Jane in NC...requesting a spinoff...

[Tullia]

I'm hoping you might have time to discuss something you mentioned in another thread:

 

[Copied and pasted from your post.] I have a preference for texts written by mathematicians not math educators.

 

I'm curious to know more about how textbooks written by mathematicians differ from those written by math educators. And, is it realistic for a parent who's not a mathematician to aspire to use materials written by mathematician? These questions are inspired partly by your post and partly by some remarks I read in reviews of math texts at Amazon.

 

oops...I should have said that I'm interested in hearing from Jane and anyone else for whom this is important.

[regentrude]

I, too, prefer texts written by not just mathematicians per se, but by people who actually use math.

One of the problems I see with math education is that often new ideas come from people who are thinking about education, but who have not the slightest idea what a person can actually do with the math that is being taught. Some ideas look nice on paper and sounds plausible - but do not stand the test when it comes to using math.

(One example: the idea that one does not have to memorize times tables but can get away with knowing only bench marks. Or that one does not have to be able to actually DO division but that it is sufficient to have understood the concept... connected math anybody???)

People who use math every day know what skills are important, and how to go about acquiring them.

In addition, mathematicians are people who enjoy math (as it is - not in a dumbed down version to be "fun"). One thing that stuck us with Art of Problem Solving is how much fun the author has with math, and how much this fun radiates from every page - without diminishing rigor.

This is quite different from the two extremes of typical math educator books: either it is "all fun and games" but fluff - or it is serious "math is good for you, hence you must suffer through the drill" which gets the job done but kills all enthusiasm.

[Jane in NC]

It strikes me that math educators are more inclined to write texts that rely on algorithms more than explanations of why things work the way they do. Some of the busy colorful texts with sidebars displaying applications that are supposed to engage kids (but often do not) exemplify this type of book.

 

I do not have experience with The Art of Problem Solving but suspect that I would love the series. The Dolciani texts are dear to my heart--they helped launch my academic career in mathematics. Mary Dolciani was a mathematician.

 

There has been in recent years a trend to make math "relevant". Of course math is relevant---one cannot do physics, biometrics, chemistry, etc. without it! But often one needs fairly complex mathematics to model simple real world processes. It is hard to make simple algebra highly relevant--and attempts to do so are often fairly lame.

 

One thing that mathematicians often bring to the discussion is beauty. A good proof, an interesting relationship, a fascinating graph can be enough for us. The "real world" is highly over rated. ;)

[Tullia]

I've looked at a couple of the AoPS books and was surprised at how different they are in appearance--there's no silly busy work or sidebars just lots of interesting questions. I, too, noticed the sense of fun. I'm more curious than ever about the Dolciani texts. What I'm gleaning from both of your replies is a sense of the combined beauty and utility of math. The disconnect between mathematicians and educators is such a waste of resources. What a shame that we don't have more mathematicians writing for and teaching in the schools.

 

Jane, your last paragraph made me smile. I know several people who define true beauty in just those terms--and they sometimes hint at a belief that those things are more real than the so-called real world. ;)

[Julie in MN]

But don't you have to balance this with someone who is actually gifted at teaching -- at communicating -- at transferring the great stuff in their brains, in an understandable way, to less advanced brains?

 

Julie

[Spy Car]

:lurk5:

[Colleen in NS]

One thing that mathematicians often bring to the discussion is beauty. A good proof, an interesting relationship, a fascinating graph can be enough for us. The "real world" is highly over rated. ;)

 

:lol: I love it!

 

I'm more curious than ever about the Dolciani texts.

 

You MUST search for the 1960s editions. :D I've been on a 2.5 year hunt for these, and am almost done collecting. My son started the algebra a few weeks ago, and LOVES it.

[dhudson]

I think anyone who feels passion and love for a subject will show that in how they teach or write about a subject. I agree that a good educator can make a subject interesting but I have experienced teachers who have felt true passion for a subject and they are the teachers I remember.

 

We like programs that are written by mathematicians.

