Mathematics includes things like number sense, weight and measurement, geometry, fractions, and problem-solving skills. At the earliest levels this involves such skills as learning the numbers and being able to count, one-to-one correspondence, identification of shapes, sorting and categorizing, recognizing patterns, being able to add to and take away from a set, and recognizing when sets are the same or different. Until a student has mastered some of these basic concepts, higher level mathematics can’t be done.
Active Learning lends itself to mathematics instruction readily. For example, using “sets” of materials such as spoons, cups, or keys that are on rings and hung on a Position Board or in a Little Room allows a child to become familiar with one and more than one.
Playing with various shapes helps the child to become familiar with different shapes. Give the child a variety of blocks or other shaped objects to explore. Add texture to the shapes or collect shapes made of different materials to make the activity more interesting.
Materials that have different weight, size, color, shape, density, and flexibility allow a child to begin to understand the notion of categories. Later as the child becomes ready for constructive play using various materials for sorting or stacking builds on the notion of same and different.
You can count anything and you can measure anything. Playing with various sizes of containers at a sand or water table helps the child learn about the concept of volume and weight. Having opportunities to play with measuring tapes, ropes with knots tied at regular distances, and playing with different sizes of shoes, hats, mixing bowls, balls, helps develop the concept of size.
Taking objects out of a container and putting objects in a container help the child become familiar with addition and subtraction. At first the child may only take objects out, and the adult puts the objects in the container. The adult can count the objects as you put them in and introduce counting in the process.
Taking things apart and putting things together is another important skill that can help a child begin to be ready to learn about fractions. Puzzles not only teach shape, they also can teach part-to-whole. When a child has developed motor skills that allow for puzzle work, using simple wooden puzzles can be a good activity.
Learning about patterns is important. Give the child opportunities to explore Elastic Boards made with beads or buttons strong in various repeating patterns. Make texture boards where patterns are formed such as soft, scratchy, smooth for the child to explore.