4.1

## Macmillan Education

Skip to 0 minutes and 0 secondsHello, it's me again. I hope you enjoyed the third week. In week 3 we introduced the two key maths education principles from other parts of Asia. Firstly the Two Basics, which emphasises how knowledge, skills and understanding all go hand in hand. And secondly, Variation, which refers to making well-thought sequences of tasks to highlight concepts. It again was nice to see you engage with the content. And it was also good to see that you appreciated, for example, the interview with professor Gu about variation. Especially here in England variation has become more and more popular recently. Some people might even say that it has almost become *too* popular. And you know what happens with things that get too

Skip to 0 minutes and 56 secondspopular: you get discussions about what 'real' variation is and what is not. I want to stress that I don't think the point should be that there is an imposed rule for this. The key element for me is that by sequencing tasks randomly we're missing out on something. We can rather think about structured, well thought out sequences of tasks. Then we can have the

Skip to 1 minute and 23 secondsbest of both worlds: on the one hand plenty of practice and then on the other hand conceptual understanding by using this variation. It was pointed out, though that making such sequences can be a very time-consuming affair and I agree with that. I would not recommend we all reinvent the wheel. It is one of the reasons why I am so enamoured by good quality textbooks where design and mathematics education experts create quality materials. Another big theme connected to Two Basics, knowledge and skills, was how procedural fluency and conceptual understanding go hand in hand. No one really disagreed with that but of course in the context of the classroom this doesn't mean you might start with one or the other.

Skip to 2 minutes and 16 secondsJust as long as you eventually do both. The article by Rittle-Johnson and others points out that there is not a lot of evidence on the order in which you best can do skills and/or understanding.

Skip to 2 minutes and 31 secondsSo the question then is: when start with what? I think this depends on many variables like prior knowledge and even the topic can make a difference. I remember teaching different types of topics, of course mostly at secondary level, and sometimes I would start with the understanding and then we do a lot of practice and sometimes I would start with a lot of practice and then hopefully and eventually understanding would come automatically. In a sense, Week 4 highlights an underlying feature of

Skip to 3 minutes and 7 secondsmost of the principles mentioned: that 'practice makes perfect'. And this is not practice in the sense that you can perform a routine, although nothing wrong with that of course, but in a way that genuinely reinforces procedural fluency and conceptual understanding. Finally, this week we will pull together some ways in which some Asian countries have tried to integrate principles like these in their education systems through professional development for teachers. I hope you will enjoy this fourth and last week and I will see you in the discussion and comment sections.

# Recap of Week 3

Welcome to Week 4!

In Week 3 we focused on the Two Basics and Variation theory as Asian mathematics teaching methods. Based on the experiences of Educators and learners, in this video, we provide a summary of Week 3, and respond to some of the comments and questions made during the week.

In Week 4 we will look at one final principle and then explore how Asian countries manage to integrate these principles into their classroom activities. The key term here is ‘professional development’. We will give some examples from a variety of countries.

We hope you enjoy this final week!

This video will be uploaded on Friday, the 21th of September, 2018.