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An increase in general quantitative literacy and discipline-specific Physics Quantitative Literacy (PQL) is a major course goal of most introductory-level physics sequences—yet there exist no instruments to assess how PQL changes with instruction in these types of courses. To address this need, we are developing the Physics Inventory of Quantitative Literacy (PIQL), a multiple-choice inventory to assess students’ sense-making about arithmetic and algebra concepts that underpin reasoning in introductory physics courses—proportional reasoning, covariational reasoning and reasoning about sign and signed quantities. The PIQL will be used to not only to assess students’ PQL at specific points in time, but also to track changes in and development of PQL that can be attributed to instruction. Data from early versions of the PIQL suggest that students experience difficulty reasoning about sign and signed quantities.
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A Cross-Sectional Investigation of Students’ Reasoning About Integer Addition and Subtraction: Ways of Reasoning, Problem Types, and Flexibility
In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis of the WoRs also led to the identification of 3 problem types: change-positive, all-negatives, and counterintuitive. We found that problem type influenced student performance and tended to evoke a different way of reasoning. We showed that those with more experience with negative numbers use WoRs more flexibly than those with less experience and that flexibility is correlated with accuracy. We provide 3 types of resources for educators: (a) WoRs and problem-types frameworks, (b) characterization of flexibility with integer addition and subtraction, and (c) development of a trajectory of learning about integers.
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- Award ID(s):
- 0918780
- PAR ID:
- 10123107
- Date Published:
- Journal Name:
- Journal for research in mathematics education
- Volume:
- 49
- Issue:
- 5
- ISSN:
- 1945-2306
- Page Range / eLocation ID:
- 575 - 613
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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