http://www.washingtonpost.com/opini...expense/2011/11/21/gIQAe76ywO_story.html
Closing the achievement gap, but at gifted students� expense
By Michael J. Petrilli and and Frederick M. Hess
Washington Post
December 15, 2011

President Obama�s remarks on inequality, stoking populist anger at �the rich,� suggest that the theme for his reelection bid will be not hope and change but focus on reducing class disparity with government help. But this effort isn�t limited to economics; it is playing out in our nation�s schools as well.

The issue is whether federal education efforts will compromise opportunities for our highest-achieving students. One might assume that a president determined to �win the future� would make a priority of ensuring that our ablest kids have the chance to excel.

To Obama, however, as for President George W. Bush, such concerns are a distraction at best. Last year the Education Department�s civil rights division announced that it would investigate local school policies that have a �disparate impact� on poor or minority students � signaling a willingness to go to court if department officials think that school systems have too few of such children in gifted programs or Advanced Placement courses. This bit of social engineering ignores the unseemly reality that advantaged children are statistically more likely to be ready to succeed in tough classes than are low-income children raised in households with fewer books and more television.

The result is a well-intended but misguided crusade to solve via administrative fiat the United States� long-standing achievement gap: the dramatic differences in test scores between white and minority students and between middle-class and poor youngsters. The message to schools was unmistakable: Get more poor and minority children into your advanced courses or risk legal action by Uncle Sam.

Then, in September, the president offered states and school districts flexibility around onerous provisions of the No Child Left Behind Act � linked to certain conditions. Among these: States must explain how they are going to move more students into �challenging� courses. The effect will be yet another push to dilute high-level classes.

<end of excerpt>

Along those lines, has anyone who's 30-ish or older looked at high school math books recently? The current trend is to fill them with colorful, distracting graphics and countless examples of Why We Use Math! and Fun Facts! and suchlike. The geometry text that my son's school uses is so full of the extraneous stuff (2-3 distractions per page), it's difficult to focus on the math. Plus, the challenging problems that used to make up the last 20-25% of exercises in a given section are gone. It's as though no one is allowed to be good at math. Almost all of the questions are superficial and simplistic. DS studies independently, and we use an old book.


This trend is a sorry example of how algebra and geometry have been diluted in the name of "accessibility." I don't understand why schools can't just teach basic geometry and honors geometry or something like that. But I guess it wouldn't be fair or something.

I agree that many textbooks used in public schools have too many distractions and have noticed that textbooks purchased by parents (often homeschoolers), such as Singapore Math or Saxon or Art of Problem Solving have less fluff. A good set of math textbooks with challenging problems are those co-authored by Dolciani http://www.welltrainedmind.com/forums/showthread.php?p=1787181 . One "human interest" feature in Dolciani's books are 1-page descriptions of the life and work of great mathematicians. They cannot appear in modern textbooks, because almost all of them were white men.

I'm gifted in math and it always came easy, but that didn't keep me from inquiring as to why we were learning about imaginary numbers. It seemed pretty useless when I was in high school, and my math teacher did not provide a very satisfying answer. Other children have a lower threshold for motivation to learn math they don't see the point of. These children need inspiration. Ideally, the problems themselves would pertain to useful applications of math. Figuring out how many years it will be before Jill is twice as old as Bill is not interesting or important, but math books are filled with those kinds of questions. Ohms law could be taught in algebra and used to answer similar questions... and the circuits could be built and the answers checked with a voltage meter.


My school had honors geometry and regular geometry. I think the expectation was the students from honors geometry would never take trigonometry... I know I never did.

Our grade school uses Everyday Math from the U. of Chicago as its textbook. Has anyone seen that? It seems muddled and confusing. Sometimes my kids have to do things like "write a sentence about how you liked this exercise" or "Write a sentence about how math helps you every day."
Duh!
However, in our local G/T program which starts in 4th grade and my kids have qualified for, they can ultimately take two years of AP Calculus at our local public high school, so I guess I can't complain TOO MUCH.

The teachers at our elementary school had to use Everyday Math, and they hated it. They felt like it focused on the wrong things, was often confusing, and - like you said - they thought some of the homework questions were less than helpful.

