If you teach in the
early years, the odds are your classroom is full of physical learning
materials. From plastic letters to wooden blocks, these materials provide
children with the hands-on experience that is so important for their learning.
But why is hands-on experience important for learning? It seems obvious, but this
is a question that researchers have spent many decades trying to understand. This
question becomes even more troublesome when considering subjects such as Maths.
Why should learning something as abstract as fractions or tens and units, be
supported by manipulating objects like blocks or tiles?
Froebel’s gifts c1820s. That
different from what we use 200 years later?
Gesturing when solving a maths
problem
Why does 1+8 make the same as
2+7?
In one study[6] with 104 children, 62% of children gestured
when explaining this relationship. By watching video clips over (and over…)
again, it has been possible to code the types of gestures children use. Gestures
generally fell into two types – those that looked like children were
manipulating imaginary objects, and those where children seemed to be
indicating points along an imaginary line running left to right. This is significant, because these gestures
relate to interaction with two different types of maths materials – physical
materials, and number lines. Traditional theory might suggest that the less
able children’s gestures simulated actions with objects and more able
children’s gestures simulated actions with a ‘less-concrete’ number line. This
was not the case. Indeed, our research is examining how the opposite may be
true for this particular problem.
Gesturing when explaining maths
As a researcher, I
love to take a small study and generate a major theory that goes well beyond
the evidence. In journals, I get caught out, so here I have a chance. I believe
my research supports theoretical work in cognitive science saying that all
numerical concepts are grounded upon two major ‘metaphors’ – that we conceptualise
numbers as ‘collections of objects’ or as ‘points along a path’. But I also
believe that we draw differently upon these metaphors depending on the problem
at hand. Want to add numbers? It’s maybe better to think of them as being along
a line, which you can ‘count up’ or ‘count down’. Want to solve a fraction
problem? Then you may find it easier to think of numbers as collections you can
‘break’ into smaller collections.
If, as I believe, we
draw upon these two metaphors in different ways for all number concepts – from
counting to calculus – that would suggest we need to think carefully about the materials
we provide throughout children’s development. It would contend the traditional
move away from ‘concrete’ objects.
So where was I? Oh, what
is the importance of hands-on learning? It is possible that our hands-on
experiences of moving objects into collections or walking in steps along a path
(then linked to tracing arcs along a number line) are internalised into our
very concepts of number. Consequently, when explaining our thinking about
numbers we often simulate these experiences – observable in our gestures.
·
Think
critically about what materials children are using and how that relates to the
way you can talk about different number ideas.
·
Encourage children
to increasingly imagine these materials in their heads
·
Don’t let
children (or adults) stigmatise physical materials as being for the less able
·
Look at
how children gesture. Teachers don’t have video cameras and hours to analyse
gestures but even in real time, they can provide an interesting window into
children’s thinking
·
Look at
how you gesture to children. Research tells us that teachers very often gesture
and naturally change their gestures according to children’s understanding. Yet
when’s the last time you had gesture training?
·
Think
critically about technology. How do they change children’s physical actions? Do
you think that matters?
The main message
however is we now have a way to examine and understand questions that have been
in education for decades. There are implications for classrooms, but no
definitive solutions yet. What we do know is that once we are able to see how
children gesture to express their thinking in a classroom each day, we are in a
strong position to contribute to our understanding of the importance of
hands-on learning; and the relationship between our minds and bodies.
Bio:
Dr Andrew Manches is a Chancellor’s Fellow in the
School of Education, University of Edinburgh.
He has 20
years experience working with children, first as a teacher, then as an
academic. His research focuses on the role of interaction in thinking, and the
implications this has for early learning and new forms of technology. He was awarded a Future Research Leader grant
by the Economic Social Research Council to conduct his research.
1 McNeil, N. M., &
Jarvin, L. (2007). When theories don't add up: disentangling the manipulatives
debate. Theory into Practice, 46(4),
309-316.
2 Wilson,
M. (2002). Six views of embodied cognition. Psychonomic
Bulletin & Review, 9(4), 625-636.
3 Iverson,
J. M., & GoldinMeadow, S. (1997). What's communication got to do with it?
Gesture in children blind from birth. Developmental
Psychology, 33(3), 453-467.
4 Goldin-Meadow,
S. (2000). Beyond words: The importance of gesture to researchers and learners.
Child Development, 71(1), 231-239.
5 Brooks,
N., Barner, D., Frank, M., & Goldin-Meadow, S. (2012). Gesture in Mental
Abacus Calculation. SILC Showcase.
from http://www.silccenter.org/index.php/showcase/167-showcase-november-2012-gesture-in-mental-abacus-calculation
6 Manches,
A., & Dragomir, M. (2015). Gesture as
a means to examine the role of physical interaction in early numerical
development. Paper presented at the Paper presented at the 2015 annual
meeting of the AERA, Chicago, US.