Stanford Math Course coming, anyone else interested?

[onaclairadeluna]

 

 

I should qualify this by saying that in my state, gr 7-12 math teachers have something like 33 hrs of math beyond College Algebra/Trig. As an engineer, to get a math cert I would have to take Real Analysis in addition to showing that I recall enough of my education (Calc 1 thru ODE plus stats) as well as the 18 credits of pedagogy etc. 

 

I was going to ask "Where in the world are you from?" but then I saw a reference to the Regents exam. It doesn't surprise me that NY has higher standards for its teachers. That is not what is expected in CA.

 

They really require teachers to have Real Analysis? To teach 7th grade???? I am astounded at the gap here. In CA you don't need anything close to that even to teach AP Calc. I think it's something like College Algebra, Geometry (which seems to be the geometry equivalent of College Algebra) Stats, and Calculus. Plus the underwater math sculpture and interpretive dance.

 

Honestly for most of the math curriculum I don't think you need to have too many upper division math courses. But my concern is that when you set the bar too low you encourage teachers who are not all that enthusiastic for mathematics. 

[onaclairadeluna]

The institution my friend and I talked with did want us (both engineers) to have Real Analysis as part of the certification path for those with Master's degrees in other areas. If I remember correctly, the prof I spoke with felt understanding Rings was important, especially in districts that have accel and honors math sections. Searching quickly, it seems to be req'd for the Master's:http://catalog.cortland.edu/preview_program.php?catoid=18&poid=2544&returnto=1289. A program for Bachelors w/cert in Math 7-12:       

 

7th grade is a widely varying year. Some schools have sections of R. Integrated Geometry, others have a lot of remedial and there's plenty in between. NY splits a lot of algebraic concepts between Gr. 6 and Gr. 8 for those not on an accelerated path. It's pretty important to get the terminology correct or the students get confused later.

I think it's great to have teachers with a math background. I am just surprised that the teachers actually have it. Surprised in a good way. 

[Pen]

Doing my best.  :001_rolleyes:

 

I was really only just looking for her actual research because she kept making claims that "the research shows... and I thought she was doing a terrible job of explaining why "the research shows" etc. I honestly was not trying to dig up dirt, just to figure out why her conclusions were so counter intuitive to my experience with GT kids. 

 

But I'll walk away now. "Nothing to see here. Move along."

 

Like you, I'd much rather have a focus on awesome people and how they are promoting great math education. Does anyone know Richard Rusczyk? :001_wub:  

 

Do you think there is a way to get a major university to hire him to teach one of their edx courses? Though his focus is on gifted students, I think that a problem solving approach is exactly what all students need. Also I think that referring to it as a "problem solving approach" is much clearer language than "mistake friendly culture". 

 

That brings me back to the piece of the course that I like. She seems to be advocating this problem solving approach for all students. I think this is a terrific idea. I have always thought that lower performing students have the ability to work problems. Perhaps they need different problems than gt kids, but they can still think. Often teachers are so focused on raising test scores that they just drill lower performing kids on test taking skills: reading comprehension, terminology, how to eliminate wrong answers and make a good guess.The focus for these kids is raising scores "by any means necessary". Which often means just training them to make good guesses and grab for answers. (I don't think this is nearly as prevalent in the homeschool community thank goodness, but it does exist in the schools and in our charters.)

 

What she seems to be advocating is that we actually try to teach these kids the math. I like that idea. But unfortunately this doesn't seem to be what other people are getting from the course. So that is a worry. 

 

I am surprised she hasn't mentioned Li Ping Ma's book. 

 

 

I like "problem solving approach" as a term.

 

My guess is you could contact Rusczyk and as if he'd be willing to teach such a course if the opportunity presented itself.  Some  major universities, such as Princeton, Rusczyck's and my alma mater, but no, I do not know him, do not have education departments and may consider that beneath them like courses in basketweaving and underwater math sculpture perhaps  (I do not think that Harvard, Yale, MIT or Cal Tech have them either),, so I do not know how he himself would feel about it, nor what time he has available along with running a company.

 

If he said yes, though, you could suggest it to several major universities that have education departments.  I think Teacher's College at Columbia tends to be interested in gifted kids' education.

[Chrysalis Academy]

PS to above--also doing the Sumdog is a good chance to practice it being okay to be wrong and make mistakes!  And for me to be okay with that.  

 

I wonder if freezing up on things like that could already be a sign of math stress and phobia building up?  I've noticed now as it is in summer that for the USA flagged avatars many more appear to be boys.  (From Australia where it is school year, they seem more even.)   But, like this is something boys like to do for fun (and thus maybe get better) while girls feel it as a stress?

That's definitely true in dd7's case - that freezing up is a sign of existing math stress.  She had a really stressful year of ps 1st grade, with a teacher who was inconsistent and used shame as a classroom management technique.  Like I said, her conceptual understanding of math is great, but she doesn't move that fast, and apparently it wasn't fast enough for her teacher  when they started multi-digit subtraction, so the teacher sat down beside her (presumably with kind intentions, to see if she was having trouble and to help).  Well, Mo got so anxious she just froze up completely, so after school that day the teacher tells me she needs to remediate basic subtraction.  Well, when we got home and worked on the problems (after some tears and chocolate chip cookies), she flew through the problems effortlessly, zero mistakes.  So the problem isn't subtraction, it's anxiety.  Very sad in a 6 year old.

 

The gender difference idea is really interesting, too - I got Boaler's book from the library and was skimming through it last night, and she talked about gender differences they had observed, with girls really wanting to know why things worked and being puzzled/frustrated when they didn't, whereas the boys got into the competitive angle of doing as many problems as they could as quickly as possible to be the fastest and best.  I'm sure this is an overgeneralization, but it piqued my interest for sure.  I only have girls, so my sample is skewed, but they both hate timed tests, and they didn't like sumdog when I tried it with them, even though that isn't timed.  They don't like video games either, though, so I think this just isn't the way to reach them, maybe.

[Pen]

Doing my best.  :001_rolleyes:

 

I was really only just looking for her actual research because she kept making claims that "the research shows... and I thought she was doing a terrible job of explaining why "the research shows" etc. I honestly was not trying to dig up dirt, just to figure out why her conclusions were so counter intuitive to my experience with GT kids. 

 

But I'll walk away now. "Nothing to see here. Move along."

 

Like you, I'd much rather have a focus on awesome people and how they are promoting great math education. Does anyone know Richard Rusczyk? :001_wub:  

 

Do you think there is a way to get a major university to hire him to teach one of their edx courses? Though his focus is on gifted students, I think that a problem solving approach is exactly what all students need. Also I think that referring to it as a "problem solving approach" is much clearer language than "mistake friendly culture". 

 

That brings me back to the piece of the course that I like. She seems to be advocating this problem solving approach for all students. I think this is a terrific idea. I have always thought that lower performing students have the ability to work problems. Perhaps they need different problems than gt kids, but they can still think. Often teachers are so focused on raising test scores that they just drill lower performing kids on test taking skills: reading comprehension, terminology, how to eliminate wrong answers and make a good guess.The focus for these kids is raising scores "by any means necessary". Which often means just training them to make good guesses and grab for answers. (I don't think this is nearly as prevalent in the homeschool community thank goodness, but it does exist in the schools and in our charters.)

