[Maths-Education] importance of physical materials for
mathematics in elementary school
Paul Ernest
P.Ernest at exeter.ac.uk
Mon Jun 25 10:53:06 BST 2007
Hi Keith (and everybody)
Your first point is an important one; any pedagogy or pedagogical tool can
be performed ineffectively, without coherent aims and little gains
In the 80s we saw how 'investigatory maths' could be both great - in some
cases - but also directionless, without conclusion or learning outcomes
Nevertheless, with regard to manipulatives: they can offer great potential
benefits for a number of theoretical reasons
1. the enactive stage in Bruner's theory of curriculum progression.
Enactive experience can get deep into our embodied/body based learning and
understanding. and provide a basis for Iconic, them Symbolic understanding
Eg, cutting out fractions, partitioning sweets; using pie/pizza diagrams
for fractions; then symbolic fractions (various forms)
Bruner based his theory on a combination of Piaget and C S Peirce
Enactivism now has a big life of its own, using, eg, body based metaphors
as a basis for understanding
2. SEN work emphasises learning styles - enactive/visual/auditory/written
enactive suits some learners very well (and this sortof ties in with
Gardner's multiple intellgeive theory)
3 Structured concrete materials or concretely presented starting points
can provide a shared, discussable, graspable (in both senses) basis for
building mathematical activities (and concepts)
Admittedly careful attention needs to be directed at bridging such
activities into more general understandings or the efforts can be wasted
4. Games often have a concrete element and these can be good learning
media. Here's an old ref.
Ernest, P. ‘Games: A Rationale for their Use in the Teaching of
Mathematics’, in P. Ernest, Ed. Mathematics Teaching: The State of the
Art, London, Falmer Press, 1989
Jones D.K. wrote:
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> Arthur Baroody once wrote that "manipulatives don't come with
> guarantees" and more recent work continues that theme (see references
> below); for example Patricia Moyer concludes her study of 10
> middle-grade teachers (in the US) by saying that the teachers' uses of
> manipulatives "was little more than a diversion in classrooms where
> teachers were not able to represent mathematics concepts themselves".
>
> There's also research in other fields (such as science education) where
> physical activities are being compared with computer-based activities
> (see references below). For example, Klahr and colleagues recently
> concluded from their study that "children were able to learn as well
> with virtual as with physical materials, the inherent pragmatic
> advantages of virtual materials in science may make them the preferred
> instructional medium in many hands-on contexts".
>
> So maybe the question is about how, and in what contexts, experience
> with physical materials can be suitably combined with computer-based
> activity...
>
> And, in terms of work in design technology (and maybe in mathematics?),
> there are going to be interesting research questions when (or if?)
> school students get to use the upcoming range of 3D printers - see, for
> example:
> http://en.wikipedia.org/wiki/3D_printing
>
> Keith
> ---------
> Keith Jones
> University of Southampton
> School of Education
> UK
>
> UoS Mathematics Education Research Group
> http://www.crme.soton.ac.uk
>
>
> --------------
> Klahr, D., Triona, L.M. and Williams, C. (2007) Hands on what? The
> relative effectiveness of physical vs. virtual materials in an
> engineering design project by middle school children. Journal of
> Research in Science Teaching, 44(1), 183-203.
>
> Triona, L. M., and Klahr, D. (2003). Point and click or grab and heft:
> Comparing the influence of physical and virtual instructional materials
> on elementary school students' ability to design experiments. Cognition
> and Instruction 21: 149-173.
>
> ------------
> Baroody, A. J. (1989). Manipulatives don't come with guarantees.
> Arithmetic Teacher, 37(2), 4-5.
>
> Clements, D. H. & McMillen, S. (1996). Rethinking "Concrete"
> Manipulatives. Teaching Children Mathematics, 2(5), 270-279
> Online at:
> http://investigations.terc.edu/relevant/RethinkingConcrete.html
>
> Gilbert, R. K., & Bush, W. S. (1988). Familiarity, availability, and use
> of manipulative devices in mathematics at the primary level. School
> Science and Mathematics, 88, 459-469.
>
> Merseth, K. K. (1978). Using materials and activities in teaching
> addition and subtraction algorithms. In M. N. Suydam & R. E. Reys
> (Eds.), Developing Computational Skills (pp. 61-77). Reston, VA: NCTM.
>
> Moyer, P. S. (2001). Are we having fun yet? How teachers use
> manipulatives to teach mathematics. Educational Studies in Mathematics,
> 47, 175-197.
>
> Prigge, G. R. (1978), The differential effects of the use of
> manipulative aids on the learning of geometric concepts by elementary
> school children, Journal for Research in Mathematics Education, 9(5),
> 361-367.
>
> Raphael, D. and Wahlstrom, M. (1989), The influence of instructional
> aids on mathematics achievement, Journal for Research in Mathematics
> Education, 20(2), 173-190.
>
> Ross, R. & Kurtz, R. (1993). Making manipulatives work: A strategy for
> success. Arithmetic Teacher, 40, 254-257.
>
> Sowell, E. J. (1989). Effects of manipulative materials in mathematics
> instruction. Journal for Research in Mathematics Education, 20, 498-505.
>
> Thompson, P. W. (1992), Notations, conventions and constraints:
> contributions to effective uses of concrete materials in elementary
> mathematics, Journal for Research in Mathematics Education, 23(2),
> 123-147.
>
>> -----Original Message-----
>> From: maths-education-bounces at lists.nottingham.ac.uk
>> [mailto:maths-education-bounces at lists.nottingham.ac.uk] On
>> Behalf Of Katherine Mackrell
>> Sent: 25 June 2007 04:10
>> To: maths-education at lists.nottingham.ac.uk
>> Subject: [Maths-Education] importance of physical materials
>> for mathematics in elementary school
>>
>> **************************************************************
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>> This message has been generated through the Mathematics
>> Education email discussion list.
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>> I have just met a Serbian teacher who informs me that there
>> is pressure to
>> remove the use of physical materials in design technology in
>> elementary
>> schools and to replace these with computer software.
>>
>> Much as I love 3D computer software, I share his concern with
>> regard to
>> students' basic understanding of 3D space and the impact that
>> this change
>> might make on students' mathematics. Could people please
>> send me arguments/
>> references, etc that would summarise the importance of using physical
>> materials for developing mathematical understanding at the
>> elementary level?
>> It's so obviously important to me that I'm not quite sure
>> where to start!
>>
>> Thanks
>>
>> Kate
>>
>>
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>>
>
>
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Best wishes
Paul
__________________________________________________
Paul Ernest
Emeritus Professor, Philosophy of Maths Education
Leader, Doctoral Programme in Maths Education
University of Exeter
School of Education and Lifelong Learning
St Lukes, Heavitree Road
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Office: Holnicote 107
Phone: +44-(0)1392-264749
Fax: +44-(0)1392-264736
Email: p.ernest at ex.ac.uk
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