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Mathematical modelling as a vehicle for eliciting algorithmic thinking

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Abstract

Developing students’ competence in algorithmic thinking is emerging as an objective of mathematics education, but despite its inclusion in mathematics curricula around the world, research into students’ algorithmic thinking seems to be falling behind in this curriculum reform. The aim of this study was to investigate how the mathematical modelling process can be used as a vehicle for eliciting students’ algorithmic thinking. To achieve this aim, a generative study was conducted using task-based interviews with year 12 students (n = 8) to examine how they used the mathematical modelling process to design an algorithm that solved a minimum spanning tree problem. I observed each students’ modelling process and analysed how the task elicited the cognitive skills of algorithmic thinking. The findings showed that the students leveraged their mathematical modelling competencies to formulate a model of the problem using abstraction and decomposition, designed their algorithms by devising a fundamental operation to transform inputs into outputs during the working mathematically transition, and debugged their algorithms during the validating transition. Implications for practice are discussed.

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Data availability

The data used in this study are not available to the public due to the constraints imposed by the Ethics Approval process at Queensland University of Technology.

Notes

  1. Algorithmatising tasks invite students to create, test, and revise algorithms in response to a given problem (Moala, 2021).

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Authors and Affiliations

  1. School of Teacher Education and Leadership, Faculty of Creative Industries, Education and Social Justice, Queensland University of Technology, E Block, Level 3, Victoria Park Road, Kelvin Grove, Brisbane, QLD, 4059, Australia

    Timothy H. Lehmann

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  1. Timothy H. Lehmann
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Correspondence to Timothy H. Lehmann.

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Appendices

Appendix 1

Each year, the school runs a fete to raise money for charity. Each house runs a stall that prepares and sells a unique food item that requires cooking equipment. However, the locations of each stall do not have access to electricity. All stalls must therefore be connected to the source of electricity located next to the rear entry of the Administration Building.

Your task is to design an algorithm that calculates the minimum length of electrical cable needed to connect each stall to the source of electricity.

figure a

Scale 1:1000.

Note: The source of electricity is identified for the reader by the star in this map, which did not appear in the map provided to the students.

Appendix 2

Suppose the location of each stall is changed for the fete next year, and these changes are reflected in the following vertex-edge graph. Use this revised graph to ensure that your algorithm will find the shortest length of cable for the new arrangement of stalls.

figure b

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Lehmann, T.H. Mathematical modelling as a vehicle for eliciting algorithmic thinking. Educ Stud Math 115, 151–176 (2024). https://doi.org/10.1007/s10649-023-10275-4

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