 

What she seems to be advocating is that we actually try to teach these kids the math. I like that idea. But unfortunately this doesn't seem to be what other people are getting from the course. So that is a worry. 

 

I am surprised she hasn't mentioned Li Ping Ma's book. 

 

 

2 more thoughts on this.  I cannot currently access the Stanford Course at all, and have never (I presume due to dial up connection) been able to access the discussion part.  But maybe instead of walking away from the Stanford course just yet it would help if you were to post something about Rusczyk and link to AoPS website--maybe the books or articles area for the 20,000 or so people who are taking that course to see it?   I do not know the protocol and whether people do that sort of thing since I have not had access to the discussions part. 

 

 

On Ma's book, it is in the recommended resources at the back of Boaler's book.

[Pen]

That's definitely true in dd7's case - that freezing up is a sign of existing math stress.  She had a really stressful year of ps 1st grade, with a teacher who was inconsistent and used shame as a classroom management technique.  Like I said, her conceptual understanding of math is great, but she doesn't move that fast, and apparently it wasn't fast enough for her teacher  when they started multi-digit subtraction, so the teacher sat down beside her (presumably with kind intentions, to see if she was having trouble and to help).  Well, Mo got so anxious she just froze up completely, so after school that day the teacher tells me she needs to remediate basic subtraction.  Well, when we got home and worked on the problems (after some tears and chocolate chip cookies), she flew through the problems effortlessly, zero mistakes.  So the problem isn't subtraction, it's anxiety.  Very sad in a 6 year old.

 

The gender difference idea is really interesting, too - I got Boaler's book from the library and was skimming through it last night, and she talked about gender differences they had observed, with girls really wanting to know why things worked and being puzzled/frustrated when they didn't, whereas the boys got into the competitive angle of doing as many problems as they could as quickly as possible to be the fastest and best.  I'm sure this is an overgeneralization, but it piqued my interest for sure.  I only have girls, so my sample is skewed, but they both hate timed tests, and they didn't like sumdog when I tried it with them, even though that isn't timed.  They don't like video games either, though, so I think this just isn't the way to reach them, maybe.

 

 

Yes.  Other aspects of the gender difference also started striking me.  I was blown away by that idea of 2/3 or so of males not caring about the "why" and just wanting to get on with it.  My ds is in that group (wonder how he will deal with AOPS which I assume has a lot of why)--I had assumed it meant he wasn't interested in math because he ignores me every time I try to show him some wonderful interesting "why" of things.  And I am now having to rethink that and consider that for him "interest in math" may show up as wanting to answer questions fast enough to get to shoot as many alien invaders as possible, and amass virtual gold coins and upgraded avatar and rank levels.  And then, when I said this to my mom, she said she found in interesting in view of that girls often do better in math in the early grades when they have female teachers most often, who may teach the way they themselves want to learn, and then at the upper levels, when math professors tend to be male, the boys shoot ahead, perhaps because the male professors teach the way boys learn.

 

On Sumdog another aspect may be that I am wrong about players gender distribution because perhaps there are a lot of girls playing, but they may favor different games, such as one that seems to be about a dress shop, which ds has never loaded.  I do see more female avatars on some games such as Snowball (a slower game in terms of answering time and involves using snowballs to knock things off sleds) and Tennis, and Jet Ski Rescue (fairly slow game and involves rescuing people in life boats), than in the more shoot em up type games.  Though I am still seeing more male ones even on what seem to be more gender neutral games.

 

And then another difference according to Boaler found in MRI studies about part of brain that is active in females versus males when solving math problems, that for males it is--I forget but some of the older closer to brainstem parts, while for females it is the, as I recall, neo-cortex, also really fascinated me.  That might go with the wanting to know why something is as it is, versus being happy with answering problems quickly in a video game.    I had previously understood that people first used the neo-cortex or cortex (I forget) as they learn a task (say driving), but then it processes in other parts once they have learned the task and it becomes automatic--and have thought that was for both genders.  So, I am not sure how that fits with the finding that females and males use different parts for math.

 

ETA While watching ds do Sumdog, it actually looked like he was using his  cerebral cortex to figure out how to get more automatic parts of his brain processing to be able to deal with the games--sort of a meta game of trying to outpsyche the computer almost like playing chess .  For example, in the Snowball game he was practicing figuring out exactly where to aim and when to release the snowballs for each sled configuration so they would knock off the things on the sled, sometime deliberately missing questions while he lined up his catapult just right ...   then, the math question answering part seems more like someone driving and no longer thinking about gas or brake--   

[mathwonk]

When I was in high school in Tennessee we practiced hard for the regional math competition, even after school, like any team. We eventually won the state. But when we saw some hard problems from NY, on a test called "Regents' test" we were told, don't worry there will nothing that hard (on the state math competition!) In college I found out the Regent's test was apparently taken by every student in NY, just to graduate! So much for my education at a private school in Tennessee.

 

Not only being deprived of significant content, but also never learning to struggle under a challenge, I was not at all prepared for the demands of a good college. I wasn't even used to studying or attending class, since in my high school, one night's study usually sufficed for a test, sometimes even without going to the classes.

 

Once, as I believe I have told before, I missed three high school physics tests while absent extendedly, which covered 110 pages of our mickey mouse level physics book. When I returned was told I had to make them up. Three days later I had almost memorized those 110 pages and got 100,100, and 97.

 

The one question I missed was not memorizing the fraction of the sun's light received by the earth. I tried to compute it by comparing the area of a sphere whose radius equalled the distance to the sun with half the area of the earth, but instead should have used the area of a slice of the earth through its equator, since that is the shape of the "hole" the earth would make in the big sphere of light. In the book, the fraction had simply been given with no explanation as to how it was found.

 

I got the multiple choice answer wrong, but I generated an idea I was very proud of. So my proud moment on that trivial test was the 3 points I lost for my one good answer.

[mathwonk]

Here is another "mistake" experience that happened today. Yesterday I typed in a hugely complicated formula for my epsilon scholars and claimed it was a polynomial which yielded 1,2,3,5,7,6 when X=1,2,3,4,5,6. This was an exercise in not taking apparent patterns for granted.

 

This morning, one of them checked it and told me he had gotten different answers, namely he got 1,2,3,4,5,6 when he put X=1,2,3,4,5,6, and he continued to check it up to X=20! always getting the same thing he input every time.

 

I was trying to patiently type my explanation to him of why he was wrong, and it could be discerned just by looking at my formulas the right way. Of course this forced me to do so, and I soon noticed that he was right!

 

I had been hurrying late at night, and made a conceptual mistake, that caused my whole complicated formula to collapse just to X, although that was not at all clear from its appearance.

 

So I thanked him heartily and typed in the correct formula, which I also checked.

 

 

So one wonderful aspect about these kids is their lack of unquestioning obedience to arbitrary authority in math. They are very respectful, (he phrased his quite justified difference with me very politely), but if I just claim something is so, they will check it or challenge it, until they themselves see it. They always want the why, and if they don't get it, they continue to believe their own opinions may well be right. And several times they have found my errors this way.

