Knowledge and Understanding 2

This report aims to examine the historical and cultural development of mathematics and how it stands today with the current decimal system and modern curriculum. Exploring the differences between numeracy and mathematics and also the recent introduction of functional skills, I shall also discuss the significance of zero and place value and how links and generalisations can be made between mathematical concepts. Furthermore, this report shall examine how teaching and learning theories influence the way in which we understand maths through the process of problem solving, generalisations, assumptions and proof, and also the common errors and misconceptions that may result from this.

THE HISTORY OF MATHS

From around 2000BC the Babylonian civilisation brought a style of mathematics which succeeded the Sumerian-Akkadian system following their invasion of Mesopotamia. As the oldest example of numeration that used place value systems, the Babylonians had an advanced number system now known as ‘base 60’. This was unlike the ‘base 10’ system that is in widespread use today, although time is still organised in this way. The Babylonians divided the day into 24 hours, each hour into 60 minutes and each minute into 60 seconds (O’Connor and Robertson, 2000). Like our own decimal system today which is a positional system comprised of nine special symbols and a 0 to denote an empty space, the Babylonians only had two symbols to produce their base 60 system. However, although the Babylonians had a fairly positional system, it also had some element of a base 10 within it. This is because the number 39, for example, was built from a unit symbol and a ten symbol (i.e. three tens and a 9). ‘Appendix A’ illustrates the 59 numbers built from these symbols.

Initially the Babylonians had a place value system without a zero feature for over 100 years. This need for the zero started to emerge when difficulties came in

References: • Allsopp, D, Kyger, M. and Lovin, L. (2007) Teaching Mathematics Meaningfully, Maryland Baltimore: Paul H. Brookes Publishing Co. • BBC News (2010) Tory Crime Figures Misleading, [Online] Available from: http://news.bbc.co.uk/go/rss/-/1/hi/uk_politics/8498095.stm (Accessed 19/04/2011) • Cockburn, A and Littler, G (2008) Mathematical Misconceptions, London: Sage Publications Ltd • Dee, L (2006) Creating Learning Materials – Level 4, Nottingham: DfES Publications • DfES (2001) Adult Numeracy Core Curriculum, London: The Basic Skills Agency • DfES (2001) Adult Numeracy Core Curriculum, Nottingham: DfES Publications • Fisher, T et al (2008) AQA Functional Maths: Teacher Book, Cheltenham: Nelson Thornes Ltd • Gates, P (ed) (2001) Issues in Mathematics Teaching, Abingdon: Routledge Falmer • Gould, J (2009) Learning Theory and Classroom Practice, Exeter: Learning Matters • O’Donoghue, J (2002) ‘Numeracy and Mathematics’, Irish Mathematical; Society Bulletin, Vol. 48, p47-55 • Peterson (2001) Importance of Place Value [Online] Available from: http://mathforum.org/dr.math/ (Accessed 05/04/2011) • Petty, G (2009) Teaching Today: A Practical Guide – Fourth Edition, Cheltenham: Nelson Thornes Ltd • Pierce, R (2011) Math is Fun - Maths Resources [Online] Available from: http://www.mathsisfun.com/ (Accessed 20/04/2011) • Swan, M (2005) Improving Learning in Mathematics: Challenges and Strategies, London: DfES Publications • Swan, M (2005) Maths4Life [Online] Available at: www.ncetm.org.uk/resources/8856 (Accessed 405/04/2011) • Thompson, D (1995) The Concise Oxford Dictionary of Current English – 9th Edition, Oxford: Clarendon Press • Westwood, P (2008) What Teachers Need to Know About Numeracy, Australia, Victoria: ACER Press Bibliography: • Confrey, J (1990) ‘Constructivist views on the Teaching and Learning of Mathematics’, Journal for Research in Mathematics Education, vol • Haylock, D (2006) Mathematics Explained for Primary Teacher – 3rd Edition, London: Sage Publications • National Centre for Excellence in the of Teaching Mathematics (NCETM) [Online] Available at: https://www.ncetm.org.uk/resources/8855 • National Research and Development Centre (NRDC) [Online] Available at: www.nrdc.org.uk • Petty, G (2006) Evidence Based Teaching, Cheltenham: Nelson Thornes • Watson, A and Mason J (1998) Questions and Prompts for Mathematical Thinking, Derby: ATM • www.geoffpetty.com