Open-ended realistic division problems, generalization and early algebra

Conference paper

Cooper, Tom and Warren, Elizabeth A.. (2003). Open-ended realistic division problems, generalization and early algebra. Proceedings of the 27th conference of the international group for the psychology of mathematics education. Honolulu, Hawaii: International Group for the Psychology of Mathemati.... pp. 245 - 253
AuthorsCooper, Tom and Warren, Elizabeth A.
TypeConference paper
Abstract

This paper explores the role of open-ended realistic division problem in the development of algebraic reasoning. A written test was administered to 672 students. From the results of this test students were selected for semi-structured interviews. The students were interviewed in pairs and were asked to explain to each other how they would solve the problem. The results of the written tests and the semi-structured interviews indicated that both students understanding of division and the real world context of the problem played an important role in abstracting generalisations.

KeywordsCurriculum and Pedagogy;--Mathematics and Numeracy
Year2003
PublisherInternational Group for the Psychology of Mathemati...
Web address (URL)https://files.eric.ed.gov/fulltext/ED500931.pdf
Open accessOpen access
Research or scholarlyResearch
Page range245 - 253
Research GroupSchool of Education
Additional information

Bronze open access.

Place of publicationHonolulu, Hawaii
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https://acuresearchbank.acu.edu.au/item/8v140/open-ended-realistic-division-problems-generalization-and-early-algebra

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Warren, Elizabeth and Young, Janelle. (2002). Parent and school partnerships in supporting literacy and numeracy. Asia-Pacific Journal of Teacher Education. 30(3), pp. 217 - 228.