id: 05948992
dt: j
an: 2011f.00393
au: Richardson, Kerri; Carter, Tyrette; Berenson, Sarah
ti: Connected tasks: the building blocks of reasoning and proof.
so: Aust. Prim. Math. Classr. 15, No. 4, 17-23 (2010).
py: 2010
pu: Australian Association of Mathematics Teachers (AAMT), Adelaide, SA
la: EN
cc: E43 U63
ut: problem solving; reasoning; foundations of mathematics; teaching methods;
thinking skills; geometric concepts; concept formation; manipulative
materials
ci:
li: http://www.aamt.edu.au/Webshop/Entire-catalogue/Australian-Primary-Mathematics-Classroom
ab: Summary: 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
studentsâ€™ 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.) (ERIC)
rv: