Shirley M. Matteson

Mathematical Literacy and Standardized Mathematical Assessments.

Mathematical literacy is an important skill that is gaining the attention of mathematics educators. Students are increasingly challenged on standardized assessments to read, create, use, and comprehend numerous mathematical representations as a way of demonstrating mathematical literacy. Test items assessing algebra concepts from the Texas Assessment of Knowledge and Skills (TAKS) test for Grades 3 through 8 were used for the study. The study examined the frequency and categories of external representations used to present and solve assessment items. The analysis showed a heavy emphasis on verbal representations even though algebra items were to use verbal, numerical, graphical, and symbolic representations. The variety of representations on assessments has implications for professional development opportunities for mathematics educators.

Extricating Justification Scheme Theory in Middle School Mathematical Problem Solving.

Abstract Twenty middle grades students were interviewed to gain insights into their reasoning about problem-solving strategies using a Problem Solving Justification Scheme as our theoretical lens and the basis for our analysis. The scheme was modified from the work of Harel and Sowder (1998) making it more broadly applicable and accounting for research developments in the cognitive sciences. During cognitive interviews, students reasoned about their solutions to four contextualized problems. We use student interview excerpts to define the four major categories of Mechanistic, Authoritarian, Language, and Visual of the justification scheme and to elaborate on the various sublevels. Analysis of cognitive interview transcripts revealed combinations of justifications leading to both successful and unsuccessful problem-solving strategies. The major difference between these strategies was the ability to correctly select a representational aspect of the problem that triggered a correct solution strategy.