Underpinning the Two Basics with research

So welcome to this video on the research basis for another one of those key pedagogical approaches in especially China, called the Two Basics. This is a philosophy that very much belongs especially to mainland China. And I think it’s good that we explain exactly what it is, but more importantly in this video what the research basis is. I assume you’ve watched the previous video from Professor Fan, and you understood what the Two Basics actually is. The Two Basics as a typical characteristic of mainland China has been applied there, and many experiments have been carried out, such as mathematics education experiments especially in a region called Qingpu. Two Basics means basic knowledge and basic skills.

Basic knowledge includes mathematical concepts, properties, laws, formulas, axioms, theorems and mathematical ideas and methods included in the contents. So that’s the knowledge. Basic skills are the skills of operation. Data processing, simple reasoning, graphing and so on. So you can already hear reasoning, for example, also seen as a skill. The Two Basics are key The emphasis on basics and training in education is the basic characteristics and experience of Chinese traditional education, which also is the accumulation and reflection of Chinese traditional culture. Some sayings that are quite

popular: “practice makes perfect”, “while learning the exhilaration”, “gained new insights through reviewing old material”. So that I think clearly depicts the philosophy the Two Basics also guides the design of textbooks. Some characteristics of these textbooks may be a gradual and step-by-step approach, for example through a spiral approach and that means that you revisit topics after a certain while or different representations. We already talked about that. The concrete pictorial abstract as well which relates to contexts with knowledge structures, and some review and reflection it also includes some rigorous definitions and layout lots of examples and exercises. Examples are an important part of a so-called worked example effect in the work of for example a psychologist called John Sweller.

Of course you might think that this sounds quite logical. Maybe you’re already using it in your classroom, or as a parent you can see it in the textbooks that your child are using. But you will be glad to hear that also contemporary research emphasizes that this is a good approach. I will discuss some sources concisely and show you why we think and that research supports this. The first example comes from Professor Fan’s own book on how the Chinese learn mathematics. Some other examples will stem from cognitive psychology, for example research on how procedural fluency and conceptual understanding are related. Let me start with the psychology example.

About 15 years ago Rittle-Johnson, Siegler and Alibali wrote an article about conceptual understanding and procedural skills and how they were related, and they very much emphasized that it was an iterative relation between the two. You can see this in this diagram. So on the one hand you have procedural fluency, and on the other hand you have conceptual understanding, but both reinforce each other. And often actually saying well we need to start with one of them first and then the other one follows is a strange question, because they actually go hand in hand. You can see this in this abstract of the article as well.

This iterative approach where one reinforces the other and where hand-over-hand understanding and skills improve seems to be a key feature also in East Asia. So this idea that in Asia they just practice a lot and that means they score very well in international assessments probably is not correct. It is both understanding and skills hand in hand. Another name is Jon Star. He also noticed that procedures and understanding were often put against each other. And he thought how can I actually reconceptualise how can I think in a different way about these two things, and make sure that it’s not seen as conflicting but that they actually reinforce each other.

This element is also apparent in something called the Math Wars, which in the 80s was especially in the USA a very big thing. People were one group said skills needs to be the main thing we do, and other groups said understanding and it really was a very big deal. And you can still see the results of that now to be honest and still a lots of people fuelled about exactly this. And he thought well actually procedures and understanding are both important, and we can both do them at a more superficial level and at a deeper level. And superficial probably is not what you want.

Although practicing sometimes can work quite nicely, but we also should aim to maybe have a deeper level for both procedures as understanding. So he really tried to reconceptualise it and to get away from the idea that you actually only need one of these two things. They actually are both needed> Perhaps we could say that this culminated in a 2015 review paper from actually Rittle-Johnson, who was one of the authors of the article I mentioned from 15 years ago. Schneider and Jon Star again in this review they looked at all the literature that had appeared on conceptual understanding and procedural fluency. And again this review said that both types are very important, and that both types of knowledge are bi-directional.

So again procedural knowledge conceptual knowledge they both reinforce each other. What they also saw is that alternative orderings of instruction on concepts and procedures have rarely been compared with limited empirical support. So even if we would think oh we need to start with one of them first and then the other, there is actually not a lot of research on this ordering what is better to do first. And it’s a little bit of speculation. But I would say that it also depends very much on the topic that you’re actually teaching. In my own research I also experienced that skills and understanding go hand in hand.

fFor example, with Professor Fan I wrote an article about algorithms algorithms are often painted in a negative light, because you perform a certain recipe and you don’t really know what you’re doing while performing this algorithm. And we in this article I think a write that actually algorithms procedures go hand in hand with understanding. So we shouldn’t be saying one is bad one is good, but actually reinstate them and make sure that algorithms procedures and understanding indeed go hand in hand. There is a link to this article in the course as well.

So again starting from the definition in the beginning of what the Two Basics is and the previous video on the Two Basics, we conclude that the Two Basics are essential for a good mathematics education. Both procedural fluency and conceptual understanding mutually reinforce each other. We would therefore say that rather than discuss what is more important also depending on the topic at hand. both need to be central. It is not necessary to choose one only do skills, only do procedures or only look at understanding. You do both. Based on the literature we conjecture that this also is part of the excellent East Asian performance.