We believe that in every area of study, children learn best in context. The City and Country School Mathematics Program is designed to provide that context. The Lower School program offers many possibilities for contextual learning. When 2s and 3s are learning about comparisons, a teacher at the water table might say, “Your bowl was full. Now it’s empty. Which other bowls are full?” Young children are also taught to pour a half of a cup of juice for snack; milk helpers need to recognize that one milk serves two children. In these ways, the City and Country Math Program teaches concepts in context, beginning at the earliest ages.
Since C&C's unit blocks are all fractional units or multiples of one another, they present many opportunities for learning mathematical concepts such as numbers, symmetry, patterns, mapping, measurement, sorting, classifying, spatial orientation, multiplication, fractions, and geometry. Through repeated exploration and experimentation with the unit blocks and other materials, the children come to intuit these concepts, then hone their understanding of them. And because children at City and Country have ample time to work with the materials, learning becomes an integral part of their daily lives. By the time fractions are formally introduced at age seven, the children are simply being given the language and symbols to illustrate ideas they already understand and have been thinking about since they were two years old.
Our goal is to help children think mathematically and then learn facts and algorithms when the time is right. Manipulative materials, traditional workbook pages, and many teacher-made materials and games are used to reinforce concepts. We encourage children at all ages to explore different ways to find answers, to describe their mathematical thinking, and to compare and discuss their observations and approaches to solving problems. When all children are asked to talk about math and comment on their thinking in a problem-solving situation, math becomes an active process.
In the Middle and Upper School, the Jobs Program
provides children with further opportunities to apply their math skills in real life settings. Making change in the 8s’ Post Office reinforces two- and three-digit addition and subtraction, whereas higher priced supplies in the 9s’ Store requires the children to have their multiplication facts at their fingertips. By the 10s and 11s, the children are exploring geometric shapes using protractors and three-dimensional scale models. Two- and three-step problem-solving schemes involving fractions, decimals, and percentages are developed and refined. In the 12s, the children execute simple proofs using Euclidean geometry. By the time they graduate, they have completed the equivalent of Algebra I, with an understanding of rational and irrational numbers and the ability to solve linear and exponential equations with variables.
As John Dewey pointed out long ago, learning is not either-or when it comes to concepts versus memorization. Our math program seeks to join the two in a way that makes sense for the learner, enabling him or her to use math as a tool for practical problem solving in school and in life.