Rationally speaking, it’s been a great research project

The Rational Number Project is wrapping up, but even after 23 years, questions remain. In the world of research that’s good, not bad.

“It’s the longest-lasting federally funded cooperative research project in the history of math education,” says Tom Post, professor of math education and a principal investigator on the project for 18 years. “But the more questions you answer, the more you find when you have a great research topic.”

And rational numbers qualifies as a great topic, Post says. (For the mathematically challenged, “rational numbers” refers to concepts including fractions, decimals, ratio, and measurement.)

Post and his colleagues wanted to find out the best ways to teach rational numbers, methods that would best help children learn about these basic concepts. Through this work and other research, Post has become a strong believer in concrete, constructivist systems for teaching math based on theories of cognitive development.

What that means in the classroom is creating an environment within which the mathematics occurs. Instead of worksheets filled with fraction exercises, for example, students read a story about children planning a bike trip. Students then do a series of calculations involving fractions or some other math concept that allow them to determine the best choices for the bike trip plan.

How the research has been done

The researchers in the study, funded by the National Science Foundation, examined, among other things, proportionality and the contributions of multiplication and division understandings to rational number concepts.

“We then proceeded to concern ourselves with the design of effective professional development programs for teachers that are based on the research,” Post says. “We’ve also designed appropriate assessment practices to help us evaluate these approaches.”

The project included 10 to 12 years of studies with children, Post says, “looking both at how they come to understand these concepts and, perhaps even more importantly, how they come to misunderstand them.

“People are realizing, for example, that fractions—how they’re being taught and how students continue to struggle with them—are a major problem. Something needs to change and our work with the Rational Number Project points in a constructivist direction for that change.”

What has resulted from the research

The project has culminated with almost 90 papers and articles produced (see them online at cehd.umn.edu/rationalnumberproject). It also has led to three mathematics courses designed specifically for elementary teachers who traditionally do not have significant math backgrounds, and two curriculum textbooks for teachers that reflect classroom teachers’ suggestions as to how rational numbers should be taught to children.

Post and his co-investigators, including Kathleen Cramer, associate professor of math education in the college, have produced a CD that contains all of the published articles connected with the project.

Other universities involved in the 23-year project are: Northern Illinois University, Purdue University, University of Wisconsin-River Falls, University of California-San Diego, University of Michigan, and Universite of Osnabruck, Germany.

What others say about the Rational Number Project

Richard Lesh, R.B. Kane Distinguished Professor, associate dean for research, and director of the School Mathematics and Science Center in the School of Education at Purdue University, says, “This sustained research effort is one-of-a-kind in the fields of mathematics, science, and technology education, and it is unquestionably one of the most influential bodies of work in the field of mathematics education.

“It has radically influenced the ways mathematics educators think about what it means to ‘understand’ basic mathematical concepts—ranging from fractions, to ratios, to rates, to proportions—that are among the most troublesome for students to learn in the entire K–16 mathematics curriculum.

“Insights from Post’s work have significantly influenced the famous Curriculum Standards that were published by the National Council of Teachers of Mathematics. They have been used as the main theoretical foundations for innovative curriculum materials ranging from books to software for children and/or their teachers.

“Furthermore, Post (and the Rational Number Project in general) has provided a launch pad for dozens of people who have developed into leaders in the mathematics education community. His work also has strongly influenced the national curriculum materials for countries such as Israel, Taiwan, and the Netherlands—whose students typically rank among the best in the world on international assessments of educational achievement.”

Kathryn B. Chval, acting head of teacher enhancement with the National Science Foundation, says, “Professor Tom Post’s research on student and teacher learning in the domain of multiplicative concepts, relationships, operations, and problem situations has been utilized by authors who have written mathematics curricula and by facilitators of professional development for teachers. His commitment to the schools, teachers, and children in Minnesota is witnessed by his work on two Teacher Enhancement projects funded by the National Science Foundation, providing support structures for teachers and helping them advance their mathematical knowledge and teaching practice.”

Beatriz D’Ambrosio, chair of the Research Advisory Committee of the National Council of Teachers of Math, and math education professor at Indiana University-Purdue University, Indianapolis, says, “Tom Post has pioneered research in children’s understanding of rational numbers. His collaborative research in this area has helped advance both theory and practice. He is one of the few researchers in mathematics education who has an established research agenda and worked tirelessly for several decades to advance the knowledge base, thereby making significant contributions to the mathematics education community.”

Thomas Carpenter, math education professor, University of Wisconsin, Madison, says, “The Rational Number Project has been one of the longest continuous focused programs of research in mathematics education and represents a model for the field. It is one of a collection of projects that have pioneered the way for integrating a deep analysis of mathematics content, the study of the development of children’s understanding of that content, and instruction that supports that development.”

Why this research matters

“By creating an environment where kids can talk about the mathematics, the teacher allows the students to internalize the math,” Post says. “This approach takes mathematics from simple exercises to activities that allow for reflection, working with others, and truly understanding the concepts. This is kid-friendly material with academic validity.”

March 2003