Blog

A blog, largely about what we have been discussing in our monthly online meetings (readings, seminars and experience-sharing sessions). Please discuss posts on the JISCmail list (Sign up)

 

  • Reflections on the Manchester Workshop by Robbie Bickerton, Troy Astarte & Gemma Crowe

    Reflections on the Manchester Workshop by Robbie Bickerton, Troy Astarte & Gemma Crowe

    Robbie Bickerton:

    The HIDIM workshop in Manchester was a valuable opportunity to exchange ideas and hear different perspectives. I came to this workshop as a mathematician with an interest in history and the different contexts underlying mathematical developments. The workshops was a great opportunity to connect with others who have similar interests and learn from their expertise and suggest areas for collaboration. In particular it is exciting to see how such discussions around history, diversity and bias can be embedded into the teaching of maths going forward.

    Troy Astarte:

    Perhaps it was the theming of this workshop around co-creation, but I noticed a distinctly reflective tone creeping into many discussions—on- and off-stage—as participants thought about their relationships with students in a deeper way than in others. Indeed, the presence of some students grounded our talk in real student experiences in a way that reporting on outcomes didn’t quite provide. Perhaps we should seek to have regular student members of the working group? We must also remember, however, that the students who are sufficiently keen not only to engage in co-creation but to travel to a workshop outside of term-time might not fully represent the entire cohort! On a more personal note, I enjoyed the discussions of neurodiversity and queerness coming in, and I believe this was the event that I have attended with the highest proportion of non-binary people outside specifically queer spaces. Small wonder I felt comfortable in the space!  

    Gemma Crowe:

    Tom Coleman (University of St Andrews) gave an excellent talk entitled “Student-staff co-creation for accessibility and inclusion”, in which he discussed three student co-creation projects. The talk was followed by a closely related panel discussion on co-creation projects. Many of the outputs from these projects are now available on the HIDIM repository (https://www.mathshist4edi.org.uk/). Here are some of my thoughts and takeaways from these discussions. “Guide rather than a boss” This was a quote from Tom about how we approach student-staff co-creation which really stuck with me. It gives students more agency, but I think, crucially, it helps to bridge the gap between students and what can often feel like the ‘intimidating’ lecturer. I think it can be easy to forget as staff that as a student, approaching staff can be daunting for students. However, leaving students somewhat in the dark with no guidance at all may also prove unproductive. Projects as modules? There are pros and cons to running these projects as credited undergraduate courses. There can be better engagement and motivation, and staff have direct contact with students. On the other hand, marking can be difficult and time-consuming. Feedback from students Two points were made about what students found enjoyable or helpful in these projects. One was the sense of community created by working in pairs or groups and exchanging ideas. The other was enthusiasm from their teachers! Having an open line of communication throughout meant that staff were approachable and helped break this barrier. Tom also emphasised in his talk how much we can learn from students that we otherwise wouldn’t think about – for example, the STARMAST website gained more attention and awareness through a social media campaign by the university. Setting up projects Student-staff co-creation can be a win-win: students gain valuable experience and skills for career development, as well as pay for their contributions. Staff get fresh ideas and innovation, direct feedback on course material and engagement of students, and most importantly, create high-quality resources with the students. In terms of finding students to work with, it was noted that grades don’t mean everything. Students who find the work more challenging may also be the best candidates and will get the most out of projects like these. One thing to consider is to seek out ‘keen’ students (e.g. those who come to office hours) who may have a more personal investment in the project.
  • Registration open for Manchester Workshop, 7-8 Sept
    In person registration and online registration are now open for our 2-day workshop in Manchester on 7-8 Sept, and we look forward to seeing lots of you there. This workshop will run from mid-morning (11.00 coffee, 11.30 session start) on Monday 7 Sept., until mid afternoon (15.00 finish & tea) on Tuesday 8 Sept. We hope this will enable many participants to attend with only one night away from home. Registration, teas/coffees and lunches are free, and we can offer some help with travel and accommodation costs for those, especially students and independent scholars, who do not have other sources of funding. The main focus of the workshop is on student-staff co-creation of resources that draw on history of maths to promote inclusivity and decolonisation in the maths curriculum. The programme will include:
    • A presentation from Sayori Ghoshal (Max Planck Institute, Berlin) on the historical development of statistical sciences,  and their impact on community identity formation in colonial and postcolonial India
    • A presentation from Tom Coleman (St Andrews) on the “Inclusive Activities” project at St Andrews
    • A panel discussion between staff-student co-creation teams, including Rehan Shah (Queen Mary University of London), Isobel Falconer (St Andrews), Ciarán Mac an Bhaird (Maynooth) plus students (names to be confirmed)
    • Lightning talks and/or short presentations from attendees
    • Collaborative resource development & upload, review and improvement of the HIDIM repository
  • June 5 2026 – Experience sharing with David Pritchard

    Title: Mathematics in Society: two years of teaching it (mostly) wrong?

