Theme 3: Building on students’ thinking

Effective teachers provide maths learning experiences that enable students to build on their existing proficiencies, interests and experiences.

Effective teachers identify what students know and can do and build on these proficiencies rather than  identifying and filling gaps. They connect learning to what the students are thinking, and to do this they must enable the students to make their thinking and reasoning visible. Students’ misconceptions and errors must be revealed and used as building blocks for teaching. Teachers must skilfully make connections for the students, and ensure that relevant and meaningful tasks provide an appropriate challenge to the student.

By recognizing competencies and making connections to what the students already know, a teacher will focus on next steps, achieving a positive conceptual learning trajectory for the student rather than implementing a more fragmented procedural gap filling approach.
 

           

Exemplars:

The reflection time also meant that I was building on the students’ thinking each time I worked with them because I had recorded key pieces of their thinking during that reflection time. This meant that rather than them having to ‘change gear’ or ‘catch up’ with what we were doing each day it directly built on the place we had finished the previous day.
The year 3 children benefited from an environment that allowed them the opportunity to work independently but also collaboratively in pairs. Discussions with partners engaged the children in their thinking and helped to reinforce the learning tasks.
‘Pairs and small groups are not only useful for enhancing engagement; they also facilitate the exchange and testing of ideas and encourage higher order thinking’. (Anthony, G. & Walshaw, M., 2009, p.9)
The emphasis during these sessions was on ‘doing’ (making, showing, sharing and explaining) rather than recording, with very little being actually written by the students. Children were consistently required to explore others' understanding of concepts and justify their own. They had opportunities to see what the other students were doing and were challenged to explain their thinking. They had access to this equipment during lessons and were encouraged to use equipment to explain their thinking to others.

 

Reflection: using a “think buddy-mentor” to reflect on the content of the session and self assess; the focus here was to develop metacognition through thinking about what was happening in our heads and explaining it from the buddy’s perspective.
We began by ‘roaming the known’ – revisiting learning they felt comfortable with and had success with. We moved to the next steps quite easily and revisited these every week. We talked a lot about how we achieved an answer and what other ways we could solve problems.
Students respond well to effective teacher questioning which challenges their mathematical thinking and gives the teacher insights about the students.
Each session started with a quick “warm-up” fun and competitive (but non-threatening) game with knowledge that the children already had. They were always racing against time, me and the other children in the group. I was surprised at the assumptions I had made about the knowledge I thought children already had. I was also surprised how long it took for the children to make this knowledge automatic. It simply does not happen without repetition, repetition and more repetition. The knowledge was also linked explicitly to the strategy teaching. It was really important to keep reminding the children of this – “What knowledge do we have that will help us with our strategy work?”