## The interplay of factors involved in shaping students’ opportunities to learn mathematics

### Leading team

### Project members

- Dr. Michal Ayalon
- Miriam Carmeli
- Tammy Eisenmann (Ex. Ph.D. student)
- Tova Kvatinsky (Ex. Ph.D. student)
- Dr. Naomi Robinson
- Boaz Silveman (Ph.D student)

### Summary

In many countries, including Israel, a common response to calls to improve mathematics teaching and learning is the development of new curricula. However, the curriculum is only one factor involved in shaping students’ opportunities to learn mathematics. Numerous research studies highlight the prominent and indispensable role that teachers play in influencing how the curriculum is enacted in the classroom, and they underscore teachers’ central role in determining the nature of the learning experiences provided to students – a role that no curriculum program by itself can fulfill. Research also reveals that aspects not directly or solely related to the curriculum or the teacher, such as classroom-related aspects, are also involved in shaping students’ opportunities to learn mathematics. Yet, not much is known about how these factors interact. To date, the interplay of these factors has received little research attention and is often considered “noise” by researchers. This research program focuses purposely on studying the interactions among curricula, teachers, and classrooms in different situations. To study these interactions, we compare mathematics teaching and learning in different classrooms of the same teacher as well as of different teachers, and examine the enacted curricula, the teaching practices, the classroom culture, etc. All studies that belong to this research program – entitled Same Teacher – Different Classrooms – use the same novel research methodology: multiple case studies in which each case includes a teacher who teaches mathematics using the same curriculum program or syllabus in two classrooms. In this way, some aspects are kept relatively constant. The findings of the study show differences in mathematics taught between classrooms of teachers using the same textbook, but in different teaching approaches, as well as between different classrooms of the same teacher.

### Links for further reading

- Even, R. (2008). Offering mathematics to learners in different classes of the same teacher. In O. Figueras, & A. Sep?lveda (Eds.), Proceedings of the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education, and the XX North American Chapter (Vol. 1, pp. 51-66). Morelia, Michoac?n, M?xico: PME.
- Eisenmann, T. & Even, R. (2009). Similarities and differences in the types of algebraic activities in two classes taught by the same teacher. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 152-170). New York: Routledge.
- Even, R. & Kvatinsky, T. (2009). Approaches to teaching mathematics in lower-achieving classes. International Journal of Science and Mathematics Education, 7(5), 957-985.
- Even, R. & Kvatinsky, T. (2010). What mathematics do teachers with contrasting teaching approaches address in probability lessons? Educational Studies in Mathematics, 74, 207-222.
- Ayalon, M. & Even, R. (2010). The nature of transformational algebraic activities addressed in different classes of the same teacher. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the 32nd Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. VI. pp. 178-185). Columbus, Ohio: PME-NA.
- Eisenmann, T. & Even, R. (2011). Enacted types of algebraic activity in different classes taught by the same teacher. International Journal of Science and Mathematics Education, 9, 867-891.
- Ayalon, M. & Even, R. (2012). Argumentative activity in different beginning algebra classes and topics. In C. Smith (Ed.), Proceedings of the British Society for Research into Learning Mathematics 32(3).
- Even, R. (in press). The interplay of factors involved in shaping students’ opportunities to engage in mathematics. In Y. Li, E. Silver, & S. Li (Eds.), Transforming Mathematics Instruction: Multiple approaches and practices. Springer.