
06618989
j
2016e.00583
Pierson Bishop, Jessica
Lamb, Lisa L.
Philipp, Randolph A.
Whitacre, Ian
Schappelle, Bonnie P.
Leveraging structure: logical necessity in the context of integer arithmetic.
Math. Think. Learn. 18, No. 3, 209232 (2016).
2016
Taylor \& Francis (Routledge), Philadelphia, PA
EN
F40
C30
integer arithmetic
mathematical structure
doi:10.1080/10986065.2016.1183091
Summary: Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a formal, algebraic way, leveraging key mathematical ideas about inverses, the structure of our number system, and fundamental properties. We identified the use of carefully chosen comparisons as a key feature of logical necessity and documented three types of comparisons students made when solving integer tasks. We believe that logical necessity can be applied in various mathematical domains to support students to successfully engage with mathematical structure across the K12 curriculum.