Every organism is born with at least one mechanism that it uses to insure its survival. For humans, one important mechanism for survival is intelligence. By nature, human beings are intelligent. Central to this intelligence is the ability to recognize patterns and relationships. It is this ability which enables us to understand the world and the way things work. The ability to understand patterns and relationships enables us to predict what is going to happen or what could happen as we ponder alternative courses of action. Therefore, young children are born with a capacity to explore and discover patterns and relationships. However, just as our capacities for language, for control of movement, and all our capacities need to develop through activity over time, so the capacity to recognize pattern and relationships develops through experience and practice. As a result, it can be observed that young children have a natural interest in exploring patterns and relationships. They can be seen sorting, organizing, matching, and putting things together and taking them apart. They love to work with puzzles, play with blocks, and use their minds to find the various ways things can go together. To this end, it is helpful to provide the children with a variety of materials they can manipulate.
As mentioned, children enjoy sorting, classifying, organizing, and making sense of their environment through finding similarities and differences in objects. They like to group things, pile them, examine them, manipulate them, and organize them. Therefore, children like to have things to sort and ways to sort them. Various objects can be collected and set out on sorting trays to serve this interest. Over time, different objects can be provided on the trays. For example, children love polished rocks, shells, and buttons. The objects can be piled in the middle, and the children like to sort them into separate piles, based on shared characteristics.
The constructive triangles are a set of triangles which can be placed together to form a variety of shapes. In this way, children can combine shapes together and form other shapes.
Children like to make patterns and designs from little colored wooden block shapes. Each shape has at least one side in common with the other shapes.
Children enjoy making tile patterns out of colored geometrical shapes. All the basic shapes are represented. For each individual shape, many separate pieces are provided. Each shape is also provided in two colors. All pieces have at least one side which is a common length.
To begin, children are given a simple shape such as a square. They are given a container containing many yellow squares and many blue squares. Their challenge is to see if they can cover an area with squares without having any gaps between the pieces. If they can, they can then experiment by making patterns with the two colors of square tiles.
After creating tile patterns made from one shape, the children can try combining shapes to discover what tile patterns they can make by placing different shapes together.
After working with two dimensional shapes, children like to explore the patterns and relationships between three dimensional pieces. Below children are laying out the pieces from two 3 dimensional puzzles. The first is a binomial cube, and the second is a trinomial cube. These materials give the children experience exploring abstract mathematical patterns and relationships which are represented in concrete form.
The Binomial and Trinomial Cubes
In doing a three dimensional puzzle, it helps to lay the pieces out in an organized fashion. In the pictures to the left, the children are organizing the pieces by size shape and their relationships. The color on the shapes helps draw attention to the relationship between pieces.
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