Moving among levels of abstraction is an important skill in mathematics and computer science, and students show similar difficulties when applying abstraction in each discipline. While computer science educators have examined ways to explicitly teach students how to consciously navigate levels of abstraction, these ideas have not been explored in mathematics education. In this study, we examined elementary students’ solutions to a commonplace mathematics task to determine whether and how students moved among levels of abstraction as they solved the task. Furthermore, we analyzed student errors, categorizing them according to whether they related to moves among levels of abstraction or to purely mathematical steps. Our analysis showed: (1) students implicitly shift among levels of abstraction when solving “real- world” mathematics problems; (2) students make errors when making those implicit shifts in abstraction level; (3) the errors students make in abstraction outnumber the errors they make in purely mathematical skills. We discuss the implications for these findings, arguing they establish that there are opportunities for explicit instruction in abstraction in elementary mathematics, and that students’ overall mathematics achievement and problem-solving skills have the potential to benefit from applying these computer-science ideas to mathematics instruction.
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Applying Levels of Abstraction to Mathematics Word Problems
In many discussions of the ways in which abstraction is applied in computer science (CS), researchers and advocates of CS education argue that CS students should be taught to consciously and explicitly move among levels of abstraction (Armoni Journal of Computers in Mathematics and Science Teaching, 32(3), 265–284, 2013; Kramer Communications of the ACM, 50(4), 37–42, 2007; Wing Communications of the ACM, 49(3), 33–35, 2006). In this paper, we describe one way that attention to levels of abstraction could also support learning in mathematics. Specifically, we propose a framework for using abstraction in elementary mathematics based on Armoni’s (2013) framework for teaching computational abstraction. We propose that such a framework could address an enduring challenge in mathematics for helping elementary students solve word problems with attention to context. In a discussion of implications, we propose that future research using the framework for instruction and teacher education could also explore ways that attention to levels of abstraction in elementary school mathematics may support later learning of mathematics and computer science.
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- Award ID(s):
- 1738677
- NSF-PAR ID:
- 10183085
- Date Published:
- Journal Name:
- Techtrends
- ISSN:
- 1201-0073
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s11528-020-00479-3
