Mathematics is what we do when we organize our thinking about our lives in order to reach a more precise level of understanding. For children at the Antioch School, this is a process of discovery and acquisition that is overlapped and re-experienced in many ways as they progress from Nursery on through the Older Group.
In the Nursery, it is apparent that math originates from children's organic awareness of their own internal rhythms. This understanding grows, expanding out of the personal to include the rhythms, patterns, and progressions in the world around them. This, in turn, becomes the basis for a growing linear comprehension of their world.
Nursery children are busy laying mathematical foundations. They accomplish this by sorting, counting, doing one-on-one correspondence, engaging in ordinal sequencing (1st, 2nd, 3rd. . .), making simple computations, all while using a logical approach to their problem solving.
The rhythms, patterns and frequencies of music, counting friends for snack, setting times to take turns, experiencing the geometry of objects as they build with blocks, the endless pouring of sand and water – all of these help create a foundation for the children's mathematical understanding.
Refining and building upon this foundation, Kindergartners focus on using those skills that they developed in the Nursery. They continue to put more of the pieces in place with calendars, clocks, sorting equipment, scales, measuring cups, measuring tapes, graphs, and daily schedules.
Math is still very concrete and tied to their surroundings. They use math to ask practical questions (could a blue whale really fit inside The Antioch School?) and then figure out the answers, sometimes inch-by-inch, in their growing need to quantify and sort the world around them.
With this foundation in place, children in both the Younger Group and Older Group continue to refine their mathematical thinking, moving on to a symbolic – and ultimately abstract – understanding of their numerical world.
In the Younger Group, number concepts are explored as the children work with real objects, such as cuisenaire rods. They discover numbers can be represented in more than one way and still have the same value. They explore congruence. Continuing on, they connect the concept of a number – using real objects – with its numerical symbol. They read and write larger and larger numbers.
With this symbolic appreciation of numbers in place, Younger Groupers move into mathematical operations: addition, subtraction, multiplication, and division. They learn math facts. They find out how to employ a variety of strategies for their work on paper. They also practice mental calculations without paper.
As Older Groupers, the children continue to refine and develop their math understanding, appreciation, and skills. They learn to calculate using long division, decimals, fractions, negative and positive integers, and percents. They use statistics – graphing data and finding the mean, median and mode. Children in the Older Group continue to use their measurement and geometry skills, calculating perimeter, area, and volume. Some children move into algebra and trigonometry.
In both the Younger Group and Older Group, children do formal work on mathematical concepts, operations, and manipulations. This happens both independently and in groups. They also get together informally to work on math problems. In collaborating in this way, and sharing their individual mathematical strategies, they expand their personal awareness of other approaches and different minds.