A detailed description of the task can be found here.
We began the session by discussing Task 3: Decimal Interviews which we had carried out in pairs at school in previous weeks. I think a lot of us had been astounded by the number of misconceptions that students had; some of the key points are below:
- doing investigations on a calculator to try to find the rule
- sometimes needed to use a closed question to elicit a response
- in multiple choice questions, pupils tried to find the 'teacher pattern' rather than the 'mathematical pattern'
- something about a zero made pupils believe a number was much smaller
- introducing a conflict can elicit response and thinking
- correct answer may not necessarily mean correct thinking
- anticipate certain misconceptions and plan probing questions
- wait time: need to give students the time to think before asking
- some students feel the need to answer every question, even when the question is not directed at them
- choosing example is important: it appeared a lot of the students had been exposed predominantly to decimals that had a value of less than 1
We then had a long discussion about a number of activities that may relate to the concepts of ratio and proportion. One particular question stirred a lot of responses:
Student A got 9 out of 10 for this test. Student D sat the same test but his teacher marked it on a different scale. Student D got 93 out of 100 for his test. Did someone do better? If so, who?It was also discussed that introducing conflict may serve to increase motivation of the students and forcing them to address their misconception, e.g. are 2/3 and 3/4 the same?
After this session we were encouraged to read further literature on the topic:
Resnick R. B. et al. (1989), Conceptual Bases of Arithmetic Errors: The Case of Decimal Fractions, Journal for Research in Mathematics Education, 20 (1) 8-27