Edited August 12, 2011 by dhudson
Didn't want a kitten to die

[onaclairadeluna]

But don't you have to balance this with someone who is actually gifted at teaching -- at communicating -- at transferring the great stuff in their brains, in an understandable way, to less advanced brains?

 

Julie

 

I think mathematician vs. educator is another false dichotomy. A great mathematician can be a great educator (AoPS is a great example of this). The problem is that many math texts are written by people who are neither. The best educational materials are written by people who are well versed in their subject and who are good at communicating. It would be terrible indeed to have to choose one over the other.

 

If you are teaching elementary math you don't necessarily need to be a PhD (see LiPing Ma) but it is nice to have someone who has a deep love and understanding of the subject putting together the curriculum. I think it's love vs. money and not mathematician vs. teacher.

 

My daughter has been nagging me to give her hard math "like her brother" and the other day I thought to show my son the math I am giving her. He got right away that it was fabulous and told her. I have no idea if her curriculum was written by mathematicians but it has the secret handshake of mathematically beautiful geeky joy that I always look for in a math curriculum. That's all that really matters to me.

[Jane in NC]

But don't you have to balance this with someone who is actually gifted at teaching -- at communicating -- at transferring the great stuff in their brains, in an understandable way, to less advanced brains?

 

Julie

 

I have been privileged to know some brilliant mathematicians and scientists. Admittedly not all but many are able to communicate with us lesser mortals. But this does not imply that all are expected to write high school or even college texts. The advantage for those who do is that they know and understand where the material is headed. Those who do not see the larger picture resort to algorithms, the "get 'er done" approach.

[FaithManor]

I agree with Regentrude and Jane 100%. Though I survived my high school math program with mostly A's and high B's, I had not developed any fundamental appreciation for higher mathematics. In college, I met my dh, the math major, and he began showing me his texts...such a WORLD OF DIFFERENCE! Math became so interesting. I went from feeling fairly incompetent in math, despite good grades, and never having a class higher than trigonometry/analytical geometry to teaching myself some differential calculus because of a section on it in Goedel, Escher, and Bach: The Eternal Braid, a book being heavily discussed amongst a bunch of us looney musicians. It was made possible by the introduction to math through the eyes of authors who loved math and used it every day in practical career applications.

 

Now I enjoy studying math, using it, teaching it, etc. but I do not use typical high school texts. We love Singapore in the younger years and I keep some Rod and Staff around for the extra problems and their real world, farming word problems since we do some hobby farming here and live in an agricultural area. But, it's Singapore that shines and then off to college texts.

 

When we switched from the standard "fare" of high school algebra books to a college level text written by someone who ADORED math, well, that's when the light went on in dd's eyes. It was a turning point for us. We were later given a "high school" trig/pre-calc book and tried to use it since it was free. We had a book burning! I am not kidding. I burned the book because I considered it an act of cruelty to foist it off on another innocent teenager! :lol: I think I danced with glee as it entered the flames.

 

Faith

[Tullia]

....When we switched from the standard "fare" of high school algebra books to a college level text written by someone who ADORED math, well, that's when the light went on in dd's eyes. It was a turning point for us. We were later given a "high school" trig/pre-calc book and tried to use it since it was free. We had a book burning! I am not kidding. I burned the book because I considered it an act of cruelty to foist it off on another innocent teenager! :lol: I think I danced with glee as it entered the flames.

 

Faith

 

There are exceptions to most rules. :D

[Julie in MN]

The problem is that many math texts are written by people who are neither.

 

Now that is not gonna be good!

 

You know, I'm thinking that this particular thing does happen when a "company" starts producing a textbook for every level. And there is a demand for that -- folks want to stick with one company all the way through, to prevent gaps and such. But I wonder if that is going to automatically mean dispassionate authors?

 

I'm a bit biased on the "complete curriculum" issue because I love Mr. Firebaugh of Math Relief, and he just and only does what he is gifted at -- teaching high school algebra. But I feel he gets left out because he doesn't have a "complete curriculum."