    A recent review of our first-year curriculum at the University of Strathclyde gave us the opportunity to introduce a new module, Mathematics in Society. This is a core module for students on single-honours mathematics and statistics degrees, which aims to address a perceived lack of “soft” skills; at the same time, it aims to broaden students’ understanding of mathematics, drawing on resources from the history of mathematics.
    Content and approach
    The starting point for students is the question “What is mathematics, anyway?” (We warn them that we will not answer this!) Specifically, we pose questions such as “where do mathematical ideas come from?”, “who gets to spend their time doing mathematics?” and “where do people think mathematically?” Successive blocks look at mathematics and games, mathematics and government, mathematics and art, and mathematical modelling. Throughout we interpret “mathematics” as widely as possible, stressing the porous boundary between academic and non-academic mathematical activities. The spirit of the module is closest to that of Jacqueline Stedall’s The History of Mathematics: a Very Short Introduction (OUP, 2012), with some influence from Francis Su’s Mathematics for Human Flourishing (Yale, 2020). We don’t attempt to give an overall historical picture; we don’t focus on the names and stories behind the mathematics that students already know; and we don’t try to train students as historians. (It is a full-time job to steer students through the school/university transition and train them as mathematicians.) We do try to give students a historically informed sense of mathematics as a human activity, which is situated in specific contexts and cross-fertilises with other activities, and to encourage them to think carefully about sources and evidence. For example, in the “mathematics and art” block, we touch on topics such as weaving (as an art form and a technology, with discussion of patterns and algorithms), mathematics as a status indicator in art (with reference to the recently reinterpreted portrait of the Jamaican landowner Francis Williams), and the mathematical construction of average or “ideal” human beings (from da Vinci’s Vitruvian Man to eugenics). In a seminar, we compare the work of Marjorie Rice and Roger Penrose on tilings, using the area of recreational mathematics to discuss who counts as a mathematician and why.
    Reflections
    1. When we broadened the definition of mathematics, more diverse examples (at least along the axes of gender and of culture/nationality) followed naturally. We didn’t feel we were struggling to include “token” diversity.
    2. Students’ baseline knowledge was lower than we had anticipated. They generally found the history of mathematics interesting, but had little prior sense of who did what when. This suggests that the challenge isn’t to directly confront perceptions of mathematics as a white/Western/male monopoly, but to give students a framework for thinking about mathematics in which those perceptions don’t thrive.
    3. Students’ initial writing skills were often poor, they struggled to read texts of more than a few hundred words, and we had to start from scratch when it came to using and citing sources. However, students often responded thoughtfully in group discussions.
    4. Topics involving “fairness” and identity were often engaging – among the best work we’ve seen so far was a group essay on mathematics and ethics. However, the language of “politics” turned many students off immediately. I suspect that terminology needs to be very carefully chosen: to frame our goals as, for example, “decolonising the curriculum” easily alienates students who are sympathetic to the ideas but not the jargon.
    5. We had the luxury of being able to design low-stakes assessments, including individual and group writing and discussion sessions, which give students multiple routes to pass the module. Partly because of this and partly because we include peer review for all written work, we have so far seen very little sign of LLM-assisted dishonesty.
    6. However, breaching the familiar assessment “contract” based on worked examples caused anxiety. When students didn’t see an immediate connection between the content of lectures and the tasks set in assignments, some of them panicked and a few disengaged. This showed up strongly in the student feedback.
    I don’t think we’ve yet got this module right, and we’ll continue to experiment with topics and presentation. One major regret is that the themes in this module aren’t picked up directly in subsequent years – which is inevitable given the pressures on the curriculum. However, if we have succeeded then our students have at least glimpsed a larger and more inclusive mathematical world.
  • May 15 2026 Seminar – by Rowena Ball

