What do you think of when you picture a maths classroom in China? Perhaps a perfectly disciplined environment with an emphasis on direct instruction and a singular focus on rote learning. Or maybe lessons where teachers spend all their time talking while their students do nothing but listen.
But what is really happening in Chinese classrooms? Few teachers and researchers have spent time observing lessons in China, and that means there are many misconceptions about teaching and learning there.
In our book, we present an in-depth analysis of Chinese primary maths classrooms by looking at lessons learned from so-called “master teachers” across five Chinese provinces. These educators are seen as the most adept teachers in their region, and play a leading role in professional development within and across schools.
To understand what makes them successful, we collected data from 70 master maths teachers, more than 3,000 primary-school students, and teaching research events at school, municipal, provincial and national levels.
We wanted to find out more about the quality and characteristics of master maths teachers’ teaching, the quality of mathematical learning among their students in affective, metacognitive and cognitive domains, and the teaching and learning mechanisms that underpin excellent performance in these domains.
So, what did we find?
Modelling
Master teachers do a lot of modelling at the front of the classroom in a highly interactive manner, and use this as a basis for a shared discourse. They also use multiple representations for one mathematical fact. For example, when teaching a topic like fractions, teachers model example calculations and also exemplify these examples with visual models, where fractions are represented as area, line and sets.
Mastery, but not as you know it
Master teachers only move on with a lesson once the class has reasoned the very essence of the focal task or topic in depth. In other words, mastery does not just mean that all children are proficient but that they are engaged in both the procedural and conceptual knowledge of a topic. Proficiency is just a threshold. This is not always the case in what others call mastery. The assumption here is that every student deserves to and can have in-depth engagement with mathematical content.
Variation
Master teachers use variation (such as counter-examples) to help scaffold fundamental understanding. For example, when encountering new concepts like triangles, teachers vary the types of triangles so students learn what their properties are. Teachers also show examples of objects that might be mistaken for triangles but are not triangles. Such variation supports students’ procedural and conceptual understanding.
Focus on mathematical structures
Mathematical structures are at the core of the lessons, with constant abstracting and generalising, and the teacher gradually unfolding the essence of mathematical knowledge on the board. Rather than presenting a structure in one go, something which sometimes happens when using pre-made slides, mathematical structures are gradually constructed on the board.
As a result of these practices, we found that Chinese students generally did better in maths tests than their more senior English counterparts (although it must be said that the English data was quite old). We also saw that the Chinese students demonstrated good metacognitive awareness and that they scored highly on affective outcomes like school belonging, engagement in learning and enjoyment of maths.
How to develop master teachers?
These approaches seem to be successful. But how do we develop master teachers in the first place The answer, we believe, lies in more effective professional development.
One big difference between China and the UK is the presence of a reliable and valid system for continuous teaching improvement and teacher growth. For example, the practice of “Keli”, in which lessons are polished for public demonstrations and competitions, supports the development of exemplary lessons.
Teachers also come together in research groups and professional development events to learn with and from each other, especially expert teachers and renowned master teachers. All teachers read, reflect, write and publish their experiences, but master teachers do more of it. This is seen as an important element of being considered a master teacher.
All of this requires strong support from colleagues, school leaders and official bodies that focus on teaching research. Chinese master teachers extensively study the curriculum and textbooks with attention to lesson planning. Although this also, to some extent, happens in England, the support structures in China are much stronger, with master teachers seen as role models but also staying grounded, recognising that there always is something new to learn.
Most importantly, ideas are not set in stone; even master teachers keep practising and keep changing, modelling a virtuous cycle of continuous development.
Master Mathematics Teachers - Educational and Professional Excellence in Chinese Primary Schools is available now, free
Dr Zhenzhen Miao is assistant professor in mathematics education at Jiangxi Normal University, China, and authored the book with Dr Christian Bokhove, professor in mathematics education at the University of Southampton, and David Reynolds, emeritus professor of education at Swansea University and distinguished professor of education at Hangzhou Normal University, China
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