 

So somehow to me the moral is that asking why, and trying to understand why, i.e. asking yourself why, is key to weeding out falsehoods and errors. Just memorizing the answer is very risky behavior. (And I always need to check my work.)

[Pen]

When I was in high school in Tennessee we practiced hard for the regional math competition, even after school, like any team. We eventually won the state. But when we saw some hard problems from NY, on a test called "Regents' test" we were told, don't worry there will nothing that hard (on the state math competition!) In college I found out the Regent's test was apparently taken by every student in NY, just to graduate! So much for my education at a private school in Tennessee.

 

Not only being deprived of significant content, but also never learning to struggle under a challenge, I was not at all prepared for the demands of a good college. I wasn't even used to studying or attending class, since in my high school, one night's study usually sufficed for a test, sometimes even without going to the classes.

 

Once, as I believe I have told before, I missed three high school physics tests while absent extendedly, which covered 110 pages of our mickey mouse level physics book. When I returned was told I had to make them up. Three days later I had almost memorized those 110 pages and got 100,100, and 97.

 

The one question I missed was not memorizing the fraction of the sun's light received by the earth. I tried to compute it by comparing the area of a sphere whose radius equalled the distance to the sun with half the area of the earth, but instead should have used the area of a slice of the earth through its equator, since that is the shape of the "hole" the earth would make in the big sphere of light. In the book, the fraction had simply been given with no explanation as to how it was found.

 

I got the multiple choice answer wrong, but I generated an idea I was very proud of. So my proud moment on that trivial test was the 3 points I lost for my one good answer.

 

 

For some reason my family has done several moves between NY and CA while someone was in high school.  My father went from NY to CA and the academic difference between the states was such that he was skipped ahead 2 years.   I went from CA to NY, and found the academics in private and special public (like Stuyvesant) schools to be far, far ahead of what I had seen at either private or public in CA where I was.  Possibly the Bay Area and maybe a few other places would be more like NYC.  But where I am now in Oregon and I think in large parts of the country the education in general, and math in particular is not at a very high level.

[mathwonk]

Of course part of it, as we are discussing here, is not just what, but how it is taught. If it is taught appropriately for the student, where he/she is at the moment, I have had the experience that almost any level topic can be taught at a very young age. But I question whether anyone knows just how that should be done in all situations, certainly I don't,

 

One thing bothering me a bit now, is that in teaching my epsilon students, who are ages 8,9,10, I am coming up with alternative ways to explain things that I believe would have worked on my college classes better than what I did.

 

At the time I was teaching in college however, I tended to present the material either as it had been done to me, or as it was in the book. This was largely unsuccessful, statistically speaking.

 

Of course the interest level from the other side of the room also played a role, compounded by the pressure of grades. I often was told by a student that he/she liked my course, found it interesting and challenging, but their scholarship demanded a higher grade than they were getting and they were therefore dropping out anyway, in favor of an easier course, or easier section.

 

Some professors responded by making grades available with almost no commitment from the student. I had a student email me in advance of one of my favorite graduate courses, still in the situation of possibly being canceled for insufficient enrollment, and he bargained with me that he would sign up if and only if I would not require any work from him.

 

I indignantly refused, but eventually calmed down and offered to let him audit the class. He answered with gratitude, signed up anyway, and became of the best students in the class. He subsequently thanked me in his thesis for "some of the most memorable lectures I have heard", the nicest thing anyone has said about my teaching in my memory. That never happened before or since. So each situation may be unique to some extent.

[Pen]

This course having had the effect of deciding me to get AOPS, does anyone have a recommendation on whether I should get Pre-algebra in addition to Introduction to Algebra?  

 

 In a more regular high school text son would be at Algebra 1.   He can do the problem solving type of questions in the pretest for Intro to Alg from AoPS, and some of the problems in the first (chapter 5 excerpt that I pulled up to look at) --However, there are some things like rates and Pythagorean Theorem that he has not had yet and would have to be filled in.   ETA: I can do things like show with squares beyond a right triangle how the theorem fits, and can show him the four 90 deg. angles on a square totalling 360 degrees, and how half of that will total 180 degrees, and so on.    What I told him, getting him emotionally ready for this next step,  is we would start with the Algebra, that it is a hard program where getting 100% is not expected and that he will be expected to work on and think about the problems,  but that if it is way, way too hard, then he can go to Pre-algebra if  needed, and he liked that idea.   His best friend  finished Saxon prealgebra and is going into Saxon algebra and there is some competition so he does not want to be behind (he is 11, so not actually "behind" in math, but the friend is 3 months younger.  He does not want to do "prealgebra" and may be willing to work hard to not have to , so  I am thinking that with the work hard idea, and competition to help, that doing the Algebra course (we will take more than one year for it) and filling in other information as needed is likely to work.    

 

Is the AOPS Pre-algebra wonderful enough that it makes sense to have it as a resource/reference book even if he does not use it as a main text?  We do have Lial's prealgebra available as a reference, and ds had been doing Jousting with Armadillos which is based on Jacobs' Introduction to Algebra, also he has done a lot of Balance Math.  I do not want excess that costs money and will not be used, but so many of you seem to rave about the pre-Algebra book, it makes me wonder.

 

(Post edited to try to make it make more sense.)

[regentrude]

This course having had the effect of deciding me to get AOPS, does anyone have a recommendation on whether I should get Pre-algebra in addition to Introduction to Algebra?  

 

 In a more regular high school text son would be at Algebra 1.   He can do the problem solving type of questions in the pretest for Intro to Alg from AoPS, and some of the problems in the first (chapter 5 excerpt that I pulled up to look at) --However, there are some things like rates and Pythagorean Theorem that he has not had yet and would have to be filled in.

My kids both went straight into AoPS Intro to Algebra from Saxon 8/7, no problem. Rates are thoroughly explained in the chapter on rates. I do not see where he would need the Pythagorean theorem in algebra 1 at all; that is covered in geometry, and will be introduced and proved there.

 

I found that proficiency in arithmetic with fractions and decimals, positive and negative, was all that was needed to succeed in Intro to Algebra. Do not be discouraged if you find chapter 2 quite tough; we supplemented with some more practice problems because both my kids were making careless mistakes (signs, parentheses), mainly due to lack of maturity. I found that all material was well explained.

[onaclairadeluna]

   He can do the problem solving type of questions in the pretest for Intro to Alg from AoPS, and some of the problems in the first (chapter 5 excerpt that I pulled up to look at) --However, there are some things like rates and Pythagorean Theorem that he has not had yet and would have to be filled in.   ETA: I can do things like show with squares beyond a right triangle how the theorem fits, and can show him the four 90 deg. angles on a square totalling 360 degrees, and how half of that will total 180 degrees, and so on.    

(Post edited to try to make it make more sense.)

 

I haven't seen the Pre A book yet (I am getting it for my daughter though) but it sounds like he is ready for Algebra.

