Learning and Assessing Mathematics through Reading and Writing

Michael J. Bossé and Johna Faulconer

Students learn mathematics more effectively and more deeply when reading and writing is directed at learning mathematics. Although reading and writing in mathematics may necessitate more skills and practice to master, the mathematical learning derived from reading and writing mathematics far outweighs the burden it places on teachers and students. This paper explores the vital role of purposeful reading and writing in the mathematics classroom and outlines some techniques to promote successful integration of reading and writing in mathematics.

Focusing on Units to Support Prospective Elementary Teachers' Understanding of Division in Fractional Contexts

Hyung Sook Lee & Paola Sztajn

This theoretical paper proposes a way to extend the partitive and measurement interpretations of whole number division to fractional contexts focusing on the issue of units. We define the unit-changing and unit-keeping interpretations for division and suggest a stronger and earlier focus on the concept of units in courses for prospective elementary teachers. As we highlight the importance of the concept of unit, we use the proposed interpretations in the analysis of one example that emerged in our methods course, discuss the idea of inverting and multiplying, and suggest implications for teacher education.

David's Understanding of Functions and Periodicity

Hope Gerson

This is a study of David, a senior enrolled in a high school precalculus course. David's understandings of functions and periodicity was explored, through clinical interviews and contextualized through classroom observations. Although David's precalculus class was traditional, his understanding of periodic functions was unconventional. David engaged in sense making behaviors even though these behaviors were not encouraged or explicitly taught. A careful analysis of his work revealed that DavidÕs understandings of functions, function notation, and periodicity were compartmentalized. However, David was able to skirt compartmentalization through flexibility in problem solving, translation between representations, and transfer of mathematical information from one representation to another.