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Underpinning the Bar Model method with research

How does the bar model method fit in contemporary research on learning?
- Cognitive psychology
- Education research (Singapore, Utrecht)
So welcome to this video on the research basis for the Singapore bar model method. I might refer to it as the model method or the bar model method and it’s known in different names but I assume you know the basics of the model method, because you hopefully have watched the previous video on the bar model method by Professor Fan and you now understand what the bar model method actually is. The method is quite specific for for example calculating ratios, proportionality, percentages but it can also be seen that the visual aspect of the model method very much fits with the previous theme, the Concrete-Pictorial- Abstract approach.
Of course you might think that the application sounds quite natural and quite common but this is not the case. You will be glad to hear that there has been a lot of research actually on the best way or good ways to actually study ratios and proportionality and there is quite a lot of contemporary research, that seems to indicate that it’s actually quite a good way to learn ratios and proportionality. I will discuss some research articles concisely to support the statement that it’s actually a good thing and that the model method works. One part of the literature is very much connected to Asian mathematics education.
Take the overview article which is linked in the course by Kho and others - later on you will even see a video by the actual originator of the model method Dr. Kho himself - it provides an overview of the origins of the model method. In Singapore in 1979 there was a big reform of mathematics and this included a so-called “primary mathematics project” led by Dr. Kho Tek Hong and the model method has been widely implemented in textbooks in Singapore as well. It was part of that project and it also was implemented in textbooks and it’s now finding its way to other parts of the world.
The model method, also known as bar modeling, is partly based on the part-whole and comparison models which are pictorial forms of Greeno’s part-part-whole and comparison schemas for addition and subtraction of word problems. In the Singapore primary mathematics textbooks the part-whole and comparison models were further developed to include multiplication and division as well as fractions, ratios and percentages. These types of models enable students to visualise the problem structure and make sense of the quantitative relationships in word problems. We could look at the model method as a sort of pre-algebraic method; the integration of the model method with the algebraic methods can be shown diagrammatically and you can see the diagram to the right.
You can see how words, a word problem, might be translated in a pictorial element, which will then feed into a more algebraic or abstract element and together they will lead to a certain solution. So in that sense it is very much a tool to go from a word problem to a solution via different representations. I think you can also recognise some of the Concrete-Pictorial- Abstract in here as well. So when students are using the model method to solve word problems we think, and the research shows that as well, that students are guided through three phases of problem solutions.
This theoretical framework is based on the processing model for solving arithmetic word problems presented by Kintsch and Greeno already in 1985 and on their observations of teachers and children who used the model method to solve word problems. So you read the text as you can see at the top of the diagram then you represent the information in arithmetic expressions and equations which is in the bottom left of the diagram and then on the bottom right you represent the information in the structure of a model this was the theoretical framework that Kintsch and Greeno used.
Of course the solution of word problems is contingent upon sound conceptual knowledge and also knowledge of what is a part and what is the whole so-called part-part-whole relationship of numbers, an integrated and well-organised knowledge base so you need some basic skills and also some metacognitive processes. The authors of the article, Ng and others interviewed heads of departments and teachers to see how the model is introduced by schools and their teachers in a primary setting. What important points to look for when drawing the model for a given problem? And also how our children taught to solve for the value of the unknown if they are neither taught to construct nor taught to transform equations? That’s what they tried to find out.
They also tried out the problems with students and teachers. An example of such a problem you can see here. The model method then is a problem solving heuristic that requires children to reflect on how they could accurately represent the information presented in word problems. First in terms of a drawing and then a series of arithmetic questions. The art of representation first has to be taught; the children’s responsibility is then how to choose them and to use them. And using these examples, were integrated in Ng and other’s research. OK you’ve now seen what the model method is and we’ve also emphasised what it can do and what it can’t do. And also what research actually underpins it.
It is important to realise that although we know the model method now mainly from Singapore, this whole week is actually about Singapore and its influence on worldwide mathematics education, the underpinning ideas again like CPA have a long history coming from for example the USA and Western Europe. For example the Institute where I did my PhD the so called Freudenthal Institute also has done a lot of work with fractions, proportionality and ratios. It is great that this idea of the model method is now being adopted worldwide.

This video demonstrates how the Bar Model method fits in contemporary research on learning.

The method is widely used for calculating ratios, proportionality, percentages, but it can also be seen that the visual aspect of the model method fits very much in the Concrete-Pictorial-Abstract approach as well. It has its roots in Greeno’s part-whole and comparison models.

In Singapore primary mathematics textbooks these ideas were extended to multiplication and division, as well as fractions, ratios and percentages. The models enable students to visualise the problem structure and make sense of the quantitative relationships in word problems. The Model method, then, can mainly be seen as a problem-solving heuristic that requires children to reflect on how they could accurately represent the information presented in word problems, first in terms of a drawing and then as a series of arithmetic questions.

This method is used in teaching in Singapore but the method is also used worldwide.

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World Class Maths: Asian Teaching Methods

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