 

And by the way, I have no idea about whether he's a mathematician or passionate about math. I just know he's good at teaching algebra -- a really good teacher :)

 

Julie

[regentrude]

You know, I'm thinking that this particular thing does happen when a "company" starts producing a textbook for every level. And there is a demand for that -- folks want to stick with one company all the way through, to prevent gaps and such. But I wonder if that is going to automatically mean dispassionate authors?

 

 

I do not think the fault lies with the company, but rather with the process how school textbooks are developed. The Colleges of Education are full of people who think about education and want to improve pedagogy, but frequently lack the in-depth understanding of the content material. They have no mathematics background themselves, are in their educator bubble and have no idea what math is used for - yet come up with new ideas for curricula that teach math better.

(The result are things like Connected Math.)

[swimmermom3]

What a wonderful thread. I tend to prefer to use books by writers to teach writing than books by writing teachers. I never thought about applying that to math.

[Colleen in NS]

What a wonderful thread. I tend to prefer to use books by writers to teach writing than books by writing teachers. I never thought about applying that to math.

 

And I never thought about that with regards to subjects outside of math (and I only thought about it with math, thanks to Jane). Thanks for pointing that out - good food for thought for me!

 

Colleen (who will be looking at previously bought-ahead books through this new lens now)

Edited August 15, 2011 by Colleen in NS

[Julie in MN]

I do not think the fault lies with the company, but rather with the process how school textbooks are developed. The Colleges of Education are full of people who think about education and want to improve pedagogy, but frequently lack the in-depth understanding of the content material. They have no mathematics background themselves, are in their educator bubble and have no idea what math is used for - yet come up with new ideas for curricula that teach math better.

(The result are things like Connected Math.)

 

Well, yes, I really dislike some of those modern math textbook series. My oldest (public schooled) son had to spend one year in something called "Core 9" since he'd had algebra I & II, and that's all they had to offer him. It was about widgets and bits of math applied to "fun, imaginary" stuff -- why they couldn't apply it to real stuff I never could understand.

 

However.... I'm not just thinking of unfortunate math series. How about good series, like Saxon, Lial, Jacobs (not sure if Singapore would apply since Singapore potentially could draw from several authors)... how does the fact that they're trying to teach "everything" impact the quality of both their enthusiasm for the topic and their teaching ability on each and every topic? (I'm thinking about algebra & higher math, and as elementary math seems like a single topic.)

 

Julie

[onaclairadeluna]

What a wonderful thread. I tend to prefer to use books by writers to teach writing than books by writing teachers. I never thought about applying that to math.

 

I am a music teacher. Most music teachers play music. We are musicians. Some great, some mediocre but almost all of us (and all of the good ones) play music. I don't know what happened with math that people that do and love math don't seem to go into teaching as much. Probably mathematicians are just terribly disgusted at the state of mathematics education.

 

Funny little schools of education are just half the problem. My son takes those awful standards tests every year. Last year he was almost in tears after the test. Actually not tears he was actually mad, very emotional. I tried to get him to calm down so he could tell me what made him so upset. Apparently there was a probability problem, something that could have been really interesting. But the test makers actually gave the formula. They took the one interesting part of the problem away and left just the calculation part. No wonder mathematicians veer away from education.

 

It would be like substituting band class with a class that you have to take quizzes about musical instruments. Clarinet is to flute as trombone is to

a)food processor b)doughnut c)french horn d) workbook

 

Then to prepare you for the test someone puts you in a room with a clarinet and tells you to play around and see if you can make a sound.

[Tullia]

I am a music teacher. Most music teachers play music. We are musicians. Some great, some mediocre but almost all of us (and all of the good ones) play music. I don't know what happened with math that people that do and love math don't seem to go into teaching as much. Probably mathematicians are just terribly disgusted at the state of mathematics education.

