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ERIC Number: EJ906682
Record Type: Journal
Publication Date: 2010
Pages: 7
Abstractor: ERIC
Reference Count: 12
ISSN: ISSN-1326-0286
Connected Tasks: The Building Blocks of Reasoning and Proof
Richardson, Kerri; Carter, Tyrette; Berenson, Sarah
Australian Primary Mathematics Classroom, v15 n4 p17-23 2010
Finding patterns, and making and justifying conjectures are considered the building blocks of mathematical reasoning and proof. Curriculum revisions in the United States and Australia place increased emphasis on problem solving and reasoning in the primary school curriculum. A number of curriculum resources for teachers are available but under current reform efforts, primary teachers require additional ideas to extend problem solving and reasoning in their classrooms. The authors have conducted teaching experiments with Grade 5 students that engaged them in generalising and justifying rules using three pattern-block tasks. The majority of students were able to successfully generalise to find an explicit rule, and to justify their rules. Individually, students in Grades 3 and 4 have also successfully completed the pattern-block tasks. They attribute the success of these students' reasoning activities to the three tasks that shared common features, known as connected tasks. Connected tasks share relationships, contexts, properties, and/or operations. These types of tasks are one way to encourage reasoning and proof throughout each grade level. The authors describe the pattern-block tasks as examples of connected tasks that share relationships and contexts. They describe how pattern blocks can be used to engage students in a variety of open-ended challenges. (Contains 5 figures and 3 tables.)
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:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Elementary Education
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Australia