3.1

Macmillan Education

Skip to 0 minutes and 0 secondsHello! I hope you enjoyed the second week. In week two we introduced to key

Skip to 0 minutes and 10 secondsmaths education principles from Singapore: the Concrete-Pictorial-Abstract approach and the Bar Model Method. And like last time this video tries to pull together some of the points you queried in the comments and discussions. For example regarding the CPA approach, some mentioned that concrete manipulatives can sometimes also be a distraction. I thought that was a very good point. Yes, we must be careful that using concrete materials does not become a gimmick but if we make sure it doesn't and carve out a good sequence going from concrete towards the abstract, I think the evidence shows that it can work really well.

Skip to 0 minutes and 54 secondsOf course it also must be noted that the inclusion of concrete materials can be really tricky because, well, you need a lot of them, sometimes, and they can be quite costly. I think that might be the reason why in some cases the concrete phase has become more like a 'concrete pictures' phase in which pictures of real things represent the concrete. The 'pictorial' then often is more a stylised version of the concrete thing. Like for example maybe a photograph of a Lego block and then maybe a picture of a Lego block and then you go to the abstract notion.

Skip to 1 minute and 34 secondsIt was interesting to see that several learners seem to have used some of the methods mentioned before, although perhaps not exactly in the same way. There were numerous comments that seemed to appreciate the Bar Model method as well. However, some of you queried when to actually use the bar model. I would, for example, never require using the bar model if you can readily calculate the sum. A pictorial approach is not a replacement for the other modes, concrete and abstract, they all complement each other. Being able to use the representations for better mathematics, that's what it's all about.

Skip to 2 minutes and 16 secondsTherefore, assessing whether students can use the bar model effectively might be useful in the beginning but later on we need to keep in mind that the bars are a tool to aid mathematics they're not an end in itself. In the next week, in this week we're going to talk about two particularly effective principles from

Skip to 2 minutes and 43 secondsChina: Two Basics and Variation Theory. Two Basics comes from mainland China and emphasises the importance of knowledge and skills and how they are closely linked with conceptual understanding. Variation Theory states that through the use of variation in sequences of tasks, both procedural fluency and conceptual understanding can be reinforced. I hope you will enjoy the third week and I will see you in the discussion and comment sections.

Recap of Week 2

Welcome to Week 3!

In Week 2 we focused on mathematics education in Singapore. Based on the experiences of Educators and learners, in this video we provide a summary of Week 2, and respond to some of the comments and questions made during the week.

In Week 3, we will move on to other Asian mathematics teaching methods. Singapore is not the only country that does well in international comparisons. Other East Asian countries and jurisdictions such as Japan, China and Hong Kong also excel.

This video will be uploaded on Friday, the 14th of September, 2018.