Problem-Based Learning in Math Home Page

What is Problem-Based Learning?

A Problem to Solve

Problem-Based Learning is apprenticeship for real-life problem solving (Stepien, Gallagher, &Workman, 1993; Stepien & Gallagher, 1993). The central concept of Problem-Based Learning, PBL, is that students will learn content as effectively as through lecture by attempting to solve realistic problems (Ward & Lee, 2002). Learning begins with a problem to be solved, and the problem is posed in such a way that students need to gain new knowledge before they can solve the problem (Roh, 2003). In PBL students assume the roles of scientists, historians, doctors, or others who have a real stake in the proposed problem (Stepien & Gallagher, 1993). Students now acquire information from resources other then the teacher. Teachers are guides; helping students to answer the posed problem. Students are active participants in their learning, constructing new knowledge on top of concepts and ideas they already know.

More specific information about the teacher and student roles is discussed in Unit II.

Benefits of Problem-Based Learning in Math

Problem solving skills

PBL, by definition, helps increase students’ problem solving skills. Students must use the skills that they have and expand on them by exploring, questioning, and investigating. When using problems as the center of learning, a shift takes place from “doing” the activity to “thinking” about relationships among mathematical ideas and how they connect to help students make sense of these ideas (Trafton & Midgett, 2001). The teacher can only be a guide; students must learn to direct themselves.

Creativity

Creativity is the high-dimensional human ability or skill to think up something new, and has drawn much attention in every field of education that attempts to cultivate the fundamental power of thinking and reasoning (Kwon, Park, & Park, 2006). When a problem is posed that does not have an immediate solution, students are forced to think creatively. Different types of problems also expand creative thinking; the more variation in problems, the more variation in thinking.

Make connections

Since students are not given all of the information, like with lectures, they must draw upon what they know and find connections in order to make progress. At every step along the way, students must pose questions, look for patterns, and make connections between the current problem and the mathematics they have learned in previous units (Alper, Fendel, Fraser, & Resek, 1996). Students can also make connections between mathematical ideas that are familiar to them by solving new problems in a variety of different settings (Erickson, 1999).

Key Factors for successful Problem-Based Learning in Math

Motivation

One of the main goals of PBL is to get the students more involved in their education, give them some ownership. But in order for PBL to be an effective strategy, students must be motivated to fully participate. They can only get out what they put in. This same idea applies to teachers as well.

Another issue with motivation deal with how engaging or interesting the posed problem is. Teachers usually have their own sense of what problems are interesting to solve, and they are not ususally the same types of problems that students are eager to solve.

Time

Time is also a key factor to condsider when it comes to PBL. There are not many resources, curriculum plans or textbooks, available which encourage PBL. Few teachers have the time or the motivation to prepare all new materials for classes (Ward & Lee, 2002). PBL activities can also require more time for investigation then is allotted for in a class period.

Changing roles of teacher & student

In traditional classrooms, teachers are the experts and pass on their knowledge to the students through lectures and structured activities. PBL switches the roles of both teacher and student. Teachers must step back from “being in the driver’s seat” and allow the students to take over. This is challenging for some teachers who like to have control of the class. The teacher is now a guide, not a director. As for the students, they now have to branch out on their own and contend with problems in a less structured environment. This is contradictory to how they have been taught throughout their schooling.

Think About It

Do you see some of the possibilities for PBL in your classroom?
What other benefits or key factors do you think would be present when implementing PBL?

Continue on to Unit II: Teacher & Student Roles

Resources

Roh, K. H.(2003). Problem-Based Learning in Mathematics. ERIC Digest. www.eric.ed.gov
Stepien, W. & S. Gallagher.(1993). Problem-Based Learing: As Authentic as It Gets. Educational Leadership, 50(7), 25-28.
Stepien, W., S. Gallagher, & D. Workman. (1993). Problem-Based Learning for Traditional and Interdisciplinary Classrooms. Journal for the Education of the Gifted, 16(4), 338-357.
Ward, J. & C. Lee. (2002). A Review of Problem-Based Learning. Journal of Family and Consumer Sciences Education, 20(1), 16-26.

Course Links

Problem-Based Learning in Math Home Page

Unit I: What is Problem-Based Learning?

Unit II: Teacher & Student Roles

Unit III: Planning & Activities

Additional Resources