Can the math people comment on this?

[shanezomom]

I periodically check Dr. Hung Hsi Wu's essays to see what's new in his efforts to reform math education in the U.S. The link below is from a presentation to educators and policy makers in October, and it is a quick and straightforward read. In it, he offers specific examples of where textbook school math has done more harm than good. He suggests a new paradigm for math education, and in other publications points out that we have created a false dichotomy between conceptual and traditional math. His goal is for math to be taught "correctly."

 

Can you math folks look at this link and comment? (I promise, it really is quick and enjoyable.) A shout out to Nittany Jen and dh, dereksurfs, etc.

 

http://math.berkeley...unty-2012-2.pdf He starts out addressing California standards, but it applies to the entire U.S.

 

I know only textbook school math and I am lousy at it. I am always intrigued that I might have had a better understanding if I hadn't been taught by rote. I would liked to have been able to teach Singapore up to ds's current 6th grade level, but I was messing him up. We have turned to Thinkwell, which is pure traditional textbook, Life of Fred, and now maybe Tabletclass Math after reading dereksurfs' posts.

[regentrude]

I tried understanding what he wants to say and I gave up. It is a bunch of "educese". I can't say I found it enjoyable at all.

I do not even understand what "textbook math" is supposed to mean - you can teach any math with or without a textbook, there are excellent textbooks and lousy textbooks.

His explanation of fraction addition seems unnecessarily complicated. Yes, the LCD does not belong in a DEFINITION of addition, but certainly in an effective algorithm.

 

I don't get his point, and I do not wish to waste more time trying to figure it out.

[snowbeltmom]

In it, he offers specific examples of where textbook school math has done more harm than good. He suggests a new paradigm for math education, and in other publications points out that we have created a false dichotomy between conceptual and traditional math. His goal is for math to be taught "correctly."

 

I don't think textbooks are to blame. In order for math to be taught correctly, we need to ensure that our nation's teachers understand math well enough to teach it. Imo, we have too many teachers, especially at the elementary level, that are not qualified to teach math. The new paradigm for math should be insisting that experts are teaching math in the classrooms, which unfortunately is not happening in the vast majority of classrooms today.

[wendyroo]

I'm an engineering person, rather than strictly math, but I have taken a lot of math classes along the way so I will offer an opinion.

 

I think the crux of the issue comes down to:

"But it will not materialize unless we have teachers who

have the requisite content knowledge to make it hap-

pen: how to teach the addition of fractions properly

(without LCD), how to define the slope of a line cor-

rectly (without reference to two chosen points), etc.,

etc."

 

Right now there is some percentage of teachers who truly understand math and regardless of standards and textbooks I think they teach it as accurately and effectively as possible. They are already emphasizing that the slope of a line is the same no matter where you measure it along the line. And some of their students understand that.

 

There is also some percentage of students who truly care about learning and understanding math. I did, and it used to drive my teachers nuts because I was asking them questions to which the answers were not neatly spelled out in the book. But most of those students are going to persevere anyway - they are going to figure out why the book says to use LCD to add fractions. They are going to think about slope and the slope formula and graphs of lines and realize that the slope of a line must be constant.

 

I tutored students preparing for the SAT, ACT, GRE and GMAT for years and years. In my opinion, some of them triumphed in math despite their education. Some of them were failed not by specific standards or textbooks, but by a string of poorly educated teachers and a societal bias that math is hard and not all that necessary. But, I think, a third group of students managed to eke out rudimentary mathematical skills BECAUSE they were taught the rote methods. No matter how many times I explained the concepts of slope or adding fractions, some students never truly grasped them. For that group, the concrete formulas were all that stood between them and mathematical incompetency. It would be cruel to never give them a sure way of determining slope because we would rather they intuit a method.

 

Which takes us back to the quote about properly educated teachers. I don't think any well educated teacher sticks strictly to the standard or the words written in the text book - at least, I hope not. I hope they are using their well-educated discretion to add or subtract material to best fit the students that are in front of them. I hope that a good teacher using a TSM text still shows fractions being added on a number line and I hope a teacher teaching under CCSSM would still mention LCD as a useful fraction adding tool if it appeared that is what would most benefit her students.

 

Good standards and texts are good. Teachers who actually understand math are better.

