This week I had the privilege of spending the morning at a nearby child care center, and while I was observing the preschoolers interacting with each other in the sandbox, at the play dough station, and making crafts, I heard a lot of math.  I heard things like “your string of cheerios is longer than mine” and “that play dough noodle is shorter than the others” and “there are about 100 bubbles.”  The math I heard was almost entirely unstructured, unplanned, undirected, unsolicited, and perhaps even unintentional.  Did the incidental nature of the comments make them any less math-like than if the teacher had been teaching children about length and quantity?  Not at all! 

Math is all around us.  Patterns, measurement, operations, probability, and quantity are but a few math-related topics that infiltrate our daily lives, often without our awareness.  We make judgments about speed, estimate how much of something we will need, determine how much change we should receive, and categorize objects by size or shape.  Children are capable of many of the same math activities we engage in daily at a much younger age we might guess, even though they may lack the vocabulary or representational skills for communicating their math ideas.  Perhaps one of the best ways to capitalize on children’s emerging math interests and abilities is to recognize them when they emerge through play.  By learning to hear math comments as they happen during play, we can turn a moment that occurs naturally, and in the context of fun, into a teachable moment.  A teachable moment might mean providing children with the relevant math vocabulary they were searching for, or challenging them to try a new mathematical strategy such as skip counting, estimating, or solving simple operations.

Over the course of the next few blogs, I will give examples of some math concepts that might arise naturally, and provide some suggestions for how to elaborate and expand upon the concepts.  I will start with one example this week, so please stay tuned for more!  And please let me know if you have other examples of math moments, or suggestions for creating or capitalizing on teachable moments.

• Jenny and Chloe are playing with beads when Jenny suddenly declares that she has more than Chloe.  You could work with the girls to group the beads into small groups (of 2, 5, or 10) and practice skip-counting, and if a different quantity is indeed established, you could talk about how many more beads one of the girls will need in order to have the same amount as the other girl (simple operations such as addition and subtraction).  You could also work with the girls to categorize the beads by color or shape. Finally, you could help the girls to create various patterns with the beads, such as: red, yellow, purple, blue, red, yellow, purple…

As a child, I adored school.  All summer I looked forward to that first day of school, you know, the day in which everyone came back full of stories about their summer adventures and wearing their new clothes.  I loved opening the pages of a brand new notebook, seeing the crisp lines just waiting for new words and ideas to be written on them.  I loved the smell of the paper, the sounds of classroom life, and the thrill of organizing my school supplies into my desk or locker. 

This love of school translated into a life-long love of learning, and I believe that sometime the most profound learning occurs outside the classroom.  Although my favorite subjects in school were English, biology, drafting, and physical education, I also enjoyed learning from experiences such as camping, riding horses, and construction.  I learned a lot about business, mechanics, environmental issues, and subcultures by driving a 100-ton haul truck at a copper mine in the summers to fund my college education.  There were some subjects that did not come as easily for me, including math.  With a notable touch of irony, I decided to pursue a graduate degree in psychology, studying children’s mathematical development, perhaps in an effort to understand why I occasionally struggled with math myself.  I became intrigued by children’s early mathematical abilities, the contexts in which children could demonstrate their abilities, and the implications for cognitive development.  During my doctoral and postdoctoral studies, I examined how young children acquire new mathematical ideas, how they might represent mathematical concepts in their minds before they can use symbol systems, what children’s strategies indicate about their mathematical reasoning, and what types of contexts and interventions help children learn mathematical concepts.

Underlying my interests in children’s mathematical development are the beliefs that children are capable of much more than we often give them credit for, that how we ask children about math can influence what they are able to tell us, that math surrounds us in everyday life, that being comfortable with mathematical concepts is necessary for many careers and life choices, and that learning about math can and should be fun!

As a Learning Designer for LeapFrog, it is my pleasure to help infuse math and science content into fun, engaging, and educational products.  When children interact and play with math and science, they can learn new concepts; think about numbers, shapes and patterns in new ways; become confident learners, and make meaningful connections in novel ways.  But perhaps more importantly, children can realize the fun and excitement of learning.