At the end of last year I was asked to speak at The Educational Collaborative for International Schools (ECIS) Educators Conference in Copenhagen. The theme of the conference was Cultivating Curiosity, not just from the viewpoint of inquiry as a catalyst for learning, but also in trying to understand how curiosity can be nurtured and grown in order to transform the lives of children.
“It is a miracle that curiosity survives formal education.”
Albert Einstein
The focus of my presentation was on problem solving, investigating and using and applying mathematics in the primary curriculum. When mathematics is taught through problem solving, using contexts that are meaningful and relevant to pupils, their curiosity is sparked and they are more likely to be motivated.
Children are born with an innate curiosity. However all too often this natural inquisitiveness becomes stifled once they enter formal education. The hierarchical nature of mathematics, and the demands of the curriculum in particular, often mean that some pupils can quickly become disengaged from the subject.
“Education is not the learning of facts, but the training of the mind to think.”
Albert Einstein
Mathematical problem solving involves constructing thoughts and actions in order to help move from looking at the problem towards finding a solution. A problem is something we do not instantly know the answer to, and often do not immediately know how to go about solving: a problem is only a problem when the solution isn’t self evident.
Putting pupils in thought-provoking situations where the means to a solution is not immediately apparent and giving them experience of that slightly uneasy feeling of being in the dark, is vital in helping to develop their problem solving, thinking and inquiring skills. It also helps to develop pupils’ understanding of mathematics as involving more than rote learning, often having more than one solution, and being about reasoning and experimenting, working systematically, generalizing, and proving and explaining.
“If I had an hour to solve a problem, I’d spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.”
Albert Einstein
When planning for mathematical problem solving, we need to consider offering pupils three different types of learning experiences.
• Learning about problem solving: In order to solve problems, pupils need to be taught problem solving, reasoning and thinking skills, such as predicting, generalising, estimating and working logically and systematically.
• Learning through problem solving: This involves a discovery approach to learning where pupils solve problems in order to learn, or develop further understanding of, a particular mathematical concept or skill.
• Learning for problem solving: Pupils engage in challenges that require them to use and apply their mathematical knowledge and skills to solve real-life, everyday problems.
“I have no special talents. I am only passionately curious.”
Albert Einstein
As teachers, we not only need to impart knowledge, which alone can have a very short-term effect on a child’s learning and development, but we must also develop in our pupils a sustainable appetite for learning.
Not all children are highly curious, and what might stimulate curiosity in some pupils might result in anxiety for others. It is our job to recognize these differences and manage the classroom or other learning environment to accommodate all pupils. With this in mind, the following strategies can stimulate the curiosity that leads to children becoming life-long learners.
• Using curiosity as ‘a hook’
• Utilising curiosity-arousing resources
• Modelling strategies, methods and behaviour
• Allowing adequate thinking time
• Providing pupils with choices
• Making teaching and learning experiences relevant and meaningful
• Promoting an atmosphere for questioning
• Creating a nurturing environment that encourages intellectual risk-taking
• Ensuring the right amount of stimulation: ‘zone of curiosity’ verses ‘zone of anxiety’
• Developing HOTS (Higher Order Thinking Skills) not providing MOTS (More Of The Same)
• Encouraging discussion and communication
• Fostering pupil exploration and discovery
• Cultivating originality and independence
• Nurturing perseverance and reflection
And finally, to paraphrase Pólya *
Pupils need to engage in a wide range of open-ended and investigative challenges if they are to appreciate that mathematics can help them solve everyday problems. As teachers we need to integrate into the heart of our teaching the problem solving and thinking skills necessary to equip pupils to be autonomous problem solvers of the future. We must develop and refine pupils’ communicating, reasoning and problem solving skills, not just in mathematics but across all subjects of the curriculum, and ignite and nurture in our pupils a genuine interest, and curiosity, in the world around them.
To paraphrase Pólya: if a teacher focuses on pure mathematics, s/he stifles pupils’ interest and hampers their intellectual development. But if s/he challenges pupils’ curiosity by setting problems proportionate to their knowledge, and helps them solve these problems, s/he gives them a taste for, and some means of, independent thinking.
* George Polya, a Hungarian mathematician
and author of ‘How to Solve It’ (1945), a small
volume describing methods of problem solving.
Peter Clarke
Series Editor: Collins International Primary Maths
