Document Type

Article

Publication Title

Journal of Numerical Cognition

Publication Date

2021

Keywords

blended theory, problem features, entrenchment, integer addition, cognition, elementary

Abstract

In this study, we explored second and fifth graders’ noticing of negative signs and incorporation of them into their strategies when solving integer addition problems. Fifty-one out of 102 second graders and 90 out of 102 fifth graders read or used negative signs at least once across the 11 problems. Among second graders, one of their most common strategies was subtracting numbers using their absolute values, which aligned with students’ whole number knowledge-pieces and knowledge-structure. They sometimes preserved the order of numbers and changed the placement of the negative sign (e.g., −9 + 2 as 9 – 2) and sometimes did the opposite (e.g., −1 + 8 as 8 – 1). Among fifth graders, one of the most common strategies reflected use of integer knowledge-pieces within a whole-number knowledge-structure, as they added numbers’ absolute values using whole number addition and appended the negative sign to their total. For both grade levels, the order of the numerals, the location of the negative signs, and also the numbers’ absolute values in the problems played a role in students’ strategies used. Fifth graders’ greater strategy variability often reflected strategic use of the meanings of the minus sign. Our findings provide insights into students’ problem interpretation and solution strategies for integer addition problems and supports a blended theory of conceptual change. Adding to prior findings, we found that entrenchment of previously learned patterns can be useful in unlikely ways, which should be taken up in instruction.

Funding Source

This research was supported by a National Science Foundation CAREER award DRL-1350281.

Comments

First published in Journal of Numerical Cognition (2021): https://doi.org/10.5964/jnc.6563

This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License, CC BY 4.0, which permits unrestricted use, distribution, and reproduction, provided the original work is properly cited.

DOI

10.5964/jnc.6563

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