infants & toddlers
development:  how math helps your child's brain develop

What family member hasn’t taken delight as they sit with a child who chants, "one, two, three …" when asked to count or in answer to the question, "how many?"  This playful interaction is easily recognized as an important milestone.  It is a step in the development of "mathematical power."

As described by National Council of Teachers of Mathematics, mathematical power "includes the ability to explore, conjecture, and reason logically; to solve routine problems; to communicate about and through mathematics; and to construct ideas within mathematics and between other intellectual activity." Mathematical power also involves "the development of personal self confidence and a disposition to seek, evaluate, and use quantitative and spatial information in solving problems and in making decisions." "Students’ flexibility, perseverance, interest, curiosity, and intuitiveness also effect the realization of mathematical power."  Mathematics is second only to reading in the amount of time spent and money budgeted in elementary school curricula.

Mathematics is a language with its own set of symbols and rules for communicating. These symbols are abstract and represent the very nature of mathematics as a way of thinking. Mathematics is a powerful tool that has usefulness in virtually every aspect of daily routines. Mathematics is a system of relationships that supports the appreciation of patterns that recur in our world, in how things work, in art and in nature.

Mathematics should continue to have a central role in the early childhood and elementary school curriculum. For a subject that is clearly so vital, "mathphobia" – an anxiety or fear of mathematics - is a condition no child should have to experience.  The anxiety associated with mathematics is often associated with how math is taught and teacher/parent attitudes. Knowing how children learn and understanding how the brain searches for, processes, and then organizes information is critical to providing appropriate learning experiences.

Only when a concept is meaningful to a child can the symbolic language of mathematics begin to be introduced and have meaning.  Active involvement in experiential learning is the cornerstone of meaning construction. Such learning is developmental and requires time.  Children need time to think and extract mathematical concepts from the authentic experiences that teachers provide. Children need time to play and explore materials, independently, through free exploration before they can attend to reflection and mathematical concepts.

Have you ever observed young children playing with "Fruit Loops" or other dry, colored cereal?  When they sort the cereal pieces into colors, arrange them into repeating patterns (yellow, green, orange …yellow, green, orange...) or otherwise explore, they are using the cereal pieces as manipulatives to assist in their independent learning. As children engage in activities like this, supported by interaction with other children and adults, they begin to think about what they are observing and make connections from one activity to another and then generalize to the world about them.  This is the beginning of "metacognition" or thinking about thinking.  The attitude of the teachers towards these and later mathematical activities is key to the success, attitudes and enthusiasm of the children towards themselves as "mathematicians."

As children enter into the world of formal classroom education, while knowledge of basic "arithmetic" facts is essential - like the learning of the letters of the alphabet and their associated sounds and uses, thinking, problem solving, and other higher mathematical tasks are the goals.  Critical thinking skills and the appreciation that there are multiple ways to arrive at an answer are critical products of good learning experiences.  Children should have a variety of such experiences using art, music, language (written and spoken), drama and other physical activities in large and small groups, as well as individual, learning settings. Activities should allow children to experience and express themselves visually, auditorally, kinesthetically, and emotionally. Since it is well known that all learning is enhanced by realistic challenges and suppressed by anxiety, the learning environment should be a welcoming and safe place that promotes risk taking while providing inviting challenges and authentic hands-on experiences.

So, what can we do as parents to support our children in their personal development of "mathematical power"? In selecting toys for children, choose items that involve sorting and patterning activities with colors, shapes and sizes. Recognize that authentic learning experiences are not always "neat" and true immersion is sometimes "messy."  The old mudpie making of days-gone-by in the backyard was truly a mathematical experience. Activities using various sized containers with water, rice, sand and clay provide children with invaluable exploratory opportunities for learning about dry and liquid measurement and relative capacities of containers.  Let your child help in your daily living activities such as cooking, laundry, shopping and visiting the library.  Develop one-to-one correspondence by specific use of language, such as, "Please give me three spoons."  Model counting out three spoons.  Language and modeling in any activity will support your child’s development of mathematical power and general competency.   Laundry provides for sorting activities by multiple attributes such as color, types and ownership of clothing (mommy’s, daddy’s, etc), and things that come in pairs.

When your child goes to pre-school ask what types of activities are planned and provided to develop "mathematical power" and what types of manipulatives are used.  Visit the public library with your child and look for picture books and stories with mathematical relevance such as Benny’s Pennies and The Very Hungry Caterpillar.  As your child enters elementary school, continue to ask questions about the mathematics curriculum.  Ask about "Family Math Night" or think about initiating one through your PTO.

Mathematics is a language, a tool, and a system of relationships that supports daily living experiences.  Knowing how children learn, being able to provide for meaningful experiences and advocating for children through school involvement and the asking of key questions will all go a long way in developing your child’s mathematical power!

Resources for Parents and Professionals

  • Poems To Count On-32 Terrific Poems and Activities to Help Teach Math Concepts by Sandra Liatsos (Scholastic, 1995)
  • Hickory Dickory Math-Teaching Math With Nursery Rhymes and Fairy Tales by Cecelia Dinio-Durkin (Scholastic, 1997)
  • Gobble Up Math-Fun Activities to Complete and Eat by Sue Mogard and Ginny McDonnell (The Learning Works, Inc. Santa Barbara, CA, 1994)
  • The Math Chef by Joan D’Amico and Karen Eich Drummond (John Wiley and Sons, Inc., 1997)
  • Math Wizardry for Kids by Margaret Kenda and Phyllis Williams (Barron’s, 1995)
  • Math Art- Projects and Activities by Carolyn Ford Brunetto (Scholastic,1997)
  • Look Around! A Book About Shapes by Leonard Everett Fisher (Viking, 1987)
  • Sea Shapes by Suse MacDonald (Harcourt Brace Jovanovich, 1994)
  • Twelve Ways to Get To Eleven by Eve Merriam (Simon and Schuster, 1993)
  • Inch By Inch by Leo Lionni (Astor Honor, 1960)
  • Eating Fractions by Bruce McMillan (Scholastic, 1990)
  • Ten Black Dots by Donald Crews (Greenwillow, 1986)
Dr. Maureen Ruby is a teacher at the A. W. Cox Elementary School in Guilford, an adjunct professor at Southern Connecticut State University and was a Department of Education, and Connecticut State Teacher of the Year Semifinalist in 1999-2000. She is the mother of four school-aged children.


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