“The idea that learning mathematics requires little or no thought, as students are only required to reproduce procedures, suggests that students are engaging in ritualistic acts of knowledge production rather than thinking about the nature of the procedures and the reasons why and when they might be applied.” (Boaler, 2000, p.189)

This supports the argument for promoting ‘multiple perspectives’  in mathematics. If our students are taught one approach to solving a problem and are not encouraged to explore other ideas, to formulate their own strategies and discuss these with their peers, then essentially mathematics becomes a restricted subject.

“This idea follows a way of thinking that has been appearing in the last few decades, that doesn’t consider knowledge as given, established and transmissible, but where higher order and the critical thinking skills are privileged, where lectures are substituted by dialogue and discovery methods. Within this perspective problem solving tasks are powerful tools for teachers to use in their classroom. In particular patterns challenge students to use higher order thinking skills and emphasise exploration, investigation, conjecture and generalisation.”(Vale and Barbose, 2009, p.9)

I quote the above book extensively as I feel it contains a power message which encourages teachers to move away from single approach methods of learning mathematics towards finding a variety of solutions and being able to provide mathematical explanations for these different strategies. It provides opportunities to bring creativity and exploration into the classroom and when in my opinion, when children have the freedom to investigate and learn through trial and error, their motivation and enjoyment of the subject increases.

By providing multiple perspectives to a problem, teachers are also catering for the variety of learning styles within the classroom. Throughout my teacher training, one thing that has become clear is that it is my job to be able to discuss, explain and promote topics in different ways in order to provide equal learning opportunities for my students. If we do this with our teaching, surely we should encourage our children to do this with their learning. We want to encourage our pupils to think deeper about problems. We want them to have the confidence to analyse, predict, apply knowledge, reflect and evaluate. Even if their new strategy is unsuccessful, the learning gained from reflecting upon their work, thinking about what they could do differently next time and comparing strategies with peers is hugely beneficial.

The following video is an example of an alternative way of teaching students percentages. There is a strong focus on the use of reading skills and using the words of the question to break down the order of the calculation. For reasons stated above, it is important to present a variety of methods to solve a problem. Firstly, teachers must model solving the problem by using different approaches before children attempt them and consequently go on to formulate their own strategies. Teachers need to put in place the basic foundation of knowledge, as without this, children wouldn’t have the prior learning experiences and ‘basic ideas’ to assist them in trying to find alternative solutions.

My next blog will explore the notion of ‘basic ideas’ and what this means in terms of having a profound understanding of mathematics.

Sources

Boaler, J. (Ed) (2000) Multiple perspectives in mathematics teaching and learning. Greenwood: Praeger

Vale, I. and Barbosa, A. (2009) Multiple perspectives and contexts in mathematics education. Escola Politecnico de Viana do Castelo: Projecto Padroes. Available at: https://www.academia.edu/1485703/Patterns_multiple_perspectives_and_contexts_in_mathematics_education Accessed: 21.10.15

Extra reading and links

Lanarkshire resource – Problem solving and enquiry for secondary mathematics.