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3.4

## Macmillan Education

Skip to 0 minutes and 0 seconds Professor Fan: We know you as the person who invented the model method in the early 1980s, so we would like to hear from you so what is the general background, or the origin, or the history when you put forward such a method or theory about the model method? So, can you give us some historical background, why? Dr.

Skip to 0 minutes and 51 seconds Kho: In the early 1980s, we were trying to improve strength. Maths education tried to improve in-class materials, teaching methods and also provide digital learning to revamp maths teaching and learning methods in Singapore. So, the model method actually is trying to help students to make sense of the abstract concepts and skills, in particular in solving problems. They do not know the meanings of problems. Then, they will be difficult to solve the problems. So, provide the visual approach okay, I mean to help students to solve and understand the problem just by drawing a picture, a pictorial model okay. So, to help them understand the problem, analyse the problem and solve the problems. So, it’s a means to provide something concrete and pictorial.

Skip to 2 minutes and 19 seconds Professor Fan: So, in the early 1980s, did students in Singapore perform very well in mathematics, or they were not as good as now? Dr.

Skip to 2 minutes and 32 seconds Kho: It’s actually, the level of basic numeracy was low. Then that’s why we want to change. We want to revamp the education. Then we, actually, the effort of the approach worked. We provide the material, advocating the concrete-pictorial approach. The concrete pictorial model or comparison, which are which are actually also parts of the model method.

Skip to 3 minutes and 22 seconds Professor Fan: Thank you. So Dr. Kho if someone does not know model method at all, how will you concisely describe what is model method? Dr.

Skip to 3 minutes and 35 seconds Kho: Model method initially called Model Drawing Method. (Professor Fan:okay) It means you draw a model, draw a picture, we call it pictorial models. Draw pictures. Nowadays people also call it bar modelling. Actually you draw bars to represent quantities, whether they are known or unknown, you just draw bar to represent here. Then we analyse the quantities compare quantities using the bars. (Professor Fan: okay) So we have this part-whole model and comparison model as basis of model method. They are also extended to other maths concepts, like fraction, ratio and so on.

Skip to 4 minutes and 37 seconds Professor Fan: So Dr. Kho can you give us some examples to explain how the model method can be used in mathematics classrooms? Dr.

Skip to 4 minutes and 58 seconds Kho: So it is a visual approach. The model is a part-whole visual approach to help students understand, analyse and solve the problems, whether it’s a fraction problem even a ratio problem. Suppose you see two quantities

Skip to 5 minutes and 19 seconds okay in the ratio 2:5. So you draw two bars, one bar comprising 2 units, the other bar comprising 5 units. Then the ratio is 2 units to 5 units. And then we can use bars to support model to concrete the unknown, even and the given data. Then we use this on the model to calculate the unknown data. So, this is about the basic use of the model. The model drawing can be used to solve complicated, complex problems which require higher levels of algebraic skills. They develop and enhance the active thinking of students.

Skip to 6 minutes and 20 seconds Professor Fan: Thank you very much. So if someone in other countries they want to use model method, for example he is a novice teacher, so can you give some suggestions or advices for those teachers who would like to try this method? Dr.

Skip to 6 minutes and 41 seconds Kho: Because the model method is for active learning. So, we would suggest teacher to allow students to draw their own models rather than giving them the models to solve the problems. Students have opportunities to draw models on their own. And the model the students draw could be different also. So, the students should be given opportunities to articulate how they draw. Then to compare and share their ideas and how they use the model to solve problems. This active learning is useful if you adopt a model drawing method in teaching. Students should be challenged to solve different and new problems through mathematic thinking to the pictorial representation.

Skip to 8 minutes and 12 seconds Many children are able to solve the problems, if they are given the chance to do the so-called pictorial thinking rather than abstract thinking alone. Pictorial thinking will enhance and improve their abstract thinking.

# Interview with Dr Kho

This is an interview by Professor Fan with one of the key people involved in the development of the Bar Model method, Dr Kho Tek Hong. He is the inventor of Bar Model method in Singapore.

Dr Kho received a PhD in mathematics from the National University of Singapore, then worked as a school teacher. He then worked in the Ministry of Education, as the leading curriculum designer. After that, he was principal curriculum specialist for numerous years. He created the Bar Model method in the 1980s while he was working in Ministry of Education, and responsible for Singapore’s mathematics curriculum development.

Although the video is in English and is subtitled, you may also want to refer to the transcript.

You may still have some questions about the Bar Model method after watching the video. You can ask them in response to this video. The teaching team will try to answer any questions you still have and choose some of them for the Week 4 recap video.