Research on Mathematics Education

Catherine D. Bruce, Trent University cathybruce@trentu.ca, www.tmerc.ca

This research summary highlights three related themes that have emerged in my research in collaboration with other Ontario researchers, teachers, students and education partners.

1. There are key characteristics of high quality, effective professional learning.

In our research over the past decade we learned that effective Professional Learning (PL) models embed learning in the classroom context and construct knowledge through collaborative experience and practice in cycles of goal setting, planning, practicing, and reflecting. In PL models, such as the Collaborative Inquiry and Learning in Mathematics program and Lesson Study, the classroom becomes the primary and legitimate site of teacher professional learning.

Key characteristics of effective Professional Learning include the following:

To learn more, read: Bruce, C.D. & Ross, J.A. (2010, August). External review of collaborative inquiry and learning in mathematics. Final report submitted to the Ontario Ministry of Education. Peterborough, ON: Trent University (132 pages).

Bruce, C. & Ladky, M. Using design research to test and enrich a Lesson Study model: A close examination of the complexities of the lesson study cycle, Paper presentation: American Education Research Association, Denver, CA.

2. Effective Professional Learning in mathematics leads to increased teacher efficacy and student achievement.

Teacher Efficacy is the teacher's belief that (s)he has the ability to help students learn mathematics and is tightly connected to student achievement. With high quality professional learning opportunities, teacher efficacy can increase. For example, in a three-year Collaborative Action Research program teachers engaged together in identifying a problem in their mathematics programs, developing a plan (an intervention) for addressing the problem, implementing the plan and assessing impact of the intervention, with the support of knowledgeable others (researchers and mathematics education experts). All teacher groups had increased teacher efficacy. However, teachers benefited more from collaborative action research if:

1. They recognized the importance of, and engaged in, data collection, analysis, and related reflection processes;

2. The action research that was rigorous and/or led to changes in their conceptual understanding;

3. The teachers worked in schools that supported and encouraged professional learning;

4. They had prior experience participating in research activities.

Student Achievement: In an Ontario study on the impact of a classroom-embedded Professional Learning (PL) program for Junior grades mathematics, we found that the complexities of context, prior learning experiences, goal setting, and persistence of teacher participants all factored into what and how teachers learned.

This graph and table show how two districts varied in their student achievement scores from pre-test to post-test. In District B, the student achievement scores began high and remained constant from pre-test to post-test while District A had student achievement scores that rose dramatically from pre-test to post-test, surpassing those of District B. One of the main distinctions in these two districts was that District A engaged in significant between-session activities, while District B did not.

To learn more, read: Bruce, C., Esmonde, I., Ross, J., & Gookie, L., Beatty, R. (2010). The effects of sustained classroom-embedded teacher professional learning on teacher efficacy and related student achievement. Teaching and Teacher Education, 26 (8).

Bruce, C. D. & Ross, J. A. (2008). A model for increasing reform implementation and teacher efficacy: Teacher peer coaching in grade 3 and 6 mathematics. Canadian Journal of Education, 31(2), 346-370.

Bruce, C.D., Flynn, T. & Peterson, S. (submitted). Examining the impact of participant roles on collaborative action research: a cross-case analysis, Educational Action Research.

3. Researched lesson sequences and learning tools, focusing on difficult mathematics concepts, offer students from a range of academic ability levels a way to build deep understanding.

Precise learning tools, structures, and developmentally based learning sequences are a fruitful area of research focused on student understanding of challenging mathematics concepts (such as understanding fractions, trigonometry and linear growing patterns). In a series of interconnected studies on the effects of CLIPS learning objects, we are finding positive effects of carefully researched and designed learning sequences, particularly when on-line and off-line tasks are integrated together. We theorized that a technology-based learning resource could provide the sequencing and scaffolding to support deep conceptual understanding and to support teacher instruction in key areas. For example, a development team of teachers, researchers and educational software programmers designed five sets of fractions activities in the form of a sequence of learning objects (called CLIPS). As part of a larger mixed-methods study, 36 observations as well as interviews were conducted in four classrooms, grades 7-10. Four students were selected by their teachers for CLIPS fractions use from each of these four classrooms because the students were experiencing difficulty with fractions concepts. CLIPS use contributes to student achievement provided the conditions enabled an effective learning environment and students experienced the full sequence of tasks in the CLIPS. Three interacting contexts affected successful use of CLIPS: technological contexts (such as access to computers with audio), teaching contexts (such as introductory and ongoing activities that prepared students for the CLIPS activities) and student contexts (such as the level of student confidence and opportunities to communicate to a peer during CLIPS activities).

To learn more, read: Bruce, C. & Ross, J. (2009). Conditions for effective use of interactive on-line learning objects: The case of a fractions computer-based learning sequence. Electronic Journal of Mathematics and Technology [online serial] 3(1). Available http://www.radford.edu/ejmt.

Ross, J.A., Ford, J. & Bruce, C. (2008). Needs assessment for the development of learning objects. Alberta Journal of Educational Research 53(4), 430-433.

Bruce, C. (2007). Student interaction in the math classroom: Stealing ideas or building understanding? Research into Practice: Ontario Association of Deans of Education. Research Monograph 1 (premier edition),1-4.