Inquiry and mixed attainment classes
  
Mathematics is the most heavily setted subject in the secondary school curriculum. The most recent reliable figures published for England show over 80% of classes for students aged between 11 and 14 were set and, no doubt, the percentage was higher for older secondary students. Mike Ollerton characterises setting as "educational apartheid" in which the powerful exercise control over the powerless. Bottom set students are taught "repetitive, procedural, fragmented, disjointed, simplified mathematics" (Watson et al.); top set students are accelerated through the curriculum often to their detriment (see here for a selection of research papers).
  
It is, therefore, welcome that more maths departments today are considering mixed attainment classes. However, an examination of the reason for the growth of interest suggests there remains cause for concern.
  
The main reason is the mastery movement’s promotion of mixed attainment teaching. Supporters of mastery argue that students should move through the curriculum together, studying the same topics from the same materials. Yet, students are not treated equitably in the mastery classroom. Only when a topic has been 'mastered' do students get the opportunity to solve problems and reason deeply. Inevitably this two-stage model of learning leads to a two-tier classroom. Students who do not master a topic as quickly as their peers are denied access to the creative aspects of mathematics. As NRICH says here, mastery "may be insufficient for developing the potential of young mathematicians."
  
The problem with the mastery approach is its insistence that solving and reasoning provide an opportunity to apply new knowledge; it rejects the notion that learning can occur in the process of solving or reasoning. Yet, it is when students are involved in a mathematical process that learning new knowledge becomes relevant and meaningful. When mastering a procedure is part of a wider aim to solve a problem or put forward a convincing argument, students are less likely to question the need to practise and more likely to become fluent in that procedure.

   
Inquiry Maths was devised and developed in mixed attainment classrooms. Its design is ideally suited to promote learning at multiple levels:
  • Students’ questions and observations about the prompt unite the class in a mathematical process that ranges from relatively basic definitions and procedures to more sophisticated conjectures;
  • The regulatory cards allow students to determine their own access points to the inquiry; 
  • The teacher introduces new knowledge for an individual, a group or the class when required by the development of the inquiry; 
  • The inquiry pathways involve students working on a common aim from different directions and at different levels of mathematical reasoning. 
The unity of purpose guarantees equity as all contributions add to the findings of the inquiry. Each student's selection of an approach and mathematical level (guided by the teacher when necessary) ensures challenge and progress for all.
  
Mixed attainment classes have their roots in social justice. Justice is not served by restricting one set of students to knowledge acquisition, while their peers move on to creative tasks. As Jerome Bruner says here, students should learn by both 'leaping' and 'plodding':
   
Let him go by small steps. Then let him take great leaps, huge guesses. Without guessing, he is deprived of his rights as a mind. (p. 531)
  
The current mastery classroom consigns some students to plodding. The rights of learners are being denied. The philosophy of inquiry, in contrast, promotes inclusiveness, cohesion and equity.

Andrew Blair 
November 2016