What do I teach?Mathematics, Numeracy or

Maths

David KayeLearning Unlimited

Webinar 5 – April 29th 2014

Thought experiment:Consider this quotation from Roseanne Benn

Mathematics is a social construct

It did not develop in a cultural or social vacuum

It is not a body of truth existing outside human experience

It is a construct or invention rather than a discovery

It is social in nature

It is value laden not value free

There are different mathematics in different societies reflecting the different needs of those societies.Benn, R. (1997 & 2002) Re-read these statements replacing “mathematics” with “numeracy”

Introduction

Why ask this?

Will look at definitions and statements - but always ask

“How does this relate to what and how I teach?”

Mathematics

What is mathematics?

Professor Adrian Smith (2004)Making Mathematics Count

There are positive senses in which mathematics is special. First, by virtue of its fundamental nature as a universal abstract language and its underpinning of the sciences, technology and engineering, mathematics has a claim to an inherently different status from most other disciplines

Professor Adrian Smith (2004) cont.

Secondly, as we have set out above, mathematics is fundamentally important in an all-pervasive way, both for the workplace and for the individual citizen.

Roger Bacon (1266)

Opus Maius

He who knows not mathematics cannot know the other sciences nor the things of this world . . .And, what is worse, those who have no knowledge of mathematics do not perceive their own ignorance, and do not look for a cure. Conversely a knowledge of this science prepares the mind and raises it up to a well authenticated knowledge of all things.

Lars Gustafsson & Lars Mouwitz, (2005)ALM11 conference proceedings

Mathematics is to be found everywhere, but to the individual it appears to be almost nowhere, a situation usually referred to as the relevance paradox of mathematics. An adult who feels anxiety and suffers learning blockages when faced with this subject is therefore likely to conclude that the subject is meaningless; it neither improves understanding of the environment nor adds to practical knowledge.

Jeff Evans (2000)

Adult’s mathematical thinking and emotions

Despite the time elapsed and the changes occurring, both in the educational world and outside, since [1976], many current commentators still appear to share a traditional view of ‘mathematical ability’. It is seen as involving a set of abstract cognitive ‘skills’, which can be applied to perform a range of tasks, in a variety of practical contexts. This is considered to take place through a relatively straight-forward process of transfer.

James R Newman (1956)

Commentary on The Foundations of Mathematics

Mathematical statements are compelling, but their force is of a special kind; they are true, but their truth is uniquely defined. . . . Mathematics cannot be validated by physical facts, nor its authority impugned or subverted by them. Yet there is a vital connection between the propositions of mathematics and the facts of the physical world. . . .

James R Newman (1956) cont.

. . . Counting and measuring in the everyday world invariably parallel mathematical propositions but it is essential to distinguish between mathematical propositions and the results of counting and measuring.

Marcus du Sautoy (2003)The music of the primes

Mathematicians can’t bear to admit that there might not be an explanation for the way Nature has picked the primes. If there were no structure to mathematics, no beautiful simplicity, it would not be worth studying.

Alfred North Whitehead (1925)Mathematics as an Element in the History of

Thought

When we think of mathematics, we have in our mind a science devoted to the exploration of number, quantity, geometry, and in modern times also including investigation into yet more abstract concepts of order, and into analogous types of purely logical relations. The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities.

Alfred North Whitehead (1925) cont.

So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction.

Before we look at meanings of “numeracy” remember there are a number of other terms that are commonly used in these debates

Quantitative Literacy

Mathematical Literacy

School Mathematics

Functional Mathematics

Maths

Adult Numeracy Core Curriculum (2001)

• ‘Mathematics equips pupils with a uniquely powerful set of tools to understand and change the world’ (The National Curriculum, (QCA). Changing the world may not be the immediate goal of adult learners, but being numerate - acquainted with the basic principles of mathematics is essential to functioning independently within the world.

Cockcroft (1982: para 39)

'We would wish 'numerate' to imply the possession of two attributes. The first of these is an 'at-homeness' with numbers and an ability to make use of mathematical skills which enable an individual to cope with the practical mathematical demands of his everyday life. The second is ability to have some appreciation and understanding of information which is presented in mathematical terms, for instance in graphs, charts or tables or by reference to percentage increase or decrease.

