Reasoning with proportion

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Abstract reasoning rather than rule-following helps lower-attaining students, new evidence suggests

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A student’s ability to deal with the concept of proportion significantly influences their success in science subjects.

Unfortunately, at secondary level, many students are still developing their understanding of proportional reasoning. These students rely on concrete reasoning (CR) methods, like rules and algorithms, to solve proportion problems, rather than abstract reasoning (AR), which experts in proportional reasoning use.

Within chemistry, proportional reasoning is important to understand many numerical topics, most notably stoichiometry.

Some reports in the chemistry education research literature have shown that students who can successfully solve stoichiometry problems using CR may not understand the chemical concepts conveyed by a balanced equation. Others suggest heavy reliance on CR methods could hinder the development of the higher order, and more desirable, AR.

An abstract curriculum

In a new study, Michael Page and his team from California State Polytechnic University, US, investigate whether implementing a chemistry curriculum favouring AR can support students at all levels of mathematical attainment to learn chemistry. The study involved around 270 US high school students and two teachers. A control group of students received instruction through CR, for a whole teaching year, whereas another group were taught using AR. The researchers used students’ performance in state and district chemistry exams to measure their learning gains.

The teachers, along with university lecturers and undergraduate thesis students, formed a learning community in order to standardise their approach to teaching chemistry using AR. This was particularly important as both teachers normally teach with CR methods, such as dimensional analysis, which is common in the US.

In addition to stoichiometry, they tried teaching gas laws, pH, solutions, thermodynamics, reaction rates and equilibria with AR methods.

The study’s results showed that instructional approaches rich in AR were as good as or better than CR-based approaches across all of the topics. The AR methods seemed to particularly support the development of students who had lower levels of mathematical attainment. Given the likely lesser-developed proportional reasoning skills of these students, you might conversely expect these students would better succeed with CR instructional methods.

Teaching tips

The most easily recognised CR-based approach, dimensional analysis, is not widely adopted in high school chemistry in the UK. Instead, most teachers already favour approaches rooted in AR. However, the validation of AR-based approaches is useful and leads to a number of reflections:

By adopting an AR approach in our chemistry teaching we are helping students to develop their proportional reasoning.
When we teach concepts rich in proportional reasoning using rules or algorithms, it might inhibit students’ development of proportional reasoning.
We might tend to teach an algorithm or a rule to weaker students, so that they can get the correct answer, perhaps without the understanding. This study suggests this is not necessary for such students to succeed.