Skip to 0 minutes and 0 seconds So welcome to this video with the last important concept, pedagogical concept. But you will actually notice, as we’ve done in previous videos, that there is quite some overlap because there is a an integrated vision you could say in Asia on mathematics. This one is about how ‘practice makes perfect’ and how actually, like The Two Basics, procedures and algorithms go hand in hand with conceptual understanding. I hope you realise that in all these
Skip to 0 minutes and 34 seconds videos this was a theme: in Variation Theory it was important that procedures and understanding went hand-in-hand in the way that tasks were designed. In the Two Basics it was important that both went hand-in-hand as well. In the concrete-pictorial-abstract approach on the one hand you had the concrete aspect on the other hand you had the abstract approach, so these things really go very much hand-in-hand. That already indicates that practice is deemed quite important in China and actually in Asia. Also recall the statements from a previous video from Chinese traditional culture ‘practice makes perfect’, ‘while learning the exhilaration’ or ‘gain new insights through reviewing old material’.
Skip to 1 minute and 27 seconds We covered for example the article by Rittle-Johnson, Siegler and Alibali where there was an iterative relation between conceptual understanding and procedural skills. They go hand-in-hand. A review of the empirical evidence in that article showed that mathematics learning indicates that procedural knowledge supports conceptual knowledge as well as vice-versa and thus that the relations between the two types of knowledge are bi-directional. But they also said that the order of these two things was not the most important thing and actually that there wasn’t much research on this. When you really say they go hand-in-hand they go hand-in-hand. Both are equally important. There are more sources that say that practice is important. Perhaps you’ve heard the work from Anders Ericsson.
Skip to 2 minutes and 17 seconds He is an expert on expertise; he’s an expert on experts.
Skip to 2 minutes and 26 seconds He studied elite experts: musicians, chess players to see how they became experts. And his conclusion was that they all practice something called ‘deliberate
Skip to 2 minutes and 39 seconds practice’: they were practicing with a certain focus and they kept on practicing and by doing that they became more and more expert. Another important result in psychology is the testing effect or sometimes known as retrieval practice. The testing effect is the finding that long-term memory is increased when some of the learning period is devoted to retrieving the to-be-remembered information through testing with proper feedback. I know that testing sometimes has had a negative connotation but if you do it well, testing can actually help your learning. Especially if you then get feedback on how you did and you can improve this. The effect is also sometimes called, as I mentioned before, retrieval practice. So it already has the word practice in it.
Skip to 3 minutes and 32 seconds Or sometimes practice testing or test enhanced learning. Although this is a secondary example, I have seen this in my own research as well. Here you can see an example from my own research in secondary mathematics where repeated practice of solving equations at home in an online technological environment, with numbers that kept on changing, were randomised, with some feedback as you can see here. If you made a mistake or you needed a hint, contributed to increased skills and understanding. So again, retrieval practice, testing effect, ‘practice makes perfect’! Like all other Asian principles we conclude that practice is essential in good mathematics education, both procedural fluency, so practice and skills, and conceptual understanding mutually reinforce each other.
Skip to 4 minutes and 28 seconds So you get the best of both worlds.
What does research say about practice?
This video will explain how the previous weeks have shown that practice is one of the key features of Asian maths pedagogy, and will reinforce this by describing research on the importance of practice: practice makes perfect.
There are several sources that confirm this importance. Work by Rittle-Johnson and colleagues shows how procedural fluency goes hand in hand with conceptual understanding: practice leads to understanding, understanding reinforces meaningful practice.
These insights also align with research on ‘deliberate practice’ and ‘the worked example effect’: presenting more worked examples will help create the skills needed for solving mathematical tasks.
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