Torquetum

 

The authors ran a very interesting study in three stages. The first stage was a short assessment of three MC questions involving the relationships between equations and their representative graphs, the first two only linear, the third linear and quadratic. The questions were quickly answered and easily graded. The second stage was giving summaries of student responses back to the class for discussion (not led by the lecturer). Directly after discussion the students were asked to write about the questions. One group was asked to write about the underlying concepts necessary to answer the questions correctly. The second group was asked to write about why students might have given incorrect answers. These written responses were also evaluated. The third stage of the study was to ask the students to answer a survey (strongly agree/disagree Likert style) testing hypotheses developed during the first two stages. The findings are interesting and point, yet again, to the student tendency to want to do calculations even if the question might not require them - “blind attraction to processes” (p. 379) - and also to the expectation that similar problems should have been encountered before. Interestingly, the students in the second writing group wrote more than those in the first, but did not make many references to actual underlying concepts. The authors stress that if you want students to write or talk about underlying concepts you need to make that explicit.

 

The authors present the design of this study as a way of using writing to encourage reflection without it taking a lot of time or being difficult to grade. I agree and would like to try this myself. Running effective writing assignments in a maths class can be very hard to get right. The authors make reference to cognitive conflict and how resolving a cognitive conflict can lead to cognitive growth. “It is not the intent of this article to explore the efficacy of using writing or conflict resolution in the mathematics classroom but to take that as given …” (p. 373).

 

 

This is quite a lengthy paper which I shall summarise very briefly. The authors disagree (as many do) with the notion that students can transfer problem solving techniques from typical classroom problems (word problems, usually) to workplace problems, which are ill-structured. They conducted interviews with approximately 90 professional engineers about problems they had encountered and how they had solved them. The authors develop 12 themes which emerged from the interviews, such as “most constraints are non-engineering” and “Engineers primarily reply on experiential knowledge”. The authors close with suggestions for education, such as using PBL (problem based learning). This requires huge commitment from staff and wide ranging reform, however, and can be hard to achieve. Other than that they give suggestions on how to make classroom activities more like workplace situations.