Grouping things according to common traits is a basic operation in mathematics and science. Teachers provide and label material to sort and match. They encourage children to collect and sort things e.g. in the school, around the neighbourhood and at tidy-up time.
Seriation orders objects by difference (e.g. smallest to largest) or a repeating sequence or pattern (e.g. alternating red and blue beads) Teachers promote this by providing materials whose attributes can be easily compared. Children read and act out stories that feature graduated qualities. For example after reading The Three Bears children may choose objects for Mama, Papa and Baby Bear based on variations of size, pitch or loudness.
Number involves classification, seriation, one-to-one correspondence and conservation of matter. To build number concepts teachers provide materials that encourage comparing and counting; materials with numbers on them (cards, board games) and materials that fit together in one-to-one correspondence. Teachers listen to the kinds of things children commonly compare (amount of materials, age), comment on the sets of corresponding materials that chlidren generate, use written numbers and support children who are interested in writing numbers themselves.
To expand preschooler's awareness of space, teachers enable them to move freely around the classroom. They engage children in spatial exploration with materials to fill and empty, fit together and take apart, shape and arrange and set in motion. To focus on spatial awareness throughout the day, teachers engage children in talking about how they made things and encourage them to crawl, roll, bounce and lie on their backs to view the world from different perspectives.
Preschoolers measure time subjectively but as they form mental representations they see time in more symbolic ways. They remember the past, anticipate the future and become aware of sequence and pacing. Teachers supply appropriate time related materials including things to signal stopping and starting. They include living things indoors and outdoors to show natural life cycles of plant and animal life. Other experiences that promote time concepts include music activities e.g. moving at different rates, asking children to describe intentions and activities in time related language.