The Relationship of Implicit Theories to Elementary Teachers’ Patterns of Engagement in a Mathematics-Focused Professional Development Setting

As elementary teachers aim to deepen their mathematical understandings, they engage in a relearning process that involves not only revisiting but also reconstructing their knowledge. To do so, meaningful engagement in immersion and practice-based experiences is required. This exploratory case study investigated the engagement patterns of two elementary teachers with varying implicit beliefs as they participated in a professional development that focused on relearning mathematics. Data were collected on the two participants in the form of video narratives, observation protocols, and interviews. Attention was given to their patterns of engagement in collaborative group settings as the participants moved through different phases of the professional development lesson. Results indicated that the engagement patterns of the two participants closely aligned with learning behaviors described in the implicit beliefs theory. In this way, the results suggested an extension of the implicit theories model to the relearning context. Additional implications and future questions are provided

An Emergent Framework: Views of Mathematical Processes

The findings reported in this paper were generated from a case study of teacher leaders at a state-level mathematics conference. Investigation focused on how participants viewed the mathematical processes of communication, connections, representations, problem solving, and reasoning and proof. Purposeful sampling was employed to select nine participants who were then interviewed and observed as they presented a session at the conference. Participants\u27 statements revealed differences in their views of mathematical processes. The analysis led to an emergent framework for views of mathematical processes that includes three levels: participatory, experiential, and sense-making. Implications are shared for mathematics methods instructors, professional learning, and research. Discussion also relates the framework to the Standards for Mathematical Practice