Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic

Autor/inn/en	Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.
Titel	Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic
Quelle	In: Mathematical Thinking and Learning: An International Journal, 18 (2016) 3, S.209-232 (24 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1098-6065
DOI	10.1080/10986065.2016.1183091
Schlagwörter	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 + Suchen Sie Ihr Suchwort? Zahlenraum; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathematik; Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Denkfähigkeit; Abstraktes Denken; Denken; Mathematische Formel; Interviewing; Interviewtechnik; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin; High school; High schools; Oberschule; Studentin; Mathmatics sikills; Mathmatics achievement; Mathematical ability; Mathematische Kompetenz; Pilot project; Modellversuch; Pilotprojekt
Abstract	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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01