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We report on one aspect of the validation process of our mathematical knowledge for teaching college algebra at community colleges MKT-CCA instrument using cognitive interviews with 16 participants 

We report on one aspect of the validation process of our mathematical knowledge for teaching college algebra at community colleges MKT-CCA instrument using cognitive interviews with 16 participants 

Using Balacheff’s (2013) model of conceptions, we inferred potential conceptions in three examples presented in the spanning sets section of an interactive linear algebra textbook. An analysis of student responses to two similar reading questions revealed additional strategies that students used to decide whether a vector was in the spanning set of a given set of vectors. An analysis of the correctness of the application of these strategies provides a more nuanced understanding of student responses that might be more useful for instructors than simply classifying the responses as right or wrong. These findings add to our knowledge of the textbook’s presentation of span and student understanding of span. We discuss implications for research and practice. 

We report on the relationship between community college instructors’ performance on an instrument measuring mathematical knowledge for teaching college algebra with their teaching experience and their frequency of using specific tasks of teaching. The findings support the argument that the instrument assesses critical knowledge for teaching college algebra. We propose further work based on these findings. 

We report on the relationship between community college instructors’ performance on an instrument measuring mathematical knowledge for teaching college algebra with their teaching experience and their frequency of using specific tasks of teaching. The findings support the argument that the instrument assesses critical knowledge for teaching college algebra. We propose further work based on these findings. 

In this paper, we examine the relationships between teachers’ subject matter preparation and experience in teaching and their performance on an instrument measuring mathematical knowledge for teaching Algebra 1. We administered the same instrument to two different samples of teachers−high school practicing teachers and community college faculty − who teach the same algebra content in different levels of institutions, and we compared the performance of the two different samples and the relationships between the measured knowledge and their educational and teaching background across the samples. The comparison suggested that the community college faculty possess a higher level of mathematical knowledge for teaching Algebra 1 than high school teachers. The subsequent analyses using the Multiple Indicator Multiple Causes (MIMIC) models based on our hypothesis on the factors contributing to the differences in the knowledge between the two teacher samples suggest that experience teaching advanced algebra courses has positive effects on the mathematical knowledge for teaching Algebra 1 in both groups. Highlighting the positive effect of algebra-based teaching experience on test performance, we discuss the implications of the impact of subject specific experience in teaching on teachers’ mathematical content knowledge for teaching. 

In this essay we reflect on the evolution of a strategy designed to gather data about students’ actions with dynamic textbooks in university mathematics as part of a two-year long, federally-funded, large-scale exploratory study. We present the context of the study, and how that context generated both opportunities and challenges to obtain information about student actions with these textbooks. The evolving process of data collection has provided insights into the relationship between researchers, participants, context, and data collection systems, and the ways in which these inform each other.