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 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.
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.