Tackling mathematical misconceptions in science

The disconnect between mathematical understanding in maths lessons and its application in scientific contexts continues to be a challenge. Research shows that students who perform well in maths can struggle to transfer these skills to scientific problem-solving, highlighting a fundamental issue in cross-curricular learning.

The transfer problem

Some science teachers assume that maths skills taught in mathematics lessons will automatically transfer to science contexts. Osborne (2014) calls this the ‘vaccination model of mathematics’. In fact, even students who excel in maths and physics fail to make substantial links between these contexts (Woolnough 2000). To support students in making these connections science teachers need to research and anticipate the common mathematical misconceptions (EEF 2017).

Common mathematical misconceptions affecting science

Several persistent misconceptions significantly impact students' performance in scientific calculations:

Decimal place value: Students frequently misunderstand decimal notation, for example believing that no numbers exist between 2.2 and 2.3, or that 0.625 is larger than 0.9. These misconceptions directly affect measurement recording and data manipulation.

Operations with decimals: Hart et al. (1981) found that only 13-18% of students aged 12-15 could correctly identify which operations yield larger results across whole numbers and decimals.

Students were asked to ring the option that gave the biggest answer:

1. 8 x 4 OR 8 ÷ 4
2. 8 x 0.4 OR 8 ÷ 0.4
3. 0.8 x 0.4 OR 0.8 ÷ 0.4

The common misconception that "multiplication makes bigger", causes systematic errors when working with values less than one. This led many students in the survey to believe that 8 x 0.4 was greater than 8 ÷ 0.4 for example.

Significant figures: Students commonly confuse decimal places with significant figures and fail to apply leading zero rules correctly. For example, 0.0020490 contains five significant figures, not seven, as the leading zeros serve only as placeholders.

Evidence-based pedagogical approaches

The Education Endowment Foundation (2022) recommends several strategies that science teachers can implement to reduce the impact of mathematical misconceptions:

Think Aloud protocols: Research suggests that verbalising cognitive processes during problem-solving provides effective modelling for students. When approaching examination questions, teachers should explicitly articulate their reasoning, making implicit thought processes visible to learners.

Fading techniques: Pritchard (EEF, 2022) notes that "for many pupils the leap from a single worked example to independent practice is too great." Graduated scaffolding (providing fully worked examples followed by partially completed problems) supports students in developing independent problem-solving capabilities. This strategy is called fading because worked examples are gradually faded from the bottom up.

Visual representations: Tools such as double number lines support students in understanding proportional relationships and unit conversions, addressing difficulties with concentration calculations and similar proportional reasoning tasks.

Recommendations for practice

Science teachers need to explicitly teach mathematical skills within scientific contexts rather than assuming all students are competent. Collaborating with mathematics departments and sharing common misconceptions and pedagogical strategies, strengthens cross-curricular coherence. Ultimately, effective science education requires not just content knowledge, but the ability to apply mathematical reasoning within scientific frameworks - a distinct pedagogical challenge requiring targeted instructional approaches.

References used in the presentation:

Clegg, A. and Collins, K. (2023) Grappling with Graphs: A Guide for Teachers of 11-16 Science. Hatfield: Association for Science Education.

Clegg, A. and Collins, K. (2023a) GCSE Science (9-1) Maths in Science Practice Pack. London: Collins.

Dabell, J. (n.d.) '20 Classic Maths Misconceptions' [Blog post]. Available at: https://www.ncetm.org.uk (Accessed: 5 February 2026).

Education Endowment Foundation (2017) Improving Secondary Science: Guidance Report. London: Education Endowment Foundation. Available at: https://educationendowmentfoundation.org.uk/education-evidence/guidance-reports/secondary-science

Education Endowment Foundation (2022) Improving Mathematics in Key Stage 2 and 3: Guidance Report. London: Education Endowment Foundation. Available at: https://educationendowmentfoundation.org.uk/education-evidence/guidance-reports/maths-ks-2-3

Fisher, D., Frey, N. and Lapp, D. (2011) 'Coaching middle-level teachers to think aloud improves comprehension instruction and student reading achievement', The Teacher Educator, 46(3), pp. 231-243. doi: 10.1080/08878730.2011.552660

Hart, K., Brown, M., Kerslake, D., Küchemann, D. and Ruddock, G. (1981) Children's Understanding of Mathematics: 11-16. London: John Murray.

Mulholland, M. (2022) 'Teaching Problem Solving', in Improving Mathematics in Key Stages Two and Three: Evidence Review. London: Education Endowment Foundation, pp. 42-51.

Ness, M. (2016) 'Reading Comprehension Strategies in Secondary Content Area Classrooms: Teacher Use of and Attitudes Towards Reading Comprehension Instruction', Reading Horizons, 55(1), pp. 58-84.

Osborne, J. (2014) 'Teaching Scientific Practices: Meeting the Challenge of Change', Journal of Science Teacher Education, 25(2), pp. 177-196. doi: 10.1007/s10972-014-9384-1

Shulman, L.S. (1986) 'Those Who Understand: Knowledge Growth in Teaching', Educational Researcher, 15(2), pp. 4-14. doi: 10.3102/0013189X015002004

Woolnough, J. (2000) 'How do students learn to apply their mathematical knowledge to interpret graphs in physics?', Research in Science Education, 30(3), pp. 259-267. doi: 10.1007/BF02461632