ERIC Number: EJ978130
Record Type: Journal
Publication Date: 2012
Professor's Page: Is Understanding a Proficiency?
Australian Primary Mathematics Classroom, v17 n1 p19-20 2012
The everyday use of "proficient" carries connotations of having reached a level of expertise. One would not describe someone stumbling through a rendition of "Chopsticks" as a proficient piano player; but novice pianists work on musical proficiencies--practicing scales or playing a polka--in parallel. They do not put off playing the polka until they can play scales fluently. Like learning to play the piano, becoming mathematically proficient means engaging in certain actions even before one displays full competence with these actions. Becoming a proficient mathematician means working with all of the proficiencies (fluency, reasoning, problem solving and understanding) from the beginning. This challenges the popularly held view (myth even) that children first become fluent in adding, creating equivalent fractions, naming shapes, or whatever and only then can apply this to solve problems, or reason about it. One needs continuously to challenge this "fluency first" view as otherwise building the other proficiencies into mathematics lessons may be put off to some later (and again often mythical) time when learners are "ready" to engage with them. In other words, taking the stance of the proficiencies as actions means moving from seeing school mathematics as a body of knowledge for learners to acquire, to seeing it as an activity to engage in; or, in the words of Brent Davis, moving from seeing mathematics as preformed to mathematics as performed. In this article, the author discusses what these proficiencies look like in action. Paying attention in mathematics lessons to a good balance of the actions involved in fluency, problem solving and reasoning will lead to connected, robust, related understanding.
Descriptors: Expertise, Problem Solving, Mathematics Instruction, Primary Education, Foreign Countries, Teaching Methods, Mathematics Curriculum
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: email@example.com; Web site: http://www.aamt.edu.au
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Elementary Education; Primary Education
Authoring Institution: N/A
Identifiers - Location: Australia