# An Approach that Works

We now have ample evidence that traditional, lecture-based forms of mathematics instruction do not work for most students. Passively listening to someone else explain mathematics is a poor way to learn it. To help students learn, they must be actively engaged in making sense of the mathematical ideas.

# What Does this Mean in Practice?

Effective active learning happens when students:

- are involved in making meaning of the new mathematical ideas they encounter,
- challenged to discover relationships among and uses for the mathematical ideas they know, and
- prove their own theorems.

Learning by Inquiry is a pedagogical approach with a long pedigree, rooted in the work of Dewey and Piaget. It is a structured approach to learning mathematics, leading students through a succession of ever more challenging problems and proofs that force them to build a coherent understanding of mathematical ideas and concepts. Its goal is nothing less than equipping them to determine when and how particular techniques or approaches might be used in solving an unfamiliar problem. It takes the focus off the instructor and onto the students who spend class time wrestling with problems and proofs they have never seen before, but have been carefully chosen so that they can find their way through to a solution.

Mathematical learning by inquiry can be described as integrating three components into the teaching and learning process:

- Active Learning: Students work, independently and in guided groups, on challenging problems relevant to the concept to be learned.
- Meaningful Applications: Students explore applications that are meaningful to their degree and career pathway and relevant to the concepts to be learned.
- Academic Success Skills: Students participate in problem solving, persistence, and learning from mistakes in a manner that enables a growth mindset for continued productive engagement throughout their education and careers.

A **ninety-second introduction to Learning by Inquiry** by Michael Starbird, University of Texas Distinguished Teaching Professor in the Department of Mathematics at the University of Texas at Austin:

Dr. Jo Boaler of Stanford University explains Learning by Inquiry in mathematics with secondary students: