Chemical calculations can leave students feeling lost. Use these tips to help them find the way

Chemical calculations, such as those found in kinetics or thermodynamics topics, are notoriously challenging for students. To solve these, students need to apply knowledge of chemistry and mathematics. Often teachers feel that their students just can’t do the maths, but the challenges are more nuanced.

The mathematical modelling cycle (MMC) is a framework used to understand how students solve problems in contexts such as chemical calculations. The first step in the cycle involves mathematisation – a student translates a real model, such as a chemical reaction, into a mathematical model by constructing mathematical relationships using appropriate parameters, such as rate constants. In the second step, mathematical work is performed, such as algebraic operations, to generate a mathematical result. To close the cycle, the mathematical result is evaluated by validating against the initial real model.

An important aspect of the MMC is acknowledging the contribution of extra-mathematical (or discipline-specific) knowledge, to the problem-solving process.

Problem-solving trajectories

As part of a study, researchers from Sweden have further developed the MMC and used their extended MMC to visualise student problem-solving trajectories. This has provided insights into how students succeed, or otherwise, when working on chemical calculations.

The researchers observed pairs of second-year chemistry and chemical engineering students as they attempted to solve a set of tasks in chemical kinetics. Students were given tasks on steady-state approximation, and needed to apply varying degrees of chemistry and mathematics to answer the questions correctly.

Teaching tips

• To improve students’ success in chemistry calculations, it’s necessary to drill them and get them to practise mathematical fluency in both a context-free and a chemistry setting.
• Use prompts to help your students identify the chemistry knowledge presented in questions which is both relevant and irrelevant to solving a particular problem.
• Explicitly refer to the extended MMC, or other such frameworks, to help demystify the process for your students. This approach could improve students’ metacognitive awareness.
• Discuss the importance of deliberation and evaluation of each step of the problem-solving process to help prevent students from making the errors highlighted in this study.
• Use explicit prompts to help students evaluate their final mathematical result.
• Develop trajectories and case studies that are appropriate for your own teaching. These will help you understand how your students are tackling problem-solving questions and improve your feedback. The case studies in this paper, describing various problem-solving trajectories, will help.

They captured students’ problem-solving processes using a think-aloud protocol. They used video to record students as they asked them to verbalise what they were doing, using a smart pen to capture students’ pen strokes. A qualitative evaluation of this data, using thematic analysis, led to the development of an empirically derived, extended MMC. The extended MMC includes descriptions of various subprocesses students engage in, such as indicating phases of deliberation and evaluation in both the mathematisation and mathematical work parts of the cycle.

In the classical MMC, extra-mathematical knowledge is only invoked during processes preceding the construction of the mathematical model. In this study, the extended MMC shows that extra-mathematical knowledge plays a significant role during the entire MMC, including the mathematical work phase. The researchers used the additional detail in the extended MMC to analyse the problem-solving trajectories that students took during their attempts at reaching a solution. This approach allowed them to visualise students’ transitions between different processes and their use of extra-mathematical knowledge.

They used the extended MMC to diagnose the origin of students’ difficulties in the tasks. For example, in one of the presented case studies, despite being sufficiently mathematically proficient, students struggled to construct the correct mathematical model because they used only mathematical reasoning and didn’t employ their chemistry knowledge.

This study details how important it is for students to develop mathematical fluency in a context-free environment, such as in a maths classroom. However, the significance of using extra-mathematical knowledge throughout the problem-solving process also shows the importance of developing mathematical fluency in a chemistry context.

Reference

S Ye et alChem. Educ. Res. Pract., 2024, 25, 242–265 (https://doi.org/10.1039/D3RP00168G)

Fraser Scott