Monday, September 27, 2010

to count to 100

Last week while I was off at Mandt training my fellow kindergarten co-teachers were in a math in service learning about the changes to our K math curriculum. Turns out they decided to add a bit to our already heavy standards- which may or may not have been fine in itself, but I'm not sure anyone took into consideration that we are teaching kindergartners. They are five years old. Sometimes they pick their nose. They are scared of the dark. Some of them don't like to flush the toilet by themselves. Trust me, I'm all for high standards, but I also firmly believe in setting a strong foundation so that our children will be able to reach high standards later in their school careers.

When I was getting my masters I remember reading a study on the downfall of US math textbooks- compared with other countries US math text books try to cover too much in one year. Other countries focus on smaller topics but truly dive into those topics so their children have a firm understanding of the concept. In the US we try to cram to much into one year of school, leaving students unprepared to use the math they've spent a year struggling to learn. (If I have time I'll dig up the article to site it.)

Still, my district decided to up our standards, which includes teaching kindergarten students 1/2 and 1/4. This use to be a requirement in first grade and I remember how hard it was to teach it to six and seven year olds. A year earlier? And why? Just because we'll feel better about ourselves if we can point to our kindergartners and say they are learning fractions?

Another one of the new standards is that the children are all expected to count to 100. This doesn't seem too bad, especially if you are a parent of a child who is already able to do this backwards and forwards. The three and four year olds I worked with this summer had no problem counting to 100. But if you've just entered school and have never been taught how to count? There's a lot to learn.

What does it take for someone to be able to count to 100?

1.First you need to be able to count to 10. The names for all of those numbers must be in your long-term memory.

2. You need to understand that when you count to 10 each numeral has a corresponding name attached to it. These numbers are different than letters. Ten and 10 are the same thing.

3. More importantly, though, the word ten and 10 must correspond to a set of 10 objects. The word Ten and the numeral 10 mean something- they exist when there is a group of 10.

4. How do you determine that there is a group of 10? You have to be able to count to 10, and you have to know that each object is counted once. One object is equal to one number. For some of our children this is such a difficult concept- they can count to 10, but they don't understand that they are saying numbers- they are just sprouting off words they've heard adults say. This also means they have to be able to control their fingers and eyes to point to each object once and give it a value.

5. So, now we can point to a set of objects and give each one a value, including ten. Next we have to learn our teen numbers. 11, 12, 13. There is something about the number 13. Perhaps five year olds sense it is unlucky and don't want to say it. Regardless, they always seem to skip 13.

Because the teen numbers have funny names that don't fit a pattern this is really just memory- over and over again, counting sets of objects. Correctly. 15 comes after 16. Really, it does. 11-20 have to go into long-term memory.

6. When they can get to 19 (hallelujah) it's time to apply the patterns. While learning about the numbers' names, the corresponding numeral and how to count sets of objects accurately, kindergartners are also learning patterns. Things repeat. Colors can repeat, shapes can repeat, and numbers can repeat. You can make your own pattern- you can read someone else's pattern- you can finish someone else's pattern. You can have AB patterns, or ABC patterns. You can clap patterns. You can sing patterns. Patterns are everywhere.

7. Math is all about patterns, and kids are not ready to count to 100 until they understand patterns. Our number system is really a abcdefghij pattern- over and over again.

8. They understand that numbers repeat- after every 0 in the ones place there is a 1, then a 2, then a 3. Next they need to learn the tens places. They need to learn to count by 10s so they know the names of the ten sets- 20, 30, 40, 50, 60, etc. And they have to remember those names in order, while understanding that even though I said a "5" was called five, once it is in front of another number it is called "fifty". Unless it is behind another number, then it is a something-five. Once they know that they can apply the repeating numeral pattern until they get to 100.

9. And finally, after slow and steady development they can count to 100.

And that is only how to count to 100 orally. I left out learning how to form letters correctly and how to write 23 so that the 2 comes first and the 3 is second, and that the 3 is facing the right direction with two small circles stacked on top of each other. That's a whole other step. And then there is knowing that we can put groups of objects together to make a bigger number, and then we can take that big group and put it into two smaller groups to get two smaller numbers- the beginning of addition and subtraction. I'd rather kids spend a lot of time firming up their beginning understanding of adding and subtracting instead of memorizing how to count to 100 before they are ready. They can add small numbers before they can count to 100- and that is ok. It's where they should be. Once they can do it with small numbers they can do it with larger numbers.

Most of our kindergartners come in with no number sense. Some know their numbers to five, and if they were lucky enough to be in our head start program they can count to 20. But most? They know we use numbers to count, but they don't understand that counting means giving one object a value, or pointing to each object when you count. Some have no problem counting a set of 10 objects as "1, 2, h, 5, 18, a, n,"

Before we really focused on counting to 20. If they can count to 20 without a problem they'll have no difficulty moving on to 100 later. But we gave them a firm number sense base with 20. With a firm base they'll have no problem quickly learning the pattern of counting to 100 in first grade.

Now? We'll teach them to count to 100. It might not be pretty and we might stress out a lot of kids, forcing them to skip steps they're not developmentally ready for. Brushing over steps might hurt their number sense when they're ready to add or subtract. It might not give them that firm understanding of numbers they'll need to be successful in first grade. But we'll do it because our teachers are awesome and we rise to the occasion.

 But really, why are we doing it?


Your Teacher said...

Similarly, there is new pressure is on first grade teachers to get our students to count by 2s to 100 without a visual aid. A skill that requires a much firmer understanding of skip counting and deeply rooted memorization of the two digit numbers than most of our students are ready for.

Today we were looking at a 100 chart just to see what patterns students noticed. After some promising observations I decided to try for a baseline measurement of this new benchmark with each even number on a 100 chart a bright red (odds in gray) and me pointing to each very slowly. I realized most could not say the correct name of the number to which I was pointing, much less understand what we were doing.

Needless to say, we will be going back to figuring out that tens/ones number naming pattern from 20-99 and the ever elusive place value concept before I start to push them to do the very impressive sounding but really not helpful parlor trick of counting by 2s to 100.

jwg said...

I get it. The schools are now being run by all my day care parents who thought they had a genius on their hands because the kid could count to 30. Imagine their shock when I asked the kid to hand me 5 blocks, and got 9.Enough already!

magpie said...

I love Number 7.
So many parents scratch their heads and complain there isn't enough rote learning of times tables.
Maths isn't quite like learning a song.

Doing Differentiated Math said...

Since I've been working with the new common core standards, I've been struggling with similar issues-- there may be fewer standards, but standards we are asked to address and quite complex. Inspired in part, by your thinking, I am linking to your post here:

Many thanks!