Known in education circles as the ‘maverick mathematician’, Zoltan Dienes believed in the power of learning mathematics through games. His influential theory left a lasting impact on the field and underpins the maths mastery approach today.
Going against the idea that young children are unable to learn complicated mathematical structures, Zoltan Dienes used games, songs and dance to bring maths to life.
“Give me a mathematical structure and I’ll turn it into a game.”
So, who was Zoltan Dienes?
Zoltan Dienes (1916–2014) was an internationally-renowned Hungarian mathematician and education psychologist who believed that mathematical structures could be effectively taught to primary-aged children through the use of manipulatives, games and stories.
Echoing the earlier ideas of educational psychologist Piaget, Dienes believed mathematics is defined by structures and patterns.
He observed that key mathematical concepts are based on the same thinking and processes found in larger conceptual systems. And by introducing these structures at the primary level, he saw the possibilities of guiding children to higher-level thinking a lot earlier than you’d expect.
In classrooms across the world, Dienes observed how inventing game rules that match the rules found in mathematical systems take advantage of children’s natural tendency for game-based learning.
Dienes also found that concrete manipulatives were another way to effectively introduce complex mathematical concepts. He designed Base 10 blocks (often called Dienes blocks) to help children learn the underlying systems of mathematics in an engaging way.
Why Zoltan Dienes believed in mathematical learning through games
If you teach with Maths — No Problem! you don’t have to look far to find Dienes’ influence. It’s right there in the Anchor Task, where learners are asked to explore mathematical ideas in a playful way and come up with multiple ways to solve a problem.
Dienes strongly emphasised the need for exploration before structured learning and practice. But is that all that games achieve in the maths classroom?
Here are three reasons Dienes believed that games could be an effective learning tool.
1. Games increase learners’ enjoyment and motivation
In his work, Dienes stresses that children don’t have to reach a certain developmental stage to experience the joy of mathematics. What really matters is that children learn how to think.
“The reason mathematics is boring in schools is because no real mathematics is taught in schools.”
Teaching maths through games can appeal to learners who see maths as unapproachable and tedious. Learning through games helps children see that understanding mathematical patterns and relationships can be an enjoyable and motivating experience.
2. Games develop learners’ problem-solving skills
Fun games like Snakes and Ladders, Cards, Monopoly and Scrabble hide mathematical rules and structures that help even young children develop higher-level problem-solving skills like:
- Trial and error methods
- Simplifying difficult tasks
- Looking for patterns
- Making and testing hypotheses
- Proving and disproving
In one study, influential teacher and researcher Edith Biggs noticed that games improved the conceptual understanding and problem-solving skills of learners aged 7–13, especially among more advanced learners in the group.
Other studies found that games with mathematical elements encourage children’s problem-solving behaviour — whether or not they had those skills beforehand.
On top of that, games are a valuable assessment tool. By paying attention to learners’ chosen strategies during the game, you can better diagnose where children are in their learning.
3. Games help learners practice and reinforce mathematical skills
Not only do games help develop learners’ problem-solving skills, they also give learners an opportunity to practice and reinforce their mathematical skills.
Learners thrive when they have a set goal they need to reach, even if the path to victory isn’t easy. That’s why challenging games are also fun games. Children get to think about all the strategies they could use, and if their strategy fails, they’re encouraged to try again.
Placing value on effort and perseverance rather than smarts or success build essential skills later in life. When children get positive feedback on their hard work, they gain a sense of optimism and an awareness that they can learn and grow as they meet new challenges.
Introducing difficult abstract symbols in the primary years can be confusing, and can interfere with the learning process. Mathematical games paired with the use of manipulatives encourages deeper thinking — without the drudgery of rote learning.
Dienes was an early pioneer in democratising learning and problem solving. Throughout his life, he never strayed from his mission: to understand how children learn by meeting them where they are.
Games. A Rationale for Their Use in the Teaching of Mathematics in School, Mathematics in School Vol. 15, No. 1 (Jan., 1986), pp. 2-5 (4 pages)
Lawlor, A. (2014) ‘For mathematician and teacher Zoltan Dienes, the play was the thing’, The Globe and Mail [online]. Available at: https://www.theglobeandmail.com/news/national/education/for-mathematician-and-teacher-zoltan-dienes-the-play-was-the-thing/article16701934/ (Accessed: 21 July, 2020)
Sriraman, B. (2007) ‘A Conversation With Zoltan P. Dienes’, Mathematical Thinking and Learning’, 9(1), 59–75 [online]. Available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.508.3380&rep=rep1&type=pdf
(Accessed: 18 July, 2020)
Reed, K. E. and Mercer Young, J. (2018) ‘Math Games to Excite Young Minds’, DREME [online]. Available at: https://dreme.stanford.edu/news/math-games-excite-young-minds (Accessed: 21 July, 2020)
Ernest, P. (1986) ‘Games: A Rationale for their Use in the Teaching of Mathematics in School’, Mathematics in School [online]. Available at: https://pdfs.semanticscholar.org/2c2c/ee2bf63918e1a4932323952a92268f97ec17.pdf
(Accessed: 21 July, 2020)