by

Zhenzhen Miao and David Reynolds

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This post was an invited piece published early 2017 on the BBC’s My Perfect Country blog. The blog webpage is not available now, so I repost and archive it here for everyone interested in effective mathematics teaching to read.

We would like to share with you some characteristics of Chinese maths teaching found in the Effectiveness of Mathematics Teaching (EMT) project which involves over 500 Year-5 children and 19 maths teachers from Southampton, England and Nanjing (a city near Shanghai), China. With the quantitative results published and widely publicised, here we will illustrate some details about how the Chinese maths teaching functions. You will be able to read the complete report in our book to be published this year. [17/4/2018: now published]

In a Chinese maths class, all pupils are expected to be active thinkers. Chinese teachers are more active in posing questions so as to generate solutions among pupils but *less* active in providing solutions. The duty of looking for an answer or solution to a given problem is on the pupils’ shoulders. The degree of a Chinese teacher’s input and support gradually decrease as she/he guides the class through the lesson. For instance, in the EMT study, the first exemplary task in Teacher CN4’s lesson on Data involved the collaboration between the teacher and the pupils; the following three tasks then saw a decrease of the teacher’s input and an increase of pupils’ independent effort; for the last task, the pupils worked in an absolutely independent fashion and completed it over a very short period of time – 33 seconds, all done!

Another typical feature of maths lessons in China is the existence of lots of metacognitive discussion promoted by the teacher and carried out by the pupils particularly before and after each task. Before tackling a problem, pupils are asked to think what they must bear in mind while looking for a solution and why. This is often generated through intensive questioning and reasoning in the whole class. Teachers are also constantly encouraging pupils to open their minds, come up with multiple solutions to every single problem and explain them to the class. So doing, children learn to think and tackle a given problem from different angles at deeper levels. A common phenomenon in every classroom is that during every independent work period (often 2-3 min per each), the teacher circulates very quickly through the class, checking everybody’s work and identifying and picking up typical work samples (correct and wrong). She/he then shows the work samples through the projector and asks pupils to comment on them. Through an intensive round of whole-class Q & A, pupils’ classwork is naturally turned into teaching material. Stimulated by the teacher questioning, pupils think and talk about issues as to what the appropriate methods and correct results are, why certain mistakes have been made by themselves or other pupils and what measures should be taken to avoid similar mistakes in their future problem solving.

Across all Chinese maths classes, children show their solid foundation and absolute readiness for the new content to come in. Chinese teachers seem to be more aware and confident of their pupils’ level of knowledge and thus make more accurate ‘prescriptions’ for their capacity of learning the new content. If a teaching plan is a hypothesis, then Chinese teachers are good at making accurate ones, which is all down to their profound and thorough knowledge of mathematics and its teaching methods.

Chinese teachers believe that a lesson should be both teacher-guided and child-centred (in Chinese: 教师为主导，学生为主体).

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Chinese teachers believe that a lesson should be both teacher-guided and child-centred (in Chinese: 教师为主导，学生为主体). The teacher is there to ensure that the lesson is heading in the right direction, leaving the main job of mathematical reasoning and problem solving to pupils themselves through asking lots of interconnected questions. It is through whole-class interaction and brainstorming that the guidance of the teacher and the central role of* every* pupil simultaneously come true.

It occurs to us that Chinese maths teaching is more progressive than the methods applied in Britain and many other Western countries. Both caring about every individual pupil (equity and democracy), the English maths teachers spend more time teaching individuals rather the whole class and allocating about a half of the lesson time for children to work on their own, but the Chinese maths teachers stick to active interaction with the whole class in about three quarters of the lesson time, breaking the remaining lesson time into a few small segments for independent work and inserting them between whole-class interaction/discussion periods. The English approach means that there are always some children being excluded from the interaction with their teacher, whereas the Chinese methods ensure that every single pupil is included in the interactive teaching process.

In the English maths class, it might seem that the teacher gives the children entire freedom, but the focus on interaction with individuals and independent work before children can be *truly* independent means that some children are from time to time excluded from the democracy of equal learning opportunities. In the Chinese maths class, it might appear that all individuals are most of the time taught together, but it is essentially through whole-class interaction with the teacher that their rights to learn the same content as everybody else are equally respected and realised.

Both believing in the importance of hands-on activities through which children learn by doing, English teachers, despite apportioning a huge chunk of lesson time for pupil “independent” work, have to re-teach many individuals who at times get stuck and choose to come back to their teachers throughout the practising time; Chinese teachers, apparently seeing the thinking and reasoning process as the heart and soul of hands-on work for *mathematics*, embed such hands-on activities naturally into the whole class interaction time, and structure the interaction with logically interconnected mini-questions. Through answering lots of questions during the whole-class interaction time, Chinese children’s mathematical thinking becomes highly observable, which in turn constantly feeds back to the teacher and guides the dynamics of the teaching and learning process.

English maths teaching is more about the teacher demonstrating the correct way of doing mathematics and pupils learning to do it in the same way. Chinese maths teaching is more about the teacher developing the mathematical knowledge gradually in pupils’ minds through intensive interaction with the whole class.

Chinese maths teachers seem to have found a better path towards a truly progressive education, with the characteristics that Dewey proposed a century ago realised, such as hands-on, child-centred, teacher-guided, teacher as a facilitator (rather than a demonstrator), relevant to children’s life. Maybe, the Western world has been misinterpreting – rather than understanding and developing – Dewey’s thoughts on education from the very beginning.

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