Do you know how many windows there are in your house? Probably not by heart... but if you give it some thought, you will be able to come up with an answer. And your answer will be correct. That is because you have a schema - in other words, a plan - of the house in your mind. Children also have schemata in their minds. The Hejny method strengthens and interlinks these schemata, and infers general patterns from them. Children soon realize that half is also a number (0.5), and they do not find commonly “problematic” fractions problematic at all.
When children know an environment and feel comfortable in it they do not get distracted by unfamiliar things. They focus fully on the task at hand, and are not bothered by unknown concepts. Each of the roughly 25 implemented environments (family, bus journey, stepping on playground, etc.) functions slightly differently. The environment based system takes into account the children’s different learning styles and the workings of a child’s mind. The child is then motivated to experiment further.
We do not present isolated information to pupils: it is always present in a familiar schema – a schema the children can recall at any time. We do not set mathematical phenomena and concepts apart, but we adopt different strategies for solving them. Children choose on their own what suits them best and what feels most natural. You will not hear any of the typical: “But, teacher, we did that two weeks ago, we do not remember it any more...“
One of Professor Hejny’s main motives for creating a new teaching method was to protect pupils from being manipulated throughout their lives. For that reason, teachers using the method do not pass on ready-made knowledge in their lessons, but, rather, teach children how to reason, discuss, and evaluate. The children learn to know themselves what is right for them; they respect each other, know how to make decisions, and accept the consequences of their actions. Along with mathematics, they naturally discover principles of social behavior, and grow morally.
In the Hejny method, all mathematical problems are designed so that children “automatically” enjoy solving them. The right kind of motivation is the internal kind, not forced by any outside factor. Children find the solutions to the problems thanks to their own efforts. We do not take away the joy of personal success from our children. Thanks to the class spirit we foster, every pupil receives applause, even those who discover a given phenomenon or solution later than others.
We draw on the personal experience a child has been forming from the moment they were born: at home, with their parents, while exploring the world in front of their house, or with their playmates in the sandbox. We build on natural, concrete experience that a child can use to form general conclusions. For example, children “sew a dress” for a cube, automatically learning how many faces, vertices and edges the cube has, how to calculate its surface area...
Experience speaks clearly: the most effective motivation derives from a child’s feeling of success, from their genuine joy of having solved an appropriately demanding task. It lies in the pleasure they gain from their sense of progress, or in the praise and respect they receive from others. Children who have this motivation do not experience the “mathematics paralysis” that has become legendary in traditional education. On the contrary, when they see a formula, they do not react with displeasure but with enthusiasm: I know this, I can solve this!
When a 6 year old is asked to build a square using rods, they pick up a first, a second, a third rod... these are still not enough, so they take a fourth rod and build a square. Then they decide to build a bigger square. They pick up more rods, and build the bigger square, beginning to understand that whenever they want to make a bigger square they will need four extra rods. They are now on their way to discovering the formula for calculating the perimeter of a square.
The typecast image of a teacher is that of someone who possesses knowledge and skills, and lectures about them. The mathematics teacher knows mathematics, and can therefore explain mathematics to their students. Often, it really does work like this: the children listen to their teacher’s explanations, write down a few notes, listen to instructions about how to solve a new problem, and learn to use the new procedure. However, in our understanding of the teaching process, the teacher plays a dramatically different role.
If a child was forbidden to fall, they would never learn to walk. Making and analyzing our own mistakes forms a deep experience, which helps us to better remember the knowledge we have acquired. We use errors as a means of learning. We encourage pupils to identify their own mistakes, and we teach them to explain why they made them. The trust fostered between teachers and pupils strengthens the children’s delight in accomplishing their tasks.
Our textbooks present problems with varying levels of difficulty. Always allowing weaker pupils to solve some problems successfully precludes any feelings of anxiety and fear of future mathematics lessons. At the same time, we constantly provide the best pupils with further challenges, to prevent them from experiencing boredom. The teacher does not overburden these pupils with tasks. Instead, he or she assigns tasks that will keep the children motivated. The teacher chooses the tasks according to each child’s needs.
With the Hejny method, children do not need to wait for the solution to appear on the board. They work in groups, in pairs, or individually. Each pupil is able to share how he or she found their solution, and is also able to explain their working to the others. The solution emerges through collaboration. The teacher does not represent the authority who decides when the answer is right – and when the pupils can turn over another page in the book. Pupils build their own meaningful piece of knowledge, in a continual train of thought.