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# Secondary Magazine - Issue 130: From the Library

Created on 03 February 2016 by ncetm_administrator
Updated on 17 February 2016 by ncetm_administrator

# From the Library

In January it was announced that the new largest-so-far prime number had been discovered: a number with some 22 million digits. Like many of the previous discoveries of large primes, this was a so-called Mersenne prime, of the form $\inline \dpi{80} \fn_jvn \small 2^{n}-1$. But why are people looking for big primes, and who is this Mersenne that these special primes are named after? Which ones have been discovered so far and how many more primes there are to search for? Has no one yet found a formula to generate them all?

As Maths teachers, do we have the knowledge to answer these questions confidently? How important do we feel it is that we can discuss these issues in our classes? In particular, what are the arguments for the use of the history of Mathematics in classroom teaching, and what does the research say about its benefits?

John Fauvel (1991) collated a number of reasons that have been advanced for using the history of mathematics, including:

• Helps to increase motivation for learning
• Gives mathematics a human face
• Historical development helps to order the presentation of topics in the curriculum
• Changes pupils’ perceptions of mathematics
• Helps to develop a multicultural approach
• Provides opportunities for investigations
• Past obstacles to development help to explain what today's pupils find hard
• Pupils derive comfort from realizing that they are not the only ones with problems
• Helps to explain the role of mathematics in society
• Provides opportunity for cross-curricular work with other teachers or subjects

Kaye (2008) identified that while “a number of benefits to the integration of a historical dimension into mathematics education” had often been suggested, “there is little research into the effectiveness of such an approach”. She investigated a project where students were studying Babylonian mathematics. The conclusions of the research suggested that the majority of students “were able to appreciate that mathematics has developed over millennia and that there are culturally different but equally valid ways of doing mathematics” and “they were able to appreciate a human element to mathematics.” However there was “little evidence…that students came to see mathematics as a creative discipline or appreciated that they could make their own mathematics.”

Georgiou (2010) researched her own teaching of a much wider range of topics, covering both mathematics history and culture. She taught pupils from Years 7 to 10 with a range of prior attainment. The material included Egyptian numerals, the Babylonian Plimpton tablet, texts on Eratosthenes and Al-Khwarizmi, as well as the examination of the economics of fair-trade coffee. She found that students reacted intensely to the variety of written texts, with negative facial expressions to some texts and comments such as “This is English!”, but with enthusiasm for a SMILE activity resembling a comic-book page. The work on number systems drew out mathematical misconceptions as well as demonstrating quite fixed views when comparing other notations, insisting that “ours are numbers, theirs are shapes”. While the researcher emphasised the provisional nature of the findings, there were indications that positive and negative reactions were spread across the groups and that “what many students seemed to appreciate in their comments was the variety in the approach.” However, there were also significant challenges for the teacher, such as incidents of feeling exposed when discussion led into unfamiliar territory despite extensive planning: “the challenges a teacher may face with such an approach are either related to a tiring and sometimes daunting preparation or some unexpected themes emerging during the lesson.”

Given the challenge of involving historical elements into the lesson, are some teachers more predisposed to this approach than others? Goodwin et al (2014) analysed questionnaire responses from 4663 teachers in the USA. They concluded that “[t]eachers with high history scores were more likely to believe that investigating is more important than knowing facts and that mathematics is ongoing and shows cultural differences. On the other hand, teachers with low history scores were more likely to believe that mathematics is a disjointed collection of facts, rules and skills.”

Understanding how mathematical ideas developed through human history is recognised as influential in the work of Piaget. “Piagetian psychology called for historical analysis of mathematical … concepts” assuming “that the individual’s development replays that of the species” (Lerman 2000). Rogers takes issue with this and argues that “what we learn from the history of mathematics is that the richness, complexity and variety of human endeavour” is such that “differences in cultural contexts give rise to what are essentially different cognitive structures when it comes to handling number, magnitude and space” (Rogers 1997).

A report on the history of mathematics in the Higher Education curriculum argues that “[s]etting historical context can motivate and enthuse learning, but it also enriches the curriculum, shows connections between different branches of the subject, and helps to produce students with a greater sense of the breadth and, what might be termed, the creative life of mathematics as a discipline” (McCartney, 2012). What is your view on using the history of mathematics in the classroom? How do you incorporate history and how have the students reacted? Let us know your opinions and experiences: email info@ncetm.org.uk or tweet us @NCETM.

Resources

There is a wealth of resources. As well as for their quality, the following are selected for their availability and their practicality.

A new competition invites young people aged 11 to 19 to explore the history of maths for a chance to win cash prizes. Launched jointly by Plus Magazine and the British Society for the History of Mathematics. The deadline for entries is Thursday 24 March 2016.

Babylonian Mathematics – a programme of study including worksheets and videos, featuring Eleanor Robson, a leading Near East archaeologist and co-author of books on the history of mathematics.

The Approximate History of Maths – a collection of animation clips from the BBC programme.

The Story of Maths with Marcus du Sautoy – a collection of clips from the BBC series of 2008.

In a video from Teachers TV, Matthew Tosh presents a half hour introduction to the history of Maths.

Maths is good for you! “History of mathematics for young mathematicians.”

Searching the NRICH website with “History of mathematics” brings up a wide range of pages, from problems to historical articles.

In the 1990s Nuffield provided a module on the History of Mathematics as part of their A Level Mathematics course. The textbook, challenging and fascinating, is available online, hosted by the National STEM centre.

'Bite-Sized' History of Mathematics Resources for use in the teaching of mathematics

The extensive MacTutor History of Mathematics archive contains a multitude of biographies as well as articles on historical topics.

References

Fauvel, J. (1991) Using History in Mathematics Education. For the Learning of Mathematics, Vol. 11, No. 2, Special Issue on History in Mathematics Education, June, 1991, pp. 3-6.

Georgiou, I. (2010) A week with secondary mathematics through history and culture. Proceedings of the British Society for Research into Learning Mathematics 30-3.

Goodwin, D., Bowman, R., Wease, K., Keys, J., Fullwood, J., Mowery, K. (2014) Exploring the relationship between teachers’ images of mathematics and their mathematics history knowledge Philosophy of Mathematics Education Journal. Issue 28, pp. 1-15.

Kaye, E. (2008) The aims of and responses to a history of mathematics videoconferencing project for schools. Joubert, M. (Ed.) Proceedings of the British Society for Research into Learning Mathematics 28(3) November 2008.

Lerman, S. (2000) The Social Turn in Mathematics Education Research in Boaler, J. (Ed.) Multiple Perspectives on Mathematics Teaching and Learning.

McCartney, M. (ed.) (2012) History of Mathematics in the Higher Education Curriculum. A report by the working group on History of Mathematics in the Higher Education Curriculum, May 2012.

Rogers, L. (1997) Ontogeny, Phylogeny and Evolutionary Epistemology Proceedings of the British Society for Research into Learning Mathematics 17(3) November 1997.

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