Mathematics

Overview 

This module introduces the concepts and language of mathematics and develops fundamental understanding of mathematical relationships. Children discover the concept of number and they learn to think about the relationship between what is being measured and the unit of measurement required for measuring it. The main task is to help children internalise concepts of relative quantity and relative size (length, weight, volume). We aim to develop the ability to make generalisations and to see connections through the use of visual mediators.

 

Why are these skills important?

Most adults accept the practical importance of mathematical skills, and in our eagerness to have children master them are anxious to get on with the business of teaching children to count and solve number tasks. But should we begin with this? The result may be a classroom full of young children who can recite numbers up to 100, but cannot reliably count three bears. They may go through the rest of their schooling sometimes getting the right answers by following the rules, but fundamentally baffled.

A number is not a label or a digit, but the expression of a relationship between the unit of quantification and the objects or features quantified. When we look at a group of butterflies we might count three butterflies or six wings. Similarly when we measure the volume of water in a jug our answer depends on the measure we choose (24 tablespoons or 6 cups). By helping children grasp the underlying relationships we help them to unlock the mystery of number.

 

How does this module work?

What is most distinctive about the Mathematics module is the use of visual models to allow children to see “at a glance” the most basic but also the most fundamental mathematical relationships: more than, less than, equal to. Similarly, they learn to understand and to use simple conventional measures (e.g. a stick) to respond to scenarios in which they must compare the size of objects that cannot be gathered together in one place.

Finely-graded, practical activities involving a wide variety of visual mediators (pictures of objects, symbols, correspondence grids, tokens, abacuses and number lines) allow the children first to grasp, and later to internalise, the mathematical relationships they model. At first tasks are concretely supported. For example, children discover if there are as many carrots in a field as there are hungry rabbits by superimposing images of carrots on images of rabbits.

Gradually the tasks require greater levels of abstraction, replacing images of objects with symbols and tokens, and direct manipulation of objects with simple graphs. Later still, as the children internalise the visual models, they practice solving problems by “looking” with their “mind’s eye”.

 

The additional benefits of this module

What is really important is not quantity but quality – the quality of a child’s understanding of quantity. The secure counting and measuring skills required to facilitate mathematical learning are the apparently paradoxical outcomes of a teaching and learning process that does not focus on teaching children to count. Instead children learn to understand what they need to count and how to count it.

Children develop insight into why quantification matters, insight into the use of measures for comparing weights, heights or volumes, and the ability to focus on exactly what it is that they are trying to measure when they quantify.

Overview 

This module introduces the concepts and language of mathematics and develops fundamental understanding of mathematical relationships. Children discover the concept of number and they learn to think about the relationship between what is being measured and the unit of measurement required for measuring it. The main task is to help children internalise concepts of relative quantity and relative size (length, weight, volume). We aim to develop the ability to make generalisations and to see connections through the use of visual mediators.

 

Why are these skills important?

Most adults accept the practical importance of mathematical skills, and in our eagerness to have children master them are anxious to get on with the business of teaching children to count and solve number tasks. But should we begin with this? The result may be a classroom full of young children who can recite numbers up to 100, but cannot reliably count three bears. They may go through the rest of their schooling sometimes getting the right answers by following the rules, but fundamentally baffled.

A number is not a label or a digit, but the expression of a relationship between the unit of quantification and the objects or features quantified. When we look at a group of butterflies we might count three butterflies or six wings. Similarly when we measure the volume of water in a jug our answer depends on the measure we choose (24 tablespoons or 6 cups). By helping children grasp the underlying relationships we help them to unlock the mystery of number.

 

How does this module work?

What is most distinctive about the Mathematics module is the use of visual models to allow children to see “at a glance” the most basic but also the most fundamental mathematical relationships: more than, less than, equal to. Similarly, they learn to understand and to use simple conventional measures (e.g. a stick) to respond to scenarios in which they must compare the size of objects that cannot be gathered together in one place.

Finely-graded, practical activities involving a wide variety of visual mediators (pictures of objects, symbols, correspondence grids, tokens, abacuses and number lines) allow the children first to grasp, and later to internalise, the mathematical relationships they model. At first tasks are concretely supported. For example, children discover if there are as many carrots in a field as there are hungry rabbits by superimposing images of carrots on images of rabbits.

Gradually the tasks require greater levels of abstraction, replacing images of objects with symbols and tokens, and direct manipulation of objects with simple graphs. Later still, as the children internalise the visual models, they practice solving problems by “looking” with their “mind’s eye”.

 

The additional benefits of this module

What is really important is not quantity but quality – the quality of a child’s understanding of quantity. The secure counting and measuring skills required to facilitate mathematical learning are the apparently paradoxical outcomes of a teaching and learning process that does not focus on teaching children to count. Instead children learn to understand what they need to count and how to count it.

Children develop insight into why quantification matters, insight into the use of measures for comparing weights, heights or volumes, and the ability to focus on exactly what it is that they are trying to measure when they quantify.

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