Embedding algorithmic thinking into 1st year undergraduate programmes
DOI:
https://doi.org/10.21100/msor.v24i3.1686Keywords:
Algorithms, Graduate SkillsAbstract
We describe the embedding of algorithms and algorithmic thinking into a first-year undergraduate pure mathematics course at the London School of Economics (LSE). Responding to growing demand for computational thinking skills, we redesigned ‘Introduction to Abstract Mathematics’ to integrate algorithmic approaches throughout the curriculum rather than as an isolated topic. Using the Knowledge, Skills and Behaviours (KSBs) framework adapted from degree apprenticeships, we developed learning outcomes that distinguish knowing algorithms from thinking algorithmically. Our approach reformulates traditional proofs using constructive and algorithmic methods, introduces loop invariants alongside mathematical induction, and shows how algorithms can both prove mathematical statements and have their own properties proven.
References
Anderson, L.W. and Krathwohl, D.R. (2001) A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom's Taxonomy of Educational Objectives. New York: Longman.
Brown, J.S., Collins, A. and Duguid, P. (1989) 'Situated cognition and the culture of learning', Educational Researcher, 18(1), pp. 32-42.
CBI/Pearson (2023) Education and Skills Survey 2023. London: Confederation of British Industry.
Collins, A., Brown, J.S. and Newman, S.E. (1989) 'Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics', in Resnick, L.B. (ed.) Knowing, Learning, and Instruction: Essays in Honor of Robert Glaser. Hillsdale, NJ: Lawrence Erlbaum, pp. 453-494.
Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C. (2022) Introduction to Algorithms. 4th edn. Cambridge, MA: MIT Press.
Evans, J.S.B. and Stanovich, K.E. (2013) 'Dual-process theories of higher cognition: Advancing the debate', Perspectives on Psychological Science, 8(3), pp. 223-241.
Floyd, R.W. (1967) 'Assigning meanings to programs', Proceedings of Symposia in Applied Mathematics, 19, pp. 19-32.
Henderson, P.B., Cortina, T.J. and Wing, J.M. (2007) 'Computational thinking', ACM SIGCSE Bulletin, 39(1), pp. 195-196.
High Fliers Research (2024) The Graduate Market in 2024: Annual Review of Graduate Vacancies & Starting Salaries. London: High Fliers Research Limited.
Hoare, C.A.R. (1969) 'An axiomatic basis for computer programming', Communications of the ACM, 12(10), pp. 576-580.
Institute for Apprenticeships and Technical Education (2023) Developing Knowledge, Skills and Behaviours (KSBs). Available at: https://www.instituteforapprenticeships.org (Accessed: December 2025).
Kahneman, D. (2011) Thinking, Fast and Slow. New York: Farrar, Straus and Giroux.
Lave, J. and Wenger, E. (1991) Situated Learning: Legitimate Peripheral Participation. Cambridge: Cambridge University Press.
Lockwood, E., DeJarnette, A.F. and Thomas, M. (2016) 'Computing as a mathematical disciplinary practice', Journal of Mathematical Behavior, 41, pp. 171-183.
Meyer, J.H.F. and Land, R. (2003) 'Threshold concepts and troublesome knowledge: Linkages to ways of thinking and practising within the disciplines', in Rust, C. (ed.) Improving Student Learning: Improving Student Learning Theory and Practice – Ten Years On. Oxford: OCSLD, pp. 412-424.
Meyer, J.H.F. and Land, R. (2006) Overcoming Barriers to Student Understanding: Threshold Concepts and Troublesome Knowledge. London: Routledge.
O'Neil, C. (2016) Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy. New York: Crown.
Piaget, J. (1952) The Origins of Intelligence in Children. New York: International Universities Press.
QAA (2023) Subject Benchmark Statement: Mathematics, Statistics and Operational Research. Gloucester: Quality Assurance Agency for Higher Education.
Vygotsky, L.S. (1978) Mind in Society: The Development of Higher Psychological Processes. Cambridge, MA: Harvard University Press.
Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L. and Wilensky, U. (2016) 'Defining computational thinking for mathematics and science classrooms', Journal of Science Education and Technology, 25(1), pp. 127-147.
Wiggins, G. (1990) 'The case for authentic assessment', Practical Assessment, Research, and Evaluation, 2(2).
Wing, J.M. (2006) 'Computational thinking', Communications of the ACM, 49(3), pp. 33-35.
