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What do I teach?Mathematics, Numeracy or

MathsDavid KayeLearning Unlimited

Webinar 5 April 29th 2014

Thought experimentConsider 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)Adults 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 cant 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 isnt 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 Toolin 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

Valuein 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.

References

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

AgencyBenn, R. (2002) Secret Knowledge

Indigenous Australians and Learning Mathematics

(in the proceedings of ALM8)Benn, R. (1997)

Adults count too Mathematics for empowerment.

Leicester NIACECockcroft 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 (2)

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. LondonThe

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.ukEvans, 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 (3)

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 Smiths Inquiry into Post-14 Mathematics

Education. The Stationery Office LtdTout, 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 BooksWithnall, A (1995) Towards

a Definition of Numeracy (in the proceedings of

ALM1

ALM Conference Proceedingsfull references

ALM1 1994Coben, 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 1996Coben, 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

2001Johansen, 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 (2)

ALM8 2001Johansen, 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

2004Lindberg, 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

EducationALM14 2007Maguire, T., Colleran,

N., Gill, O. and ODonoghue, 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)

David KayeNumeracy Professional Development

Learning Unlimiteddavid.kaye_at_learningunlimited.co