An approach to mathematics teaching and child development

Supporting collaboration: acquiring knowledge through discussion

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.

Most knowledge emerges in children’s minds as a result of their experiences and mutual discussion. Therefore, children need to be provided with space for collaboration and discussions in their lessons. This type of communication proves highly effective.

 

A choice of working styles

Each child is unique and so will prefer a different working style. Some like to work individually, others are more successful completing tasks in pairs or groups. There is no harm in giving the children this choice when a new mathematics problem is presented. Those who want to work independently will tackle the problem straight away. Those who feel more comfortable working with someone will find a partner. Needless to say, even the former will enjoy sharing the results of their endeavors with a classmate afterwards.  

The importance of discussion

Discussion among pupils is indispensable, regardless of their stage in the learning process: whether they are just beginning to acquire a piece of knowledge, or are already confirming their own conclusions. Discussion brings out a variety of ideas, prompts, or even misconceptions that motivate a pupil to look for the correct solution.  There is no authoritative figure who decides what the truth is. The adult simply observes and allows the child to form their solution and justify it to the others. Thus, each child constantly assesses different options and keeps thinking about the problem throughout the discussion. They build up a meaningful piece of knowledge that fits into their existing cognitive structure.

The teacher’s role

The teacher gives precedence to activities that encourage collaboration between the students. Each lesson is planned so that it provides pupils with space for collaboration. A variety of task types is important not only in terms of pupil typology but also in terms of the acquisition of new knowledge.

The goal, however, is not to vary these types of task as much as possible within one lesson. It is far more important to keep the lessons effective, while not allowing any particular task type to be left out in the long run.

The teacher’s main intention is to select task types that encourage the pupils to interact. Whether this interaction takes the form of discussion in pairs, groups, or the whole class is not an issue. The diversity of tasks and working styles ensures that the lesson is enjoyable and fun. No activity is endlessly repeated.

No barriers between pupils

 

How different this approach is from the traditional class, in which a teacher strives painstakingly to stop pupils from copying.  In that class, pupils are likely to be punished for trying to consult with their classmates, which often results in the pupils building barriers, or barricades, to prevent their classmates from copying.  This fairly common scenario is entirely incompatible with the Hejny method, for which is vitally important to take any such barriers down, so that the children’s communication can flow naturally, in a civilized, objective, and seamless manner.  

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