginning of a chapter or topic to say, "Ok, here's what we'll be working on for the next x weeks, and here is why it's important and how it fits in to the big picture, and here is what you will know by the end."  So I have decided to do this, explicitly: to create a written set of goals, learning objectives, whatever you call them, at the beginning of each chapter, to explicitly discuss them.  Then at the end of the chapter, ask dd to read through them again and rate whether she feel that she can do/knows all of those things.  Again, kind of a meta-analysis of her math understanding - so she really has to think about what she's learned, and ask herself if she feels like she has mastered it.

 

 We will still do chapter tests so that we can objectively assess mastery, but I am not going to write scores on the tests, she gets really hung up and discouraged if her score is "low" - anything below 90% is low to her.  Instead I'm thinking that I'll highlight mistakes (rather than x-ing them out) and give the paper back to her to correct, with assistance/discussion as needed.

 

I think these things will help us take the next step in shaking off the whole obsession with getting 100% and focus on scores that she and I both  probably do too much, and hopefully create time and space for thinking about math learning and thinking, and developing problem solving skills and focus. They are as much for me to stop and think about my teaching as for her to stop and think about her learning.

 

Anyway, that's what I'm thinking right now.  We start Monday, so we'll see how it goes!

 

Anybody else doing anything different?

 

Even before the book/course, I decided to put logic and math as a single block subject of 1.5-2 hours, and that is working well here as of earlier this summer (we are now off school for theater camp, trying to keep plants watered during heat and so on).  

 

My sense of the Railside school situation is that both sides have merit.  As I look at much of the IPM material, it may well be that it is at a lower level than expected for, say, Algebra 1.  At the same time, it may also be that the way of learning to think and getting engaged and so on did lead to better results, than a traditional curriculum in terms of engagement in material, approach to life and so on.  

 

We will be going to AoPS Intro. Algebra, and filling in with other material as needed, then back to pre-algebra only if that seems too hard.  But I am also interested in that James Tanton material.  We will also continue with Critcial Thinking Co materials, and I think the History approach from the History thread will also fit in with a critical thinking and problem solving approach.  I got a few math puzzle books, my favorite is called something like Moscow puzzles.  I am also going to see if our rural library might be a place to try to have a "math club" meeting to do some group interactive work from time to time.   But it may be that there just is not enough interest in something like that where we are.  

 

I like your idea for the Assessment for learning.  I want to do something for that, but have not yet figured out what.

 

I put written stars on what is right--and sometimes put stars on whatever I want to encourage such as writing out steps on way to an answer, or even writing neatly.  I circle what needs to be done over, or sometimes write a written note on it.   My new thing though has been choosing correct answers (or ones that I do not even know yet whether it is correct or not)  and asking for an explanation of the reasoning that went into getting that answer, "okay, lead me through it".  So that they if I ask the same thing for an incorrect answer I think it is less upsetting because it is something that is asked routinely and not just when something was wrong.  ...because I am dealing with perfectionist mindset issues.

 

But more than that I am working toward trying to get ds to become more responsible for correcting his own work.

 

Hope you'll report on how it goes!

[Chrysalis Academy]

Well, 3 days in, I can say that the main thing I'm doing differently is slowing down.  And it makes me crazy!!!  But it has noticeably relaxed and enhanced the whole math environment at my house.  

 

Instead of feeling like there is an amount we need to get through in one day, I'm taking as long as it takes to make sure she *really* understands the problem.  This means we are having a lot of "math talks" and for word problems if she makes a mistake, I look at the problem and figure out where she went wrong, and then offer questions/hints to help her figure out for herself where she went wrong and how to solve it.  And then she figures out the answer herself.  This can take awhile!

 

Partly I know there is a little slowness because there was a 5-week break with no math, and we're just getting back into the hang of school.  It will pick up a bit, I think, but I am committed to holding my own crazy back and going at the pace that facilitates understanding, as well as keeping the environment light and pleasant, not stressful.

 

I'm pleasantly surprised by how great she is doing with number sense/mental math!  This was all new in 4th grade, and very hard, and even last year I felt like she hadn't quite "leapt the brook" but now she *really* has it down.  Which is so very great.

 

So, we are moving more slowly than I had planned, but *much* more deeply, and less stressfully.  There is a lightness and fun about math hour that I fear was lacking in the past.  This is an entirely good thing.

[Pen]

Good!  Less stress, more depth, lightness and fun sounds excellent!    

 

We are waiting for our Stuff (AoPS algebra) to arrive--I thought ds would be in theater this month, but it was a dud, and now I wish I had expedited our new math stuff.    Meanwhile he is finishing up Balance Math Teaches Algebra--slowly, but that is okay since AoPS probably will not get here for another 2 weeks.  But in our case the slowly does not seem to be yielding lightness and fun.    I find ds figures out the answers in a different way than the book suggests--and often his way seems better.   Not sure then if I should dump their "proofs" and have him write out his steps or keep figuring out how to fit in to their way of doing it for the "proofs".  As between writing out the whole thing his way or just filling in blanks their way, he seems to prefer whatever is less writing to do.  But either way, the hardest part is going back and getting the steps that were taken to get to an answer written down.  And he seems to need to work it out without doing the steps as he goes.   I keep saying that even though he does not need the steps now, he needs the practice on these easy problems so that he can write the steps in an orderly way when the problems get harder.   Alas, this needing to write down the steps is not giving us a lightness and fun time at the moment...it sort of takes away from just letting the Balance Math be like fun puzzles to solve.   I am not sure what to do.

[A home for their hearts]

Can someone please tell me what you all are talking about and where to find this class?

[Chrysalis Academy]

https://class.stanford.edu/courses/Education/EDUC115N/How_to_Learn_Math/about

 

It's an online class (a MOOC) being taught by Joe Boaler who wrote What's Math Got to do With It,  and is a math educator at Stanford.  It's about how to teach math effectively.