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ERIC Number: EJ1025587
Record Type: Journal
Publication Date: 2013-Sep-26
Pages: 15
Abstractor: As Provided
ISSN: ISSN-1473-0111
From Sailing Ships to Subtraction Symbols: Multiple Representations to Support Abstraction
Jao, Limin
International Journal for Mathematics Teaching and Learning, Sep 2013
Teachers are tasked with supporting students' learning of abstract mathematical concepts. Students can represent their mathematical understanding in a variety of modes, for example: manipulatives, pictures, diagrams, spoken languages, and written symbols. Although most students easily pick up rudimentary knowledge through the use of concrete objects, we ask our students to use symbols and other mathematical notation to represent their understanding. Thus, teaching strategies that support abstraction are important for teachers' arsenals. In this paper, I use a case study of a Grade one teacher to illustrate how she uses multiple representations as a learning progression for the purposes of abstraction. I present a detailed description of one specific lesson that incorporated multiple representations and discuss her pedagogy with her four chosen representation forms. Administrators and mathematics teachers can use this case as a model for how multiple representations can be used to move students to abstraction.
Centre for Innovation in Mathematics Teaching. 5th Floor Rolle Building, Faculty of Education University of Plymouth, Drake Circus, Plymouth, PL4 8AA, UK. Tel: +44-1752-585346; Fax: +44-1752-585344; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: Grade 1; Elementary Education; Early Childhood Education; Primary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Canada