It’s time to re-introduce one of the most popular math games that I know of: the card game called SET.

SET is a card game of logic, geometric shapes, and visual perception. It’s a fast moving game in which neither age nor academic excellence is necessarily an advantage. SET is simple and clever: each of the 81 cards has one to three icons that can be any of 3 different colors (red, green, purple), any of 3 different amounts (single, double, triple), any of 3 different shades (solid, hollow, striped), and any of 3 different shapes (diamond, oval, squiggle).

For example, a single card could have two red striped diamonds, and another card could have three purple solid ovals. Three different possible variations on each of four criteria is 3•3•3•3 = 81 different cards.

Lay the 12 or 15 cards out in a rectangular grade. The goal is to find three cards (always three) that are either all three the same or all three different for each of the four criteria (color, amount, shade, shape).

The game is actually easier to play than it is to explain, and while SET is not hard to learn, it still continues to challenge both experienced players  and novices of all ages. Because SET can be played alone or in groups of 2 or more, it is a great activity for a classroom tournament, or a family game night, or a solitaire session on a dull afternoon.

I first taught my younger son to play the game at age 7. Although I was no slouch at playing SET, this… kid… consistently beat the pants off me. Both of us delighted in a young boy being able to beat Dad so convincingly.

SET earned Game of the Year awards from numerous game organizations and magazines in the early 1990s. This game is for adults, adolescents, and kids as young as age 7.

SET isn’t a game involving quantitative math (numbers, ratios, calculations, etc.) – but it is a math game because it involves logic, perception, and visual discrimination. Visual discrimination is the ability to look at a group of items and then group or re-group – or even un-group – them according to some specific criteria. In SET, players have to find three cards that can be grouped together according to four separate criteria. The multi-tasking involved in keeping track of four separate criteria is great brain building. For the most part, all that brain-building is dominated by a game that is sheer, challenging fun.

This is a blog I’ve published before, and it’s worth posting again.

As I’ve written elsewhere, I’m convinced that the skill of skip counting is an extremely important pillar in building a strong foundation for success in arithmetic and mathematics. Recall that skip counting is counting in multiples of a number – 6, 12, 18, 24, 30, etc., or 4, 8, 12, 16, 20, 24, etc.

Skip count songs are catchy, fun songs that help plant those number-word sequences firmly into a child’s memory. We have two different skip counting albums that we carry, with different lyrics and melodies for each of the numbers from 2 through 10.

My younger son Trevor started hearing the skip count songs when he was about 16 months old.  We played one in the car and the other for the house, and we played the songs a lot – in the car during trips, sometimes at bedtime, sometimes at lunch, and often simply just in the background when Trevor was playing with toys and with friends. The catchy songs started getting stuck in his head, and before he was two years old, he could count to 20 by 2’s.

Now here, the question has to be asked: did he know what he was really doing? I’d say, No – of course not. He was just repeating a series of number-words that he knew from the skip count song for 2’s. But here’s the important piece: at least that series of number-words was firmly embedded in his memory in the proper order.

He kept hearing the songs at various times throughout his day as he grew older, and over the next 3+ years, he eventually mastered all the skip count choruses from 2 through 10. When he turned 5 years old with his summer birthday, my wife Sarah took him in for his kindergarten checkup. The nurse checked his ears and eyes and throat, and then she asked him, “Trevor, can you count?”

Trevor looked at the nurse and said, “How?”

The nurse didn’t understand what he meant and replied, “Well, I’ll just make a note that he can’t count.”

Since my wife was there, she spoke up, “No, he means what he said when he said How?”

The nurse was still puzzled, and so Trevor asked her, “How do you want me to count? By 2’s or by 8’s or by 9’s or by 4’s?”

At this point, the nurse looked at him with astonishment and said, “You can count by 4’s?!”

So Trevor replied in a sing-song-y voice, “Sure – four, eight, twelve, sixteen, twenty, twenty-four, twenty-eight, thirty-two, thirty-six, forty days Goliath had to wait.”

At this point, the nurse turned back to her check-up form and said, “I’ll put down that he can count…”

Here was a young boy who had mastered all the sequences of skip counting for each of the numbers from 2 through 10 – going into kindergarten. This was a perfect set-up for success in so many areas of elementary arithmetic.

Trevor is now an adult. He didn’t go into math or a math-related field in college. But the impact of skip count songs on this guy is noticeable. He has excellent mental math skills and great number sense. From paying attention to skip count song numbers as a child, he’s also learned to pay attention to details all over the place. He’s a very savvy young man. Other things contributed to that, and listening to skip count songs was a piece of that.

So my older son and I are discussing his suggestion of how to build a sandbox in my backyard for his kids to play in.

He’s describing kind of a ground level frame of 4×4 beams in the shape of a square, with a layer of a black plastic moisture barrier beneath, and then a slightly smaller offset frame of 4×4 beams laid into the ground.

I’m having trouble visualizing what he’s describing. So he goes to the dusty back window of his van and starts drawing a partial diagram of the sandbox he’s got in mind. Now I see what he’s talking about – there’s a picture there that I can examine.

