MATH: What's the Problem? — Text-only | Flash Special Report
Forget the overheads and film strips shown to passive students in yesteryear. Today’s technology can engage students directly in doing mathematics, support the learning of concepts, offer customized instruction and tutoring, and leave a trail of data to gauge impact. Here, we highlight two technologies whose initial development was funded by NSF in the 1990s. Both SimCalc and Cognitive Tutors have since been commercialized and their use in school districts has been studied in terms of student progress and results. To give some perspective on technology and how it can, under specific conditions, help students succeed at math are Ken Koedinger, professor of human-computer interaction and psychology at Carnegie Mellon University and Jeremy Roschelle, director of the Center for Technology in Learning at SRI International.
JEREMY ROSCHELLE:I think when people are saying, “I don’t need anymore math and arithmetic,” they’re looking at one kind of math, which is sort of shopkeeper math and maybe they’ve had enough to be a shopkeeper. When you’re looking at people who are innovators and driving the future of the economy, they’re look at math as a tool kit that allows you to do new science, engineering, and innovation, and that’s not about adding numbers.
JEREMY ROSCHELLE: You know, many parents and people have some images of what technology could bring and they think it’s fun or it’s engaging or it’s games, and all those things are nice, but, really, what the research has shown is some deeper reasons that we should use technology, and one is the ability to bring concepts to life. When you can put the concepts in a digital interactive, often dynamic, or animated form, students are much more able to really understand mathematical concepts and when they understand the concepts, they perform much better.
JEREMY ROSCHELLE: Part of math literacy is really graphing literacy because one of the representations that you see in newspapers is graphs. Part of it is being able to read tables and not just see them as piles of numbers, but see mathematical relationships in the tables. Part of it is being able to look at formulas in algebra and make some sense of that and then to relate that to the events you’re trying to explain or predict, and that’s the storytelling. So, what SimCalc really aims to do is connect these things in the experience of the students and the teacher.
STUDENT: The space between the dots gets bigger.
TEACHER: The space between the dots gets bigger. What do you mean?
STUDENT: It, like, skips – the line is –
TEACHER: Hold on. One at a time. Carson, finish your thought. Go ahead.
STUDENT: The, like, dots are closer and then once it gets [inaudible].
KEN KOEDINGER: Math is a book about being able to express yourself, to communicate ideas, but it’s also about, you know, part of communicating, you know, ideas. So, if you’re going to understand issues like interest rate. You need to be able to read mathematics, right? You need to be able to understand it as a language.
KEN KOEDINGER: Well, Cognitive Tutors grew out of past research in cognitive science and that research was on how people learn, sort of understanding how the brain works, but also on how we can get technologies to essentially simulate student learning. While it is an advanced technology and it’s tutoring students in a one-on-one way like a human tutor does, it’s not replacing the teacher. So, it has this function of being able to zero in on those needs that a student has, where they struggle and what do they not know and gives instruction just on that. That’s the technology component, but it’s also embedded in a full classroom so two days a week students are using this technology, typically. Those other three days a week they’re in a regular classroom. The materials are designed to help students appreciate why algebra is important by connecting them to real world problem solving, but what’s nice is, in the computer lab, those kids that are somewhat falling behind, they’re not left behind. They get help where they need it. Those kids that are racing ahead, they’re being challenged. They’re doing things that are interesting. So, we found that it’s not just about mathematical achievement and getting the concepts, it’s also more engaging for students because they feel like they’re really making progress. They’re having success experiences and the harder they work, the better they do.