[onaclairadeluna]

When I was in high school in Tennessee we practiced hard for the regional math competition, even after school, like any team. We eventually won the state. But when we saw some hard problems from NY, on a test called "Regents' test" we were told, don't worry there will nothing that hard (on the state math competition!) In college I found out the Regent's test was apparently taken by every student in NY, just to graduate! So much for my education at a private school in Tennessee.

 

In NY there are two different tracks Regents tracked students get a Regents diploma which is required for 4 year University (I think CC students don't need Regents classes). The tests are not really that difficult but certainly more challenging and more well thought out than tests I have observed in other states. Every year my kids and I have a little laugh at the problems with the California STAR tests, there is no comparison.

[Arcadia]

 Possibly the Bay Area and maybe a few other places would be more like NYC.  

 

Bay Area is just as pathetic, which probably explains the large numbers of math tuition centers.

 

Is the AOPS Pre-algebra wonderful enough that it makes sense to have it as a resource/reference book even if he does not use it as a main text?  

 For your 11 year old, I'll skip buying pre-algebra.  For my kids, the prealg book is a nice filler text for me to get them to focus on reducing careless mistakes and reading the questions carefully.

[mathwonk]

My grands are in the bay area and have had disastrous schools there, which were considered the best available public schools, and the parents have subsequently been forced to tryvery expensive (and much better) private schools.

[Woodland Mist Academy]

This course having had the effect of deciding me to get AOPS, does anyone have a recommendation on whether I should get Pre-algebra in addition to Introduction to Algebra?  

 

 In a more regular high school text son would be at Algebra 1.   He can do the problem solving type of questions in the pretest for Intro to Alg from AoPS, and some of the problems in the first (chapter 5 excerpt that I pulled up to look at) --However, there are some things like rates and Pythagorean Theorem that he has not had yet and would have to be filled in.   ETA: I can do things like show with squares beyond a right triangle how the theorem fits, and can show him the four 90 deg. angles on a square totalling 360 degrees, and how half of that will total 180 degrees, and so on.    What I told him, getting him emotionally ready for this next step,  is we would start with the Algebra, that it is a hard program where getting 100% is not expected and that he will be expected to work on and think about the problems,  but that if it is way, way too hard, then he can go to Pre-algebra if  needed, and he liked that idea.   His best friend  finished Saxon prealgebra and is going into Saxon algebra and there is some competition so he does not want to be behind (he is 11, so not actually "behind" in math, but the friend is 3 months younger.  He does not want to do "prealgebra" and may be willing to work hard to not have to , so  I am thinking that with the work hard idea, and competition to help, that doing the Algebra course (we will take more than one year for it) and filling in other information as needed is likely to work.    

 

Is the AOPS Pre-algebra wonderful enough that it makes sense to have it as a resource/reference book even if he does not use it as a main text?  We do have Lial's prealgebra available as a reference, and ds had been doing Jousting with Armadillos which is based on Jacobs' Introduction to Algebra, also he has done a lot of Balance Math.  I do not want excess that costs money and will not be used, but so many of you seem to rave about the pre-Algebra book, it makes me wonder.

 

(Post edited to try to make it make more sense.)

 

Not knowing your child it's hard to say, but from what you've written I would give Algebra a try. I wouldn't buy the Pre-Algebra book as a reference to the Algebra unless you find you need it.  I think the raves are most likely for AoPS, not necessarily the Pre-A book--that just happens to be the book being used.

 

 

[mathwonk]

Pen, Harvard has a graduate school of education, and many of the teachers at a good private school here in Atlanta trained there. The Harvard math department also formerly employed a well known professor who specialized in math education, supervised the low level math courses for non math types (which did exist when I was there 50 years ago), and even wrote a well known book on "reform calculus" together with other more main stream math researchers.

 

The presence of this professor focusing on education but in the math department, also provoked objections from some math professors.

 

The fundamental attitude at Harvard, at least when I was there, was that every professor was an acknowledged expert in the subject, someone who was responsible personally for significant advances in research in the field. As such they were uniquely qualified to teach in the sense that they knew what they were talking about better than possibly anyone else alive. The onus was on us to try to understand what they said. As Richard Feynman put it in his lectures to freshmen, roughly: "I am going to teach you as if every one of you were going to become a physicist, and all your other professors here at CalTech will take an analogous approach in teaching their subjects."

 

My first week at Harvard the student orientation contained the warning: "this is the first time in your lives when your professors are not being evaluated on how well you do, only you are."

 

For me personally, this did not work out at the time, but it showed me a vision of excellence, and of aspiring to excellence, that inspired me all my life. Although to me Harvard was at an inappropriately high level as an undergrad, it was perfect for me when I returned as a postgraduate student, and I then benefited enormously. At that later time, the 18 months extra training I got there launched me on a relatively successful research career for the next several decades.

 

In the 1960's, there were in fact not any official student evaluation at Harvard, other than those done by the studnt newspaper. They apparently did not care what the students thought at least not as an official matter of policy. But in later years when I made this observation at my own school as a comparison with our obsession on polling students as to whose course they liked most, I checked it out by calling Harvard. I learned they had completely changed their view, and had adopted extensive evaluations as standard procedure.

[quark]

NM!

[mathwonk]

One thing that surprised me about some schools of education, is that several, maybe most, of the best products of these schools whom I have met, have had essentially no interest in actual classroom education. I.e. some are simply interested in their research, and not on its application.

 

One very bright man I met was doing research on learning and I naively asked him when his results would find their way into the classroom. He looked at me as if I didn't get it at all. He said essentially: "I have absolutely no interest in that. I am a scientist. I am concerned simply with bringing order out of chaos."

 

So perhaps there are many different interests found among professors of education (and math).

 

Possibly the most impressive example I know of someone who combines math and education, is Uri Treisman. His dedication to making an actual difference in the outcomes for students is unmatched in my experience. If you want to check out his spectacular resume here is a link:

 

http://www.utdanacenter.org/staff/uri-treisman.php

[quark]

Bay Area is just as pathetic, which probably explains the large numbers of math tuition centers.

 For your 11 year old, I'll skip buying pre-algebra.  For my kids, the prealg book is a nice filler text for me to get them to focus on reducing careless mistakes and reading the questions carefully.

 

"the large numbers of math tuition centers...." and homeschoolers and afterschoolers. I don't know though...I think the math tuition centers are prevalent even in districts with good schools aren't they? A large number of Bay Area parents, at least the ones I know, like to cover all bases, bad schools or not. ETA: I'm trying to lead the ones I know towards AoPS! :D

[Arcadia]

I think the math tuition centers are prevalent even in districts with good schools aren't they?

Districts with good schools have plenty of afterschoolers too.  The after school care a friend's child goes to uses Zaccaro Challenge Math and does Star testing prep.

[Pen]

One thing that surprised me about some schools of education, is that several, maybe most, of the best products of these schools whom I have met, have had essentially no interest in actual classroom education. I.e. some are simply interested in their research, and not on its application.

 

One very bright man I met was doing research on learning and I naively asked him when his results would find their way into the classroom. He looked at me as if I didn't get it at all. He said essentially: "I have absolutely no interest in that. I am a scientist. I am concerned simply with bringing order out of chaos."

 

So perhaps there are many different interests found among professors of education (and math).

 

Possibly the most impressive example I know of someone who combines math and education, is Uri Treisman. His dedication to making an actual difference in the outcomes for students is unmatched in my experience. If you want to check out his spectacular resume here is a link:

 

http://www.utdanacenter.org/staff/uri-treisman.php

 

 

The ivory tower research orientation as separate from real life is frustrating  (or worse) in many areas!   

 

 Actually, a group of people with different views to all be part of teaching such a course like the Stanford one--from a top institution and on an open-ed platform where many people could participate from afar--is something I would find interesting, and perhaps it would be fruitful.  The person you mention, Treisman, along with Rusczyk, maybe Sal Khan, and others--perhaps including Boaler and Dweck could perhaps make for an interesting meeting place of ideas

 

I am not sure about getting somewhere like Harvard Dept of Ed. to host such a thing, and put it out, but I was just thinking that the Great Courses actually solicits comments on what courses people would like to see them put out.  A Great Course course would be pricey however and does not give the back and forth participation aspect that something like the Stanford one online does.

[Pen]

I looked at one of the books that got recommended by Boaler for a more integrated approach to math -- called Interactive Mathematics Program--and I saw the book intended for 9th grade.  I think it is quite good, however, for an accelerated student it might be more of an upper elementary to middle school level.  And I think for many teachers it would be hard to implement.  

 

I do not have access to its answers or teacher guide so having to guess at what it wants in some cases.  Others seemed very clear.  

 

Some things that struck me included that it gave two graphs of parabolas and wanted the students to figure out equations for them... and then figure out what the equations had in common.   I thought that might be more memorable as an approach than being given quadratic equations and then being asked to graph them.  I thought it had a helpful intro to the idea of trig, with calculating heights based on shadows, or predicting shadows based on height.

 

It also had a puzzle that left me with several possible answers, and not sure which they thought right.  Though I think my several possible may come from thinking from a fairness perspective rather than a math one

 

The puzzle was (simplified and as I recall it, with the book no longer available) that 3 travelers on the Oregon Trail stop to eat together.  Ann has 5 cans of beans. Bo 7 cans, and Cym no cans.  They agree to share all they have, and when the beans are hot, share them equally.  Cym then produces 84 cents that he has as his contribution.  How should the money be distributed, and it said that one of them thought that Ann should get 35 cents, but that the others thought that was not right.  What was right?

 

Possibilities I thought of include that there were 12 cans total, and that of the 4 cans  of beans eaten by Cym, 1 would have come from Ann so she should get  1/4 of the 84 cents, or 21 cents, and Bo should get the rest (my guess is that as a math problem that may be what they are looking for).   Or, everyone put in what cans they had and then shared the food equally, so the money also should be shared equally with 1/3 for each person, including Cym, or half to each of the others and none for Cym since Cym did not intend to be keeping any of the money, but rather to be paying for the food...  etc.       Anyway, I thought such a problem might be interesting in terms of discussion, and thinking about numbers.

[Pen]

And, thank you to everyone who answered about AOPS just Algebra or preA also!

[onaclairadeluna]

I have been really getting into the "Elements of Mathematics" curriculum lately. When my son was little, my daughter was an infant and I had limited time. I just let him read through the books and do the exercises on his own. He seemed to be getting quite a bit out of it and it was really just a supplement for the other math that I am doing. Now I am on my second child and I have more of a handle on the homeschooling twice exceptional dyslexic student thing so I am less overwhelmed. I have had more time to sit with my daughter and work through the books. I find this curriculum to be completely inspired and unlike anything else I have ever seen. 

 

I know they have a computer based version of this, not sure how well this is going for kids. I would expect it would need a teacher and one who is familiar with mathematics. 

 

Anyhow I was musing about this curriculum and how it is completely different from anything else and the relative value of teaching math for mathematicians at the elementary level and it reminded me of CSMP (slightly less advanced but equally abstract and esoteric math curriculum from the..70s? I think.) Anyhow I went to look for it and it was gone. I hope this is not permanent. A part of me just loves the little string games and mini computers. I hope that it is only temporarily down. 

 

CSMP didn't succeed because teachers couldn't figure out how to teach it. Though I just love some of the cute little ideas in this curriculum, I don't think that it really was the last best hope for mathematics. Still, it didn't seem like rocket science to me. As a matter of fact one of the reasons I never used it with my own kids was that it moved so...S...L...O...W...L...Y. Maybe they wrote it to move so slowly in an effort to make it accessible to elementary teachers. It didn't seem to work, no one could figure out how to use it. And I think, more importantly, no one could figure out why they were supposed to use it.  I can kind of see how the conversation would go... An angry parent comes in asking the teacher "Why is my son learning string diagrams and mini computers. What would this ever be used for?" and the teacher would answer "I have no idea."

 

Maybe this is the problem. Maybe people really don't understand the value of abstraction.

 

Anyhow, EM is really quite meaty. I didn't really realize it before, but now that I am working through it I am very impressed. Of course there is no way in the world that elementary teachers could work through it. When I talked to Terry Kaufman and told him my situation he told me I "might be able to get through the first few books" because I have an undergraduate degree in math. I am not really sure what type of skills you need to get through the book 0 chapters. the math is not exactly difficult but it is quite abstract. It is certainly not meant to be accessible. But I think it is the high level of abstraction that makes it so awesome. I just worked through Chapter 2 with my daughter and there is so much in there and she really understands what she is doing on a much deeper level. It's exciting, it's math. I get chills. More importantly *she* is excited. She ran to my bookshelf and dug out Chapter 3 "Sets, Subsets and Operations with Sets" and said something like "Oh boy this looks hard this is going to be fun"

 

Contrast this to AOPS, which is wonderful in a completely different way. Their curriculum lines up more or less with what kids learn in schools. You can do Algebra Geometry, Precacl Calc etc. but it is taught by throwing really hard problems at kids and giving them a chance to figure out solutions on their own. Then they give you some interesting methods that you can use. They show one way to solve a problem, perhaps it was the way you used, perhaps it is different. It has the feeling of being on a math team. Let's work these problems and then we can discuss how we went about solving them. For my son this was his first really awesome experience with math. The EM curriculum didn't challenge him quite enough (he was a little older and had an intuitive understanding of the material already). But when he started with Probability and Counting he would literally scream at his textbook (in an animated and exciting way...like he was having a debate with a good friend). 

 

These two curricula are completely different yet both wonderful and both elevate students towards the mathematics that they would use in college. EM on the one hand teaches kids to think abstractly and AOPS teaches kids to solve difficult problems.

 

I think what these two curricula have in common is that they are inspiring. challenging and passionate. I find it interesting that you can approach a topic from two completely different angles and still have such amazing results.

 

 

 

[Pen]

"the large numbers of math tuition centers...." and homeschoolers and afterschoolers. I don't know though...I think the math tuition centers are prevalent even in districts with good schools aren't they? A large number of Bay Area parents, at least the ones I know, like to cover all bases, bad schools or not. ETA: I'm trying to lead the ones I know towards AoPS! :D

 

 

I'm thinking math tuition centers may also be a function of affluence in an area.  And also perhaps population density to support them.     ?

