[Maths-Education] Do you recognise this extract?
John Mason
maths-education@nottingham.ac.uk
Fri, 24 Oct 2003 07:59:00 +0100
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Colleagues,
I am at page-proof stage of a reader assembled=20
from extracts, designed for masters students in=20
education.
I have been labouring under the belief that the=20
extract below was from a paper of Meira. But I=20
cannot now locate the source!! Do you recognise=20
it or have any ideas as to its origins?
=8A Manipulatives are not, of themselves, carriers=20
of meaning for insight. 'Although kinesthetic=20
experience can enhance perception and thinking,=20
understanding does not travel through the finger=20
tips and up the arm' (Ball 1992 p47). It is=20
through their use as tools that students have the=20
opportunity to gain insight into their experience=20
with them. Research has shown that for children=20
to use concrete representation effectively=20
without increased demands on their processing=20
capacity, they must know the materials well=20
enough to use them automatically (Boulton-Lewis=20
1998). If the user is constantly aware of the=20
artifact it is not a tool, for it is not serving=20
the purpose of enabling some desired activity to=20
move toward the desired goal state (Winograd &=20
=46lores 1986). =8A
Students sometimes learn to use manipulatives in=20
a rote manner, with little or no learning of the=20
mathematical concepts behind the procedures=20
(Hiebert & Wearne 1992) and the inability to link=20
their actions with manipulatives to abstract=20
symbols (Thompson & Thompson 1990). This is=20
because the manipulative is simply the=20
manufacturer's representation of a mathematical=20
concept that may be used for different purposes=20
in different contexts with varying degrees of=20
'transparency'.
=2E.. in many instances teachers indicated that the=20
use of manipulatives was 'fun'. Initially the=20
term 'fun' seemed to indicate that teachers and=20
students found enjoyment in using the=20
manipulatives during mathematics teaching and=20
learning. Further analysis of the data suggested=20
that embedded in teachers use of the word 'fun'=20
where some unexamined notions that inhibit the=20
use of manipulatives in mathematics instruction.=20
Teachers made subtle distinctions between 'real=20
math' and 'fun math', using the term 'real math'=20
to refer to lesson segments where they taught=20
rules, procedures and algorithms using text=20
books, notebooks, worksheets, and=20
paper-and-pencil tasks. The term 'fun math' was=20
used when teachers described parts of the lesson=20
where students were having fun with the=20
manipulatives.
Many thanks
Desperate of Milton Keynes
JohnM
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<div>Colleagues,</div>
<div><br></div>
<div>I am at page-proof stage of a reader assembled from extracts,
designed for masters students in education.</div>
<div><br></div>
<div>I have been labouring under the belief that the extract below was
from a paper of Meira. But I cannot now locate the source!! Do
you recognise it or have any ideas as to its origins?</div>
<div><br></div>
<div><font face=3D"Times New Roman" size=3D"+1" color=3D"#000000">=8A
Manipulatives are not, of themselves, carriers of meaning for
insight. 'Although kinesthetic experience can enhance
perception and thinking, understanding does not travel through the
finger tips and up the arm' (Ball 1992 p47). It is through
their use as tools that students have the opportunity to gain insight
into their experience with them. Research has shown that for
children to use concrete representation effectively without increased
demands on their processing capacity, they must know the materials
well enough to use them automatically (Boulton-Lewis 1998). If the
user is constantly aware of the artifact it is not a tool, for it is
not serving the purpose of enabling some desired activity to move
toward the desired goal state (Winograd & Flores 1986).
=8A</font></div>
<div><font face=3D"Times New Roman" size=3D"+1"
color=3D"#000000"><br></font></div>
<div><font face=3D"Times New Roman" size=3D"+1" color=3D"#000000">Students
sometimes learn to use manipulatives in a rote manner, with little or
no learning of the mathematical concepts behind the procedures
(Hiebert & Wearne 1992) and the inability to link their actions
with manipulatives to abstract symbols (Thompson & Thompson
1990). This is because the manipulative is simply the
manufacturer's representation of a mathematical concept that may be
used for different purposes in different contexts with varying degrees
of 'transparency'.</font></div>
<div><font face=3D"Times New Roman" size=3D"+1"
color=3D"#000000"><br></font></div>
<div><font face=3D"Times New Roman" size=3D"+1" color=3D"#000000">... in
many instances teachers indicated that the use of manipulatives was
'fun'. Initially the term 'fun' seemed to indicate that
teachers and students found enjoyment in using the manipulatives
during mathematics teaching and learning. Further analysis of
the data suggested that embedded in teachers use of the word 'fun'
where some unexamined notions that inhibit the use of manipulatives in
mathematics instruction. Teachers made subtle distinctions
between 'real math' and 'fun math', using the term 'real
math' to refer to lesson segments where they taught rules,
procedures and algorithms using text books, notebooks, worksheets, and
paper-and-pencil tasks. The term 'fun math' was used
when teachers described parts of the lesson where students were having
fun with the manipulatives.</font></div>
<div><font face=3D"Times New Roman" size=3D"+1"
color=3D"#000000"><br></font></div>
<div><font face=3D"Times New Roman" size=3D"+1" color=3D"#000000">Many
thanks</font></div>
<div><font face=3D"Times New Roman" size=3D"+1"
color=3D"#000000"><br></font></div>
<div><font face=3D"Times New Roman" size=3D"+1" color=3D"#000000">Desperate
of Milton Keynes</font></div>
<div><font face=3D"Times New Roman" size=3D"+1"
color=3D"#000000"><br></font></div>
<div><font face=3D"Times New Roman" size=3D"+1"
color=3D"#000000">JohnM</font></div>
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