Gifted Issues Discussion homepage Forums General Discussion APS article on math ed: A Math Paradox

http://www.aps.org/publications/apsnews/200910/backpage.cfm

I'd like to hear your reactions to this article.

I've run into this exact same thing with my DS14. It's memorization without any clear intent for understanding.

I tutored math in college. I agree with this author.

Most people will struggle with Calculus even if they are very bright. It takes a certain level of maturity to handle it and a good ability to solve problems methodically. It also takes a thorough grounding in Algebra and Trig. I always started with teaching how to solve problems using a method, then went into the nuts and bolts. I've seen D students make A's and I've seen a lot of others continue to fail.

The answer to the issue is threefold.

1. A lot of people do not belong in a technical field of study at the collegiate level. They need other technical outlets that are not primarily intellectual.
2. Many teachers are not up to the task. Most retired engineers can teach math with their eyes closed, but no amount of instruction will make most teachers' college grads able to teach it.
3. Kids should be grouped by ability based upon standardized tests. This way material can be presented in a way that is appropriate.

The fact of 1-3 means the good teachers ability to impact the right students is diluted by pushing too many kids on the wrong study track. And then most students do not get the right exposure at the right time.

Ouch. That article sparked painful memories of my first attempt at college-level calculus. I was woefully unprepared & dropped the class rather quickly.

I guess that nonsense in my senior year of sitting in the back of a classroom with a pre-calculus book to figure things out on my own with a small group of similarly ignored students didn't help me one whit.

The author's comment about maturity resonated as well. I took another crack at college a handful of years later and absolutely smoked calculus (relatively speaking). I'd had no formal math since my first attempt, so could credit nothing other than being a little bit older.

The author's three main complaints are discussed beautifully:
1. Confusing difficulty with rigor.
2. Mistaking process for understanding.
3. Teaching concepts that are developmentally inappropriate.

Looking back, I think our teachers in HS stumbled the most @ #2. There was a whole lot of memorization, but understanding? Not so much. I'm one who thrives on knowing all the why's & wherefore's -- once I get those under my belt I can run in any direction.

Determining what exactly constitutes "developmentally appropriate" for DS is going to be a challenge -- I can see that already.

Thanks for sharing this article!

I think this is an interesting article and it makes a lot of good points, but it skims over a very real problem: most adults are not developmentally ready for calculus. A currriculum path that prepares students for a science major will not work for most students. As long as we try to find a one-size-fits-all approach, we are going to fail. This article advocates a developmentally appropriate curriculum. Developmentally appropriate for whom? If we design a curriculum that is appropriate for most students it will fail to adequately prepare those with math talent.

It is true that some people confuse rigor with difficulty, but the real problem illustrated by the author's anecdotes is that the teachers were not capable of understanding the material themselves! How does he expect bright students to be prepared for calculus if they can't do rate problems in eighth grade? Or understand what an identity is? These concepts are developmentally appropriate for eighth graders on the track for scientific careers.

Yes, the focus on testing is counterproductive. But it exists because we perceive that there is a real deficiency in the ability of teachers to actually teach math! To fix this problem, we need to pay math teachers enough to buy competence for our public schools. And we need to provide developmentally appropriate curricula for different ability groups.

Of course you can't instruct students by assigning material that they aren't prepared for. I don't think that necessarily means that the material is inappropriate, but that the lack of preparation is systemic. Ganem doesn't address that. He seems to excuse teachers from knowing the material by saying that he himself found it difficult.

Articles like this are used as support for those who want to dumb down the curriculum. I don't think that's the right approach. I think we need to stop expecting to prepare everyone for calculus. I don't think that's a realistic expectation.

My impression of this editorial was similar to Cathy�s crystallized response.

Imagine the �take away� many educators would find and later mention to parents seeking math acceleration for their gifted child. Dr. Ganem should have included the �gifted caveat� as was later added by the author of �The Hurried Child� after his book had been cited as reason to retain countless kids with age peers.

I found myself bristled when reading his analogy about developmentally inappropriate skills since each of my kids walked (cruised) at six months and sight-read a fair amount at two years.

I was nodding my head in agreement at the beginning of the article as he described the problems of students not being prepared for college level math. By the end, I was bristling like delbows when I realized this would probably just be fodder to accuse parents of "pushing" children into developmentally inappropriate math.

DD7 is on a different developmental path as Grinity described so well in another post and I copied below. To me it is developmentally inappropriate to focus on the speed of her math drills. Her basic addition and subtraction speed is fast enough so it's not a hindrance as she tackles 2 digit multiplication and long division. Isn't that the whole point of math drills and not just speed for speed's sake? Grrr!

I have some further questions for the science/engineering experts here.

What is the appropriate level to introduce calculators for use in classroom math and should their use be allowed without restriction from that point forward?

I ask because my kids attend different schools with different approaches (neither could use one in their elementary/middle school math courses). My daughter was required to have a graphing calculator beginning with her freshman advanced algebra (1 and � of 2) class. My son still hasn�t been allowed a calculator in math class (high school honors geometry), including for the ITBS and other standardized tests.

Which approach is better and why? Thanks.

Well now you've got me trying to figure out what the three or four things are! LOL... If you count "factoring" as one thing (although it covers several chapters when you go into the detail of linear vs. quadratic and simple quadratic vs. completing the square and/or the quadratic equation), that's a start... then maybe "isolating a variable" could include all the rules of manipulating equations and situations where one equation will do vs. when you need two or three...

Hey, that covers most of it right there! Maybe there are only two things you need...

I just this morning started algebra with DS8. I have been dragging my feet on it, reviewing the basics because I feared he wasn't ready. But he has been acting out, and I realized that his behavior looked a lot like it looked in 1st grade when he was underchallenged. I made the switch and his behavior this morning was the polar opposite of how he has been most of the school year this year.

That's a long way of saying that I am reading this thread with interest because I'm personally trying to find that balance right now! Tips are welcome!