Following is from the September 26, 2012, edition of Education Week. Candace Walkington is an Assistant Professor in Teaching and Learning in SMU's Simmons School of Education and Human Development, specializing in mathematics education. Her research examines how abstract mathematical ideas can become connected to students’ concrete, everyday experiences such that they become more understandable.
October 4, 2012
By Sarah D. Sparks
While "personalization" has become a buzzword in education, it can be hard to determine what really makes a subject relevant to individual children in the classroom. An ongoing series of studies at Southern Methodist University suggests learning students' interests upfront and incorporating them into lessons can get struggling students to try harder and substantially improve their performance in algebra.
"You don't think the words, the little details of context, will make a difference when you are solving a math problem, but it really does," said Candace A. Walkington, an assistant professor of teaching and learning at Southern Methodist in Dallas and the lead researcher for the reports. The most recent of them is expected to be published later this year in a special issue of the Journal of Educational Psychology on advanced learning technologies.
The studies, which were discussed at a recent meeting here at Carnegie Mellon University, highlight one way to boost learning in algebraic expression, a concept considered critical in the Common Core State Standards but which educators say is perennially challenging to students. The study found that personalized math problems not only made it easier for students to understand what was being asked, but also helped boost the confidence of students who may have been intimidated by the subject.
Word problems at any level can be challenging, but Michael Shaughnessy, a mathematics and statistics professor at Portland State University in Oregon and the immediate past president of the National Council of Teachers of Mathematics, said it is particularly difficult for students to make the switch from looking at a concrete arithmetic problem—the cost of a sweater on sale for 20 percent off, say—to the generalized arithmetic in algebra, such as an equation for finding the cost of any item in a storewide 20 percent-off sale.
"That process is one of the harder things in the algebra trajectory to do," Mr. Shaughnessy said.
Steven Ritter, the founder and chief scientist at Carnegie Learning Inc., a Pittsburgh-based publisher of math curricula, had seen similar problems while designing his company's Cognitive Tutor software. Administrators found students who had learned how to identify an equation using a positive slope in one word problem showed no transfer of skills to identify a problem using a negative slope. Small changes to contextual details completely threw them.
In one high-poverty Texas school using the software, Ms. Walkington thought she saw a reason why students weren't making those logical connections. Many didn't relate to the question scenarios, which were often about harvesting grain or building greenhouses.
"If [a student is] already pretty fluent in math and has a high level of interest in math," Ms. Walkington said, "it doesn't really matter how you dress up the problem, they see it as what it is: a math problem, linear equation in this case."
Struggling learners, by contrast, often had little self-confidence in math. They weren't sure how to approach problems and often wouldn't even attempt them, even if they had just completed similar problems in class.
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