Then I asked him, “Could you picture in your mind what you were describing, before you drew the diagram?” He said, “Sure. You couldn’t though, could you?”

“Nope,” I admitted. And I realized why he could visualize his diagram and why I couldn’t.

He was starting with the picture in his head, then using words to describe what he saw.

I was starting with his words, then trying to create a picture in my mind. The process in my head was the reverse of the process in his head.

So why could he so easily picture in his mind how a sandbox could be built?

Experience.

He’s had a lot of experience working with beams and studs and frames. He spent two summers in college doing construction and remodeling with some very experienced remodelers, plus he spent 2-3 years in high school and 3+ years in college working in the technical side of the school theater departments – building sets, putting up doors and door ways, constructing stairways, framing stud walls with sheetrock layers and plywood.

Experience. Based on that experience, it was easy for him to picture in his mind’s eye the kind of sandbox he thought would work.

That was experience that I didn’t have. He’s probably forgotten more about construction than I will ever know.

There is at least one area where I have enough experience to picture in my mind’s eye what’s going on: in algebraic factoring of quadratic expressions.

What prompted this blog was that I was creating some algebra problems for my SAI students to factor. In SAI, we use pieces to show elementary age students what quadratic factoring is. Many times it’s easier for me to picture the pieces for 2x2+ 7x + 6 than it is to write out those symbols.

So why is it easy for me to picture those algebra pieces but not the 4×4 beams? Experience. I’ve got a lot more experience with algebra pieces than I do with wood beams.

I can picture what I want in my head, then use words and symbols to describe what I’m already seeing.

That’s the advantage of SAI: we give your child the experience of working with math in ways that train them to see in their mind’s eye what they can then describe with words and symbols.

Songs help form memory. Songs help prompt memory.

A long time ago, my then 6-year-old son Brandon and I were playing catch in the front yard. As we threw the ball back and forth, I could hear him singing softly to himself. He was practicing the chorus for the 3’s song from the set of skip counting songs we had.

But he wasn’t singing the whole chorus. As we threw the ball back and forth, I could hear him singing, “Three, six, nine, twelve, …” – but then he stopped at twelve as he threw the ball to me.

I threw the ball back to him, and as he kept going through the motions of catching and throwing, he continued singing softly, “Three, six, nine, twelve, …” But he was stuck at twelve.

This happened several more times. Finally, I realized what was going on. He was trying to recall the rest of the 3’s chorus – but he couldn’t. He was stuck on the number that came after twelve.

Then I further realized something very positive was occurring here.

His mind was searching for completion. He was seeking that sense of satisfaction and completeness – that we’ve all experienced – of trying to remember that next line in a song.

He was wrestling – as 6-year-olds do – to figure out the number that comes after 12 when counting by 3.

This is not an automatic thing for a child only in first grade.

This momentary brain-freeze he was having was actually working in his favor.

His brain was searching and seeking – maybe even doing some mental calculating – to try to determine that next number. This sense of incompleteness was driving him, motivating him, urging him to find that next number.

I kept quiet and let him wrestle with this.

After a few more throws, he finally found it: “…, fifteen!” – and then the rest all poured forth – “…fifteen, eighteen, twenty-one, twenty-four, twenty-seven, that’s how many wheels I count.

He had a huge grin on his face.

So consider what was happening here. Like all songs, skip count songs provide the sing-song-y scaffolding that both forms and prompts memory. As with other songs we enjoy, our brains want to recall the whole song – every word, every line, every stanza, the whole chorus.

This dynamic was helping Brandon master the powerful skill of counting in multiples.

What was cool was that he wasn’t singing the 3’s chorus because his father told him to. He was singing the 3’s chorus because he liked it. Because his mind was searching for that sense of completion. While he was outdoors. Playing catch. Having fun.

Way cool.

It was the Monday morning session of one of our SAI classes about ten years ago. A fifth grade girl I’ll call Zosha plopped herself down in her seat in front of me and wrote on a piece of paper, “I hate math. I hate math.”

Hmm, I said to myself – “Well, this should be interesting. We’ll just do our normal, day-one activities and see where things go.”

So we did exactly that. All the students went through the usual hands-on activities with lots of work with color, shape, size, texture, music, and games. In SAI, we do math in ways that make sense. If you were present in our SAI sessions, you’d hear teachers explaining algebra to the students and then asking, “Is that a rule – or does that just make sense?” The kids get it. They see that they’re doing algebra in ways that simply make sense.

So as the morning unfolded, I didn’t pay any special attention to our I-hate-math girl. In fact, I forgot about her written remark altogether. Unfortunately – or perhaps fortunately, as things turned out – I didn’t get a chance to even ask her how the session went for her.

The next morning, I saw Zosha come in to the classroom – with her mom right behind her. The mom marched right up to me and said, “I don’t know what you did yesterday… – but you did exactly what I was hoping would happen: she could hardly wait to get back here this morning.”

My reply? I said, “Yep – that happens several times every summer. But thank you for mentioning it.”

Zosha is the perfect example of our goal in SAI: to use algebra to turn kids on to math.

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