The same or Not the same--that is the question!

People often think of math as being about numbers, calculating and manipulating numerals. But 5 - 2 = 3 doesn't have any meaning by itself. However, if you have five dollars and want to buy a slushie and candy bar for two dollars and wonder if you'll have enough left for a slice of gas station pizza, then the 'math' has meaning.

But the language of math begins long before we ever reach numeral manipulation. When we look at an object and declare it to be big or small, we're doing math, we're measuring. When we describe an object as round or square, we're doing math, we're doing geometry. When we locate an object as inside or beside or behind something else, we're doing math, we're doing visual-spatial graphing. Likewise, when we compare two items and declare them to be the same or to be not the same, we're doing math. "Equals" = "the same as." 5 - 2 is the same as 3. It's part of the language of mathematics.

That is one of Jman's new language lessons we're addressing with the ProLoQuo2Go. To begin our study of the language of mathematics, we started with 'the same as' and 'not the same as.' I programmed two button choices for him into the P2G. Each button speaks not just one word, but the complete sentence, "They are the same" or "They are not the same." I could have chosen to use the words 'same' and 'different,' but by using 'the same' and 'not the same' we achieve two purposes. First, it comes closer to 'equals' and 'does not equal' and will therefore translate better into traditional math symbols down the road. Second, it introduces the language concept of 'not,' which we can develop more generally in other areas of language studying. "The boy is jumping." "The boy is NOT jumping." And so, Jman's first math language lesson is learning to appraise when things are "the same" or "not the same."


So, Jman has two options on his ProLoQuo2Go--'They are the same' or 'They are not the same.' My next task was to find things for us to compare. I gathered a variety of objects I intended to use--cards, pick up sticks of different colors, bear counters of different colors. I quickly decided against the cards because while the numbers might be the same, the colors might be different, or at the very least the suits would be different (unless I used two decks of identical cards). There were too many potential attributes to compare, so I decided against the cards for now. I decided to use the bear counters. I have two different style of bears, but I have plenty of each style in each color, so I could easily generate lots of pairs that were exactly the same.

Now, I should clarify one point, perhaps. Jman KNOWS when things are exactly the same and when they are not. That was not the issue or the lesson I was trying to teach. What I was trying to help him learn is what LANGUAGE to use in order to share with someone else the observation that things are the same or not the same. This wasn't a lesson to learn about 'sameness' but a lesson to learn the language about sameness.

When I sat down with Jman and the bag of bears, Jman was in no way interested in comparing a pair of bears and saying whether they were the same or not the same. I demonstrated a few times for him (Guided Demonstration), but he would have none of it. He either wanted to play with the bears (sorting or lining them up or setting them up like bowling pins), or he wanted the bears put away. And so, thus ended lesson one of "the same or not the same."

The next day I decided to try our 'same game' with coins. I grabbed some pennies, nickels, dimes, and quarters. Jman was more cooperative and interested this time, in part because he'd asked for the computer and I had told him we were doing a few things first. Yes, sometimes bribery is your friend.

I placed a couple of pennies together, and punched into the P2G, "They are the same." Jman watched. Then I put together a couple dimes, and together we punched, "They are the same." Next nickels, and Jman happily punched in "They are the same," and ditto with quarters.

Okay, we'd covered 'the same,' and he seemed interested and cooperative, so I put together two different coins. Jman promptly punched in, "They are the same." Um, no. They are NOT the same. I erased his error and punched in "They are not the same." He didn't care. I tried again with a couple other different pairs of coins, but he was done. Lesson over. You can't teach a kid who has checked out.

The next day, Jman and I were stopping by the drive thru for some french fries. I pulled out two one dollar bills to pay for them, and while we waited I showed them to Jman and pointed out that they were 'the same'--they both had numeral one's and they both had the same picture of George Washington. "They are the same." Jman listened but didn't comment. And we got our fries and drove home.

Back at the house, SB3 brought me a pair of identical yellow wood blocks from a knock-off Jenga game. I commented to SB3 that they were the same. He of coursed loved the acknowledgement and the attention, and maybe he'll learn "the same" faster too. :)

I turned to Jman, who was eating his fries, and showed the two blocks to him. I commented again to Jman, "They are the same. They are both yellow." Jman finished his fries as I gathered a pair of red blocks and a pair of blue blocks to go with the yellows. Then we sat down together and Jma (again hoping for the computer, which he did get after this) himself selected the two yellow blocks and punched into the ProLoQuo2Go "They are the same." I offered two reds, and he qucickly and enthusiastically shared "They are the same." Ditto for blue.

And then I grabbed two of different colors, and Jman quickly and easily identified "They are not the same." Woo-hoo! He was quite pleased and having much fun. I don't know if his excitement was about his being 'right' or if it was mostly in anticipation of getting some computer time, but either way, he was happy and participating. I pulled out several more pairs of matching or not matching blocks, and he quickly and correctly identified each pair as being the same or not the same. Hooray!

We called it a day and he happily began watching Animaniacs on the computer for a while I made some modifications to the 'same' choices on the ProLoQuo2Go. I added in buttons for "color" and "shape." This week coming up, we will try to help him expand and differentiate not only when things are the same or not the same, but clarify whether they are the same color or not the same color, and later whether they are the same shape or not the same shape. We could add choices for size, location, function, category, orientation--lots of possibilities. However, some of those will come further down the road. For now, we'll focus on same or not, color, and shape. Yes, he knows his colors by name, and his shapes by name as well. This isn't about teaching him those things, but about teaching him language, developing his ability to communicate thoughts and ideas with others.

As an aside, in case anyone is actually interested, I have an old used set of the Singapore Math workbooks for kindergarten. The table of contents includes, of course, the list of lessons, along with the objectives of each lesson and the vocabulary or phrases associated with each of these math objectives. Some of the langauge Jman already has (such as colors, shapes, numbers, counting, etc). But other bits of language he doesn't have, even if he understands the math concept (such as 'the same' or 'not the same'). It is from these vocabulary and phrases that I am developing Jman's math language lessons, but with as much variance and adjustment on my part as will be necessary. Think of it this way--the Singapore Math workbooks are my 'Guided Demonstration' of one way of approaching math and language. I don't have to do it exactly that way or follow their workbooks exactly as laid out. In fact, I most certainly won't, because the books are all written in from years ago. But they are serving as a simple guide to how I can approach helping Jman learn the language of math, and I'm very pleased with our first few days. It may take years for Jman to master all the language in these K workbooks, but hey, if that's what it takes, that's okay. For Jman, learning math will be more about learning the language to describe what he already knows rather than learning the 'math.' These early Singapore books are a handy reference because they have that 'language development' component that I haven't noticed being emphasized in other curriculums I'm familiar with from homeschooling Sly over the years. I don't know what the Singapore books are like after the K workbooks, but it'll be a long time before we're there anyway.

Fwiw, Jman just came up wanting the computer. I asked him to find me two things that are the same. After cleaning up the spilled counter bears that SB3 dumped out earlier, Jman selected two red bears and happily punched into the P2G while he muttered under his breath repeatedly, "They are the same." I asked for two 'different' bears, and he looked at me a little unsure. I realized my mistake and asked for two bears that were 'not the same.' He promptly pulled out a red bear and a yellow bear, muttering, 'not the same, not the same' and punching "They are not the same" into the P2G. He then pulled out two red bears again and muttered 'they are the same' as he punched in "They are the same." So, I'm guessing he's got 'the same' and 'not the same' down in his head now! Tomorrow we'll add 'color' to his sentence!