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

### Principle Investigator

Prof. Ruhama Even

### Research team – current members

Dr. Michal Ayalon

Boaz Silveman (Ph.D student)

### Research team – alumni

Miriam Carmeli

Dr. Tammy Eisenmann (Ex. Ph.D. student)

Dr. Tova Kvatinsky (Ex. Ph.D. student)

Dr. Naomi Robinson

### Summary

In many countries, including Israel, a common response to calls to improve mathematics teaching and learning is developing 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 class-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 classes in different situations. To study these interactions, we compare mathematics teaching and learning in different classes 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 Classes – 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 classes. In this way, some aspects are kept relatively constant; this enables careful examination of the interactions among curricula, teachers, and classes, which are not easily detectable.

My current research focuses on studying what might be gained and what the challenges might be when using this methodology for assessing or studying mathematics classroom instruction. By comparing mathematics teaching and learning in classes of different teachers that use the same textbook, our studies (supported in part by a two-year ISF grant) show that students of teachers who adopt different teaching approaches might not only study mathematics differently, but there might be also differences in the mathematics addressed in those classes, even tough they all use the same textbook. These differences appeared to be linked to the teacher's teaching approach. Noteworthy information was revealed when, instead of focusing solely on the comparison between teachers, different classes taught by the same teacher were compared. For example, we detected a rather surprising finding, which is contrary to the prevalent view portrayed in modern literature about teachers' tendency to focus less on developing understanding and more on mechanistic answer-finding when teaching low-achieving classes. Furthermore, our studies show that differences in the mathematics addressed in class occur not only between classes of different teachers, but also between different classes of the same teacher who use the same curriculum materials. Recently, we identified the mathematical topic as another potentially critical factor, suggesting that mathematical topics that require substantial use of deductive reasoning – in contrast with those requiring mainly the use of inductive reasoning – have the potential to generate high variation in students' opportunities to engage in mathematics across teachers and classes.

### Related publications

- 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.