NotesFAQContact Us
Collection
Advanced
Search Tips
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ904886
Record Type: Journal
Publication Date: 2010-Oct-5
Pages: 10
Abstractor: As Provided
Reference Count: 30
ISBN: N/A
ISSN: ISSN-1473-0111
Characterising the Cognitive Processes in Mathematical Investigation
Yeo, Joseph B. W.; Yeap, Ban Har
International Journal for Mathematics Teaching and Learning, Oct 2010
Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their research. Moreover, there is a research gap in studying the thinking processes in mathematical investigation, partly because it is not easy to define these processes. Therefore, this article seeks to address these issues by first distinguishing between investigation as a task, a process and an activity; and then providing an alternative characterisation of the process of investigation in terms of its core cognitive processes: specialising, conjecturing, justifying and generalising. These will help to clarify the relationship between investigation and problem solving: an open investigative activity involves both problem posing and problem solving; but the problem-solving process entails solving by the process of investigation and/or by using "other heuristics". In other words, mathematical investigation does not have to be open. The article concludes with some implications of this alternative view of mathematical investigation on teaching and research. (Contains 2 figures.)
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: feedback@cimt.org.uk; Web site: http://www.cimt.plymouth.ac.uk/journal/
Publication Type: Journal Articles; Reports - Evaluative
Education Level: Adult Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A