ERIC Number: EJ1104998
Record Type: Journal
Publication Date: 2016
Abstractor: As Provided
Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic
Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.
Mathematical Thinking and Learning: An International Journal, v18 n3 p209-232 2016
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.
Descriptors: Numbers, Arithmetic, Mathematics, Mathematics Instruction, Mathematical Logic, Thinking Skills, Algebra, Comparative Analysis, Elementary Secondary Education, Abstract Reasoning, Mathematics Activities, Mathematical Formulas, Mathematical Concepts, Interviews, Elementary School Students, Middle School Students, High School Students, Mathematics Achievement, Pilot Projects, Video Technology
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Publication Type: Journal Articles; Reports - Research; Tests/Questionnaires
Education Level: Elementary Secondary Education; Elementary Education; Middle Schools; Secondary Education; Junior High Schools; High Schools
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: DRL0918780