[Pen]

...

 

I know they have a computer based version of this, not sure how well this is going for kids. I would expect it would need a teacher and one who is familiar with mathematics. 

 

...

 

 

This?   Looks like it can be tried out  on a guest basis -- though when I tried to do that, it made my internet connection shut down altogether.

[quark]

I know they have a computer based version of this, not sure how well this is going for kids. I would expect it would need a teacher and one who is familiar with mathematics. 

 

I know a couple of families trying it and they love it. I think the online version provides solutions etc...I know the books don't right? That's stopping me from buying them...plus the price tag too. :P

[onaclairadeluna]

This?   Looks like it can be tried out  on a guest basis -- though when I tried to do that, it made my internet connection shut down altogether.

Yes. When I tried the free trial of the online program they had a few bugs. You might try it on a different operating system (no pun intended).

 

I know a couple of families trying it and they love it. I think the online version provides solutions etc...I know the books don't right? That's stopping me from buying them...plus the price tag too. :p

I know. It is very expensive. Glad to hear people are using it. Yes, the solutions. I wonder if I will hit a wall with not having a solution manual. I did with my son but I made the critical error of letting him read on his own, thinking that I could just glance in and check his work. I was able to do this through book 1 and then not so much. I just gave up. Still in spite of my lack of teaching he got quite a bit out of the books. I plan to stay with DD if she works through these books both for her and for my own enjoyment. It's quite unique.

 

Anyhow AOPS is way better as far as providing an affordable product that is usable by people. Another huge contrast between the two. I mean EM is inspired and awesome and almost completely useless. Very much like most mathematics  :P AOPS on the other hand is complete. I mean you get a whole years worth of curriculum that can be used implemented and understood for 50 or so dollars. With EM you can get the curriculum for that same amount of money but then you have to take it home and kind of decipher it. But it's still kind of fun, like getting the Rosetta Stone or trying to read the bible in Greek or something. Actually it's probably not even that hard...yet...

 

What is super interesting for me is that my very twice exceptional dyslexic type daughter is hanging in just fine with this curriculum. It has cleared up any weird confusion she had about negatives. (She was getting the rules mixed up but now she really gets them solidly). It's like the sequence just works for her. When she did chapter 1 her times tables were kind of wobbly but she just really wanted to keep up so she really worked to do all of the modular arithmetic mod 7 or mod 29 or whatever. I don't think she would have been nearly as motivated by a page of hard arithmetic.

 

I have tentatively planned on starting her with AOPS pre A in the fall. But I might work through several of these chapters first. They are really quite fun.

[onaclairadeluna]

Oh by the way if you want to see the first chapter it's here online.

 

http://math.buffalostate.edu/~giambrtm/MAT501/Chp1/Book0CHp1pg1-57.pdf

 

And Chapter 2 as well.

 

http://math.buffalostate.edu/~giambrtm/MAT501/Chp1/Book0CHp1pg1-57.pdf

[Bang!Zoom!]

Okay, the Dana center is about to become a favorite. Thanks mathwonk.

[quark]

Oh by the way if you want to see the first chapter it's here online.

 

http://math.buffalostate.edu/~giambrtm/MAT501/Chp1/Book0CHp1pg1-57.pdf

 

And Chapter 2 as well.

 

http://math.buffalostate.edu/~giambrtm/MAT501/Chp1/Book0CHp1pg1-57.pdf

 

Nice! Thank you! I think they are both Chapter 1 though. Sorry, don't mean to trouble you but I was excited that 2 chapters are available online! :D

 

I just browsed very quickly through the first few pages of the first link...good stuff. I feel like it encapsulates a bunch of the living math/ puzzle books my boy works with but all in one text...so maybe it isn't that expensive after all. If they would only include the solutions because I'm really no use helping him with this stuff.

 

Another resource we've looked at in the past and come off impressed is James Tanton's materials. Really makes you think that stuff! But he didn't have solutions either although I know he might be willing to email them if you ask nicely.

[onaclairadeluna]

Nice! Thank you! I think they are both Chapter 1 though. Sorry, don't mean to trouble you but I was excited that 2 chapters are available online! :D

 

http://math.buffalostate.edu/~giambrtm/MAT501/Book%200-Chapter%202%20%20(Integers)/pg%201-85.pdf

 

Oops, here's Chapter 2...

[onaclairadeluna]

 

Another resource we've looked at in the past and come off impressed is James Tanton's materials. Really makes you think that stuff! But he didn't have solutions either although I know he might be willing to email them if you ask nicely.

Ooh, this looks good. 

[Bang!Zoom!]

Before I bother, would a pit stop for an appendix of links shared thus far in this discussion be helpful? I can gather, give brief description and post if it would be helpful.

 

ps: Tanton is a lot of fun. :)

[Chrysalis Academy]

Before I bother, would a pit stop for an appendix of links shared thus far in this discussion be helpful? I can gather, give brief description and post if it would be helpful.

 

ps: Tanton is a lot of fun. :)

 

Yes!!!!!  TIA!

[justamouse]

 

 

The other thing that reading The Mathemetician's lament made me think was that I need a mathemetician to come teach my kids math - I have no business teaching them math, because I really don't see the deep, artistic underlying beauty of it.  Just like I have no business teaching them to play an instrument or create art.  But then I'm hosed, right? Because how many people do see math like a mathemetician?  None of the teachers my kids have had at the local elementary schools, that's for sure.  Where am I supposed to find such a person? I think I'm the best chance they've got, so I continue to struggle to turn myself into such a person, but it is a challenge.

 

I have been thinking long about a very unpopular idea amongst homeschoolers. That is the idea that homeschooling is not a perfect situation for most children. Why? Because as my children enter HS (not pertaining to my olders who went to back to PS for HS) they are not being taught by people who are masters of their subject. (the math educator/anything educator stuff is what is wrong with our schools)

 

I will never be able to teach math to my children like Mathwonk or Regentrude could. Yet, my children NEED teachers like Mathwonk/Regentrude--all of our children need *mathematicians* to teach them math. Why? Because teachers need to know art to the point of playing with it, so that they can see where the child/person will make a mistake, and anticipate that mistake, know the way to bring the person out of the mistake so that they LEARN the difference, and then show them 5 other correct paths to get the correct solution. 

 

I can hand them a book, buy them a CD package and then punt them to their father, who is a history major but has always had an easy time with math--yet that still doesn't make him the best that could teach him. 

 

In a perfect situation, a high school would be filled with teachers who are masters at their subject, and who can teach. A homeschooling parent has love, devotion, and normally is an autodidact, but still unless the parent has a mastery of the subject, they can only teach it up to that point. 

 

All that considered, our public schools are in such a horrid state, our only choice is to homeschool, but in knowing where we are weakest we need to seek out people who can teach what we shouldn't. 

 

Every year I homeschool I really wish I had put more time in self education when my kids were small--even though I thought I was!--because now that they are older, staying one year ahead of them is a full time process--and you have to. You cannot teach a book you haven't read. At least when my last graduates, I'll be fully capable of homeschooling my grandchildren. :p

[mathwonk]

Well the same thing applies to us college professors. On arriving for my first college teaching job I was told on Friday my first class was a formal logic class starting on Monday. This was a subject I had not studied since Freshman year 10 years before, and never used or thought about since. There went my weekend, and I was panicked for most of it, but it worked out, i.e. disaster was avoided.

