From Theory to Practice: Bringing Lev Vygotsky into the maths classroom

“By giving our students practice in talking with others, we give them frames for thinking on their own.”

– Lev S. Vygotsky

One of the pillars of maths mastery, Lev Vygotsky's theories are a cornerstone of the Maths — No Problem! programme. But who was Lev Vygotsky and what are his theories? And most importantly, how can we intentionally bring Vygotskian ideas into the classroom?

Lev Vygotsky (1896 - 1934)

L. S. Vygotsky was a psychologist at Moscow's Institute of Psychology who focused on developmental psychology.¹ His most influential work is Thought and Language (1934). In the 1960s, Vygotsky's work was translated from Russian and published in English, making him even more well known and influential in educational theory.

Vygotsky's work focuses on understanding human consciousness and how social and cultural factors affect it, as well as the sociocultural context of learning, specifically the important role language plays in learning.²

Vygotsky's Sociocultural Theory

“Through others we become ourselves.”

– Lev S. Vygotsky

Zone of Proximal Development (ZPD)

Vygotsky defines the Zone of Proximal Development as the space between what a child can learn independently and what a child needs to be taught from a skilled partner, also known as a 'More Knowledgeable Other.'³ Vygotsky's work expressed that the ZPD is a crucial area in the learning process, where the most important knowledge is given to later be built on and strengthened. Vygotsky emphasises that collaboration is the key to effective learning and bridging the gap that is the ZPD.

Sociocultural context of learning

Vygotsky believed social interactions and cultural experiences shape one's mind. Sociocultural theory, based on Vygotsky's work, aims to explain how societal factors and cultural contexts influence knowledge formation and cognitive growth.

We are constantly learning from those more knowledgeable than us: our parents, teachers, colleagues, and friends. This is especially true for children. Vygotsky's work puts a heavy influence on teachers facilitating learning and peer interaction. A child watches a more knowledgeable peer and follows their instructions. The child then internalises this method, drawing on it in the future to guide their problem-solving — Vygotsky called this cooperative or collaborative dialogue and it is the key to bridging the ZPD.⁴

Compare and contrast theorists

Lev Vygotsky

Sociocultural Theory

Introduced Zone of Proximal Development (ZPD), supported learning through social interaction where pupils are challenged beyond current abilities with support from others.

Jerome Bruner

Constructivist Theory of Cognitive Development

Suggested Discovery Learning, created Three Modes of Representation (CPA), coined the Spiral Curriculum for deep learning, and introduced Scaffolding for learner support.

Jean Piaget

Stages of Cognitive Development

Proposed four cognitive stages in learning, believed development driven by biology and environment, and emphasized learning through world interaction and self-discovery.

Richard Skemp

Relational vs. Instrumental Understanding

Distinguished relational from instrumental understanding, and advocated teaching for deeper mathematical comprehension, not rote learning.

Zoltan Dienes

Six-Stage Theory of Learning Mathematics

Promoted manipulatives in maths, introduced Base 10 blocks for place value, and emphasized engaging, enjoyable maths learning through games, songs, and dance.

Importance of language in maths lessons

“By giving our students practice in talking with others, we give them frames for thinking on their own.”

– Lev S. Vygotsky

Vygotsky understood the importance of language. In his work, he labels three forms of speech: social speech, inner speech and private speech. Social speech is external language used in engaging with others and communicating culture. Inner speech is thinking and communicating with oneself internally for mental reasoning. Finally, private speech is audible self-talk, such as children speaking to themselves as work through problems.⁵ Vygotsky believed that social speech and private speech formed inner speech, which expresses the importance of culture and social interactions in knowledge formation. Vygotsky was one of the first to highlight the pivotal role of private speech in cognitive development.

Vygotsky’s work also highlights the pivotal role of social language, as it shapes a child's development and reasoning. Vygotsky explains that language is the primary vehicle for sharing cultural information, such as knowledge, values, and skills.⁶ Vygotsky's term Cultural Tools refers to problem-solving methods that one acquires from social language with a More Knowledgeable Other. These tools, such as language, mnemonic systems and counting methods, are imperative to developing higher-thinking.⁷

Language is a powerful tool, not just a way to communicate, but also a vehicle for thinking, learning and problem-solving.

Practical applications in the modern classroom

“The teacher must adopt the role of facilitator not content provider.”

– Lev S. Vygotsky

Model problem-solving

Leading guided practice and modelling problem-solving for your pupils allows them to build their understanding through implicit learning. By watching how a More Knowledgeable Other solves a problem, a pupil can mirror the process, growing their conceptual understanding until they have bridged the ZPD.

After leading guided practice, you can gradually move pupils to independent work as their skills and confidence grow. During modelling session, try thinking out loud so that pupils can understand the thought process behind each action and concept.

Support pupils with appropriate scaffolding

ZPD is often seen as synonymous to scaffolding. ZPD is the gap between what a pupil can do independently and what they can do with assistance. Scaffolding is the idea of providing pupils with the right amount of support so that they can stretch their understanding to new heights.

Each pupil's ZPD is different and their ZPD moves as they gain more knowledge. Adapting your lessons and guidance to include various levels of understanding opens the lesson up to each pupil. Figure out where each pupil's ZPD is and provide the necessary scaffolding to support them. Scaffolding can look like guided instructions, manipulatives and collaborate work.

Manipulatives are a great tool to have in maths lessons. They provide pupils with concrete representations for abstract concepts, assisting those who require more guidance to build conceptual understanding.

Encourage collaborative learning

Making a point to add group work to your maths classes will encourage pupils to assist each other. Arrange pupils so that more knowledgeable pupils are seated with those still learning and are able to model for their partners. Encourage pupils to explain their thinking, ask questions and assist one another.

During your maths lessons, hold space for maths conversations and reciprocal teaching so that pupils can work together to solve problems and become more familiar with maths language. Through these conversations, try relating maths to pupils' lives and cultural contexts in order to make the maths more engaging and encourage deeper understanding of the concepts.

Adding these simple Vygotskian ideas to your lesson plan can greatly improve the way your pupils learn, providing them with a strong, well-rounded mathematical education built on the theories of expert mathematicians and educators.

Provide productive struggle

Lev Vygotsky's concept of ZPD, which is essentially Productive Struggle — the concept of giving pupils' problems just challenging enough to stretch their current abilities. Through making mistakes pupils practice implicit learning which allows for deeper understanding rather than rote-learning.

Encourage positive learning experiences when pupils are struggling by making sure the work is not too challenging, normalising struggle, creating a respectful classroom culture, and incorporating diverse activities that appeal to a variety of learning styles into your practice. By creating space for productive struggle in your classroom, you are creating resilient problem-solvers who learn from their mistakes.

Having the proper educational material can make your life exponentially easier as a teacher. With a programme like Maths — No Problem! which is built on the proven best practices such as Vygotsky's theories, and has each lesson planned out with supportive teaching guides, mathematics teachers can save time and focus on teaching, and meet the necessary attainment levels.