August 30, 2006

My First Fan

Back in April, I took to task an article in the St. Paul Pioneer Press which bought into the defeatist educrat crititicisms of Minnesota's plan to teach algebra to all 8th graders. One of my criticisms was that the article interviewed a bunch of kids instead of real experts. One of those kids was Therese Harrah.

Therese Harrah is in algebra this year and thinks about half her classmates could take the class. She also thinks there's a big fear of math out there that students could overcome by taking good notes, following directions and taking the problems one step at a time.

"People think it's really hard because of all the equations, variables and exponents," Therese said. "But as soon as you learn how to break down the solutions in different parts, it's not that hard."

Here's what I wrote.
Poor Therese has already bought the "blame the student" meme. It's the kids' fault they didn't do well. They need to take better notes, follow direction better and solve the problems systematically. Isn't this the teacher's job? To, you know, teach how to do this stuff?

Algebra really isn't very hard. So long as you've mastered elementary math. Then it's just a matter of "learn[ing] how to break down the solutions in different parts" according to little Therese. Of course, you learn how to do this by being taught how to do it. It's only hard if you're not taught how to do it well. And, if you're not taught it well, you can forget about calculus. And, if you can't do calculus well, then you can forget about a career in math, science, or engineering -- i.e., the high-paying careers.
Lo and behold, four months later Terese Harrah (or at least someone from St. Paul who found this blog by googling her name) has responded.
umm... excuse me?? i'm that "little therese". not kidding. i'm the girl in that article. i didn't say that it was the students fault, but, c'mon, not every 8th grade student is perfect! do you expect evry student to take perfect notes and always study for tests? no way! it's not the students fault, or the teachers. mary hoffman is a great teacher who actually got me to enjoy math. she works hard and loves her job. so it's not the teachers fault, and it's not entirely the parents fault either. it's a combination of all three. i don't pay attention in class, i get a poor grade. the teacher doesn't teach, i get a poor grade. the parents don't help or support, it affects my grade. so don't go around saying, "poor little therese got it wrong" when in fact you don't have YOUR story straight!
I think Therese has been reading The Education Wonks.

I'll just point Therese to this post and see if she can figure out the correct solution for herself by breaking down the solution problem into different parts and solving.

Parental support is always a good thing. But, if the material was being presented properly in school, the need for parental support would be greatly diminished. Parental support is a crutch for inadequte teaching.

Of course, students do need to pay attention. But, how well they pay attention is a function of how well the material is being taught and how well previous teachers have taught previous material. As it turns out, kids who have difficulty manipulating algebraic expressions usually haven't learned how to manipulate fractions all that well either. So what are they doing in algebra class? I'll answer that: not paying attention because they are lost.

In order to do algebra these kids have to learn not only algebra and all the math they didn't learn in previous years. Learning algebra is difficult enough by itself. The problem is exacerbated because these kids are likely lower performers and have a difficult enough time in the first place.

This is a common misconception about how kids learn. Teachers make this same mistake all the time, so you can't blame Therese for faliing into the same trap.
Many teachers believe that lower performers are something like crippled children. They can walk the same route that the higher performers walk, but they need more help in walking...

The information these teachers receive about low performers is that they do not retain information, that they need lots and lots of practice, and that they don’t seem to have strategies for learning new material. Ironically, however, all these outcomes are predictable for students who receive the kind of instruction these students have received. High performers receiving instruction of the same relative difficulty or unfamiliarity would perform the same way. Let’s say the lower performers typically have a first-time-correct percentage of 40%. If higher performers were placed in material that resulted in a 40% first-time-correct performance, their behavior would be like that of lower performers. They would fail to retain the material, rely on the teacher for help, not exhibit self-confidence, and continue to make the same sorts of mistakes again.
From Student-Program Alignment and Teaching to Mastery, pp. 14-15.

Don't feel bad Therese, even the mighty EdWonk has stumbled on this same issue.

7 comments:

rightwingprof said...

Of course, when he transfers to business school, he'll find himself in the same situation, just with stats and analysis instead of calculus.

(-:

KDeRosa said...

And, then its either drop out or down to some cushy B.A. major.

In engineering school we had to take calc, linear algebra, differential equations, statistics and probability, and numerical methods. A regular picnic I tell you.

rightwingprof said...

Typically what happens first is they want to do a marketing major. Then they find that marketing is probably the most data analysis intensive major in the school (I guess they think if you go into marketing, you sit around drawing up storyboards all day). Then they leave the business school.

Business isn't engineering, but it's not a good fit for a mathphobe. And as I'm beginning to discover, not all business schools are created equal.

MikeZ said...

I'll have to side with Therese on this one. If you read again what she said, you'll see that she said "[students] think it's hard ... but as soon as you ... it's not that hard".

I do not see where you got the "she bought the blame the student meme". Is 'second-order differential equations' hard? You bet. So is brain surgery - until you figure out how to do it. You might say that differential equations aren't that hard, if you've got differential and integral calculus down pat. But the argument breaks down somewhere - I cite as an example the recent proof of the 4-color theorem - a long proof that is so difficult to follow that only the writer and maybe one or two other mathematicians can follow. If X is easy provided only that you've done X-1, then we should all be geniuses.

Learning is the process of working through the hard stuff until it becomes easy.

She said "... taking good notes and following directions...". Just where do you think those come from? From the teacher. That's how teachers teach - by presenting information and methods. The other end of that communications channel is the student, who takes notes, follows directions (the teacher's notes and directions), and with luck, thinks about the notes and directions and asks whatever questions are needed to resolve things not understood.

As far as "breaking down the problem", that's how the real advances in the world are made. Newton, for example, broke his problems down to basics. (I leave Newton's methods as an exercize for the reader.) Read Polya's "How to Solve It" - "break it down" is right there at the top of the list.

"I'll just point Therese to this post and see if she can figure out the correct solution for herself by breaking down the solution problem into different parts and solving."

I assume you're looking at the fractions. Sorry, but that is the level down to which harder problems are solved. My suggested method would be:

2/3 + 3/4 = .666666 + .75 = 1.41666 = 1 + .41666 = 1 + 5/12 = 17/12

The other one's easier.

KDeRosa said...

Hi MikeZ

I was referring to this line "She also thinks there's a big fear of math out there that students could overcome by ..."

I'm calling this the blame the student meme because Therese is blaming the students fo rtheir fear of math and suggests that they are responsible for overcoming it. The problem lies within them.

I don't disagree that Therese's suggestion wouldn't be helpful, especially the breaking down part.

I do disagree that the students are the cause of the problem. The most likely source of the problem is inadequate teaching. Most algebra problems are a result of inadequately learned elementary math. At that age the teachers I contend that the schools need to take responsibility for student learning.

I assume you're looking at the fractions.

I was actually referring to the post for the proposition that elementary math was the underlying cause of the algebra problems.

therese_harrah said...

hello, this is therese harrah. now that i'm in high school i have experienced even more teaching styles (and some students methods). and now that i've gotten over pre-teen angst (lol. i was pretty touchy then), i can see you do have a point. i'm so sorry for my snotty letter and hope you continue to keep posting your blog.

therese_harrah said...

i also want to add that i was not saying that it was the students fault. Sure, if you have teachers who have ineffective teaching methods, or parents that don't/can't support your education, that affects the way you learn. But students do contribute a huge part to this equation. If a student does not want to learn, than no amount of effective teachers and motivating parents are going to make them get good grades. also, if a student wants to do well on an exam but doesn't take notes, they will still do poorly. the bottom line- you can't be successful if you don't want to or try to, no matter how many people wish you would succeed.