Gifted Issues Discussion homepage Forums Learning Environments Conceptual mathematics

Someone here recently responded to a post that I wrote asking a similar question. Her answer was that many of the teachers don't fully understand what's behind the algorithms they teach. I agree, and think that this sad fact forces many of them to follow the recipes in the books.

Also, many teachers with a good understanding of the subject teach the old algorithms behind closed doors. Many of them are frustrated with conceptual mathematics too. Here's a good perspective from a math teacher.


Val

I agree completely (hence my original post).

Here is yet more insight on questions surrounding elementary mathematics education and what prospective teachers learn. Or don't learn.

Kriston was right about the challenges of teaching a group of kids with different abilities and learning styles --- and of course, this is prima facie evidence of the need for ability grouping. But I guess ability grouping diminishes self-esteem or something. Though I don't know how, as constant struggling/constant boredom because it's too hard/easy don't seem like self-esteem builders to me.

A lot of the mental math stuff is really important --- after all, it's great to be able to multiply 88*5 in your head. But using these approaches as the only way to learn multiplication seems silly, because they break down when you have to do complex calculations. Even with a calculator, setting up such calculations is difficult if kids (and adults) don't understand the foundational stuff.

<sigh>

Val

Is anyone familiar with the McGraw-Hill high school math sequence called, Contemporary Mathematics in Context: A Unified Approach?

This is a highly conceptual approach as well. I just wondered if anyone had run across it and, if so, what they thought of it.

Did anyone see this article from the New York Times back in March? Here is a quote from what the Bush administration wants to do to improve math...

http://www.nytimes.com/2008/03/14/education/14math.html?_r=1&em&ex=1205726400&en=43d6c2db14891c1f&ei=5087%0A&oref=slogin


Does anyone else read this and think, "Adding and subtracting whole numbers by the end of 3rd grade????" I think I read somewhere??? recently that, over the last 25-30 years, American textbooks have been dumbed down by two complete grade levels. I wondered what other people thought of this? I distinctly remember becoming proficient in long division in 4th grade. (and 35 years ago I was in a very backwoods, southern, small town that was not known for its stellar educational results. Gifted was a completely foreign concept.)

Another link that I wanted to share about the future of math is from the Washington Post entitled, Accelerated Math Adds Up To a Division Over Merits. It describes D.C.'s goal to accelerating math for everyone so that 80% of kids get algebra 1 by 8th grade.

http://www.washingtonpost.com/wp-dy...ml?nav=rss_print&sid=ST2008060303480


I was not a part of this group discussion when these articles were published, so maybe they have been already hashed out. But I thought they were relevant and was curious as to what others thought.

acs: Sorry... I haven't heard of the McGraw-Hill sequence. I did have "Unified Math" a very, very long time ago... back in the dark ages of the 70's.

California is going to require that all students take algebra I in 8th grade soon. It's a ridiculous idea; 56% of them take it now and a woefully low percentage manage to pass. I have to get the kids in a few minutes and so can't find the number now, but will look later.

The problem is that the maths courses in 3rd - 7th don't create students who can work with numbers. They emphasize memorization at the one extreme and the conceptual stuff we've been discussing here, and very little middle ground. Of course, this approach falls to pieces in algebra, which is easy if you have a solid grounding in the basics and very difficult to impossible if you don't.

I remember doing multiplication in 3rd grade, long division in 4th grade and fraction manipulations in 5th. Each topic was previewed the year before. My son's 2nd grade class was still doing basic addition last November. <sigh>


Val

Dottie and Val,
Not to play devil's advocate or anything... I'm just woefully ignorant and terribly naive... But could this new algebra requirement actually be a good thing, in that it may force these schools to see how shaky a foundation they have laid for math?

Maybe this will be a wake-up call to the schools that they need to revamp their 3rd-7th math in order to get those kids ready for the challenges of algebra?


Am I giving them too much credit for assuming that, if there is a problem, the solution is to strengthen the math skills, instead of watering them down? Or is this another instance of the schools mandating something without the faintest idea of the how to get from point A to point B?

That's my take on it. Our district sees a problem with math instruction at the elementary level but they are just flailing around and likely to grab onto the latest fad...

I agree. And given that too many teachers don't understand the foundations of mathematics, the problem isn't likely to improve anytime soon.

And the US marches on further into Mediocrity-land.

I read somewhere that Algebra I is now what pre-Algebra I used to be. By extension, Algebra II is what Algebra I used to be. So kids who take Algebra I only, get to college w/ Algebra I on their transcript, take an Algebra college level class (which you need REAL high school ALgebra I) and are woefully unprepared.

Some states are worse off than others in regards to their math curriculum. Illinois is apparently the absolute worst for low math standards on their state standards test by 8th grade according to at least one comparative study.

Here is the contrast between a question deemed *proficient* for 4th grade from IL and one from MA.


http://www.illinoisloop.org/trib_dumb_isat.html