Harvard references that I used for the Level 5 Maths ADTLLS, Developing Role of Numeracy / History of Mathematics essay. (Part of Module 1: Approaches to Mathematics learning and teaching).
Most of the references below are not available online so you will need to order the books and journals through your college library. Other references to on-line sources are listed separately under History and development of mathematics and numeracy teaching links
- Cohen, P. (1999), A Calculating People. London: Routledge.
- Department for Education and Employment (2001), Adult Numeracy Core Curriculum. London: Basic Skills Agency. (Now been replaced by the updated 2009 online version at the Excellence Gateway – see our separate external link).
- Department of Education and Science, Central Advisory Council for Education (1959), A Report (The Crowther Report). London: Her Majesty’s Stationery Office.
Fasanelli, F. (2000), The political context. In: Fauvel, J. and van Maanen, J. (eds.), History in mathematics education: the ICMI study. Dordrecht: Kluwer Academic Publishers, p38.
- Fauvel, J. and Gray, J. ed. (1987), The History of Mathematics: A Reader. London: Macmillan Press Ltd.
- Fauvel, J. and van Maanen, J. ed (2000), History in mathematics education: the ICMI study. Dordrecht: Kluwer Academic Publishers.
- Sewell, B. (1981), Use of Mathematics by Adults in Daily Life. London: Advisory Council for Adult and Continuing Education.
- Swain, J. at al. (2005), ‘Beyond the daily application’: making numeracy teaching meaningful to adult learners. London: National Research and Development Centre for Adult Literacy and Numeracy.
Here’s some random paragraphs showing how I used the references in my essay:
Mathematics has been studied as a distinct subject for over four thousand years (Fauvel, 2000, p. xvii). Indeed, tally marks on a bone dated between 6500-9000 BC provide even earlier evidence of proto-mathematic activity (Fauvel, 1987, p5).
A knowledge of the history of mathematics is important. In 1959 Crowther (cited by Fasanelli, 2000) acknowledged that it helps students appreciate that ‘much of what is taught today as a finished product is the result of centuries of groping or of spirited controversy’.
Crowther was responsible for the word ‘numeracy’ entering the English corpus in 1959. In his report on English education, he described it as ‘the mirror image of literacy’ (DES, 1959, par.398) and linked it with scientific literacy. Cohen (1999, pp5-6) explains that in the 1950s there was great concern that the ‘humanities and the sciences were diverging into two cultures, each unable to comprehend the other …’. Being ‘innumerate’ was not considered a lack of basic skills but more a higher level deficiency preventing proper communication between academics in different disciplines.
A small research project commissioned by Cockcroft to inform his report – later verified by a much larger Gallup poll (Sewell, 1981, cited in Cockcroft) – confirmed that maths anxiety impacted on all social groups and educational classes.
Two years later, Swain led research into exactly what made numeracy teaching meaningful to adults (2005). The results perhaps signal yet another change in direction for numeracy teaching. Although Swain acknowledged that numeracy teaching is most ‘meaningful to [adult] students when it is related to their own purposes and needs’ he found that numeracy did not have to be ‘functional’ and that the quality of students’ engagement with mathematical problems, whether real or abstract, was key. Moreover, the role of the teacher was discovered to be crucial: at least as important as mathematical content. (Swain, 2005, p.8).
Swain’s recommendations for government (2005, p.12) included an overhaul of the Adult Numeracy Core Curriculum (DfEE, 2001). The post-Moser emphasis on functional numeracy resulted in many mathematical gaps and students were not getting the provision they wanted. New forms of assessment were also recommended: multiple choice tests were no longer deemed adequate due to the ‘sole emphasis’ on getting the correct answer (with no guarantee of learners gaining an understanding of underpinning concepts) and no true assessment of ‘functional’ ability.
‘The test questions mostly take the form of traditional algorithms, inserted into artificial contexts, often quite irrelevant or even incomprehensible to students from other cultures’. (Swain, 2005, p12)
In the 50 years since the appearance of ‘numeracy’ there has been much change. Today, decisions on what is taught are ‘ultimately political’: based on social context, along with the needs of teachers and employers. (Fasanelli, 2000, p38).
The Crowther Report (and associated surveys) is now available on Derek Gillard’s excellent Education in England site where you can also find other key educational documents including the Warnock Report 1978 (Special Educational Needs), the Cockcroft Report 1982 (Mathematics Counts), the Swann Report 1985 (Education for All) and other classics. All make fascinating reading.