eric.ed.gov har udgivet:
Contemporary state math standards emphasize that students must demonstrate an understanding of the mathematical ideas underlying the computations that have typically been the core of the elementary school math curriculum. The standards have put an increased emphasis on the study of fractions in upper elementary grades, which are the years during which students build a strong foundation in fractions concepts. At the same time, the National Mathematics Advisory Panel (2008) cites limited understanding of fractions as the key reason for the high failure rate in algebra courses. Longitudinal data from both the United States and the United Kingdom have demonstrated that knowledge of fractions in the elementary grades plays a powerful role in subsequent success in algebra, the gateway to math achievement in high school. Members of the Regional Educational Laboratory (REL) Southeast Improving Mathematics Instruction Research Alliance saw teachers’ lack of in-depth knowledge of fractions concepts as a major challenge in their teaching these concepts to their students. Alliance members indicated that teachers would benefit from a professional development program that focused on building a deep understanding of the mathematical ideas underlying fractions and of how to apply those ideas in the classroom. This large-scale study investigates the effectiveness of such a program to help inform future district and state investments in professional development. Members of the REL Southeast Improving Mathematics Instruction Research Alliance formed a work group and selected Developing Mathematical Ideas (DMI) as the professional development program that seemed best suited to develop in-depth teacher knowledge of fractions and that could be scaled up in a large number of districts simultaneously. Developed by the Education Development Corporation, DMI is designed to help teachers think through major mathematical ideas and examine and reflect on how their students develop and understand the ideas. Teachers examine vignettes of classroom teaching and examples of student work from their own classes and from the classes of other participating teachers. Teachers also work on fractions problems designed to promote their own understanding of fractions concepts. The primary goal of the study was to assess the impact of DMI on grade 4 students’ and teachers’ understanding of fractions. The study was conducted during the 2014/15 school year using data from 84 schools in eight school districts in three states (Florida, Georgia, and South Carolina). Participants included 4,204 grade 4 students and 264 grade 4 teachers. Nine trained facilitators provided the professional development. The study used a randomized controlled trial, randomly assigning schools to either the treatment condition or the control condition. Teachers in schools in the treatment condition received 24 hours of DMI professional development on fractions during fall 2014. They attended eight three-hour sessions conducted over four days (two three-hour sessions per day; one day per month). In most cases substitute teachers filled in for teachers during these days; in some cases teachers preferred occasional Saturday sessions and were compensated for the additional workday. Teachers in the control condition did not receive DMI professional development but were free to participate in any type of school- or district-provided professional development in math, including fractions. About a third of teachers in the control condition indicated that they had participated in some form of professional development in fractions. The student outcome measure was the Test for Understanding of Fractions, which was administered at the end of the school year to assess students’ understanding of fractions concepts and their ability to perform computations and word problems. The teacher outcome measure was the Mathematical Knowledge for Teaching: Fractions Scale (Learning Mathematics for Teaching, 2008), which was administered to all teachers at the end of the study to assess their understanding of the mathematical ideas involved in teaching fractions and their knowledge of the typical errors and misconceptions that can develop as students learn this material. Key findings include: (1) DMI did not demonstrate any impact on student proficiency in fractions. Students of teachers who participated in DMI performed at almost the same level as students of teachers who did not participate; the difference was not statistically significant (p = 0.637); and (2) The impact of DMI on teachers’ knowledge of fractions was inconclusive. Teachers who participated in DMI performed 0.19 standard deviation better than teachers who did not participate, but the difference was not statistically significant (p = 0.051). Thus, DMI had nonsignificant impacts on students’ proficiency in fractions and their teachers’ knowledge of fractions. The finding of no impact on students’ math proficiency is common in the research literature on professional development in math. The results suggest that professional development that attempts to build teachers’ knowledge of the mathematical ideas underlying the K-8 curriculum, though theoretically compelling, does not always lead to improvements in student learning. The following are appended: (1) Study design and study sample; (2) Reliability of measures; (3) Online surveys; and (4) Data analysis.