How Jean Piaget’s theories underpin maths mastery

Jean Piaget (1896-1980) was a Swiss psychologist and genetic epistemologist (someone who studies the development of knowledge.) He began as a biologist, receiving his Ph.D. from the University of Neuchâtel in Switzerland in 1918.

Piaget is probably most known for his theory of cognitive development, which is also called developmental stage theory. He was one of the first educational psychologists to study how children develop understanding.

Prior to Piaget, teaching was thought of as “largely didactic, and focused on rote learning,”¹ says Sue Robson in Developing Thinking and Understanding in Young Children. Piaget formulated the idea that children are not merely ‘mini-adults’ or empty vessels, but rather have their own way of thinking that is fundamentally different from the way adults think. One of Piaget’s central ideas is that humans create their own understanding of the world by interacting with the objects within it.

His ideas gained traction around the world, especially after the 1950s, and were seen as “legitimising the idea of learning through play,”² says Robson.

Schema psychology in childhood development

Piaget believed children develop their understanding of the world through exploring and acting upon objects, He developed the idea of schema — or mental building blocks we use to organise our knowledge of how the world works. Learning about the world and modifying our schema to accommodate or assimilate new information is essential for survival, since we must be able to anticipate events.

Piaget believed children “make sense of their surroundings by actively interpreting their experiences,”³ say Anthony Pellegrini and David Bjorklund in their paper Applied Child Study, Knowledge is not simply acquired; it is constructed, based on an interaction between the child and his or her environment.

Piaget was a proponent of the idea that children “should be able to do their own experimenting and their own research.”⁴ Teachers can guide children by providing appropriate materials, but in order for children to understand something, it’s essential to construct it themselves, he said. What children are allowed to discover for themselves will remain with them for the rest of their lives.

That’s why mastery programs like Maths — No Problem! allow for so much time during maths lessons to explore one single topic, giving each child an opportunity to discover their own way of relating to the material, and not moving forward as a class until everyone has mastered the idea. That allows for learning that is deep, secure and long-lasting.

Anchor tasks and maths mastery

In a video about the five key theories behind Singapore Maths, renowned speaker and trainer Dr Yeap Ban Har says Piaget’s idea of letting children have ample processing time to accommodate new ideas is central to the maths mastery approach. That’s why lessons in Maths — No Problem! textbooks have an anchor task, which he defines as “a single task that is dealt with for a rather long time.”

Piaget’s theories also form the basis for the mastery approach, since learners are partially motivated by rewards but because of the active, social nature of their learning, they also draw on their own inner curiosity and drive to learn.

Inspired by Piaget and other educational psychologists, maths mastery programmes like Maths — No Problem! draw largely on the constructivist theories in ways that sustain and nurture intrinsic motivation.

Peers collaborate, anchor activities are explored and journaling enables reflection — providing an environment where the active process of learning can take place and where intrinsic motivation is developed rather than stifled, Jane Currell writes in her 2018 blog How Maths Mastery Fosters Intrinsic Motivation In Learners.

Constructing knowledge

Children learn new things by building on what they already know. Understanding how your learners construct knowledge is the key to supporting their development, she says.

“Each time one prematurely teaches a child something he could have discovered himself, that child is kept from inventing it and consequently from understanding it completely,”⁵ says Piaget as quoted in Frontiers in Cognitive Psychology.

His observations of children led Piaget to develop his famous model of the stages of cognitive development. According to the research paper Applying Piaget’s Theory of Cognitive Development to Mathematics Instruction by Bobby Ojose, these stages and their distinctive features are:

1. Sensorimotor (birth through ages 18-24 months)

• Children develop eye-hand coordination schemes and object permanence

1. Preoperational (18-24 months through age seven)

• This stage includes the growth of symbolic thought, for example the increased use of language

1. Concrete operational (ages seven to 11)

• Children can perform basic operations such as classification and serial ordering of concrete objects

1. Formal operational (adolescence through adulthood)

• Students develop the ability to think abstractly and metacognitively, as well as reason hypothetically⁶

Here are some little-known facts about Jean Piaget:

• Piaget worked with Alfred Binet, the developer of the world’s first intelligence test, and Piaget helped score the assessments, according to mental health website VeryWellMind.com
• It was his work with Binet’s intelligence tests that led Piaget to conclude that the way children and adults think is fundamentally different, which was a revolutionary idea at the time
• “My position is that human knowledge comes from what we do to objects,” Piaget said in this 1977 film. “I am a constructivist. Knowledge is not ready made. Each of us is continually creating our own knowledge. We are continually organising what we know, structuring and restructuring our knowledge.”

¹ Sue Robson, “Developing Thinking and Understanding in Young Children,” 2nd ed. (Oxford, Routledge, 2006), 16.
² Ibid, 16
³ Anthony Pellegrini, David Bjorklund, “Applied Child Study: A Developmental Approach,” 3rd ed., (Lawrence Erlbaum Associates, New Jersey, 1998), 126
⁴ Ibid, 128
⁵ Michael Vanchesky, “Frontiers in Cognitive Psychology,” (Nova Science Publishers, New York, 2006), 43
⁶ Bobby Ojose, “Applying Piaget’s Theory of Cognitive Development to Mathematics Instruction,” (The Mathematics Educator 2008, Vol. 18, No. 1, 26–30), 29