P. Beites1, A. Nicolás2

1Departamento de Matemática da Universidade da Beira Interior and CMUBI (PORTUGAL)
2Departamento de Matemática Aplicada de la Universidad de Valladolid and IMUVa (SPAIN)
The origins of Peer Instruction go back to the 1970s, at Arizona State University. David Hestenes, Professor of Physics at the mentioned university, suspected that the reason for the low class average on the exams of a colleague was that students learned problem solving without really getting the concepts. He and Halloun, one of his graduate students, developed and applied the Force Concept Inventory (FCI), which is a multiple-choice test that probes students' Physics conceptual understanding. Students didn't do very well, the results were published but a lot of instructors ignored the study. Eric Mazur, after giving the FCI to his students, was shocked. Hestenes says that ''He was the first one who took it to heart.'', [2].

Peer Instruction was developed in the early 1990s by Mazur, a prominent physicist and educator at Harvard University. In 1991, he started to design the mentioned method and, in 1997, published [3] - the Mazur's step-by-step guide for planning and implementing Peer Instruction lectures. In 2001, Mazur and Crouch (member of the Mazur Group till 2003) reported data from ten years of teaching through Peer Instruction. The results therein ''... indicate increased student mastery of both conceptual reasoning and quantitative problem solving upon implementing Peer Instruction.'', [1].

The main characteristic of Peer Instruction is the transformation of the student's role from that of a passive participant to an active participant in the teaching/learning process. This is achieved through: reading incentives, engaging every student in the material; voting events, related to concept questions, in classroom and peer students discussions. Regarding the latter, reactions from students around the room are expected when they grasp the logic. Moreover, the instructor has to embrace a new environment that involves abandoning a measure of control.

The teaching of undergraduate Linear Algebra is a concern for both Linear Algebra instructors and Mathematics Education researchers. In fact, many students master the procedures but do not grasp the concepts. Inspired by Peer Instruction in Physics, we present didactic material for teaching Linear Algebra through the mentioned teaching/learning methodology. Concretely, we construct concept questions based on students' misunderstandings in order to improve the teaching of Linear Algebra and to promote a meaningful learning. Furthermore, we reflect on their implementation, and collect students' opinions regarding traditional lectures and Peer Instruction ones.

[1] Crouch, C., & Mazur, E. (2001). Peer Instruction: Ten years of experience and results. American Journal of Physics 69(9), pp. 970-977.
[2] Hanford, E. (2012). The problem with Lecturing. Accessed February 2013.
[3] Mazur, E. (1997). Peer Instruction: a user’s manual. Upper Saddle River: Prentice Hall.