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Using NRICH Tasks Richly

NRICH's beliefs about mathematics, and mathematics teaching and learning, inform how we envisage teachers and learners working with our tasks in the classroom.

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:

  1. 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.
  2. 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 collaborative work.
  3. The teacher circulating and listening to discussion, resisting the urge to share their own ideas. They consider how they will weave together students' ideas in the whole class discussions that will follow.
  4. Teacher and students working with a shared understanding that struggle is a key part of learning, together with a belief that all students can make progress.
  5. A classroom culture in which the teacher values students exploring, conjecturing, justifying and asking their own questions, rather than solely focusing on 'getting' the correct answers.
  6. The teacher orchestrating whole class discussions in which all students participate and all contributions are valued, including partially-formed ideas. They encourage students to build on previous contributions, so that listening becomes as important as speaking.
  7. The teacher encouraging students to share their observations, questions, conjectures and visual representations of their ideas. The teacher acts as a scribe, recording students' thinking on the board and drawing attention to connections.
  8. The teacher using mistakes and misconceptions as a springboard for learning. The teacher asks questions to deepen understanding and nudge students to move from the particular to the general.
  9. Students considering new lines of enquiry, perhaps in response to ideas shared by other students.
  10. Plenaries offering opportunities to assemble different ideas, support understanding and help students to make connections.