    Title: Empirical mathematics in Australian Indigenous Smoke Telegraphy

    Link: Preprint at https://arxiv.org/abs/2603.26037

    Link: Recording of seminar

    Link: Slides

    Key words: Undergraduate mathematics, Indigenous mathematics, Smoke telegraphy

    This study is part of a research and teaching program that I lead at ANU on mathematical knowledge of non-Western and Indigenous societies. All societies that we know of developed, communicated and practised mathematics, yet it is usually assumed that Australian mathematics began in the 19th century with a colonially transplanted British-European curriculum. Documenting the rich but neglected mathematical heritage of First Nations cultures of Australia has been one of the delights of my research life.

    In the seminar I described some of the mathematics inherent in smoke telegraphy, a long-distance communications technology that was developed and practised from ancient to modern times by Aboriginal and Torres Strait Islander peoples of the Australian continent and islands. I juxtaposed aspects of that mathematics against analogous or cogent mathematical developments in European mathematics.

    The research is based on numerous archival primary sources from the 19th century and early 20th century. White colonial society was absolutely fascinated with smoke telegraphy, because it was used to track white explorers and travellers with high precision, the codes were kept secret by the Aboriginal master signallers (and are classified knowledge to this day), and across much of the continent it was a more effective system than electrical telegraphy until well into the 20th century. The research also draws on several precious pre-colonial sources from the mid to late 1600s and from 1770.

    Mathematical perception and know-how were intrinsic to smoke telegraphy. Beyond attributes such as quite complicated numerical coding, I described the use of chiral symmetry (or right- and left-handedness), which was understood and actively created by Indigenous smoke signallers, the use of frequency coding of the visible signals, and empirical knowledge of fluid dynamics.

    Why have we never heard of smoke telegraphy? What became of it? was a question asked. In the far north of Australia, beyond the reach of poles and wires and the broadcast range of radio transmitters, smoke signalling and telegraphy was still used until the 1940s, but knowledge of the finer points declined. It seems that the very real Japanese threat in WWII caused the military to suppress it, presumably for national security reasons. For a decade or so after the war smoke signals became infantilized as a Scout-camp exercise that some people’s grandparents might remember, but as a sophisticated long-distance communications technology smoke telegraphy seemed to disappear from white public consciousness, from newspapers and books, and from the published white colonial histories.

    How old might smoke-signalling technology be? is another question. Given the long cultural continuity of Australian Indigenous societies, smoke signalling as a method of long-distance communication may well be very ancient. Smoke is, of course, a natural signal, and humans would have exploited its potential very early in history. When sea levels were 80–150 m lower during a glacial maximum approximately 65,000 years ago, smoke from natural bush fires on the exposed Sahaul (Greater Australian) shelf would have been visible from several Indonesian islands and may have stimulated the original voyages to Australia. Did those voyagers who arrived safely perhaps send up smoke telegrams to be received by family and friends whom they left behind? “Arrived safely. Land of plenty. Build more outrigger canoes. Make sails. Come soon.” Was smoke signalling technology Australia’s first export to the world? Purely speculative, but not unreasonable, questions.

    Another speculative but reasonable sequitur from this study is that development of mathematical ideation in the human brain may occur at similar rates and levels in all societies, and that expression of those ideas is cultural in actuation but always serves a social purpose. Humans are a social, mathematical species.

    Australian Indigenous smoke telegraphy was a remarkable achievement on its own terms. All the evidence supports that, prior to the roll-out of electrical telegraphy, it was the most highly advanced, most effective, long-distance telecommunications technology in the world. It also affirms the cultural universality of mathematics.

    The materials and results of this study may be included in a cultural and historical introduction to first and second year tertiary mathematics and physical science courses where topics such as symmetries, groups, and the Fourier transform are studied. The systems properties of smoke telegraphy may inspire modelling and simulation problems to be set up and analyzed with modern mathematical, computational and machine learning tools. For Indigenous and minority students this study provides affirmation that mathematics is a valued part of their cultural heritage and identity and that Indigenous mathematical knowledge is rich and strong.

    Please comment/discuss the seminar and questions raised by it and the blog on the JISCmail list (Sign up)

     

  • 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.

