### Geometry and Spatial Sense

Kindergarten children can use positional words in sentences and can give directions to other students. Preschool children learn how to use words like “behind” or “next to” and can understand them, but have difficulty using them correctly. They have no problem saying, “The scissors are on the shelf next to the sink under the paper towels.” They can also locate things in three-dimensional spaces using a two-dimensional representation such as a map. For example, children can follow a treasure map around the classroom to find a bag of candy hidden under the sink. If “X” marks the spot under the sink on the map, they can translate that into the three-dimensional world of the actual classroom. They can also use toys to make a fairly accurate map of their classroom.

### Data Analysis, Probability and Statistics

Kindergarteners can use graphs in more dynamic ways than preschool children, using them to collect, analyze, and represent data. They can then use them to make decisions, such as “What snack are we going to have today?” or “What book are we going to read next?” Kindergarteners are good at making graphs out of things in their environment such as shoes, blocks, or even people. They can also use pictures to create graphs to represent data. While preschoolers can construct similar simple graphs, kindergarteners can use the information in the graph to answer questions such as: “Which group has less? Which group has more? Which group is the smallest? Which group is the biggest?” They can also compare individual factors. For example, if a graph is about a favorite color, each student can put a colored square on the board to make a stacked bar graph. They can then answer questions such as, “Do more people like red or yellow?” Kindergarteners are able to extract useful mathematical information from pictures or other visual media. These can become early versions of “word problems.” For example, children can look at pictures of houses and figure out which one has the most windows. They are able to problem solve and should be involved in what Fosnot called mathematizing, or making sense of the world using mathematics. Kindergarten is the beginning of the formal mathematics that children in the first grade and up will be involved with, such as addition, subtraction, multiplication, fractions, and decimals (Burns & Silbey, 2000).

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