Dave Tout(1997)Proceedings of ALM 3

There seems to be almost Australia wide agreement that yes, we can use that word [numeracy] to talk about what we do - it isn't downgrading what we do, it isn’t inferior to mathematics - and as we said in the introduction to the Adult Numeracy Teaching course: "numeracy is not less than mathematics, but more".

Dave Tout(1997) cont.

We believe that numeracy is about making meaning in mathematics and being critical about maths. This view of numeracy is very different from numeracy being just about numbers, and it is a big step forward from numeracy or everyday maths that meant doing some functional maths.

Kees Hoogland (2008)Proceedings of ALM 2014

From this definition we derived the concept of a 'numeracy incident'. The quantitative aspect of the world around us takes many forms. It shows up in artefacts and devices (meters, gauges, clocks, numbers, symbols), in constructions (measurements, angles, spatial attributes) and in texts (numbers, symbols, diagrams, maps, graphs, formulas).

Roseanne Benn (1997)Adults count too

Numeracy consists of being able to make an appropriate response to a wide range of personal, institutional or societal needs. . . . Here the knowledge of numeracy is seen as important, not just for utilitarian or abstract purposes, but as part of students' attempts to understand their own individual and collective lives and to make their lives meaningful.

Lena Lindenskov & Tine Wedege (2001)Numeracy as an Analytical Tool

in Mathematics Education and Research

Our two-pronged general definition of numeracy describes a math-containing everyday competence that everyone, in principle, needs in any given society at any given time:

Numeracy consists of functional mathematical skills and understanding that in principle all people need to have.Numeracy changes in time and space along with social change and technological development.

What are we supposed to teach now?

What sort of mathematics should we be teaching?

Do different people (schools of thought) mean the same thing, but use different words

How much do numeracy and mathematics overlap?

Who decides what ought to be taught?

What about “maths” then

Is “maths” simply a convenient abbreviation of “mathematics”?

Is it significant if it is used in an official document?

Is this only a UK phenomena?

Used in UK policy documents since 2011

What about “maths” then

In New Challenges, New Changes published in 2011 by a UK government department ‘maths’ is used throughout. It argues against using ‘numeracy’ as a matter of policy. In a list of key actions for improvement it states “Re-establish the terms ‘English’ and ‘Maths’ for adults” as the first key action.

The education and Training Foundation (April 2014)

As a result of these concerns about the achievement of maths GCSE among learners in England, a number of policy changes have been initiated. The Department for Education(DfE) and the Department for Business, Innovation and Skills (BIS) plan to expand maths teaching in the FE sector, where most vocational subjects are taught, so that from September 2014 onwards:

GCSE maths or ‘stepping stone’ qualifications towards it will be taught to all students up to the age of 19 who do not hold this qualification at grade C or above; and Level 3 core maths will be taught to the 22% of students who have achieved maths GCSE before embarking on a level 3 vocational course.

Defining Numeracy

I want to use “numeracy” as I feel it enables questioning and inclusion, rather than acceptance and exclusion.

When do you think we should use numeracy, or mathematics or maths?

What difference will it, or can it, make to what we teach?

What do I teach? Mathematics, Numeracy or Maths

Which term?

When is it used?Where is it used?About what?Who is using it?For what purpose?

Diana Coben (2002)Use Value and Exchange Value

in Discursive Domains of Adult Numeracy Teaching

Numeracy is a notoriously slippery concept. There is no shortage of definitions but there is, crucially, a shortage of consensus, with the term meaning different things in different educational and political contexts and in different surveys of need.

Defining numeracy at ALM1 (1994)

Alexandra Withnall

The final sentence states:

“Numeracy must remain a fluid term capable of re-conceptualisation according to the contexts in which it is used and by whom”.

Bacon, Roger (1266) Opus Maius quoted in Fauvel J, Flood R and Wilson R (eds) (2000) Oxford Figures: 800 Years of the Mathematical Sciences Oxford University Press Oxford (p 2; citation p 272)

Basic Skills Agency (2001) Adult Basic Skills Core Curriculum. London: Basic Skills Agency

Benn, R. (2002) Secret Knowledge: Indigenous Australians and Learning Mathematics (in the proceedings of ALM8)

Benn, R. (1997) Adults count too: Mathematics for empowerment. Leicester: NIACE

Cockcroft Committee (1982) Mathematics Counts: A Report into the Teaching of Mathematics in Schools. London: HMSO.

