With the rise of the ‘nanny state’ childhood has become so much safer than it ever was before. I have very fond memories of my youth and in particular, time spent climbing the rocket ship in the local park. The rocket ship was the pinnacle of playground equipment. They were four stories tall, made of steel and were accessed by a series of ladders which passed through a trapdoor set into the floor of each level. The external structure was a grid of steel bars through which the young explorer could view the world far below. At the top, there was a wheel with which to steer the rocket and an escape shoot, in the form of a slippery dip exited from the second level. The real challenge was climbing to the top, not via the relative safety of the internal ladders, but up the outside, with nothing but clean air between you and the ground far below.
The rocket ships have all but disappeared from our playgrounds, replaced by smaller, safer structures, with less rusted steel, fewer sharp edges and surrounded by a sea of soft-fall material to ensure any accidents result in little more than a bruised ego.
There is a tendency to do the same with cognitive challenges. We are so keen to make learning easy and accessible that at times we completely remove the challenge. We wrap our learners in the cognitive equivalent of cotton wool. We manage the difficult parts of the curriculum with strategies to make the learning readily accessible while teaching students short cuts and strategies to make the hard parts easy. We provide endless scaffolding of processes with pro-formas and checklists until the task is reduced to a set of simple steps, manageable with no real mental effort. We then applaud the success achieved and yet wonder why our learners are unable to apply their learning to new situations or transfer their skills from one discipline to another.
We seem to be most guilty of this in Mathematics; although programmes which teach students to structure their writing through highly formulaic methods and texts which reductively simplify concepts from the sciences and humanities are just as guilty . The moment a child appears to be struggling with a concept the concerned teacher will intervene, providing an easy three-step method for solving the problem. Indeed, it is more likely that the three-step method will be introduced before the learner gets anywhere near a problem.
In her book 'Mathematical Mindsets’, Jo Boaler shares the importance of learning from mistakes and shows how when we are engaged with challenging learning and making mistakes, we grow our brains. "If we believe that we can learn, and that mistakes are valuable, our brains grow to a greater extent when we make a mistake.” (Boaler. 2016 p13) It is in these moments when we are struggling with concepts and ideas, when we are confronted by what Piaget refers to as ‘disequilibrium’ that we enhance our cognitive powers. Disequilibrium is the circumstance when we are confronted by information that does not fit with our existing knowledge structures. In these moments we are confronting new learning and this can be uncomfortable and yet it is only by passing through moments of disequilibrium that we achieve learning. These moments are likely to be bookmarked by the mistakes that we make and yet if we have the right mindset towards mistakes we are able to benefit from these moments.
It must be understood that the key here is not just the mistake but the conditions under which the mistake was made. If students are not challenged, if the teacher’s pedagogy is focused on making the learning easy, the child will not benefit from making mistakes. We are not helping our students by removing the cognitive struggles required for brain growth. Worse when we reduce challenging maths to a series of procedural steps we deny our students the opportunity to see the beauty of mathematics as a creative endeavour; as a powerful tool for solving problems. “One of the problems with our current version of mathematics education is that students are given repetitive and simple ideas that do not help them to move into the important state of disequilibrium.” (Boaler. 2016 p18)
Research by Manu Kapur (2014) shows that students are better able to develop a deep understanding of mathematical concepts when they are allowed to fail on their first attempt to learn new ideas. The experience of failure better activates prior knowledge and prepares students for subsequent instruction. This requires that students are presented with sufficiently challenging material and that it is presented in ways that allow for failure. Kapur (2015) also suggests that students are best served by opportunities to generate problems as a part of their mathematical learning and that doing so assists with conceptual understanding and transfer of learning to new situations.
"When mathematics is taught as an open and creative subject, all about connections, learning, and growth, and mistakes are encouraged, incredible things happen.” (Boaler. 2016 p20)
Undoubtedly our children need to learn in a safe environment. But this should not mean our classrooms are modelled on our playgrounds; devoid of risk, challenge or the possibility of making mistakes. Our children need to know that learning occurs when we are challenged, that the real learning occurs because of the hard parts. They need to know that they will be judged positively as learners when they make mistakes and that getting the answer right does not enhance their worth. We create the safe environment our students need not by making learning easy but by making it hard and then celebrating the challenges along the way more than the successful conclusions.
We need to bring the rocket ships back into our classrooms and then smile as our learners try to climb up the outside.
By Nigel Coutts
Boaler, J. (2016) Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching. Wiley; Kindle Edition.
Kapur, M. (2014) - Productive Failure in Learning Math. Cognitive Science 38 pp1008-1022
Kapur, M. (2015) - The preparatory effects of problem solving versus problem posing on learning from instruction. Learning and Instruction 39 pp 23-31