CAREER: Coherence as a Basis for Understanding Teachers’ Mathematical Knowledge for Teaching

Principal Investigator: 
Project Overview
Background & Purpose: 

The proposed research activities focus on investigating mathematical knowledge for teaching from the perspective of coherent understanding. To this end, this mixed methods research effort will begin with the development of a series of profiles of understanding that characterize the relationship between the amount of content knowledge participating teachers have and the ways in which they have mentally organized that mathematics. Then, profiles of understanding will be linked to observable classroom practices to develop profiles of practice that capture the interrelationship between understanding and practice.

Setting: 

Middle school classrooms with data collection beginning in Spring 2012.

Research Design: 

The project will generate evidence that is descriptive [case study, observational, and clinical interviews]. Original data are being collected on middle school mathematics teachers using assessments of learning, observation [personal observation and videography] and survey research [paper & pencil and face-to-face]. Instruments or measures being used include clinical interview, LMT for proportional reasoning, and the Proportional Reasoning instrument from Diagnosing Teachers' Multiplicative Reasoning.

Analysis will include using Epistemic Network Analysis to understand how teachers make sense of proportional reasoning and the interactions of that knowledge to their classroom practices. This effort will include qualitative and quantitative analysis of clinical interview data. Analysis will also include consideration of the relationship between the ENA results and the results of the two nationally-validated instruments designed for measuring teacher knowledge to determine the relationship between quantity of knowledge and organization of knowledge. Hill's LMT data will be reanalyzed using a mixture Rasch model (she used a traditional IRT model).

Findings: 

Findings will be posted as they become available.