Coben , Diana (2002) Use Value and Exchange Value in Discursive Domains of Adult Numeracy Teaching in Literacy and Numeracy studies – an international journal in the education and training of adults, vol 11, no 2 pp25 – 35

References

Department for Business, Innovation and Skills (December 2011) New Challenges, New Changes further education and skills system reform plan: building a world class skills system. London

The Education and Training Foundation (April 2014) Research And Development Framework - Invitation To Tender Specification Document ‘Research and analysis to inform the improvement of maths skills in the post-16 vocational sector’ www.etfoundation.co.uk

Evans, Jeff (2000) Adults’ Mathematical Thinking and Emotions - a study of numerate practice. London: Routledge Falmer. (p 2)

Gustafsson, L. & Mouwitz, L. (2005) Adults and Mathematics – a vital subject (in the proceedings of ALM11)

Hoogland, K. (2008) Towards a multimedia tool for numeracy education (in the proceedings of ALM 14)

Lindenskov, L & Wedege, T (2001) ‘Numeracy as an Analytical Tool in Mathematics Education and Research’, Centre for Research in Learning Mathematics (Publication No. 31), Roskilde University, IMFUFA, Roskilde

References (2)

Newman, James R (1956) Commentary on The Foundations of Mathematics in Newman, J R (1988) The World of Mathematics vol. 3 Redmond, Washington Tempus Books of Microsoft Publishing (re-issue p 1588)

du Sautoy, Marcus (2003) The music of the primes – why an unsolved problem in mathematics matters London Fourth Estate – Harper

Collins Publishers (p6) Smith, A (2004) Making Mathematics Count – The report of Professor Adrian Smith’s Inquiry into Post-14 Mathematics Education. The Stationery Office Ltd

Tout, D. (1997) Some reflections on adult numeracy (in proceedings of ALM 3)

Whitehead, Alfred North (1925) Mathematics as an Element in the History of Thought in The World of Mathematics;, Volume One I, ed. James R Newman (1956/1988) Simon and Schuster/Tempus Books

Withnall, A (1995) Towards a Definition of Numeracy (in the proceedings of ALM1

References (3)

ALM1 [1994]Coben, D. (comp)(1995) ALM1 (Proceedings of the Inaugural Conference of Adults Learning Maths - A Research Forum) London: Goldsmiths College, University of London in association with ALM.

ALM3 [1996]Coben, D. (comp)(1997) Adults Learning Mathematics - 3 (Proceedings of ALM3 the Third International Conference of Adults Learning Maths - A Research Forum) London: Goldsmiths College, University of London in association with ALM.

ALM8 [2001]Johansen, L Ø. & Wedege, T. (comps)(2002) Numeracy for Empowerment and Democracy (Proceedings of ALM8 the Eighth International Conference of Adults Learning Mathematics - A Research Forum) Roskilde: Centre for Research in Learning Mathematics, Roskilde University in association with ALM.

ALM Conference Proceedingsfull references

ALM8 [2001]Johansen, L Ø. & Wedege, T. (comps)(2002) Numeracy for Empowerment and Democracy (Proceedings of ALM8 the Eighth International Conference of Adults Learning Mathematics - A Research Forum) Roskilde: Centre for Research in Learning Mathematics, Roskilde University in association with ALM.

ALM11 [2004]Lindberg, L. (Ed) (2005) “Bildning” and / or training (Proceedings of the 11th International Conference of Adults Learning Mathematics – A Research Forum) Göteborg. ALM and Göteborg University, Department of Education

ALM14 [2007]Maguire, T., Colleran, N., Gill, O. and O’Donoghue, J. (Eds) (2008) The Changing Face of Adults Mathematics Education: Learning from the Past, Planning for the Future (Proceedings of the 14th International Conference of Adults Learning Mathematics – A Research Forum)Dublin. ALM with CAMET (Centre for Advancement of Mathematics Education in Technology) & Institute of Technology Tallaght Dublin)

ALM Conference Proceedingsfull references (2)

David Kaye

Numeracy Professional Development

Learning Unlimiteddavid.kaye@learningunlimited.co