    Please comment/discuss the reading and questions raised by it and the blog on the JISCmail list (Sign up)

 

  • Reflections on the Manchester Workshop by Robbie Bickerton, Troy Astarte & Gemma Crowe

    Reflections on the Manchester Workshop by Robbie Bickerton, Troy Astarte & Gemma Crowe

    Robbie Bickerton:

    The HIDIM workshop in Manchester was a valuable opportunity to exchange ideas and hear different perspectives. I came to this workshop as a mathematician with an interest in history and the different contexts underlying mathematical developments. The workshops was a great opportunity to connect with others who have similar interests and learn from their expertise and suggest areas for collaboration. In particular it is exciting to see how such discussions around history, diversity and bias can be embedded into the teaching of maths going forward.

    Troy Astarte:

    Perhaps it was the theming of this workshop around co-creation, but I noticed a distinctly reflective tone creeping into many discussions—on- and off-stage—as participants thought about their relationships with students in a deeper way than in others. Indeed, the presence of some students grounded our talk in real student experiences in a way that reporting on outcomes didn’t quite provide. Perhaps we should seek to have regular student members of the working group? We must also remember, however, that the students who are sufficiently keen not only to engage in co-creation but to travel to a workshop outside of term-time might not fully represent the entire cohort! On a more personal note, I enjoyed the discussions of neurodiversity and queerness coming in, and I believe this was the event that I have attended with the highest proportion of non-binary people outside specifically queer spaces. Small wonder I felt comfortable in the space!  

    Gemma Crowe:

    Tom Coleman (University of St Andrews) gave an excellent talk entitled “Student-staff co-creation for accessibility and inclusion”, in which he discussed three student co-creation projects. The talk was followed by a closely related panel discussion on co-creation projects. Many of the outputs from these projects are now available on the HIDIM repository (https://www.mathshist4edi.org.uk/). Here are some of my thoughts and takeaways from these discussions. “Guide rather than a boss” This was a quote from Tom about how we approach student-staff co-creation which really stuck with me. It gives students more agency, but I think, crucially, it helps to bridge the gap between students and what can often feel like the ‘intimidating’ lecturer. I think it can be easy to forget as staff that as a student, approaching staff can be daunting for students. However, leaving students somewhat in the dark with no guidance at all may also prove unproductive. Projects as modules? There are pros and cons to running these projects as credited undergraduate courses. There can be better engagement and motivation, and staff have direct contact with students. On the other hand, marking can be difficult and time-consuming. Feedback from students Two points were made about what students found enjoyable or helpful in these projects. One was the sense of community created by working in pairs or groups and exchanging ideas. The other was enthusiasm from their teachers! Having an open line of communication throughout meant that staff were approachable and helped break this barrier. Tom also emphasised in his talk how much we can learn from students that we otherwise wouldn’t think about – for example, the STARMAST website gained more attention and awareness through a social media campaign by the university. Setting up projects Student-staff co-creation can be a win-win: students gain valuable experience and skills for career development, as well as pay for their contributions. Staff get fresh ideas and innovation, direct feedback on course material and engagement of students, and most importantly, create high-quality resources with the students. In terms of finding students to work with, it was noted that grades don’t mean everything. Students who find the work more challenging may also be the best candidates and will get the most out of projects like these. One thing to consider is to seek out ‘keen’ students (e.g. those who come to office hours) who may have a more personal investment in the project.
  • Registration open for Manchester Workshop, 7-8 Sept
    In person registration and online registration are now open for our 2-day workshop in Manchester on 7-8 Sept, and we look forward to seeing lots of you there. This workshop will run from mid-morning (11.00 coffee, 11.30 session start) on Monday 7 Sept., until mid afternoon (15.00 finish & tea) on Tuesday 8 Sept. We hope this will enable many participants to attend with only one night away from home. Registration, teas/coffees and lunches are free, and we can offer some help with travel and accommodation costs for those, especially students and independent scholars, who do not have other sources of funding. The main focus of the workshop is on student-staff co-creation of resources that draw on history of maths to promote inclusivity and decolonisation in the maths curriculum. The programme will include:
    • A presentation from Sayori Ghoshal (Max Planck Institute, Berlin) on the historical development of statistical sciences,  and their impact on community identity formation in colonial and postcolonial India
    • A presentation from Tom Coleman (St Andrews) on the “Inclusive Activities” project at St Andrews
    • A panel discussion between staff-student co-creation teams, including Rehan Shah (Queen Mary University of London), Isobel Falconer (St Andrews), Ciarán Mac an Bhaird (Maynooth) plus students (names to be confirmed)
    • Lightning talks and/or short presentations from attendees
    • Collaborative resource development & upload, review and improvement of the HIDIM repository
  • June 5 2026 – Experience sharing with David Pritchard

    Title: Mathematics in Society: two years of teaching it (mostly) wrong?

