Enhancing prospective teachers’ views of doing mathematics: Documenting and reflecting on mathematical investigations

ABSTRACT

Too often, students are merely consumers of mathematics, without many opportunities to engage in authentic processes of doing mathematics. As a mathematics teacher educator, I decided to provide more opportunities for my prospective teachers (PSTs) to do so. In my mathematics class for elementary education majors, the PSTs worked on two low-threshold high-ceiling doing mathematics investigations. For each investigation, the PSTs recorded their thinking in math notebooks and prepared a concluding write-up, describing their mathematical findings and personal experiences. The PSTs also completed a final written reflection describing changes in their views on doing mathematics. For 29 PSTs, I analyzed the thoroughness of their math notebooks, the quality of their mathematical work and reflections, and their perceptions of doing mathematics. A majority of the PSTs thoroughly captured their work in their math notebooks, three-fourths of them included mathematical findings of a proficient nature in their write-ups, and all of them richly described their personal experiences with the investigations. Most encouraging, the PSTs enhanced their perceptions of what doing mathematics entails as a result of engaging in and documenting their authentic experiences of doing mathematics paired with intentional reflections on such experiences. These enhancements occurred regardless of how the PSTs performed mathematically on the investigations.

KEYWORDS:

• Doing mathematics tasks
• low-threshold high-ceiling mathematical tasks
• math notebooks
• writing-to-learn mathematics