My work as a researcher, outside of my dissertation, began in 2001 when I joined the Valle Imperial Mathematics project (NSF funded). Consistent with my belief that changes in teaching practices must occur when students are not able to understand the content, this project focused on helping K-8 teachers learn how to use student thinking to guide their instruction. For five years I documented changes in teacher instructional strategies and student solution strategies. Through this work I have gained insights into the challenges that teachers face when they try to change their teaching strategies which has given clearer focus to my research agenda as I explore these issues in more depth.

One big challenge that mathematics teachers face is finding the right balance between helping their students achieve conceptual understanding and addressing all state/district content standards in a timely manner so students can excel in statewide examinations. Novice and experienced teachers alike are hard pressed to find such a balance in their classrooms with their students. One way to address this issue is for teachers to emphasize key mathematical concepts in their lessons. Essential towards achieving this end is to help teachers discover, or rediscover, the core ideas for a given mathematical concept and experience different ways of learning that same concept. The intent is to facilitate changes in instructional practices so teachers can help their students see mathematics as much more than just a set of unrelated rules and procedures to memorize before the next test.

Through my work with teachers and student teachers, I have established three strategies to help them determine the core ideas of a given mathematical concept. I am now working with teachers and student teachers to help them understand how to incorporate the core ideas of a given mathematical concept into their lessons. Of particular importance is to continue investigating and documenting how these interventions change teacher content knowledge, the strategies they use in their classrooms, and the improvement of student understanding.

I emphasize that these activities merge upon a research agenda centered upon informing the educational community of specific and effective aspects of teacher professional development in mathematics, particularly in the area of algebra, that support changes in instructional practices to enhance student learning of mathematics.