ERIC Number: EJ998826
Record Type: Journal
Publication Date: 2012
Pages: 9
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0045-0685
EISSN: N/A
Available Date: N/A
Understanding Proportional Reasoning for Teaching
Kastberg, Signe E.; D'Ambrosio, Beatriz; Lynch-Davis, Kathleen
Australian Mathematics Teacher, v68 n3 p32-40 2012
Proportional reasoning is an important cornerstone in children's mathematical development. This sort of reasoning has been shown to develop across the early years of schooling (ages 8 to 10) through the middle years (ages 11-14). In the early years, children tend to use additive reasoning to generate solutions to problems, while later comparisons rely on multiplicative strategies including the use of ratios, fractions, percents and proportions. In part this is a result of the support provided by their teachers. Yet children in the middle years, while expected to understand and be able to use ratios and percents, often over-generalise and apply missing value proportions strategies to problems that require only additive reasoning. To support development teachers can use a variety of tools including ratio tables and contextual activities the basis of which is an understanding of learners' reasoning. But understanding such reasoning and deciding which direction to take can be quite challenging. Given the challenges faced in the middle years' curriculum and the expertise the teachers have at solving proportional problems themselves, students' approaches may not be the first thinking teachers draw on as they plan for instruction. In this article, the authors contrast teacher reasoning and student reasoning in work samples. They highlight some computational and reasoning approaches 11 to 14 year old students take on a comparison problem and suggest that teachers' understanding and use of student approaches is a fruitful basis for instruction. In their efforts to understand teachers' conceptions of proportional reasoning, the authors have had many conversations with teachers and mathematics educators. The first half of this article is written as a dialogue among teachers as they examine and compare tasks using their mathematical understandings. The dialogue was crafted from the authors' experiences with teachers in their workshops, presentations and classes. The second half of the article looks closely at how students solved one of the problems. Student work is discussed as a mechanism to build teacher awareness of student reasoning and use of that thinking in instructional decision making. (Contains 10 figures.)
Descriptors: Mathematics Instruction, Mathematical Concepts, Mathematics Education, Children, Early Adolescents, Mathematics Teachers, Comparative Analysis, Mathematics Skills, Problem Solving, Mathematical Logic
Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: N/A

Peer reviewed
Direct link
