May Reading Group – by Gemma Crowe
Title: Viewing basic math through the lens of history: Undergraduates’ reflective learning in a history-augmented mathematics classroom
Link: https://doi.org/10.15663/wje.v22i4.557
Key words: Fibonacci tiling, fang cheng method, Meru prastara, non-western maths, reflective learning
This paper discusses an example of integrating history of mathematics into the curriculum, and how this affects students’ understanding and engagement.
The study was undertaken by first-year students at a university in North Central Nigeria, and focused on three topics: sequences, matrices and combinatorics. The first topic explored Fibonacci numbers, where students first wrote a historical summary of Fibonacci, before exploring the geometrical interpretation of this sequence, by forming the Fibonacci spiral. The second topic focused on the Chinese fang cheng method of solving linear equations. The relevant context in ancient China was discussed, followed by examples of these calculations. The final topic was explored through the history of maths in ancient India. Students learnt about the Meru prastara, an alternative formulation of Pascal’s triangle, which led to understanding of binomial expansions.
During the course, students were given ‘logbooks’, which were used as a form of reflective journalling. These were regularly reviewed by the teacher, who would highlight questions and reflections in class. These logbook entries were collated into a final report, of which a qualitative analysis was undertaken, to assess students’ engagement and understanding of the course.
From this analysis, students reported more concrete and intuitive understanding of abstract concepts. They were also more engaged with their learning, by seeing how mathematics can be connected to everyday applications. The historical context aided understanding of these concepts, and in some cases simplified mathematical approaches, such as the fang cheng method. Students appreciated the creative and human aspect of maths, by seeing how ancient and multicultural mathematics has led to our knowledge today.
Discussion points from reading group:
- As this study was based in Africa, why weren’t historical references from African origins used? One reason may be the difficulty in finding such resources.
- Would this reflective method of teaching be more appropriate in a HoM module? How do you incentivise students to take part in the reflective aspect of teaching, particularly if it isn’t part of their overall grade. This idea of reflective journalling was tried at St Andrews, where students’ journalling contributed to their final grade. However, this idea is only applicable in smaller courses, due to the workload on the teacher.
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