    A recent review of our first-year curriculum at the University of Strathclyde gave us the opportunity to introduce a new module, Mathematics in Society. This is a core module for students on single-honours mathematics and statistics degrees, which aims to address a perceived lack of “soft” skills; at the same time, it aims to broaden students’ understanding of mathematics, drawing on resources from the history of mathematics.
    Content and approach
    The starting point for students is the question “What is mathematics, anyway?” (We warn them that we will not answer this!) Specifically, we pose questions such as “where do mathematical ideas come from?”, “who gets to spend their time doing mathematics?” and “where do people think mathematically?” Successive blocks look at mathematics and games, mathematics and government, mathematics and art, and mathematical modelling. Throughout we interpret “mathematics” as widely as possible, stressing the porous boundary between academic and non-academic mathematical activities. The spirit of the module is closest to that of Jacqueline Stedall’s The History of Mathematics: a Very Short Introduction (OUP, 2012), with some influence from Francis Su’s Mathematics for Human Flourishing (Yale, 2020). We don’t attempt to give an overall historical picture; we don’t focus on the names and stories behind the mathematics that students already know; and we don’t try to train students as historians. (It is a full-time job to steer students through the school/university transition and train them as mathematicians.) We do try to give students a historically informed sense of mathematics as a human activity, which is situated in specific contexts and cross-fertilises with other activities, and to encourage them to think carefully about sources and evidence. For example, in the “mathematics and art” block, we touch on topics such as weaving (as an art form and a technology, with discussion of patterns and algorithms), mathematics as a status indicator in art (with reference to the recently reinterpreted portrait of the Jamaican landowner Francis Williams), and the mathematical construction of average or “ideal” human beings (from da Vinci’s Vitruvian Man to eugenics). In a seminar, we compare the work of Marjorie Rice and Roger Penrose on tilings, using the area of recreational mathematics to discuss who counts as a mathematician and why.
    Reflections
    1. When we broadened the definition of mathematics, more diverse examples (at least along the axes of gender and of culture/nationality) followed naturally. We didn’t feel we were struggling to include “token” diversity.
    2. Students’ baseline knowledge was lower than we had anticipated. They generally found the history of mathematics interesting, but had little prior sense of who did what when. This suggests that the challenge isn’t to directly confront perceptions of mathematics as a white/Western/male monopoly, but to give students a framework for thinking about mathematics in which those perceptions don’t thrive.
    3. Students’ initial writing skills were often poor, they struggled to read texts of more than a few hundred words, and we had to start from scratch when it came to using and citing sources. However, students often responded thoughtfully in group discussions.
    4. Topics involving “fairness” and identity were often engaging – among the best work we’ve seen so far was a group essay on mathematics and ethics. However, the language of “politics” turned many students off immediately. I suspect that terminology needs to be very carefully chosen: to frame our goals as, for example, “decolonising the curriculum” easily alienates students who are sympathetic to the ideas but not the jargon.
    5. We had the luxury of being able to design low-stakes assessments, including individual and group writing and discussion sessions, which give students multiple routes to pass the module. Partly because of this and partly because we include peer review for all written work, we have so far seen very little sign of LLM-assisted dishonesty.
    6. However, breaching the familiar assessment “contract” based on worked examples caused anxiety. When students didn’t see an immediate connection between the content of lectures and the tasks set in assignments, some of them panicked and a few disengaged. This showed up strongly in the student feedback.
    I don’t think we’ve yet got this module right, and we’ll continue to experiment with topics and presentation. One major regret is that the themes in this module aren’t picked up directly in subsequent years – which is inevitable given the pressures on the curriculum. However, if we have succeeded then our students have at least glimpsed a larger and more inclusive mathematical world.
  • May 15 2026 Seminar – by Rowena Ball

    Title: Empirical mathematics in Australian Indigenous Smoke Telegraphy

    Link: Preprint at https://arxiv.org/abs/2603.26037

    Link: Recording of seminar

    Link: Slides

    Key words: Undergraduate mathematics, Indigenous mathematics, Smoke telegraphy

    This study is part of a research and teaching program that I lead at ANU on mathematical knowledge of non-Western and Indigenous societies. All societies that we know of developed, communicated and practised mathematics, yet it is usually assumed that Australian mathematics began in the 19th century with a colonially transplanted British-European curriculum. Documenting the rich but neglected mathematical heritage of First Nations cultures of Australia has been one of the delights of my research life.

