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Jonathan Groves
Posts:
2,068
From:
Kaplan University, Argosy University, Florida Institute of Technology
Registered:
8/18/05


ST Math at Madison Elem. in Santa Ana, CA
Posted:
Oct 1, 2010 2:48 PM


Dear All,
I thank Michael Paul Goldenberg for sharing this information about ST Math that Madison Elementary School in Santa Ana, CA, is using to help their students learn mathematics. See the article
http://www.districtadministration.com/viewarticle.aspx?articleid=2351
for more information.
The link
http://mindresearch.net/cont/programs/demo/tours/SolvingLinearEquations/progTour.php
gives an example of one of these games that students are playing to help them learning mathematics.
Games are good ways to help motivate students to learn math and to help make learning more enjoyable for students. Traditional ways of practice and drill bore most students and do not give them much of a good reason to learn math other than possibly as a mere excuse to do work, to occupy their time with something boring to do, or to please their teachers and the administration.
I looked over some of this stuff, and this is an interesting approach to helping students learn mathematics. A visual and intuitive approach to mathematics without using mathematical language and symbolism up front is a good way to help students learn concepts and helps motivate the need for mathematical language and symbolism. Such an approach can also help students learn to see what mathematical language and symbolism say. I know that students' confusion about mathematical language and symbolism is a major hangup for them. Not only that, many students end up believing that mathematical language is meant to make math and problem solving more confusing rather than less confusing.
I can't say for sure whether the rise in test scores is a genuine sign or something fake, but that rise does indicate that perhaps this ST Math might have some promise behind it. At least it is worth looking into to see what is going on and why. It is possible to find a way to fake success like this, but it is not easy to do; otherwise, we would see big increases in test scores across the country. I could think of ways to fake success, but how to do that in ways so that the chances of getting caught are low I'm not sure.
And it is just one school, and the test scores are based on tests I wouldn't give. I would like to see tests that dig deeper into the students' understanding to see if they really understand the math and to see if their learning is longterm learning or simply the kind of learning that helps them do well on tests but then quickly evaporates afterward.
If ST Math has been tried elsewhere, I hadn't heard yet. If not or if has been tried in only a few other schools, then ST Math needs to be tested more.
So the signs aren't definite, but these signs look better than what we usually see or hear about.
Since one purpose of mathematics is translating real world problems into languages on paper so that we can analyze and solve these problems without having to carry out physical processes, we should help students to see this purpose of mathematics. That is, mathematics is supposed to make problem solving easier rather than more difficult and is supposed to help make many problems accessible that would be, for practical purposes, inaccessible without mathematics.
The games I had mentioned here from ST Math are not modeling problems, of course, and I do not mean to suggest that they are. But these games do help students develop a way to picture these ideas in their minds, and these visual representations of the mathematical ideas will help them later in using the mathematics as a way to understand our world. It is extremely difficult, if not impossible, for students to use the math outside the classroom meaningfully if they see the mathematics as nothing but symbolic manipulation. For instance, how can we model a realworld situation using mathematics if we see the math as nothing but symbolic manipulation. I have seen students who struggle with basic word problems in arithmetic, for example, but who are decent at working purely computational questions (that is, questions that explicitly mention what computation to do and no context of any kind is given). They cannot decide what operation to use because they see the operations in arithmetic in essentially the same way that we see operations in an abstract algebraic structure but nothing more. That is, the operations to them are just formal rules for "generating" a number from other numbers. Games such these, even if they don't include modeling problems, can still help students develop these meanings for operations that go beyond just mere symbolic rules.
If students can really see for themselves why we need mathematical language and symbolism, then they should be more eager to learn it. That is, mathematical language and symbolism is not, despite what many students may believe, just there for the hell of it or just there to make their teachers and mathematicians and others sound brainy. But to help make this learning effective, we should follow Clyde Greeno's and Alain Schremmer's advice about identifying the mess in curricular language and cleaning it up (see my recent post about this). Garbled and imprecise language hinder many students' learning of mathematics.
As for cleaning up curricular mathematical language, ST Math doesn't do that, of course. I had mentioned that as something we educators need to do if we are to help students become fluent with mathematical language and to help clarify to our own students what we are talking about. Clyde Greeno and Alain Schremmer and I have noticed some mess in curricular language. These discussions can be found on MathTeach and Mathedcc. For those interested, I can give more details about where to find some of this information.
I had begun noticing the mess consciously a while ago when I had noticed that curricular language does not generally make it clear what the difference is between a fraction and a ratio or what the differences are when working with real numbers as real numbers (that is, as elements of an algebraic structure) versus working with real numbers that represent counts or measurements. We can add any two real numbers, but can we add 12 liters and 14 meters? The real number division 134/23 makes sense, but what about 134 miles divided by 23 hours? Does that make sense? If it does, what does it mean? It certainly cannot have the same meaning because in, 134/23, both 134 and 23 are expressed in terms of the same unit; that is, 134 is 134 times 1, and 23 is 23 times 1. Both 1's are the same. But in 134 miles/23 hours, if it even makes sense, 134 miles is 134 times 1 mile, and 23 hours is 23 times 1 hour. But 1 mile and 1 hour are not the same thing! Curricular language does not help here because it does not generally distinguish between the arithmetic of real numbers (as real numbers) and the arithmetic of counts and measurements.
ST Math does not teach language and symbolism, so that is up to us to do. But making language and symbolism clear requires precise language, but unfortunately curricular languageat least in the United Statesis highly imprecise.
Jonathan Groves



