Measuring Task Posing Cycles: Mathematical Letter Writing Between Preservice Teachers and Algebra Students

In a secondary school mathematics teaching methods course, a research team engaged 22 preservice secondary teachers (PSTs) in designing and posing tasks to algebra students through weekly letter writing. The goal of the tasks was for PSTs to elicit responses that would indicate student engagement in the mathematical processes described by NCTM (2000) and Bloom’s taxonomy (Bloom, Englehart, Furst, Hill, & Krathwohl, 1956), as well as student engagement in the highest levels of cognitive activity described by Stein, Smith, Henningsen, and Silver (2000). This paper describes our efforts to design reliable measures that assess student engagement in those processes as a product of the evolving relationship within letter-writing pairs. Results indicate that some processes are easier to elicit and assess than others, but that the letter-writing pairs demonstrated significant growth in terms of elicited processes. Although it is impossible to disentangle student factors from teacher factors that contributed to that growth, we find value in the authenticity of assessing PSTs’ tasks in terms of student engagement rather than student-independent task analysis.