 

Funny little schools of education are just half the problem. My son takes those awful standards tests every year. Last year he was almost in tears after the test. Actually not tears he was actually mad, very emotional. I tried to get him to calm down so he could tell me what made him so upset. Apparently there was a probability problem, something that could have been really interesting. But the test makers actually gave the formula. They took the one interesting part of the problem away and left just the calculation part. No wonder mathematicians veer away from education.

 

It would be like substituting band class with a class that you have to take quizzes about musical instruments. Clarinet is to flute as trombone is to

a)food processor b)doughnut c)french horn d) workbook

 

Then to prepare you for the test someone puts you in a room with a clarinet and tells you to play around and see if you can make a sound.

 

My brother would have loved your analogy! He was a mathematician who elected to teach high school and was an amateur musician as well. His choice of profession meant financial sacrifice--for him and his family. He faced all kinds of pressure to take a job that would have paid more. The sad thing is that he was often at odds with the system even though he was blessed with colleagues, and even more important, a principal who shared his ideals. He died before we started homeschooling. I miss him. I regret not having had the time to have discussions like this with him, so I truly appreciate all of the replies.

[Colleen in NS]

My brother would have loved your analogy! He was a mathematician who elected to teach high school and was an amateur musician as well. His choice of profession meant financial sacrifice--for him and his family. He faced all kinds of pressure to take a job that would have paid more. The sad thing is that he was often at odds with the system even though he was blessed with colleagues, and even more important, a principal who shared his ideals. He died before we started homeschooling. I miss him. I regret not having had the time to have discussions like this with him, so I truly appreciate all of the replies.

 

:grouphug:

[Jane in NC]

What a wonderful thread. I tend to prefer to use books by writers to teach writing than books by writing teachers. I never thought about applying that to math.

 

I think that this may be part of the appeal of TC videos and college texts to so many on our board. People who are passionate about science, history , etc. may reach students who are less passionate about these subjects.

[swimmermom3]

I think that this may be part of the appeal of TC videos and college texts to so many on our board. People who are passionate about science, history , etc. may reach students who are less passionate about these subjects.

 

Yes Jane, being in the presence of people who are passionate about a subject and who are able to give one even a glimpse of the beauty of their subject as seen through their eyes is to me, a gift of wonder.

 

Which is part of why I am drawn into your math threads repeatedly.:D You also remind me that I must do something more for Swimmer Dude than simply following Foester, as much as he likes it.

 

Unfortunately, about the time I thought of the most perfect math tutor for ds, that brilliant, but lost soul (the teacher, not ds) was an international fugitive from the law and was being arrested at our local airport. It does not speak well of my own character that I couldn't decide which transgression I was angrier with him for: the legal and moral one or the loss of an outstanding middle school math teacher when there seem to be so few of them in the world.:tongue_smilie:

[Jane in NC]

 

Unfortunately, about the time I thought of the most perfect math tutor for ds, that brilliant, but lost soul (the teacher, not ds) was an international fugitive from the law and was being arrested at our local airport. It does not speak well of my own character that I couldn't decide which transgression I was angrier with him for: the legal and moral one or the loss of an outstanding middle school math teacher when there seem to be so few of them in the world.:tongue_smilie:

 

Oh my word!!

 

I started another thread with some rabbit holes for you and Swimmer to consider. Does he play Go?

[Mommyfaithe]

Yes Jane, being in the presence of people who are passionate about a subject and who are able to give one even a glimpse of the beauty of their subject as seen through their eyes is to me, a gift of wonder.

 

Which is part of why I am drawn into your math threads repeatedly.:D You also remind me that I must do something more for Swimmer Dude than simply following Foester, as much as he likes it.

 

Unfortunately, about the time I thought of the most perfect math tutor for ds, that brilliant, but lost soul (the teacher, not ds) was an international fugitive from the law and was being arrested at our local airport. It does not speak well of my own character that I couldn't decide which transgression I was angrier with him for: the legal and moral one or the loss of an outstanding middle school math teacher when there seem to be so few of them in the world.:tongue_smilie:

 

Oy!!:001_huh: :lol:

[swimmermom3]

Oh my word!!

 

I started another thread with some rabbit holes for you and Swimmer to consider. Does he play Go?

