Drawing inferences from learners’ examples and questions to inform task design and develop learners’ spatial knowledge

Journal article

Examples that learners generate, and questions they ask while generating examples, are both sources for inferring about learners’ thinking. We investigated how inferences derived from each of these sources relate, and how these inferences can inform task design aimed at advancing students’ knowledge of scale factor enlargement (i.e. scaling). The study involved students in two secondary schools in England who were individually tasked to generate examples of scale factor enlargements in relation to specifically designed prompts. Students were encouraged to raise questions while generating their examples. We drew inferences about students’ thinking from their examples and, where available, from their questions. These inferences informed our design and implementation of a set of follow-up tasks for all students, and an additional personalised task for each student who raised any questions. Students showed increased knowledge of, and confidence with, scale factor enlargement independently of whether they asked questions during the exemplification task.

Authors: Bentley, J; Stylianides, G

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Journal of Mathematical Behavior
• Volume: 47
• Pages: 35–53
• Publication date: 2017-07-06
• Acceptance date: 2017-06-08
• DOI: 10.1016/j.jmathb.2017.06.001
• ISSN: 0732-3123
• Keywords: learners' questions; exemplification; scaling; enlargement; mathematics; learners' examples