Mixed Methods Study of Middle School Mathematics Teachers' Content Knowledge in USA and Russia Using Sequential Nested Design

The sequential nested mixed methods study focused on comparative analysis of middle school mathematics teachers' content knowledge in two countries. The study consisted of two stages: (1) quantitative study of teacher content knowledge; (2) qualitative study of teacher topic-specific content knowledge. The initial sample for the first stage included lower secondary mathematics teachers from the U.S. (grades 6-9, N=102) and Russia (grades 5-9, N=97). The Teacher Content Knowledge Survey (TCKS) was applied to assess teacher content knowledge based on the cognitive domains of Knowing, Applying, and Reasoning, as well as addressing the lower secondary mathematics topics of Number, Algebra, Geometry, Data and Chance. The second stage - an interpretive cross-case study - aimed at the examination of the U.S. and Russian teachers' topic-specific knowledge on the division of fractions. For the second stage, N=16 teachers (8 - from the U.S., and 8 - from Russia) were selected for the study using non-probability purposive sampling technique based on teachers' scores on the TCKS. Teachers were interviewed on the topic of fraction division using questions addressing their content and pedagogical content knowledge. In order to analyze the qualitative data, we conducted meaning coding and linguistic analysis of teacher narratives as primary methods of analysis. The study revealed that there are explicit similarities and differences in teachers' content knowledge as well as its cognitive types. Findings from the first stage did not show any significant differences between the U.S. and Russian teachers' knowledge of Number (chi 2=0.347, p>.05) and Geometry (chi 2=1.293, p>.05) domains. However, there was a statistically significant difference observed in teachers' knowledge of Data and Chance (chi 2=8.003, p<.05) and Algebra (chi 2= 6.311, p<.05). With regard to cognitive types, the study reported no significant difference between the U.S. and Russian teachers' knowledge on Knowing and Applying domains (chi 2=1.707 and chi 2=0.008 at p>.05 correspondingly) whereas there was a statistically significant difference on the Reasoning domain (chi 2=19.117, p<.05). During the qualitative stage, the similarity was observed in teachers' responses to the question on important objectives of the fraction division at different cognitive domains. The most evident difference between two groups of teachers was observed on the question examining meanings of fraction division as well as attempting to prove the general statement using a numerical method, which was statistically significant in both cases (correspondingly chi 2 = 10.286 and chi 2 = 5.333 at p < .05). The results are reflected in meanings expressed and the language used by teachers while responding to topic-specific questions on the division of fractions. The study's main findings contribute to a body of literature in the field of cross-national research on teacher knowledge with a narrow focus on topic-specific knowledge. The study results may inform the field on priorities placed on lower secondary mathematics teachers' knowledge in the USA and Russia. It also suggests close comparison and learning about issues related to teacher knowledge in the U.S. and Russia with a potential focus on re-examining practices in teacher preparation and professional development.