We have seen this in our district - with a twist. As part of one of the largest school districts in the US, our high schools have a huge disparity of both dropout rates and students continuing on to college. For example, our high school has a graduation rate of around 97% and over 80% continuing on for higher education. 25% of last year's senior class graduated with over a 4.0. In contrast, another high school in the district battles dropout rates approaching 70% with paltry number of graduating seniors continuing on for higher education.

In an attempt to equal the playing field, the superintendent proposed that our mid and high school not be allowed to offer advanced academic courses that were not also available to students at other high schools in the district. After a vociferous outcry, the proposal was tabled - but not dropped.

While steps need to be taken to address the socioeconomic and social challenges that are affecting a disparity in education options for students, dumbing down all students is not the answer, either.

Huh. I'd have expected it to be the other way around. Why wouldn't an honors student keep progressing in the subject?

When I took Honors Geometry, it was the only Geometry class offered by my school. But that was a quirk of the way the school system was organized at the time. We had grades 10-12 in high school and 7-9 in junior high. If you were an honors math student, you'd have been ready for Geometry in 9th grade. If not, you'd have gotten it in high school. The honors track was laid out like this:

7th - Pre-Algebra
8th - Algebra I
9th - Geometry
10th - Algebra II
11th - Trig/Pre-Calculus
12th - Calculus

If you weren't an honors math student, there was another class they'd offer you in 7th, and you'd take Pre-Algebra in 8th. If I recall correctly, you'd then get Algebra I, Geometry, and either Algebra II or something called Business Math, your choice, to satisfy your graduation requirements. You only needed 3 years of math in your last 4 years of school.

So in my school, the Honors Geometry students were pretty much expected to take Trig... and I did. That was as far as I went, though. You know this epidemic of the lazy teachers you can't get rid of because of tenure and unions that certain politicians keep bloviating about in the media? In my public school experience I only ever met one, in my senior year, and he was teaching Calculus and AP Physics. I dropped both courses.

Wow. You have to wonder what problem they thought they were going to solve there, because the proposed solution seems to indicate that the problem is that your school is doing too well, and it needs to be dragged down to the level of the others.

I agree completely, so I think I didn't make myself clear.

The textbooks used today (well, the ones I've looked at anyway) have so much extra stuff, it crowds out actual information. Here are examples from my son's geometry book:

• LiNK
• Who uses this?
• Engineering application
• CONCEPT CONNECTION
• Why learn this?
• California Standards
• Remember!

This is on top of semi-useful stuff like "Know-It Notes," "Helpful Hints," "Standardized Test Prep!" and "Spiral Review." There are bright, distracting icons everywhere and the book is loaded with irrelevant color photographs of things like traffic signals, puppies, heroes on horseback, and the Statue of Liberty. Did you know that her index finger is 8 feet long? I do now, thanks to that book. But what this has to do with similar triangles I do not know.

There's very little space for actual text that you'd have to sit down and concentrate on. But that might be hard, and geometry wouldn't be "accessible."

I'm looking at a "challenge" problem in my son's book. It's a straightforward question about side-hypotenuse relationships in a 45-45-90 triangle (the side is 1; how long is the hypotenuse?). For those who've forgotten, the formula is 1-1-root 2.

I think that basic geometry is a really great thing for students who aren't mathematically inclined. What tears at me is that with books like the one I have on my desk, difficult geometry is out of the question.

Dude, the regular track would look like this:

geometry
algebra II
trigonometry
pre-calculus


the honors track was this:

Honors geometry (which included elements of trig)
algebra II
pre-calculus
calculus

So the honors students would not devote an entire year to trigonometry, while the other students would. When I say I never took trig, I mean that I never enrolled in a year-long class called trigonometry.

I was wondering which geometry book Val was talking about (in order to avoid it), and what she recommended instead. She answered that in an Amazon review http://www.amazon.com/Holt-California-Geometry-Edward-Burger/dp/003092345X .

I see your point. I too think it's a terrible decision to take out the difficult questions, and distract from learning actual math concepts. The extras should be there to inspire an interest in math, not to impede children from learning.

But, I can appreciate that a large triangle is similar to a small triangle in much the same way that an 8 foot finger is similar to a child's 3 inch finger. There's a lesson about scale related to that example.

