Challenging the expected: problems as written and enacted in secondary mathematics
Date
2020
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Publisher
University of Delaware
Abstract
The purpose of this study is to investigate learning opportunities students can encounter through mathematical problems as written and enacted in secondary mathematics classrooms. It is important to study learning opportunities associated with problems as written and as enacted in the classrooms because students can learn more than (or something different from) the intended mathematical learning goals of the lesson. This study is a secondary analysis of a database of videos of three secondary teachers’ mathematics lessons (in Integrated Mathematics 1) from the SMiLES project (Secondary Mathematics in-the-moment Longitudinal Engagement Study) (e.g., Jansen et al., 2019). ☐ To understand the students’ opportunities to learn about what it may mean to do mathematics, as potentially communicated through written and enacted mathematical problems, I analyzed the written and enacted problems of the lessons with the cognitive demand framework (Stein & Lane, 1996). To understand students’ opportunities to learn about who can be a part of knowledge generation in the mathematics classroom, I attended to the language use of the written and enacted problems, analyzing for open and closed language (c.f., Halliday & Matthiessen, 2014; Herbel-Eisenmann, 2007). I combined these two perspectives (cognitive demand and language use) to implement a micro-analysis that entailed written and enacted problems, which I defined as a subset of mathematical tasks, and two phases of problem enactment (work time and summary). For each of the three secondary teachers’ classrooms, I examined one case of low demand from each teacher and one case of high demand from each teacher. ☐ Results from this analysis include: (a) that teachers can raise the cognitive demand of problems written with low demand during enactment. (b) that teachers can use open language when enacting problems written at either low or high demand. (c) teachers’ problem enactment can vary across different phases of a problem. ☐ Overall, these results suggest that teachers may affect students’ learning opportunities as they enact problems through language use and shifting levels of cognitive demand. Teachers may benefit from becoming more aware of subtle ways they can shift levels of cognitive demand during problem enactment and ways they can enact language use. A contribution from this dissertation is a framework to analyze mathematical problems as written and enacted to provide insights about students’ learning opportunities related to a potentially hidden curriculum. Future research could consider the potential impact of the cognitive demand and language use has on student learning outcomes in the classroom.
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Keywords
Cognitive demand, Curriculum, Enacted problems, Open and closed language, Written problems