The National Council of Teachers of Mathematics recognizes and encourages learning through four components, which are:

1.  Relevance:  Math activities must focus on children’s interest, questions and ideas. Look for counting books with bright pictures and interesting subjects.

2.  Interaction/Collaboration:  Young children are fundamentally concrete thinkers, and require personal (one-to-one reading) and interpersonal (group reading) experiences.

3.  Problem-Based Learning: Provide challenging and motivating experiences, which leads to higher order thinking skills.  Pose realistic and interesting open-ended problems.  Ask questions in which many answers could be correct.

4.  Integrated Instruction:  This last component includes the blending of two or more activities.  Not only reading a story, but maybe making an experience chart, or drawing an art mural, or a math graph of the things in the story.

Infants: One-To-One Correspondence – The most fundamental component of the concept of number is the recognition of quantity.  This starts with babies when they start to understand that one sock goes on one foot which goes into one shoe.  A wonderful Caldecott Honor book by Nancy Tafuri is Have You Seen My Duckling? Here the only words in the book is that question.  Finding the missing duckling is the problem, which is always hiding in plain sight.

Toddlers: Spatial Relationships/Comparing Activities – Position, direction and distance are spatial relationship ideas and Blue Sea by Robert Kalan and Donald Crews is an excellent choice in comparing the sizes of fish in the sea.  Another Caldecott Honor book by Donald Crews is Freight Train in which the train moves under, over and through as it races along.  Other activities tied to the stories could be sponge painting fish or an art project where children run the wheels of trains in paint and then on paper, or possibly taking a field trip to an aquarium or a train station.

Preschoolers: Number Operation and Counting – Rational counting involves attaching each numeral name in order to a series of objects in a group.  One Gorilla by Atsuko Morozumi is an “I Spy” book where the children must find and count the 10 different animals in the woods and find the Gorilla who is always hiding in plain sight.  The book contains a picture graph that children can easily put together.  A field trip to a zoo can add interest and motivation to do research about different animals.  Start taking every opportunity to count birds and flowers outside on walks or people wearing gloves or hats when it gets cold.  The more experiences with counting, the better understanding of what quantity really means.  Encourage children to make graphs using objects from outside by color, shape, or size.  Make categories such as things that grow (seeds) or things that don’t grow (rocks).

Young children can’t internalize mathematical concepts on the basis of a single experience, but on experiences repeated over and over again in different ways and with different materials.  Also ask children to make predictions.  (What going to happen next?)  Research shows children who are good at predictions make much better choices when they grow up because they learn to think about the consequence of their actions.

Arithmetic is being able to count to twenty without taking off your shoes.