 

Just my thoughts,

Wendy

[Alessandra]

I liked what Dr Wu was saying -- he sounds a LOT like Liping Ma. Students should understand concepts, and (surprise!) so should teachers. Also, he argues that algebra in grade 9 instead of grade 8 is not dumbing down, if grade 8 standards are rote learning, rather than true understanding.

 

Thanks -- it was a nice slide show.

[kiana]

I do agree with what he has to say about algebra/geometry integration, specifically with the slope of the line. This is one of the issues that I see, that we are in such a hurry to get everyone "through" algebra 1, that rather than taking the time to explain WHY these things work, we just say "Here is how to find the slope of a line. Memorize it. Do homework about it." and so students come to college with no understanding as to why, for example, a horizontal line has 0 slope.

 

I also agree with him about needing better-educated elementary teachers.

 

I did not at all like his explanation of fraction addition. It seemed, though, that part of what he thinks is that we should *first* teach adding fractions by using denominator times denominator as the common denominator, and afterwards teach reduction to the LCD. About that, I'm not sure I agree, but I can see his point.

[regentrude]

I do agree with what he has to say about algebra/geometry integration, specifically with the slope of the line. This is one of the issues that I see, that we are in such a hurry to get everyone "through" algebra 1, that rather than taking the time to explain WHY these things work, we just say "Here is how to find the slope of a line. Memorize it. Do homework about it." and so students come to college with no understanding as to why, for example, a horizontal line has 0 slope.

 

I agree. But can anybody explain to me what this has to be with "textbook math"? Our math textbook most definitely explores this issue extensively in algebra.

[Crimson Wife]

Is he willing to throw his weight behind Algebra 1 in 9th grade to the admissions officers at UC Berkeley and the other top universities? I may agree with the general premise that students are being rushed to algebra but who's going to unilaterally disarm and have their child get passed over in favor of one who follows the "new normal" honors track of algebra 1 in 7th through post-AP math in 12th?

[kiana]

 

I agree. But can anybody explain to me what this has to be with "textbook math"? Our math textbook most definitely explores this issue extensively in algebra.

 

 

I believe what he's referring to as "textbook school mathematics" is "the mathematics in the most commonly used school textbooks" not "the mathematics in any textbook."

 

I think he could have chosen a better name for it.

[letsplaymath]

I think part of what Dr. Wu is trying to communicate is the difference between two common ways of understanding math, described in this article:

• http://astro.temple.edu/~madman/ruiu.pdf
  

 

The American school culture (the subconscious attitudes of the majority of teachers, parents, students, standardized test writers, and school board members) leans heavily toward an instrumental understanding of math -- so that is what tends to get taught, most of the time, in most schools, no matter how the textbook is written. This is what Wu refers to as Textbook School Mathematics, even though the textbooks are really only a small part of it and tend to follow the culture rather than create it.

 

The Common Core standards are attempting to swing the pendulum toward a relational understanding of mathematics. Whether they will succeed remains to be seen, but I wish them the best of success!

[Alessandra]

On rushing to algebra too soon. A while back I read some posts from Montgomery County, MD parents, who complained that their kids fell apart in high school, because all of the kids had been 'accelerated in elementary school.

 

Math is one subject that I believe should have separate tracks early, because for kids who really do get it, repeating info they know can be so boring. In our school system (a highly regarded one one), some students (about .03%, that is, one kid avery few years) take algebra in 6th grade, some (less than 10%) take it in 7th grade, another percent (don't know the number) take it in 8th grade, others in 9th grade. The school system has got stricter about letting kids into early algebra. Students who get below B in 7th grade algebra have to retake the course in 8th grade. I think that is a good way to go.

[shanezomom]

Your replies have helped me out, thanks. I think I see glimmers in our homeshool journey that there is some beauty to behold in math. I just wasn't taught that way so I am intrigued by the concepts being debated in math education.

 

I had two dried up, uninspired math teachers at critical times: a dull, old prune of a man who refused to smile and jingled change in his pockets while he "taught" us algebra in the dullest way imaginable. And our geometry teacher at a different school, was a mousy, plump little woman past retirement age who got a bit disheveled when she had to explain things to those of us who weren't getting it. You just stop asking questions when there is absolutely no pleasure in the math learning process and pray the semester will end quickly. I swear, teacher showing some enthusiasm for a subject goes a long way in encouraging the student to believe that it's even worth learning. I want to dump my math baggage so I can help our son see that math is a beautiful thing.