Making the most of NRICH activities in the classroom
NRICH's beliefs about mathematics, and mathematics teaching and learning, inform how we envisage teachers and learners working with our tasks in the classroom, and the roles they play.
Broadly speaking, we envisage that an NRICH activity will involve the students attending to the maths, and the teacher attending to the students and their mathematical ideas. This puts the students in the role of mathematicians, and the teacher in the role of facilitator.
In a classroom where rich tasks are being used to develop students' mathematical thinking and foster their mathematical mindsets, you might expect to see:
- The lesson focused around a carefully selected problem that offers opportunities for sustained mathematical exploration. The problem is presented at the beginning of the lesson, with minimal input from the teacher.
- Students being given time to think about the problem, then discussing it in pairs or small groups. Students may be sitting in groups to facilitate discussion.
- The teacher circulating and listening to student discussion, finding out what students know that might help them work on the problem, but resisting the urge to interrupt conversations with their own ideas. The teacher considers how they will weave together students' ideas in the whole class discussions that will follow.
- A classroom culture in which teachers value students exploring, conjecturing, justifying, working collaboratively, asking their own questions... rather than solely focusing on 'getting' the correct answers.
- A classroom culture in which the teacher and students believe that all students can make progress. There is an understanding that struggling is a key part of learning.
- The teacher orchestrating whole class discussions in which all students participate and all contributions are valued, even when they are partially-formed ideas. The teacher is encouraging students to share their observations, questions, conjectures or visual representations of their thinking, enabling students to see the connections.
- In these discussions, the teacher might act as a scribe, recording students' thinking on the board. They ensure that every contribution follows on from the previous contribution, so that listening becomes as important as speaking.
- The teacher using mistakes and misconceptions as a springboard to learning. The teacher asks questions, nudging students to move from the particular to the general.
- Students considering new lines of enquiry, following on from whole class discussions.
- The plenary offering an opportunity to assemble different ideas, support understanding and help students to make connections.