Relationship between cognitive types of teacher content knowledge and knowing-to act: A mixed methods study of Mexican borderland middle school teachers

Maria de los Angeles Cruz Quinones, University of Texas at El Paso


This study analyzed middle school mathematics teachers' content knowledge and its relationship with teachers' "knowing-to act" ability. Understanding what kinds of knowledge has a direct influence on teaching practices and student learning is critical in order to improve teacher education programs and professional development. An Explanatory sequential mixed methods design was used in the study. It involved collecting quantitative data and explaining the quantitative results with in-depth qualitative data. In the quantitative phase of the study, two surveys were administered to N=70 middle school mathematics teachers in the Mexican borderland to assess whether their mathematical content knowledge was related to their "knowing-to act". The correlational analysis of these surveys showed no statistically significant correlation between overall mathematical teacher content knowledge (total score on TCKS) and the "knowing-to act" ability (KtAS). However, a statistically significant correlation between the specific cognitive type of teacher knowledge - models and generalizations - and the "knowing-to act" was reported. The qualitative phase provided a deeper understanding of the quantitative results: the exploration of the "knowing-to act" enacted during mathematics instruction with four middle school mathematics teachers from the quantitative sample was conducted using a specifically designed classroom observation protocol. The analysis of the observation together with the results of the KtAS provided revealing differences among teacher's actions observed and the teacher's responses on the survey. Overall, the analysis of the qualitative data reflected findings from the quantitative phase of the study. Two main findings were reported in the study: (a) the lack of correlation between the mathematical teachers content knowledge and their "knowing-to act" during teaching mathematics, which was reflected by the data collected from the case studies; (b) a statistically significant correlation between knowledge of models and generalizations (T3), which added to the discussion that teachers who performed higher on the cognitive type 3 items of the TCKS were able to know how to act at the moment more frequently than teachers with a limited T3. This research provided in-service teachers and other participants in the education field with awareness about the active knowledge that is needed to enact the teachers' knowing-to act in teacher preparation programs in Mexico that can be used to support teachers and students in the United States. Further studies are needed in which the association and exploration of other kinds of knowledge for teaching mathematics and students learning can be analyzed. For instance, research on "knowing-to act" in the United States or other countries can also be worthy of a study; how would teachers act in KtA situations during their mathematics instruction in the USA, Canada, or Russia? In addition, this study allows comparisons among Mexico and countries where data is already collected in regards to teacher knowledge in the area of Mathematics, such as Russia, the U.S., Latin American countries, and other countries that participated in the TEDS-M Study 2012.

Subject Area

Mathematics education|Middle School education|Teacher education|Latin American Studies

Recommended Citation

Cruz Quinones, Maria de los Angeles, "Relationship between cognitive types of teacher content knowledge and knowing-to act: A mixed methods study of Mexican borderland middle school teachers" (2014). ETD Collection for University of Texas, El Paso. AAI3682455.