Analysing abstraction

Although problem solving is widely acknowledged as a key skill for scientists, the deliberate development of the skill remains a challenge. After an exam, it’s common to hear ‘That wasn’t fair – we’ve never done that before’, when the question simply required the application of knowledge that had been encountered before to an unseen example.

The application of knowledge and skills to a new problem is not such a simple task in practice, as shown in a new study by Melissa Weinrich and Hannah Sevian, which investigated students’ abstraction while solving mechanistic problems in organic chemistry. The lessons learned provide valuable insight for those who teach organic chemistry at all levels.

A key challenge for students when approaching mechanisms is understanding the symbolic representation of abstract concepts and processes, with many students adopting a join-the-dots approach to drawing a mechanism with curly arrows. Success in this is connected to the ability to derive and apply the implicit features of representations (eg the presence and influence of electronegative atoms, lone pairs, etc) rather than relying on the interpretation of explicit features such as the atoms shown in a formula and the lines connecting them.

Three approaches

Previous work has shown students adopt three reasoning approaches when solving problems. Students using ‘rule-based’ reasoning are often unsuccessful as they attempt to solve complex problems with reference to a single rule (eg nucleophiles attack electrophiles). Greater success is achieved with ‘case-based’ reasoning, where they might apply a specific reaction, and the sequence of processes it comprises, to solve a related problem. ‘Model-based’ reasoning (eg the application of the S_N 2 mechanistic model) also fosters success, allowing students to break problems down into chunks.

In this study, the researchers interviewed students after exams, using Livescribe pens to capture written work and the accompanying verbal narrative. They used representation mapping, comparing students’ ‘new instance’ representations – ie how they view the problem at hand – with their ‘stored knowledge’ representations, which relate to the resources applied by students to solve the problem. In doing this, the researchers derived the level of abstractness in approach. Phrases such as ‘I need to form a line here’ and ‘I need to get rid of this OH’ were deemed to characterise low levels of abstractness, in contrast to phrases such as ‘Oxygen is electronegative … the carbon attached to the oxygen could be an electrophile’.

While I’ve captured the essence of the study here, there is much more covered in the article itself. The data, including quotes and handwritten mechanisms, provides fascinating insight into students’ thought processes – something a simple handwritten mechanism viewed ‘after the event’ fails to convey. One of the key conclusions of the authors is that higher levels of abstraction are characteristic of students who are better able to generate plausible mechanisms and demonstrate understanding of the underlying principles, which infers important implications for educators.