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While proving, and more broadly conceived “reasoning and sense-making,” have received a great deal of attention in mathematics education research over the past three decades, recently scholars have argued for the importance of justification as a learning and teaching practice. As teachers work toward realizing goals for more equitable classroom environments, little is known about whether teachers’ conceptions about mathematical practices, such as justification, reflect an understanding of how students’ engagement in those practices can support more than just mathematical achievement. In this paper, we present findings from our analysis of interviews with 10 secondary mathematics teachers engaged in participatory action research to explore connections, and potential disconnections, between teachers’ conceptions of justification and their visions for equitable instruction. 

The construct of mathematical knowledge for teaching (MKT) has transformed research and practice regarding the mathematical preparation of future teachers. However, the measures used to assess MKT are largely written tasks, which may fail to adequately represent the nature of content knowledge as it is used in instructional decision making. This preliminary report shares initial findings into one measure of MKT in practice – mathematical errors made during planning and enactment of mathematics instruction. We analyzed lesson plans and classroom video from prospective secondary mathematics teachers (PSTs)’ supervised field experiences in college algebra course. We found that there tended be more errors related to understanding of functions (especially logarithmic), but relatively few errors happened overall during instruction. Of the errors made during planning, the majority of these errors were issues of mathematical precision. Implications for the mathematical preparation of secondary PSTs, as well as research on MKT in practice, are discussed. 

The University Teaching Experience (UTE) model is a field experience where secondary mathematics PSTs teach in a first-year undergraduate mathematics course coinciding with their first methods course (Bieda et al., Accepted). Teacher educators mentor PSTs in planning and teaching in the UTE, supporting PSTs to enact ambitious teaching practices early in teacher preparation. We report results of our assessment of PSTs’ vision for high-quality mathematics instruction (VHQMI) at the outset of the UTE, which inform mentoring of PSTs during the UTE.