Webinar 5 – April 29th 2014
What do I teach?
Mathematics, Numeracy or Maths
David Kaye
Learning Unlimited
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”.
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
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 (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. 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 (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
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
ALM Conference Proceedings
full references
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 Proceedings
full references (2)
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)
David Kaye
Numeracy Professional Development
Learning Unlimited
david.kaye@learningunlimited.co