Gifted Issues Discussion homepage Forums THINKING BIG About Gifted Education Closing the achievement gap and gifted students

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 fluently 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.