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What do I teach? Mathematics, Numeracy or Maths David Kaye Learning Unlimited


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Title: What do I teach? Mathematics, Numeracy or Maths David Kaye Learning Unlimited

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
  • It is a construct or invention rather than a
  • 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
  • Benn, R. (1997 2002)

Re-read these statements replacing mathematics
with numeracy
Why ask this? Will look at definitions and
statements - but always ask How does this relate
to what and how I teach?
What is mathematics?
Professor Adrian Smith (2004)Making Mathematics
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
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,

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
  • 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
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
Diana Coben (2002)Use Value and Exchange
Valuein Discursive Domains of Adult Numeracy
  • 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
  • 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
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
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
David KayeNumeracy Professional Development
Learning Unlimiteddavid.kaye_at_learningunlimited.co
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