Photo provided by pk2000.
Many people believe that preschool math begins and ends with counting. In reality, there are so many facets of mathematics addressed in the preschool years that truly lay the groundwork for the algebra and calculus to come!
Classification / Sorting / Seriation
Young children are often natural collectors. Observe them as they play on their own with these prized collections. Do they separate the race cars from the monster trucks? Do they sort their favorite candies into piles according to color? Do they line up their self-sheared pretzel sticks shortest to tallest? These types of activities that often come naturally (or easily with a little suggestion), and display an important early math skill. The ability to identify the different characteristics within a group, plays a key role in concepts such as recording and interpreting data, charting and graphing, and predictions and probability.
Numbers and Operations
These are the concepts many automatically think of when they think of math. Numbers, adding, subtracting. There’s more to it, however. Many children learn to “count” early, reciting a memorized list of number names, but to actually count they must understand that one number name goes to one item in the group. It also includes the concepts of “more than” and “less than” (something preschoolers grasp very quickly when candy is involved). Recognizing written numerals and connecting them with their number names is another task often overlooked as a learning objective all its own. Once again, we must remember that written numerals, even number names, are abstract concepts when compared with raw amounts – our “piles of stuff”. Children need hands on experiences, with interactive discussion, to fuse together the concept that this “pile of stuff” is the same as the word “seven”, which is the same as the numeral “7″. Once they understand the link between grouped items and quantified terms, they can advance to justifying their claims of “He has more than I do!” by saying, “He has 9 and I have 4″. Further operations can be explored to find out how, exactly, justice can prevail, and both parties end up with equal amounts.
Time and Sequence
Most preschoolers are too young to learn how to read an analog clock, but they do need to build the foundation for time and sequence by using and understanding terms such as “yesterday”, “tomorrow”, “in five minutes”, or “last week”. Sequential terms such as “before”, and “after” and ordinal numbers (first, second, third, etc.) also build the concepts of time and sequence. Recognizing the days of the week and their typical activities (“Today is Monday. We go to the library on Mondays.”) also strengthens this skill. Involving children in regular conversations about and throughout the day goes a long way in building this foundation. Talk with children about what you’re doing, what you’ll do next and about how much time has passed. Make picture schedules to show the order of routines. Talk about future and past events and make comparisons of time. (“Lunch is in one hour. That’s about as long as Sesame Street.”)
Children should be exposed to the concept of measurement, not necessarily in the sense that they would use inches and feet, but other familiar standard units. How many blocks long is your foot? Which uses more blocks to measure, the door or the window? Compare weight by using a basic balance and discussing heavier/lighter. Volume is often compared using containers in the sensory table.
In the preschool years, children begin to learn basic geometry when they learn to identify and create simple shapes, such as circles, squares, triangles, diamonds, and on and on. Children generally first learn the shapes in isolation, but then may also learn how to identify shapes within a picture (that tractor wheel is a circle) or create a new picture using shapes.
Unlocking the mystery of patterns is the foundation for many mathematic and scientific breakthroughs. It begins simply for preschoolers, with the basic ABAB pattern (circle, square, circle, square). Children first learn to complete the pattern and then learn to create it on their own. Children then progress to more complex patterns, such as ABBA, or AABBAA, and on an on. You can expose your children to patterns in riddle form with almost any repeating objects. You can use shapes cut from felt, black and red checkers, or even silverware on the table. Start out the pattern, “Here’s a fork, spoon, fork, spoon, fork. What comes next?” You can present it as a riddle or a game, “Guess the Pattern”, or even “Read My Mind”. As children become more familiar with patterns, it will not only open the door to more complex math concepts, but it will also increase logic and reasoning skills.
Fractions may seem like a concept far beyond a preschooler’s grasp, and as a formal, worksheet type concept, it is. As a foundation concept it is not. At the preschool level, children can experiment with the concept of halves, and that a whole can be divided into parts. Think of dividing an apple. You can slice one into eight slices, but you can also place them back together to reveal that you still have only one whole apple. This is a concept preschoolers can understand, and when they do, they are primed for the more complex concepts to come.
Math is a very abstract concept. The terms and operations mean little when taken out of context. (What does the word “two” mean if you’ve never held a group of two objects?) Use concrete objects as often as possible when working with young children. Take advantage of authentic experiences as they arise in the day to use math terms. (You have 5 crackers and I have 3. I have less than you do!) Encourage them to verbalize as you work together so that they can gain ownership and an authentication of the concepts, building connections in their own minds to make the concepts firm.