Pedagogy 1: Manipulatives in Computing (theory)

Manipulatives in Computing

At the moment I am quite interested in the pedagogy of Computing, what this looks like for the subject and how we can best support teachers and learners to convey core Computing knowledge. As part of this journey, I have taken inspiration from other disciplines and considered its applicability to the subject of Computing. This post, surrounds the idea of using Manipulatives, such as you might see in a Maths classroom, in Computing.

What are Manipulatives?

In the context I am talking about, manipulatives are concrete resources for teaching Maths. In the classroom, this is frequently seen in the use of multilink cubes, dienes, place value cards, fraction walls etc. There are examples of manipulatives in other areas, but the majority of research stems from the ability of concrete objects to make abstract mathematical concepts seem more ‘real’ to children.

It is worth noting here that there is a whole field of work exploring ‘Virtual Manipulatives’ which surround the idea of having access to concrete resources such as counters or dienes blocks through a computer, such as an app on an iPad, instead of on the table in front of them. This is not what I am referring to when I talk about ‘Manipulatives in Computing’, but if you’re interested in this area, try Sarama and Clements (2009).

Why do we need Manipulatives in teaching?

The origin of Manipulatives in teaching abstract concepts if based on those of Piaget (1952), who believed that children would not be capable of abstract through before having a concrete basis to build their knowledge around. Alongside this, Bruner (1964), was interested in how knowledge is stored and explained stages starting with ‘enactive – action stage’, this is where an individual learning something repeats certain actions, but could not easily explain what they were doing. Bruner’s stages do not change based on age, but merely begin transitioning in this case to the iconic (image-based) stage. Moyer-Packenham (2001) has a more detailed history of this, but with just these snippets we can start to understand why manipulatives are seen as valuable in the teaching of Maths.

From a learning theory perspective, the ability to use concrete resources when starting to demonstrate more complex mathematical understanding is crucial. Whilst you may not be able to form numbers (iconic representation) you can show your understanding the concept of ‘2’ by collecting 2 objects in a group. Equally further up the school, children may explain to you what a half is, by physically showing you. At this point, the ability to articulate the abstract concept of fractions is facilitated by an ability to show what you mean.

From these early learning theorist stages, there has been much, much more work with varying opinions. As this is not the main focus on this post, I will direct you to Carbonneau, Marley and Selig (2013) who conducted a meta-analysis comparing 55 studies measuring the efficacy of teaching Mathematics with concrete manipulatives compared to a control group. Altogether they found that manipulatives in Maths education do have a positive effect on learning compared to more abstract models, however, there is a delicate balance between the tool and how it is used. This supports other theories (Resnick & Omanson, 1987) that how the teacher uses the manipulatives on a daily basis is the most determining factor in their usefulness.

Overall, from my own experiences of teaching and my reading, it’s clear that children like having manipulatives when they’re working on problems. There is a perception that coloured items on desks makes the learning seem less mundane, however, equally the children may get distracted by such tools if they’re not shown how to use them appropriately. EVERYONE has seen a child building a tower as tall as they can with multilink at some point in their career…

But what does this have to do with Computing?

There’s already some links between using concrete tools of teaching Computing, particularly with younger children. Flick through a school supplies catalogue and the pages are littered with Bee-bots, Probots, Code-a-pillars and many more and the theory is that these tools do the same jobs.

It has to be said, there is little research in this area, and much of that is based on specifically designed products as opposed to tools that are already adopted on the large scale in the classroom. Sapounidis and Demetriadis (2013) conducted one of these studies comparing a ‘tangible user interface’ with a ‘graphical user interface’ for controlling a Lego NXT robot. Interestingly, there were some similarities with Maths. For example, in children’s interviews they showed an initial preference to the tangible, suggesting that it seemed more ‘fun’ and overall children seemed more engaged with the manipulatives they were using. Beyond this, the difference in ‘ease of use’ between the two systems was not significant. Younger children got on better with the tangible system, but this is thought to be explained more to do with their limited motor skills when using the mouse, than the conceptual nature. Older children preferred the tangible system, yet it did not make a difference on their learning outcomes.

Whether through engagement, accessibility or an explicit learning advantages, educators speak highly of the benefits of these resources on teaching children to program. I myself, am a big advocate of ‘digital making’ and ‘physical computing’ as way to inspire children and allow them to pursue their own interests. However, I have been reflecting on this pedagogy, as I said, and I wonder if there needs to be a teaching stage before this.

What went wrong?

Children throughout my KS2 classrooms can happily tell you that an algorithm is ‘a clear and detailed set of instructions like you would need to tell a computer to do something.’ They can also tell you ‘a program is a set of instructions that runs on a computer and tell it what to do.’ Brilliant we think! They’ve got it! And then I asked them ok, what is a computer? And these are their answers:

  • A piece of technology
  • A keyboard and a screen
  • A search engine
  • A machine used for work
  • A metal brain
  • A machine with a keyboard
  • Information device
  • It’s electric

Now, this could be a case that we mentioned earlier, of not having the vocabulary to explain a concept, but if I ask them to draw a computer. I get this:

Their understanding of what a computer is, is very limited.

Imagine now, that I hand them a Beebot, and I say, go and program this. If their understanding of a computer is a laptop, and their understanding of programming is instructions for a computer, how are they going to assimilate the knowledge I’m giving them about programming being sequential and precise with what they think a computer is.

Piaget argued that children need a good reason to give up on a current working theory and I would say in this scenario they are more likely to make no connection between the object and the concept you’re teaching. In their head, they’re learning to make a Beebot move, but they have no understanding of the wider view and how this relates to programming in general. Once again, this sits nicely with the theory surrounding manipulatives in Maths which pointed out many children didn’t recognise the correlation between the mathematical objects they were using and the concept. They merely learnt the procedure of moving the objects around as they’d been shown to please the adult.

Pre-programming stage in understanding

This misunderstanding led me to explore a wider application of educational theory and this is where I started to make the connections between the misunderstandings I was seeing in Computing and those that are typically seen in Maths.

The reading and research I have done, leads me to suggest that before we start with the teaching of programming, with concrete objects or otherwise, we need to first have some concept of what a computer is. From a National Curriculum perspective, this is highlighted by the KS2 strand:

  • work with variables and various forms of input and output

What is an input? Or an output? How do the children work with something that they have no concept of? All of this came together with me turning the manipulatives as a way to start introducing the more abstract concepts of what a computer was, what an input was and what an output was. My answer was to use a Raspberry Pi.

See my second blogpost: Manipulatives in Computing (in the classroom) to learn about how I used the Raspberry Pi and what the outcomes were for the children’s understanding.

References

Bruner, J.S., 1964. The course of cognitive growth. American psychologist, 19(1), p.1.

Carbonneau, K.J., Marley, S.C. and Selig, J.P., 2013. A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), p.380.

Moyer, P.S., 2001. Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in mathematics, 47(2), pp.175-197.

Piaget, J., 1952. The origins of intelligence in children (Vol. 8, No. 5, pp. 18-1952). New York: International Universities Press.

Resnick, L.B. and Omanson, S.F., 1987. Learning to understand arithmetic. Lawrence Erlbaum Associates, Inc.

Sapounidis, T. and Demetriadis, S., 2013. Tangible versus graphical user interfaces for robot programming: exploring cross-age children’s preferences. Personal and ubiquitous computing, 17(8), pp.1775-1786.

Sarama, J. and Clements, D.H., 2009. “Concrete” computer manipulatives in mathematics education. Child Development Perspectives, 3(3), pp.145-150.

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