Technology helps students understand reasoning behind math

UNIVERSITY PARK, Pa. -- Using technology in the classroom can help students succeed in math according to Kathleen Heid, distinguished professor of mathematics education at Penn State. In a recently published book chapter titled “Using Computer Algebra Systems to Develop Big Ideas in Mathematics with Connections to the Common Core Standards for Mathematics,” Heid and Rose Mary Zbiek, professor of mathematics education, discuss how teachers who use computer algebra systems (CAS) can help students better understand mathematics and effectively apply it to the world around them.

CAS is mathematics technology in the form of calculators or software that can solve complicated math problems and generate exact answers to algebra problems that students traditionally produce by hand. CAS typically include linked graphical, symbolic and numerical capability. Heid and Zbiek maintain that educators who utilize this technology to aid in the teaching and learning of math can help students learn and do more than ever before.

“Imagine having available a calculator that actually took derivatives or simplified equations or solved equations with exact answers, not approximate. That’s what’s available right now,” said Heid. “Currently, as a mathematics education community, as people who are interested in kids learning math, we are not yet capitalizing on the availability of technology in mathematics classrooms.”

According to Heid, the content of today’s school mathematics is often thought about as a list of procedures that students need to know how to do. She said that too often these procedures are learned primarily through rote symbolic manipulation, and that far too often students do not know when to use these procedures in solving real world problems. She suggests that mathematics teachers use CAS to enhance the student experience by allowing the powerful technology to do the calculating when producing those answers are not the focus of lessons. This delegation of work frees educators to focus on teaching the reasoning behind mathematics, to develop a framework that helps students see mathematics as unified whole, and to engage students in becoming real-world problem solvers. Moreover, by teaching the reasoning behind mathematics and providing students with that framework, students can develop a deeper understanding of the mechanics more quickly, according to Heid.

“Our goal is to teach mathematics so that people see it as useful, and see it as something with which they can solve problems, and technology can help us to do that,” said Heid.

In addition, Heid does not believe that technology detracts from mathematics. In fact, she said that it enhances mathematics because students are free to use technology to engage in mathematical investigations that would have in the past taken a very long time.

“Research shows that unless a math problem can be completed within a couple of minutes, students will give up on it,” said Heid. “If students have this kind of (power) at their fingertips, they could conceivably do mathematics that is far beyond what they are asked to do at this point.”

To help teachers employ this powerful tool, Heid said that the College of Education requires secondary math education majors as prospective teachers to take a class in using technology in the teaching and learning of math. Penn State is one of only a few institutions of higher learning that requires such a class in their teacher certification programs.

Zbiek and Heid’s work is published in "Curriculum Issues in an Era of Common Core State Standards for Mathematics" edited by C. Hirsch, G. Lappan and B. Reys.

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Last Updated March 21, 2013