[Maths-Education] importance of physical materials for mathematics in elementary school

[Jones D.K.]

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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> 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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