Progressions in young learners' understandings of parity arguments

Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The qualitative study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about parity arguments f...

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Bibliographic Details
Published in:Mathematical thinking and learning 2024-01, Vol.26 (1), p.90-121
Main Authors: Blanton, Maria, Gardiner, Angela Murphy, Ristroph, Ingrid, Stephens, Ana, Knuth, Eric, Stroud, Rena
Format: Article
Language:English
Subjects:
Algebra
Algebraic thinking
argumentation and proof
early algebra
elementary grades
Grade 1
learning progressions
Mathematical analysis
Mathematics Instruction
Parity
Progressions
Qualitative analysis
qualitative research
Students
Sums
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Summary:Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The qualitative study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about parity arguments for sums of evens and odds, as well as underlying concepts of pair and parity of a number. Data are drawn from classroom lessons of a Grades K-1 early algebra instructional sequence, as well as task-based interviews conducted at four timepoints during the implementation of the sequence. While most students at the beginning of the study (Grade K) did not know the concepts of even or odd and could not make any viable arguments regarding parity, by the end of Grade 1 students were largely constructing representation-based arguments to justify number parity and claims about sums of evens and odds. Results of this study align with other research that shows young learners can develop viable arguments to justify mathematical generalizations. Results also provide preliminary evidence that the instructional sequence used here can foster students' practice of argumentation from the start of formal schooling.
ISSN:1098-6065
1532-7833
DOI:10.1080/10986065.2022.2053775