It seems to me that the new text books you've described don't have a good balance between the basic mathematical principles and the (hopefully) related topics of interest. I just wanted to make a point that a good text book will have broad appeal, and that such a book should definitely highlight interesting applications of the lessons within.

The McDougal-Littell/(Jurgenson, author) book is great. You can use it for self-teaching or as a classroom text, and each section has loads of problems that get harder as you go. But lots of them are not tough, which makes it a good book for any course. There are also other books in this series (Algebra I and II, for example) that are equally good.

Oh, got it.

Our school only offered the one class, which we all called Trig, though its (abbreviated) proper name was Trig/Pre-Calc, so yeah, it wasn't a full year of Trig for us, either.

Our school wasn't rated too highly, so I don't think they could muster enough non-honors students to take a full year of Trig. There were times I flipped through someone's Business Math book, and I was horrified... this was stuff we'd done in elementary school.

I remember back when I was a teenager, it was a very popular cliche that "you'll never use Algebra after high school." This was expressed in a number of movies and TV shows at the time. I found it very de-motivating. I enjoyed the process, though, so I kept going on anyway. For someone who didn't enjoy the process, I don't know why they'd bother.

I send the opposite message to my DD. I let her know that I use Algebra all the time.

This discussion reminds me of an idea that I contemplate sometimes:

A mandate requiring that all teachers at the high school level or above have 5 years of work experience relating to the field they will teach.

No more teaching straight out of school, and not being able to answer questions about the usefulness of what you teach. Also, if you didn't learn your area of study well enough to be employed in the field for 5 years, then you probably didn't learn it well enough to teach it very well either.

Edit: Also, I'm pretty sure you can't drive without at least an intuitive understanding of calculus. You have an accelerator pedal, and a decelerator pedal after all, that you use to modify your speed and position.

I think the cliche is true for most people, as discussed in a recent essay. Students who do well in algebra will earn more than those who don't primarily because they are more intelligent on average, not because many of them will be using algebra in their jobs.

http://www.ams.org/notices/201005/rtx100500608p.pdf
What Is Mathematics For?
Underwood Dudley
Notices of the American Mathematical Society
May 2010

A more accurate title is �What is mathematics education for?� but the
shorter one is more attention-getting and allows me more generality.
My answer will become apparent soon, as will my answer to the
subquestion of why the public supports mathematics education as much
as it does.

So that there is no confusion, let me say that by �mathematics� I
mean algebra, trigonometry, calculus, linear algebra, and so on: all
those subjects beyond arithmetic. There is no question about what
arithmetic is for or why it is supported. Society cannot proceed
without it. Addition, subtraction, multiplication, division,
percentages: though not all citizens can deal &#64258;uently with all of
them, we make the assumption that they can when necessary. Those who
cannot are sometimes at a disadvantage.

Algebra, though, is another matter. Almost all citizens can and do
get through life very well without it, after their schooling is over.
Nevertheless it becomes more and more pervasive, seeping down into
more and more eighth-grade classrooms and being required by more and
more states for graduation from high school. There is unspoken
agreement that everyone should be exposed to algebra. We live in an
era of universal mathematical education.

<end of excerpt>

And if you read on, it concludes by basically saying the reason the people are more intelligent is because they learned algebra.

When I say that I use algebra all the time, I'm not referring to the quadratic equation or any particular algebraic function. I'm referring to the concept of constructing an expression based the relationships between known and unknown values to solve a particular problem. Once you've got that expression, it's usually just a matter of simple arithmetic to solve whatever problem you're trying to solve... so it's all in the expression. And the logical processes behind constructing and manipulating expressions is learned in algebra.

Also, I'd say that while the execution of higher math isn't necessary to the performance of most jobs, the understanding of higher math is essential to accessing certain concepts. Electronics engineers and technicians talk casually of sine waves, but if you don't know trig, that statement is meaningless.

When I was in school in the Navy, we spent a whole week on vector mathematics, manually calculating a firing solution to intercept an aerial target with a ballistic weapon fired from a pitching and rolling deck. We never used vector mathematics again, because that's what the computers are for. But we did acquire a deep understanding of the complexities involved in a firing solution, from which we appreciated the importance of getting a battery alignment check done properly, or the impact to the system of losing windbird or gyro data.

Here in this forum on giftedness, an important mathematical concept that helps us understand our kids is the standard deviation. You don't have to calculate it, but you do have to understand it.

