This is the fourth in a series of posts about the visit made to Shanghai by Katie and Jo (primary school teachers) and Ruth (secondary maths teacher).
While we were in Shanghai, we were interested in the use of mathematical language in every lesson we saw, both at primary and secondary levels. Each key point had vocabulary associated with it, which all students were expected to know and use as part of their reasoning.
Stem sentences were evident in every lesson that we saw. These were well planned and were displayed throughout the whole lesson. The teacher would start by engaging the class in a discussion or a problem before encouraging pupils to share their thoughts. This would then be followed by the teacher recording stem sentences/methods (often pre-printed/taken from the textbooks). These would be read aloud and then repeated by all students, including the highest-attaining, and even in secondary! In the lessons we observed, the board work was fundamental and the stem sentences were often built on as the lesson progressed.
In secondary classes, we often saw students doing the following:
Explaining their own method (with workings out) which had been completed independently and then shared with the class
Explaining another student’s method
Pointing out errors in another pupil’s work and explaining why it was wrong
Sharing steps to solve a new problem without giving the answer
In all of these aspects, the children were expected to do this using the appropriate mathematical vocabulary, which included using the displayed methods and stem sentences.
What we have taken from this is that vocabulary is truly a key area in creating stronger mathematicians. We have seen that repetition of vocabulary helps to improve long term memory, it supports pupils in explaining their reasoning and creating generalisations and it makes the explicit obvious.
The use of carefully-constructed stem sentences/methods also meant that every learner had the same experience and it wasn’t used solely as a device to extend the higher-attaining students.