In the actual task as implemented, the mixed ability of the students led to the teacher’s
decision to work at a pace that catered adequately for slow pace students but did not
extend the ‘brighter’ students to their full potential (teacher interview). Most students
(including ‘brighter’ students) reported how much they enjoyed being in this teacher’s class
and how much more they learnt than in most mathematics classes. The teacher selected a
pathway that progressed from specific examples to tabulation to discussion of a studentrecognised
pattern to algebraic manipulation to confirm the pattern. The teacher integrated
Susan’s discovery of a pattern into the whole class discussion. She acknowledged the
correctness Leon’s recognition of the complimentary variation of dimensions to retain the
same perimeter but she did not integrate this into the discussion. Leon’s explained his use
of the dimensions [9, 10] to find the width when the length was 9.6 by “moving the point
six around the corner”. This potentially could have been a precursor to a mathematical
argument based on variation within the physical context.