CAREER: Examining Prospective Teachers’ Learning of Three Mathematics Teaching Practices--Posing, Interpreting, and Responding--During Teacher Preparation

Principal Investigator: 
Project Overview
Background & Purpose: 

This project is studying the development of prospective teachers’ understanding and enactments of mathematics teaching practice, as they move from course work, to preparatory teaching, and into regular teaching positions. The project involves conceptual and empirical work related to three specific practices of mathematics teaching---posing mathematical tasks, interpreting students’ mathematical work, and responding to students’ ideas---that teachers constantly perform in classrooms. It seeks to define and then unpack these practices with greater precision and with the goal of broadening what might be considered competent performance of these practices, especially for those just beginning their formal studies of mathematics teaching. It uses cross-sectional and longitudinal study designs. The educational goal of the project is to explore ways of making these practices an object of explicit study in mathematics teacher education classrooms.


The questions investigated are pursued in various contexts. The context for the cross-sectional study is the teacher preparation program at Michigan State University. This includes the program’s courses and school field experiences. The school field experience classrooms are typically close to the campus of the University up to year 4 (senior year) in the program. Then the teacher candidates spend a year-long internship in one school’s classroom during the 5th year. These internship schools are in several geographic locations within the State of Michigan (typically within three main urban areas: Lansing, Grand Rapids, and Detroit): in the past year the program has also added internships in Chicago, Illinois. For the longitudinal phase of the project, we have two concurrent studies. One is following teacher education students at the start of the program for 2 years up to their Internship year. The other study is following 8 graduates of the program to their first and then second year of teaching. Two of these participants are teaching in Michigan while the other six are teaching out-of-state. The participants are teaching a range of grades from preschool to 5th grade in urban, suburban and rural schools.

Research Design: 

This is a longitudinal and cross-sectional study designed to generate descriptive [case study, observational] and associative or correlational [interpretive commentary, quasi-experimental] evidence. Original data are collected through diaries, journals or records kept by study subjects; observation [personal, videographic]; and survey research [self-completed questionnaire, semi-structured interviews]

The PIR paper-pencil survey has been completed by a total of about 350 teacher education students; about 120, 150, and 70 students from each of three stages in their teacher preparation program – before taking math methods, during math methods, at end of program. All students enrolled in year 3, 4, and 5 of the TE program during 2007-2008 were invited to participate. About a third of the students in each of the cohorts elected to be part of the project. This data was all collected by Spring 2008.

In the Fall 2008 we began the longitudinal phase of the project. A group of 8 students at the initial phase of teacher preparation were selected from the survey participants (based on their willingness to participate in longitudinal phase of the project, academic background and experiences such as math minors or child development majors, responses to the survey questions). Another group of 8 students graduating from the program were also selected for longitudinal study. Those participating in the survey and indicating interest in the longitudinal phase of the project were contacted via e-mail in the Fall of 2008. Those who replied and were employed with their first teaching position are included in the project.

The project is still in the process of analyzing data. Several methods are being employed. Each of the PIR tasks are analyzed using coding rubrics developed with an open-coding approach and then using multiple raters and reliability studies to stabilize the coding rubric The cross-sectional responses to each task are then compared using quantitative and qualitative analyses. The case study data (interviews, classroom observations) will be analyzed using various qualitative tools to build rich descriptions of the participants’ practices.


Based on our interviews with instructors that teach math education courses across the MTH (2 course supervisors, and 1 instructor) and TE (2 course supervisors, 1 instructor) departments we learned that all three courses focus most prominently on the practice of posing mathematics problems and interpreting students’ mathematics. We also learned that the practice of responding, however, is not studied at all in the MTH 201 course, and receives moderate attention in the last course (TE 801) of the math ed course sequence. This finding was also confirmed when the analysis was performed on the course texts and syllabi. We suspect that this is likely the case in other teacher preparation programs.

The P-I-R script generation tasks elicit an enactment of teaching practice that is more dynamic (than static). They elicit an imagined enactment that has a longer timeframe than an enactment that is suspended or frozen in time. We expect that the generated scripts from the participants in the project will tell us something about PIR practices that the other more static tasks do not. We hypothesize that the scripts of those farther along in the program will look different than the scripts from those students who had just started their formal study of mathematics teaching.

Publications & Presentations: 

Crespo, S., Oslund, J., Brakoniecki, A., Lawrence, A., Thorpe, J. (in Press). Learning to interpret students’ mathematical work: Studying (and mapping) preservice teachers’ practices. Proceedings of the 31st annual meeting of the North American Chapter of the Psychology of Mathematics Education. Atlanta, GA: Georgia State University.

Brakoniecki, A. (In Press). Mathematical knowledge for teaching exhibited by preservice teachers in responding to mathematical and pedagogical contexts. Proceedings of the 31st annual meeting of the North American Chapter of the Psychology of Mathematics Education. Atlanta, GA: Georgia State University.

Crespo, S., Oslund, J. A., & Parks, A. (2007) Studying elementary preservice teachers' learning of mathematics teaching: preliminary insights. (pp. 975-982). In Lamberg, T., & Wiest, L. R. (Eds.). Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Lake Tahoe, NV: University of Nevada, Reno.

Other Products: 

The project has generated a new sort of instrument and task items for the study of math teaching practice. Additionally the project generated its own classroom observation and interview protocols. The project is also generating pedagogical applications of some of the project tasks to be used as instructional tools with pre-service and in-service teachers.