Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-12-03T00:25:36.847Z Has data issue: false hasContentIssue false
  • English
  • Français

Focus on the Visual (The 2022 Presidential Address)

Published online by Cambridge University Press:  12 October 2022

Chris Pritchard
Chris Pritchard*
Affiliation:
14 Livingstone Avenue, Callander FK17 8EP, [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

There are visual components of mathematics that are vital to the learning of the subject and should be a focus for its teaching. One aspect is the impressive capacity of the brain to visualise, an important element in the discovery process of some prominent mathematicians and scientists. The pedagogical importance of diagrams in mathematics is considered, with examples showing their role in problem-solving, elucidation, persuasion and decision making, concluding with some particularly stimulating and revealing diagrams for use in the classroom.

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 567 , November 2022 , pp. 386 - 399
Check for updates
Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Maguire, A., et al, ‘Navigation-related structural change in the hippocampi of taxi drivers’, Proceedings of the National Academy of Sciences 97(8) (2000) pp. 4398–4403.Google ScholarPubMed
Hofstadter, D., Thoughts on geometrical thinking, Mathematics in School 36(4) (September 2007) p. 27.Google Scholar
Boutroux, P., L’imagination et les mathématiques selon Descartes, Bibliothèque de la Faculté des Lettres de l’Université de Paris, No. 10. Paris: Alcan (1900).Google Scholar
Hadamard, J., An essay on the psychology of invention in the mathematical field, Princeton University Press (1945) and Dover (1954) p. 74.Google Scholar
Penrose, R. (in conversation with Melvyn Bragg), Spacetime singularities, Oxford Mathematics Public Lecture (16 February 2021), available at www.youtube.com/watch?v=1zXC51o3EfI (especially from 1:29).Google Scholar
Atiyah, M., ‘What is geometry?’ The 1982 Presidential Address, Math. Gaz., 66 (October 1982) pp. 179–184.Google Scholar
Pólya, G., How to solve it, Princeton University Press (1945).Google Scholar
Skemp, R. R., The psychology of learning mathematics, Penguin, (1971).Google Scholar
Euler, L. P., Lettres à une Princesse d’Allemagne (Partie II, Lettre XXXV, February 17, 1791, ed. Cournot (1842) pp. 412–417.Google Scholar
Musielak, D. E., Euler and the German princess, online at https://arxiv.org/ftp/arxiv/papers/1406/1406.7417.pdf Google Scholar
Friendly, M., The graphic works of Charles Joseph Minard (catalogue of Minard’s diagrams), online at www.datavis.ca/gallery/minbib.php Google Scholar
Friendly, M. and Wainer, H., A history of data visualization and graphic communication, Harvard University Press, Cambridge, Mass. (2021).Google Scholar
Tufte, E. R., The visual display of quantitative information (2nd edn), Graphics Press (2001).Google Scholar
Bostridge, Mark, Florence Nightingale: the woman and her legend, Penguin (200th Anniversary Edition) (2020).Google Scholar
Magnello, Eileen M., Victorian statistical graphics and the iconography of Florence Nightingale’s polar area graph, BSHM Bulletin 27(1) (2012) pp. 13–37.Google Scholar
Pritchard, C., A square peg in a round hole (2016), The room in the elephant (2019), Pack up a penguin (2020), all published by The Mathematical Association.Google Scholar
Nelsen, R. B., Proofs without words: exercises in visual thinking, MAA (1993); also Vol II (2000) and Vol III (2016).Google Scholar
Anscombe, F. J., Graphs in statistical analysis, American Statistician 27(1) (1973), pp 17–21; available online at www.sjsu.edu/faculty/gerstman/StatPrimer/anscombe1973.pdf Google Scholar