Using representations of practice to elicit mathematics teachers’ tacit knowledge of practice: a comparison of responses to animations and videos

Prospective and in-service teachers’ perspectives about launching a problem

“…We align our work with prior research that has established the use of focus groups for eliciting practitioners' perspectives about issues of practice and, more specifically, for identifying elements that constitute the practical rationality of mathematics teaching (Herbst and Chazan 2003;Herbst and Kosko 2014). Focus groups enable us to consider statements that participants deem appropriate and relevant to other participants and, thus, are representative of the teaching practice.…”

“…In our case, we were able to create a representation of teaching to elicit PSTs' and ISTs' tacit knowledge about launching a task during a problem-based lesson. In addition, an examination of teachers' evaluative stances in response to a representation of teaching may aid in identifying elements that constitute the practical rationality of mathematics teaching by making explicit some of the implicit norms in teaching (Herbst and Kosko 2014). An analysis of teachers' evaluations may identify tensions and dilemmas that surface when teaching.…”

“…Our methodology is based on We use pseudonyms for the last names of the practicing teachers and for the first names of the prospective teachers G. González, J. A. Eli recent work that shows that animations are equivalent to videos when eliciting teachers' tacit knowledge of teaching (Herbst and Kosko 2014). The vignettes enabled us to elicit teachers' perspectives on launching a problem-based lesson by using a specific problem and showing contrasting choices.…”

“…The analysis of participants' evaluative stances enabled the possibility of identifying subtle differences in participants' perspectives. We based our analyses on prior work by Nachlieli et al (2009), which relied on Lemke's (1998) research regarding evaluations (see also Herbst and Kosko 2014). According to Lemke, there are seven possible types of evaluations in the English language; they are as follows: desirability, probability, normativity, usuality, importance, comprehensibility, and humorousness (see ''Appendix 3'').…”

“…According to Lemke, there are seven possible types of evaluations in the English language; they are as follows: desirability, probability, normativity, usuality, importance, comprehensibility, and humorousness (see ''Appendix 3''). However, we consider normative stances regarding the launch of a problem-based lesson as markers of elements of the practical rationality of mathematics teaching because they reflect what practitioners consider is appropriate when launching a problem (Herbst and Kosko 2014;Nachlieli et al 2009). …”