 

The same thing applies to every course I have taught, from algebra to calculus on up. I was taught calculus by a high powered professional functional analyst at an elite school where the professors experimented on us stronger math majors by throwing graduate level material at Freshmen. They pretty much blew me away, but eventually I survived by memorizing a lot and specializing in professors who tested for regurgitating well.

 

Then I arrive as professor in a non honors calculus class in a middle level state school, with students who are pretty weak compared to any I have seen, and am given a cookbook calculus book to use that I have never seen before. I either have to read it every night and follow along, or follow my own high powered training and do my own version, which then blows my own class away.

 

 

It has taken me over 40 years of teaching to arrive at the more informal, laid back, let's try whatever works, seems fun, and makes sense approach I can use now. (Moreoevr I am retired and not subject to grade scales.) And I still need lots of work on intangibles that may be natural to you, like encouragement, diplomacy, support, reasonable sense of pacing, even good handwriting, sympathy with struggles and mistakes, discipline to spend time correcting homework.

 

But that's the way things work. I think you should give yourself more credit. You are doing the same thing we did, i.e. you are teaching passionately and well everything you do know. Its not what you know but how much curiosity and interest and delight you convey in those areas you do know. And you are learning and studying continually and always broadening the scope of what you can teach.

 

Congratulations! (and thanks for the kind words).

[Pen]

You may some very important points here. We can never be complacent and believe that homeschooling automatically gives our kids a better education. It doesn't. 

 

However, the math teachers children would have in public schools would not necessarily be people like Mathwonk or Regentrude — in fact, they are highly unlikely to be at the elementary level. Public school teachers have something homeschool parents do not, namely a public trust that they know what they are doing and are doing a great job.

 

I am highly unqualified to teach my kids math. Even now, at a third grade level, I am struggling immensely to understand everything my older kid is supposed to master. I will not forget that I got there because I myself had inadequate teachers, though. I will not forget either, that the kid who is working on third grade math would be learning to count to 20 if she were in public school right now. 

 

I will homeschool as long as I can do better than local public schools (private school is not an option financially), and this I base on a real look at what the local public schools are doing, rather than on a gut feeling. Yes, my kids are still young, so I can't say how long this will go on for. Constant self-education will help, but perhaps not indefinitely. When I know I can not keep up any longer, something that will definitely happen with math and soon too, I will hire a tutor for that subject (but only if I can find a tutor who does a better job than I can do). I'll know the tutor is good if I can learn from her/him without having a panic attack. 

 

So, I suck at math (for now). I will not deny that I am immensely unqualified in this area. Does that mean I have no business homeschooling? No. Not for now, at least. I still do a better job than the public school does. My kids are more educated than other kids their age (mind you, we live in a country where formal schooling starts rather late, so that is a huge factor), their curiosity is encouraged rather than killed, and they can be themselves. 

 

I may suck at math, but I still speak five languages and develop areas of education that public schools do not touch at this stage (history, science, logic, all those languages. and even... reading, counting...). That's good enough for me. 

 

Just rambling. And justifying myself. But I do have a question for you, justamouse. You may not have math skills like Mathwonk, but you do have other great strengths that you are obviously sharing with your kids and people on this board. Do you think there is anything wrong with parents passing their own strengths on to their kids, so they are exceptionally well-educated in those areas, but to the detriment of other areas?

 

This is a genuine question, by the way, and not one that I have preconceived ideas on at this stage. At some point in recent history, parents would pass their trade on to their children and thereby essentially determined their future. Don't we still do that, in a way? All of us, parents, not just homeschool parents?

 

For example, I come from a multi-etnic background and ended up with those five languages. I write and translate, because my parents gave me that background. I was essentially pushed into being a humanities and languages person, without anyone's conscious effort. I am sure that the same thing happens to others — your parents' talents and interests are often (subconsciously in some cases) attributed to you, either by others or yourself. 

 

 

Not Justamouse, but think it an interesting question.  Really seems to be 2 questions.

 

I do not think there is anything wrong with parents passing on their own strengths to their children, so long as they do not expect their children to become junior versions of themselves, but are fine with the child having other directions in life, and also helping the child to move toward those even if they are not in the parent's own area of strengths.  I think there is actually a danger in parents not valuing their own strengths and trying to give children what they themselves lacked, and not passing on what they themselves had/have/know/can.  

 

"But to the detriment of other areas." seems to me another question.  There is only so much time and energy and resources, so in some sense anything that is being done means that for that same time/energy/resource commitment something else is not being done.   I think a decision has to be made though about what is so important it is needed, and at what level it is needed, versus what can be done less or not at all.  And that is going to depend on many circumstances.   

 

 

The other day I was driving my son and a friend of his from an activity and a conversation got onto future education and jobs--and I realized that the friend is lost as to how to go about moving toward a professional type career direction, neither parent and I guess not other relatives either having done that, while I might be just as lost trying to help my ds figure out a trades type career.  I know words like apprentice and journeyman, but have little idea how someone goes about getting into such a situation, while I think, from what the friend was saying, that the dad, who has been in a trade, is at sea trying to figure out a college type direction.

[regentrude]

. But I do have a question for you, justamouse. You may not have math skills like Mathwonk, but you do have other great strengths that you are obviously sharing with your kids and people on this board. Do you think there is anything wrong with parents passing their own strengths on to their kids, so they are exceptionally well-educated in those areas, but to the detriment of other areas?

 

This is a genuine question, by the way, and not one that I have preconceived ideas on at this stage. At some point in recent history, parents would pass their trade on to their children and thereby essentially determined their future. Don't we still do that, in a way? All of us, parents, not just homeschool parents?

 

For example, I come from a multi-etnic background and ended up with those five languages. I write and translate, because my parents gave me that background. I was essentially pushed into being a humanities and languages person, without anyone's conscious effort. I am sure that the same thing happens to others — your parents' talents and interests are often (subconsciously in some cases) attributed to you, either by others or yourself. 

 

I am not justamouse, but I'd like to share my opinion about this question anyway, because I have thought about this a great deal.

 

No, I do not find anything wrong with parents passing on their strengths to their children, sharing their talents, and creating excellence in a particular area. In fact, I believe to a certain extent all parents do this, even those of publicly schooled students. I am certainly heavily influenced by my parents' musical background; the experience of having an opera singer as a mother and being exposed to classical music from an early age on shaped my education in a way another child's would not be shaped.

This said, I find it very important that parents 1. realize the limits of their abilities and that 2. they do not push their children into their own field just because that is what they are comfortable with. I see it as progress that a carpenter's son nowadays does have options and is not by default predestined to be a carpenter again. I do find it wrong when parents limit their children's options by limiting their children's exposure and education to fields that are not the parents' own, or more generally when parents make an early decision about the child's future career path and limit the child's education so that this becomes a self-fulfilling prophesy. (For example, there are occasionally posts where a 12 year old is pegged as "clearly not going into science" and the homeschool education is tailored to be weak in math and science... this child will not even have a chance to make a different choice because he is not given the necessary preparation.)