 

No, he doesn't. I will have to look at your thread. He does not particularly like board games, but I think that has to do with an overly competitive older brother who is not always a good sport. He does however, love state testing. He took the 8th grade test instead of the 7th grade test for "fun." He talked all the way home in the car about his "process" for working with questions he did not know the answer to. He is intrigued with problems like that. Does that make any sense? I am not sure I could turn him loose in a public school system. Unlike his older siblings, he intuitively understands how to "work the system."

 

I am off to check out your Rabbit Holes. I have taken ds farther than his siblings in that he is competent and confident with regards to math, but he needs a passionate teacher to take him to the next level. He is interested in the thinking behind math, not in just being able to solve the problems for the grade. I should have done this a couple of years ago because he is at that stage where he is acutely aware of the competency of others. I taught art literacy in the schools for years and was always saddened to see the transition from bold, adventurous artist to unhappy art student with no ideas that they feel comfortable with putting on paper. This is how my son has become when we talk about looking at some of the math competitions. A couple of years ago, he would have said, "Bring it on, baby."

[Corraleno]

It would be like substituting band class with a class that you have to take quizzes about musical instruments. Clarinet is to flute as trombone is to

a)food processor b)doughnut c)french horn d) workbook

 

Then to prepare you for the test someone puts you in a room with a clarinet and tells you to play around and see if you can make a sound.

You MUST read Paul Lockhart's Mathematician's Lament!!! It's a wonderfully written 25-page rant in support of the point that Jane made about attempts to make math "relevant": that it strips all the power and beauty out of it and turns kids off instead of turning them on. The essay starts with a great music analogy:

 

A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.†Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer.

 

Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.†It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.

 

As for the primary and secondary schools, their mission is to train students to use this language— to jiggle symbols around according to a fixed set of rules: “Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. One time we had a chromatic scale problem and I did it right, but the teacher gave me no credit because I had the stems pointing the wrong way.â€

 

In their wisdom, educators soon realize that even very young children can be given this kind of musical instruction. In fact it is considered quite shameful if one’s third-grader hasn’t completely memorized his circle of fifths. “I’ll have to get my son a music tutor. He simply won’t apply himself to his music homework. He says it’s boring. He just sits there staring out the window, humming tunes to himself and making up silly songs.â€

 

In the higher grades the pressure is really on. After all, the students must be prepared for the standardized tests and college admissions exams. Students must take courses in Scales and Modes, Meter, Harmony, and Counterpoint. “It’s a lot for them to learn, but later in college when they finally get to hear all this stuff, they’ll really appreciate all the work they did in high school.†Of course, not many students actually go on to concentrate in music, so only a few will ever get to hear the sounds that the black dots represent. Nevertheless, it is important that every member of society be able to recognize a modulation or a fugal passage, regardless of the fact that they will never hear one. “To tell you the truth, most students just aren’t very good at music. They are bored in class, their skills are terrible, and their homework is barely legible. Most of them couldn’t care less about how important music is in today’s world; they just want to take the minimum number of music courses and be done with it. I guess there are just music people and non-music people. I had this one kid, though, man was she sensational! Her sheets were impeccable— every note in the right place, perfect. She’s going to make one hell of a musician someday.â€

 

The whole essay is brilliant. There is a book, too, which adds a "second half" to the online version.

 

Jackie

[Colleen in NS]

I think that this may be part of the appeal of TC videos and college texts to so many on our board. People who are passionate about science, history , etc. may reach students who are less passionate about these subjects.

 

Yup. This is partly why I jumped on the super-duper TC sale in December - I could finally get all those science lectures I've been wanting. I haven't watched them all yet, but oh boy, I've never had science teachers as enthusiastic as these professors!!!

 

Unfortunately, about the time I thought of the most perfect math tutor for ds, that brilliant, but lost soul (the teacher, not ds) was an international fugitive from the law and was being arrested at our local airport.

 

Yikes!! :lol: (I think Jane should start some online tutoring.....)