This is a 3.5-year efficacy study of the Developing Mathematical Ideas (DMI) elementary math teacher professional development (PD) program. DMI was developed by staff from Education Development Center (EDC), SummerMath for Teachers, and TERC, the STEM research and development institution responsible for this research. DMI is a well-known, commercially available PD program with substantial prior evidence showing its impact on elementary teachers' mathematical and pedagogical knowledge. However, no studies have yet linked DMI directly with changes in teachers' classroom practice, or with improved student outcomes in math. This study aims to remedy this gap.

The research questions for the study are:

1) Does participation in the Developing Mathematical Ideas (DMI) professional development program lead to increases in reform-oriented teaching?

2) Does participation in DMI lead to increases in students' mathematics learning and achievement, especially in their ability to explain their thinking and justify their answers?

3) What is the process by which a reform-oriented professional development program can influence teaching practice and, thus, student learning? Through what mechanisms does DMI have impact, and with what kinds of support do we see the desired changes on our outcome measures when the larger professional development context is examined?

The dependent variables for this study include a) teachers' pedagogical and mathematics knowledge for teaching; b) the nature of their classroom practice; and c) student learning/ achievement in mathematics.

The study uses experimental and quasi-experimental methods, working with about 195 elementary grades teachers and their students in Boston, Springfield, Leominster, Fitchburg, and other Massachusetts public schools. Volunteer teachers are randomly assigned either to PD with DMI in the first year of the efficacy study, or to a control group that will wait until the second year of the study to receive DMI PD. Both groups of teachers will be followed through two academic years. Analyses use OLS regression, hierarchical modeling, and structural equation modeling, as appropriate, to compare the two groups and to track changes over time. In this way, the project explores several aspects of a conceptual framework hypothesizing relationships among PD, teacher mathematical and pedagogical knowledge, classroom teaching practice, and student outcomes. There are multiple measures of each construct, including video-analysis of teacher practice, and a new video-based measure of teacher knowledge.

The study tests the impact of DMI in a range of districts (large urban, small urban, suburban) serving an ethnically and economically diverse mix of students. It provides much needed, rigorous evidence testing the efficacy of this reform-oriented professional development program. It also directly explores the commonplace theory that teachers' understanding of content and student thinking and their encouragement of rich mathematical discourse for student sense-making lead to improvement on measures of mathematics achievement. Findings from the study are disseminated to both research and practitioner communities. The project provides professional development in mathematics to about 195 teachers to improve their ability to teach important concepts. If the evidence for efficacy is positive, then even larger-scale use of this PD program is likely.

This project involves a longitudinal, ethnographic study of children's mathematical performances from preschool to first grade in both formal classroom settings and informal settings at school and home. The proposed site for the study is a small, predominately African-American pk-12 school. The study seeks to identify opportunities for mathematical learning by young children across multiple contexts, to map varied performances of mathematical competence by young children, to chart changes in young children's mathematical performance over time, and to design and assess the impact of case studies for teacher education that explore young children's mathematical competencies. Research questions focus on mathematical opportunities for learning in various contexts, children's development of knowledge, skills, and dispositions over time, the characteristics of competent mathematical performances, and the role of case studies in helping beginning teachers to understand young minority children's mathematical thinking. Data collected will include video tapes of classroom activities, written fieldnotes of formal and informal settings, student work, parent focus group transcripts, and children's interview performances. Analysis will involve both thematic coding and construction of case studies. The overarching goal of this project is to transform the ways that researchers think about and study the mathematical learning of young minority children as well as the quality of schooling these children experience.

This project Math Snacks: Addressing Gaps in Conceptual Mathematics Understanding with Innovative Media, led by mathematics and education faculty at New Mexico State University, is developing and evaluating effectiveness of 15 - 20 short computer mediated animations and games that are designed to: (1) increase students' conceptual understanding in especially problematic topics of middle grades mathematics; and (2) increase students' mathematics process skills with a focus on problem-solviing and communicating mathematically. The basic research question for this project is whether the planned collection of computer-mediated animations and games can provide an effective strategy for helping students learn core middle grades mathematics concepts in conceptual areas that research suggests are difficult for these students.  A second question relates to types of delivery that are effective for mathematics learning using these tools including in classrooms during extended learning time at home or in informal educational settings. The project is developing and testing the effectiveness of a set of such learning tools and companion print materials, including student and teacher guides, and short video clips documenting best practices by  teachers using the developed materials with students. A pilot study in year 3 and a substantial randomized control trial in year 4 will test the effects of using the Math Snacks web-based and mobile technologies on student learning and retention of identified core middle school mathematics concepts, as measured by performance on disaggregated strands of the New Mexico state standardized mathematics assessments. Thus the project will produce animations and games using the web and new mobile technologies, and useful empirical evidence about the efficacy of their use. One of the key features of the Math Snacks project is development of the mediated games and simulations in a form that can be used by students outside of normal classroom settings on media and game players that are ubiquitous and popular among today's young people. Thus the project holds the promise of exploiting learning in informal settings to enhance traditional school experiences.