Children learn through concrete experiences with a wide range of engaging, discovery-based activities. Parents and teachers can use a wide variety of natural materials to help stimulate children’s creative inquiry and critical thinking skills. The National Council of Teachers of Mathematics recognizes and encourages learning in four areas.

1. Relevance: Math activities must focus on young children’s interest, questions and ideas. They must be involved in the execution of the activities that helps them to go from the familiar to the unfamiliar.
2. Interaction/Collaboration: Young children are fundamentally concrete thinkers, and they require a personal and interpersonal experience to learn effectively. Vygotsky
   believed that learning depended on socialization.
3. Problem-Based Learning: This provides challenging and motivating experiences,
   which lead to higher order thinking skills by posing realistic and interesting open-
   ended problems.
4. Integrated Instruction: This last component includes the blending of two or more of the curriculum areas to help young children understand that learning in one area effects learning in many of the other areas.

Infants: Relevance Through Classification – This refers to things that are put together in a group based on common criteria such as color, shape, or size. Very young children need to have daily practice in sorting (separating) and grouping (joining). For infants use objects like fruits and vegetable which they can identify using all their senses, touch, sight, sound, smell and taste. Talk to them and tell which sense they are using when the hold or eat fruits and vegetables.

Toddlers: Problem-Based Learning Using Comparing Activities – This is where young children find relationships between two things on the basis of some specific characteristic. Natural objects such as shells, feathers, leaves or stones can be used as a bases of comparison. Forms of comparisons might include:

 large/small   big/little    long/short   hard/soft

 tall/low   heavy/light   thick/thin   more/less (fewer)

Preschoolers: Integrated Instruction Using Ordering and Patterning – This is a higher level of comparing which involves more than two things. It also involves placing things in a sequence from first to last. Start with three items and ask children to put natural items gathered on field trips in a row going from big to little or little to big. Research has shown that children who are good at prediction (i.e. What is going to happen next?) make much better choices when they grow up because they develop critical thinking skills and learn to think about the consequence of their actions.

P.S. Don’t expect young children to have an understanding of conservation of numbers (addition and subtraction). Piaget says it doesn’t happen until they are around 7 or 8.

Our Questions Are More Important Than Our Answers. (Fred Rogers)