    In the seminar I described some of the mathematics inherent in smoke telegraphy, a long-distance communications technology that was developed and practised from ancient to modern times by Aboriginal and Torres Strait Islander peoples of the Australian continent and islands. I juxtaposed aspects of that mathematics against analogous or cogent mathematical developments in European mathematics.

    The research is based on numerous archival primary sources from the 19th century and early 20th century. White colonial society was absolutely fascinated with smoke telegraphy, because it was used to track white explorers and travellers with high precision, the codes were kept secret by the Aboriginal master signallers (and are classified knowledge to this day), and across much of the continent it was a more effective system than electrical telegraphy until well into the 20th century. The research also draws on several precious pre-colonial sources from the mid to late 1600s and from 1770.

    Mathematical perception and know-how were intrinsic to smoke telegraphy. Beyond attributes such as quite complicated numerical coding, I described the use of chiral symmetry (or right- and left-handedness), which was understood and actively created by Indigenous smoke signallers, the use of frequency coding of the visible signals, and empirical knowledge of fluid dynamics.

    Why have we never heard of smoke telegraphy? What became of it? was a question asked. In the far north of Australia, beyond the reach of poles and wires and the broadcast range of radio transmitters, smoke signalling and telegraphy was still used until the 1940s, but knowledge of the finer points declined. It seems that the very real Japanese threat in WWII caused the military to suppress it, presumably for national security reasons. For a decade or so after the war smoke signals became infantilized as a Scout-camp exercise that some people’s grandparents might remember, but as a sophisticated long-distance communications technology smoke telegraphy seemed to disappear from white public consciousness, from newspapers and books, and from the published white colonial histories.

    How old might smoke-signalling technology be? is another question. Given the long cultural continuity of Australian Indigenous societies, smoke signalling as a method of long-distance communication may well be very ancient. Smoke is, of course, a natural signal, and humans would have exploited its potential very early in history. When sea levels were 80–150 m lower during a glacial maximum approximately 65,000 years ago, smoke from natural bush fires on the exposed Sahaul (Greater Australian) shelf would have been visible from several Indonesian islands and may have stimulated the original voyages to Australia. Did those voyagers who arrived safely perhaps send up smoke telegrams to be received by family and friends whom they left behind? “Arrived safely. Land of plenty. Build more outrigger canoes. Make sails. Come soon.” Was smoke signalling technology Australia’s first export to the world? Purely speculative, but not unreasonable, questions.

    Another speculative but reasonable sequitur from this study is that development of mathematical ideation in the human brain may occur at similar rates and levels in all societies, and that expression of those ideas is cultural in actuation but always serves a social purpose. Humans are a social, mathematical species.

    Australian Indigenous smoke telegraphy was a remarkable achievement on its own terms. All the evidence supports that, prior to the roll-out of electrical telegraphy, it was the most highly advanced, most effective, long-distance telecommunications technology in the world. It also affirms the cultural universality of mathematics.

    The materials and results of this study may be included in a cultural and historical introduction to first and second year tertiary mathematics and physical science courses where topics such as symmetries, groups, and the Fourier transform are studied. The systems properties of smoke telegraphy may inspire modelling and simulation problems to be set up and analyzed with modern mathematical, computational and machine learning tools. For Indigenous and minority students this study provides affirmation that mathematics is a valued part of their cultural heritage and identity and that Indigenous mathematical knowledge is rich and strong.

    Please comment/discuss the seminar and questions raised by it and the blog on the JISCmail list (Sign up)

     

  • 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.

    Please comment/discuss the reading and questions raised by it and the blog on the JISCmail list (Sign up)

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Tags

fang cheng method Fibonacci tiling Indigenous mathematics Meru prastara non-western maths reflective learning Smoke telegraphy Undergraduate mathematics

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