Examining the Mathematical Knowledge for Teaching Involved in Pre-service Teachers’ Reflections

Oct. 01, 2013

Source: Teaching and Teacher Education, Volume 35 (October, 2013) 146-156.
(Review by the Portal Team)

This study seeks examine the mathematical knowledge for teaching involved in reflection.
It addresses to the following research questions:
(1) What aspects of mathematical knowledge for teaching do pre-service teachers include and emphasize in their reflections on teaching mathematics?
(2) What insights do pre-service teachers’ reflections provide into their mathematical knowledge for teaching?

The participants were twenty-four elementary pre-service teachers, who completed the integrated mathematics content and mathematics education course during the time of the study.
Data included four reflective journals written by 24 pre-service teachers over the course of four weeks.


The first finding of this study indicates that mathematical knowledge for teaching is involved in reflection and supports the analytic quality of reflection, thus making reflection more productive.
The strength of preservice teachers’ knowledge, then, may be a factor in the analytic quality of their reflection.
To strengthen pre-service teachers’ knowledge and improve the analytic quality of their reflections, teacher educators need to specify that the knowledge needed for teaching is also involved in reflection.

To make this connection, teacher educators can merge theoretical models for teacher reflection and teacher knowledge.
One way for teacher educators to merge teacher reflection and teacher knowledge is to design prompts that explicitly ask pre-service teachers to address content, teaching, and students in their reflections.
Designing focused prompts specifies the knowledge involved in teaching, assists pre-service teachers in making connections between teaching and reflecting, and provides pre-service teachers additional opportunities to strengthen the knowledge needed for teaching and reflection.

Furthermore, pre-service teachers lacking motivation for reflection might benefit from class discussions about their reflections to assist them in elaborating on the interesting complexities involved in their own teaching.
During these discussions, teacher educators can model how to analyse problematic situations, motivating pre-service teachers to learn how to use their reflection to find solutions
to the problems involved in their own teaching.

The second result is that focus on content promotes knowledge integration.
This study highlights how content is pivotal in helping preservice teachers integrate the aspects of mathematical knowledge for teaching in their reflections.
Teacher educators must support pre-service teachers in making the content involved in teaching the focus of reflection.

The last finding of this study shows how pre-service teachers’ reflections can provide a diagnostic tool that sheds light on their mathematical knowledge for teaching.
Overall, the pre-service teachers in this study included common content knowledge most often in their reflections followed by specialized content knowledge, knowledge of content and teaching, and knowledge of content and students.
The aspects the pre-service teachers included most often may be the aspects they are most knowledgeable of.
In this study, the pre-service teachers included knowledge of content and students less frequently than the other aspects, suggesting that their knowledge of this aspect was weaker.

Ball et al. (2008) explain that one of the tasks of teaching associated with knowledge of students includes listening to and interpreting student thinking.
Teacher educators should distinguish listening from interpreting to build on what pre-service teachers know how to do, listen and describe.
Teacher educators, for instance, could model for pre-service teachers the difference between listening and interpreting using video of students engaged in solving mathematical tasks.
Asking pre-service teachers to view video to describe student actions and then model for pre-service teachers how to interpret what student actions mean may provide the scaffolding pre-service teachers need to move beyond listening toward interpretation.


The author concludes that the ability to analytically reflect on practice assists teachers in using their reflection to become effective teachers over time.
Focusing on the specific knowledge involved in reflection further supports pre-service teachers in learning how to analytically reflect on their teaching.
Teacher reflection and teacher knowledge should be viewed as integrated components of teacher preparation to support pre-service teachers in learning how to use their knowledge to reflect on their practice.

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59, 389-407.

Updated: Mar. 11, 2015


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