Math

Mixed Ages

What We Saw: A teacher was helping children in a sorting activity with leaves they had collected the day before. She helped one child to sort the leaves into two piles of yellow and brown. When another child decided to put her leaves away, the teacher encouraged her to count them as she put them in the bag. Together they counted to 5. While they were counting they talked about which leaves are big and which are little.

What It Means: The teacher supported the cognitive abilities of recognition, recall, categorizing and counting. All of these skills are important in mathematical development. Mathematics connects with all other curriculum areas and can be easily integrated throughout the day. The National Council of Teachers of Mathematics (NCTM) published Principles and Standards for School Mathematics (2000), that contains five content standards and five process standards directed to teachers of children pre-kindergarten through second grade. To learn more about these standards visit their web site at www.nctm.org

Preschool

What We Saw: The classroom keeps a thermometer outside and as a regular part of the routine the teacher brings it in so she can discuss the temperature with the children. The teacher comments to the children, "The thermometer says its 20 degrees. That's cold. Can you feel how cold that is?" She passes the metal thermometer to the children. She brings down a chart that is a record of the week's temperature. She says, "On our chart, can you show me where 20 is?" One child points to a number. "You are going too high," she suggests. "You need to go down." She helps a child to select the number 20, and she draws a line across a bar graph at that point. She then has one of the children color in the bar.

What It Means: Young children encounter measurement in many contexts every day as they explore and try to make sense of their world. Teachers can extend their learning by providing daily opportunities to measure something in the environment, discuss it and visually represent its attributes. Through this process, children learn to recognize that many things have measurable properties that are represented by a corresponding unit of measurement such as degrees, feet, pounds, etc. They also start to make comparisons by experiencing how a measurement can vary from day to day.

Preschool

What We Saw: The children had made a paper chain. One teacher asked the group, "How many green links do you think are on the chain?" Several children responded with estimates that the teacher then repeated. "Next, the children and teachers counted the green links in unison. One teacher repeated the activity for the red links, and then asked the children to remember the pattern they developed before they guessed how many white links were made. One boy answered, "We made, red, green, white, white." "That's right," replied the teacher. "Red, green, white, white. Now think about that, and tell me how many white links you think there are. Remember, there were 17 red ones, and 17 green ones." The children answered with several estimates, many of numbers greater than 17.

What It Means: Mathematics is the science and language of patterns. Thinking about patterns helps children make sense of mathematics. Research has shown that learning experiences focusing on the concept of patterns facilitate children's ability to make generalizations about number combinations, counting strategies, and problem solving. When children are encouraged to see patterns in their world and connect them to mathematics, they are more apt to remember what they have learned and transfer the knowledge to new situations and problems.

Preschool

What We Saw: Two children were playing in the block corner. One called to their teacher and said, "Come over here and see what we did." The teacher went over and noticed that they had built blocks all around a baby doll. The teacher commented, "Your baby is safe now because she is inside the blocks." The children were so excited that they began to jump around the structure, but they did not know what to do next. The teacher asked them, "What else do you want to make for your baby?" They thought about it, then began to build their blocks up very high. One child said, "We will build a very, very tall crib for the baby to sleep on." When finished, they placed the baby on top of the blocks, and everything came tumbling down. The children laughed and one said, "The baby fell down and is hurt." The teacher responded, "It was too high for the baby, try again." The children began to build some more.

What It Means: Math concepts are being learned here. Children must learn the basic prepositional concepts such as inside / outside, on / under before they can master more advanced concepts, like ordering objects from little to many or from short to long. Eventually this leads to the understanding of numbers, and then onward to arithmetic. But mathematical learning starts with experiences like this one, where an interested adult helps children begin to label their own creations with words like "inside" and "on top of" which describe relationships between objects. Social skills are being learned here. Instead of making their own individual block structures, the children cooperated in a joint project. Two and 3-year olds often play together in the block corner, but it is usually parallel play, in which each builds their own project. By age 4, truly cooperative play is possible, as we see in this classroom. They must negotiate a plan and act in concert, no small thing! They are learning to take into account the viewpoints of other people. This teacher did only a little, but what she did was important and skillful. First she provided a fantasy meaning to the structure ("Your baby is safe now…"), which was highly motivating to the children. She encouraged independent thinking by asking them an open-ended question. In the end, she encouraged them to think of a better solution, so the baby wouldn't fall.

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