 

Specifically for our family: Both DH and I are physicists and obviously can teach math and physics well to our kids. But I am very aware that I am in no way competent to teach French, since I am not fluent - thus I must outsource French if I want my child to learn it. I am aware that I possess a limited background in literature and history, and this I must seek out resources that compensate for this lack of expertise: I let college professors who are experts in their subject teach my children history and literature via TC lectures. I have in previous discussions written that I do not consider this "teaching", but rather "facilitating": I can only teach what I know, but I can facilitate my child learning things that are beyond my own expertise. I know that some homeschooling parents do not agree with this, but I consider it an important distinction.

Secondly, we are very concerned of anything we might do subconsciously to influence our children towards a career in science. I would not wish my kids to choose physics because they felt that they needed to do this to please us, or because we have given them an education that did not prepare them well for a different option. Now, of course my kids grow up with a different perspective on science and with more experience than other children, and this may well influence their path; but I do not believe I, as a parent, have the right to make a conscious choice that limits my child's possibilities.

 

ETA: Btw, I have wrestled quite a bit with the fact that I will, most likely, not be able to give my children the high quality well rounded public education I myself received in school in Germany, where I was taught by teachers who knew their subjects. I know, however, that I will be able to give them a better education than they would receive in the local public school - thus my decision to homeschool is the right one for our specific circumstances. If I lived in a city with better schools, I might choose differently.

[mathwonk]

Here is another personal remark, for give me: as a math oriented guy who had less opportunity than available today, my kids will tell you I pressured them to do math, sort of hoping they would become the famous mathematician i wasn't, with my expert help.

 

This backfires. My more intelligent friends instead supported whatever inclination their children had, rather than pushing their own agenda. Fortunately my children resisted and chose their own directions.

 

This sensitivity to the needs of the student is in my opinion far more valuable than designated expertise, that may well be different from what is wanted by the child.

 

This forum abounds with people who are trying to provide what is appropriate rather than what they would choose themselves, More power to you.

 

(I had not yet read Regentude's fine post when writing this.)

[Pen]

Before I bother, would a pit stop for an appendix of links shared thus far in this discussion be helpful? I can gather, give brief description and post if it would be helpful.

 

ps: Tanton is a lot of fun. :)

 

Yes!

 

Thanks for the Tanton link!

[Pen]

...

 

So, I suck at math (for now)....

 

I may suck at math, but I still speak five languages ...

 

 

 

 

A couple more thoughts--I am glad you added the "for now" and I am wondering, from the word you used whether Danica McKellar's Math Doesn't Suck  might help.  And also wanted to mention that I think The Great Courses: Mastering the Fundamentals of Mathematics is pretty good.

 

 

Languages are super important and helpful, I think, and can open a lot of doors.  I don't think math should be ignored, but if you can pass languages on to your child that is a huge plus, and not to be taken lightly.  Particularly for a child who turns out to enjoy that it would likely be as good or better to have that than a STEM direction.  My $0.02.

[justamouse]

I don't think there's ANYTHING wrong with passing familial strengths down. Not at all. HOWEVER, a Liberal Arts Education would open up doors for my child that my own family might not be able to. And, the alternative is that our familial strengths may be perfect for the child, for it's his own strength, also. 

I am not saying that I'm going to every do anything other than homeschool, either. I'm just saying that there are advantages, and criticisms, and to truly do best by our children, we need to acknowledge the gaps. 

And, Regentrude is right, we have to facilitate as they get older, but unless that is a capable tutor, I still think it's not the perfect solution (which may not be found this side of heaven or without millions of dollars). I have many Teaching Company classes, but, as excellent as they are (and friends and I were just talking about the differences between the online Yale courses and TC--Though I LOVE the Yale course, TC is far more detailed and the college level we'd consider college level work-My 14 yo will be using the Yale course this year with ease) they are sill not the perfect, which is a tutoring/dialogue with a master professor.

But, then, kids right now have lecture halls with hundreds plus students and do they get much more?  

We don't have the perfect, we all have to do with what we have, and so we do the best by them as we can.

[Pen]

Oh no...   Now that I see the James Tanton site, I am wondering if his Algebra might have been a better choice than AoPS---   At least it looks like another good alternative!

 

ETA:  or...at least  I like the way he was explaining things on the quadratics part...I'm not really sure which of his books would be "algebra"...

 

 

I liked what he had to say here.   Reminds me a bit of the Lament, but different too.

[Chrysalis Academy]

Oh no...   Now that I see the James Tanton site, I am wondering if his Algebra might have been a better choice than AoPS---   At least it looks like another good alternative!

 

ETA:  or...at least  I like the way he was explaining things on the quadratics part...I'm not really sure which of his books would be "algebra"...

 

 

I liked what he had to say here.   Reminds me a bit of the Lament, but different too.

:001_wub:  So much more encouraging than the Lament!!

[Bang!Zoom!]

Somewhere in those links I was carried into quadratic estimation and patterns and was happy as a lark the entire day.  That was like a flipping opera!   :drool:

[quark]

Oh no...   Now that I see the James Tanton site, I am wondering if his Algebra might have been a better choice than AoPS---   At least it looks like another good alternative!

 

ETA:  or...at least  I like the way he was explaining things on the quadratics part...I'm not really sure which of his books would be "algebra"...

 

 

I liked what he had to say here.   Reminds me a bit of the Lament, but different too.

 

How we came across Tanton is that during kiddo's algebra 1 course, he became very enamored by number theory. He did some AoPS but wanted more. After he finished algebra 1, I googled around and found Tanton's site and emailed him to ask what he would suggest for my younger child who had finished algebra 1 and was thirsting for more materials on number relationships and patterns. He replied:

 

As for what might be good for your son, there are two possibilities.

1. Under LEARN TO THINK I have three books (which do already come with soluitions) that I have written for middle-schoolers with some algebra under their belts. It is a review of ideas, but getting at them from the viewpoint of a mathematical thinking, rather than rote doing. I suspect your son would a) go through them quickly but B) enjoy them! (They really do represent a different way of thinking to the traditional approach.)

2. The real book that you might want to look at is THINKING MATHEMATIC! Volume 1: Arithmetic = Gateway to All. (I can send you a file of the solutions. Just let me know.) This book is surprisingly advanced for its elementary content and is quite a challenge. (My LEARN TO THINK series is based on this book, but toned down.) This might be a good thing to look and plan to work through together. You can find it at www.lulu.com/spotlight/jtanton. Of course, after this is volumes 2, 3, 4, ... After this, your son will be done with all of highschool mathematics AND thinking like a true mathematician!

 

I took his advice and we worked our way very slowly through the first volume...some of it was too easy and some of it was at the other extreme! Even after he had finished a rigorous algebra course. I left it on the shelves for kiddo to work on on his own once he was ready for the harder parts. Then, I think we lost the book! lol. I can't seem to find it.

 

FWIW, I would go with AoPS and use Tanton's as a supplement.

[Chrysalis Academy]

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