I didn't get that message. Maybe I missed the part you're referring to, but I read this:


Getting better at reasoning doesn't make you inherently smarter. It just means you're better at a skill you develop by doing maths. If I practice skating every day, I'll get better at loop jumps and backward three-turns, but my innate abilities won't change.

I agree that you can develop a skill. You don't have to have innate mathematical abilities to use the skill.

Just like understanding derivatives. I can use an example of an option on a house to explain derivatives to someone who never had calculus and they get it. But the example is a derivative.

Ren

I tell my students that people who take more math classes than they have to are more likely to get a job that lets them wear jeans to work and pays well, too. That's what I got from my experience in 17 jobs before I became a teacher! ; )

Well, I became a teacher in my mid-thirties. Five years experience in my field was difficult because so few jobs are tied to an academic field. In a recession, that five years becomes even tougher to get. I guess you could say I did that, if you define my field very loosely, and include the graduate assistant work in university.

After I switched careers and became a teacher, I had to work in education for about 8 years before I got the chance to actually teach a class that was related to my undergraduate and graduate major fields (6th grade social studies, as it happens). Of course, about half of teachers leave the profession within their first five years, and teachers who are assigned outside their area of expertise are even more likely to leave. I'm still teaching because I am unusually stubborn.

Having been on both sides of the fence, I will say this. People in education have a tendency not to value education and experience outside of that field. People outside of the field of education really have little idea what is involved in education. But the real problem with your plan is that it is difficult to retain people who worked in another field before becoming a teacher, because people with experience and skills that are recognized by the world outside the school doors are less likely to be satisfied with the working conditions and pay of a teacher.

I have often had the opposite thought, that nobody should be allowed to enter a teacher training program until they have actually worked inside a K-12 school, even if it is just as a part-time Educational Assistant for a semester. But if we did that, I wonder if we might have an even tougher time staffing our classrooms.

To be clear, I'm not saying that a math teacher needs to work as a mathematician, nor that a history teacher needs to work as a historian. If a would-be math teacher has 5 years experience in engineering, or a hard science, I would accept those as related fields. Similarly the would-be history teacher could work in politics.

Beckee, What you say is true that people who have success outside of teaching may want to stay there, or return there after trying teaching. Salaries may have to be raised to account for the fact that the bar has been raised in one way. On the other hand, Finland has a high bar for teachers, but their compensation isn't drastically higher than it is in the US, from my understanding (by many accounts, it's lower). Also, there are perks to teaching regarding summer vacations, and job satisfaction that aren't found in other industries.

The point is to let the market assess the understanding these teachers gained in the subjects they studied instead of developing subject specific tests for all teachers, while giving the teachers experiences they can relate to their students. Did you ever ask your math teacher the usefulness of understanding imaginary numbers? Could they answer? Mine couldn't. I think he said they were "used in engineering" but had no idea how, and could offer no example. He was generally a good teacher, but my motivation suffered because of his ignorance. (Luckily I didn't need much motivation to grasp math.)

Since you're a teacher with at least some outside experience, perhaps you can comment on whether or not you relate those experiences to your students in a way that enriches their education. My sister-in-law relates my engineering experiences to her math students because she has none of her own (she'd be perfectly capable of acquiring some.)

I notice this in textbooks as well. It drives me crazy. But this may be partly a question of learning style, I think. I like a clear, linear flow of text and hate it when I can't tell what ot read first or when things go off-topic in little boxes. I HATE those DK books for the same reason, but plenty of people seem to adore them. I wonder if some of this is an adapatation for kids who are on the web all the time.

The purpose of textbook publishers these days is to convince educators that the new books add value, so they'll keep buying new books every year. Those images you're talking about aren't intended for the consumption of the child, they're intended for whoever makes purchasing decisions in the local school districts. Upper-management types are often delighted by bright, shiny objects.

It's not like the fundamentals of geometry change drastically every year. We're still pretty much studying Euclid and Pythagoras at that stage.

Don't get me started on math textbooks. I volunteered in all of my kids' classrooms during their elementary years. The 3rd & 4th grade books their school used were ridiculous.

Pages crammed with so many unnecessary graphics that they were a distraction issue for those kids with focusing problems. And they had numerous errors.