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Elementary pre-service teachers in an upper-division algebra mathematics content course explored graphing through the use of Calculator-Based Rangers™ (CBRs). This study explores how they used the Distance Match feature of the technology to engage in algebraic thinking. Operating CBR technology, pre-service teachers’ perceptions regarding how position/time graphs represent algebraic concepts was explored with an emphasis on physical movement. Using an inductive approach for qualitative data, the pre-service teachers’ reflections regarding the use of CBRs were analyzed. Specifically, patterns and structures were discovered through coding of the pre-service teachers’ raw descriptions of their movements. Using the data sources (a reflection and assignment), the results showed increased understanding and beneficial affordances with the use of CBRs. However, the pre-service teachers failed to connect the graphs thoroughly to numeric representations and described slope only superficially. For example, movement was not contextualized using numbers but rather using verbal descriptions. Implications are provided for the integration of CBRs as tools for enhancing pre-service teachers’ knowledge for teaching mathematics with technologies

WOS: 000297741300005, This article reports an analysis of 44 prospective middle school mathematics teachers' pre-existing knowledge of rigid geometric transformations, specifically the geometric translations. The main data source for this study was the participants' responses to the tasks that were presented during semi-structured clinical interviews. The findings of the study revealed that prospective teachers had difficulties recognizing, describing, executing, and representing geometric translations. The results indicated that teacher candidates held various views about the geometric translations: (1) translation as rotational motion, (2) translation as translational motion, and (3) translation as mapping. The results further revealed various interpretations of the vector that defines translations: (1) vector as a force, (2) vector as a line of symmetry, (3) vector as a direction indicator, and (4) vector as a displacement. Although many of the teacher candidates interviewed knew that a vector has a magnitude and a direction, this knowledge did not generally lead them to conclude that vectors define translations.