id: 06618989
dt: j
an: 2016e.00583
au: Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre,
    Ian; Schappelle, Bonnie P.
ti: Leveraging structure: logical necessity in the context of integer
    arithmetic.
so: Math. Think. Learn. 18, No. 3, 209-232 (2016).
py: 2016
pu: Taylor \& Francis (Routledge), Philadelphia, PA
la: EN
cc: F40 C30
ut: integer arithmetic; mathematical structure
ci: 
li: doi:10.1080/10986065.2016.1183091
ab: 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 K‒12 curriculum.
rv: