Kindergarten, Counting and Cardinality 1/3

Opinion – time to launch

There is a certain satisfaction in following a path to math competence, even though we may not recognize the path. We probably came this way, but we may not have “seen the forest for the trees,” or vice versa. In any event, pointing out a few trees and flowers to students will be satisfying. And as we teach, we will notice that we are also learning. This phenomenon has already been noted, but there is no substitute for the experience. A couple of points to remember: showing and doing count for more than just telling; getting students to show us and do for themselves will be as important. Practice, practice, practice, but the practice should be fun, and when attention begins to stray, that’s usually an early warning that practice is over.

If your student is following a formal course with a professional teacher, try to coordinate these posts with the pace of the class. The teacher should be able to help. Don’t worry if that doesn’t come naturally. There is so much depth and breadth in math that your child is going to be learning no matter what.

If you are home-schooling your child, find his rhythm – neither too slow (he is bored) nor too fast (he is confused). If you don’t wind up exactly where and when the formal classes do, remember that it will be the quality of learning – an appreciation and an affection for math as well as a reasonable amount of retention, especially for problem-solving processes – that will ultimately carry the day.

CCM Lesson of the Day: Counting and Cardinality (K.CC), 1/3/1

Notice that there are four parts to this lesson. Each part will take some time, but you are the coach. You can let your imagination, experience, and observations (of your child) be your guide for how fast to go and whether to combine any of these sections. Make no mistake though, there is a lot to learn.

Know number names and the count sequence.

  Count to 100 by ones and by tens.

Borrowing from an earlier post, consider these complications in our number system:

  - Where do the names of numbers such as ten, eleven, and twelve come from?

  - Why does the spelling change from three and five to thirteen and fifteen?

  - And from two, three, four, five to twenty, thirty, forty, fifty?

  - And then there is zero – is that even a number?

The point is that our number system, from the perspective a child who doesn’t yet know it, is quite random. Therefore, learning the number system is an exercise in memorization. It is very interesting to me that memorization, which some educators devalue, is thrust upon us at the very start of the trail to math competence. That leads me to simply accept that memorization plays a prominent role in learning math just as it does in learning any academic subject.

Yes, there are patterns that will become visible over time, but there also many exceptions to the way we say the numbers in English. I suggest that you and your child practice saying the numbers in order, out loud every day until they are embedded in that formative brain. There is no reason that fingers and toes (or blocks, beans, marbles, etc.) should not be recruited into the process but don’t worry, future lessons will ascribe symbols and meaning to the numbers.

   Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

This exercise helps to reinforce the memorization and to reveal patterns (and pitfalls) as indicated by some of the random aspects above. Don’t forget to count by tens because it is not obvious that after learning “one, two, three,” we would say “ten, twenty, thirty.” That’s just the way we count around here, but I’m sure that took you and me some time and practice to learn when we were in Kindergarten.

   Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects).

This is where we start to link written characters, so-called Arabic Numerals, to numbers. Note that we start at 0 and that the difference between writing 1 and 10 is significant, even though the written numbers only differ by a 0. Most of us have 10 fingers and 10 toes. Any ideas on how to use that fact as part of the teaching the number of objects represented by each and every number from 0 through 20?

One key here is that the ten decimal digits (0, 1, 2, … , 9) must be memorized; no exceptions. A second key is that 10 through 99 are represented by two decimal digits. As we memorize these numbers, there should be many opportunities to point out examples in documents, newspapers, signs, etc. Let your children know that you like them to do this.

Definitions

Count: Count (the verb) means to enumerate the cardinality of a group (or set) of items.

Cardinality: the cardinality of a set is the number of elements in that set.  The set {dog, cat, chair} has a cardinality of 3.  The set {3, 6, 9, 12} has a cardinality of 4.

Example

When I count the number of fingers on one hand, the result is 5 (fortunately for me).