Thinking About Thinking About Math

Home Sweet Home is a humming hive of math activity in any given corner, whether teacher lead (snack fractions, Blokus game) or centers (sorting bears, dividing magnatiles, building with blocks, folding paper) or outside play (how many scoops of sand fill this bucket).

What children think about amounts, proportion and ratio, and how they compare and classify objects is of interest to the Early Childhood Educator. What is mathematical learning? How can adults support an open ended learning environment for math inquiry?

There is a lot of adult anxiety over academic preparation of children. This is understandable in an era of high stakes testing. How can adults ensure that math learning is developmentally appropriate? Young children may recite rote labels for symbols without comprehension of what numbers these symbols may represent, and this standard and other narrow objectives of canned curriculum can distract teachers from appreciating how mathematical thinking is authentically represented in young children's play. What do we know about how children construct this knowledge, and what can we do to enhance and support it without imposing a 3rd grade agenda on kindergarten?


"If our brains can represent numbers only approximately, then how were we able to "invent" numbers in the first place? The 'exact number sense' is a uniquely human property that probably stems from our ability to represent number very precisely with symbols. This reinforces the point that numbers are a cultural artifact, a man-made-construct rather than something we acquire innately." (Andreas Nieder)


Young children naturally map out numbers logarithmically. Numeric competency is achieved through instruction by adults and changes children's perception to a linear approach. Is it wise for preschool to advance this linear instruction? It is important and necessary to ponder this question, especially when this impacts children before the age of six years.

As adults, specifically adults in a developed, Western country, we live and work with both a linear and logarithmic understanding of quantity. The linear seems evident, but the logarithmic is also apparent, for example in the way we perceive one hundred as much more than three in the number of gallons of oil spilled on a beach, but one million does not feel like much less than one billion gallons of oil cleaned up out of a bay - the higher the numbers are, the closer together they may be perceived. This may also be illustrated in that many people clump millionaires and billionaires in the same elite circle, although one is one thousand times richer than the other. Many indigenous cultures maintain reliance on logarithmic perceptions for survival. This aides strategies for safety, health and defense. For example, tribes considered illiterate can judge at a glance, within grains, the cups of rice to be cooked, without measurement.

Could it be that we have suppressed our logarithmic intuition in our dependence on linearity? What are the consequences of this linear way of being?

Parents are invited to engage in discussions on math education within our Home Sweet Home community. We are blessed with the talent and expertise of many parents who are elementary and high school educators that can further our conversation.