“What are you drawing?” I asked the nine-year-old boy.
“I’m making a scale,” he replied
Puzzled, I then asked him, “Why are you making a scale?”
“I want to keep track of what I think about doing math with you.”
Abrupt as it was, that was my very first interaction with Matthew. His father had greeted me on the front step of their home when I first met the family. Meanwhile, Matthew was hiding, peeking at us from behind the front door and running around inside.
“He has a hard time with math,” his dad told me with evident sadness in his voice. He said that Matthew, a highly energetic boy, had a really tough time focusing on math.
I sat down with Matthew and, as I thought about everything his father had said, it occurred to me that the boy’s scale was actually a good idea – and from my standpoint, an excellent teaching tool. So I decided to draw a scale as well.
Matthew saw me doing this and asked, “What are you doing?”
“I want to record how much I like tutoring you,” I answered calmly. Suddenly he looked surprised. I started at a 5. He started at a 4. I was not intimidated. I actually felt hopeful (maybe that’s just my nature).
Before the family invited me to help, Matthew’s family had tried numerous programs and schools. They had little success. When he turned 9, he became resistant to math instruction altogether. The tutor that they hired before me had quit in frustration because of Matthew’s frequent meltdowns. write my essay
After our scales were completed, I asked him what he thought about math. “I can do some math,” he said quietly. “But a lot of it is confusing.”
“Can you show me some problems you can do?”
“I can do 2 plus 2 and some others. I like those.” He wrote out his doubles – from 1 + 1 = 2, to 6 + 6 = 12. “That’s all I know,” he sighed. “I know some other math but right now I can’t remember it.”
When he was finished writing out the doubles that he knew, I wrote out 3 + 4. “Can you do this problem?” I asked.
“I’m really not sure, but I’ll try.” He wrote 6 as his answer. “Is it right?” he asked.
“I don’t know…we’ll have to figure it out for sure,” I said. He looked at me strangely, and I began to draw some dots next to the numbers. “Can you count these dots?”
He replied, “Counting is one thing I can do – I can count to a billion! But I never tried it because it would probably take a couple of days!” He laughed, and so did I. This time, he wrote 7 as his answer.
Then he got out his scale – and drew a line to the number 9. I immediately responded by indicating a 7 on my scale, and I could tell that the wheels were churning in his mind. We were just getting started. We had a lot of work to do.
Matthew’s problem was that he didn’t know what numbers meant, and this frustrated him. I quickly learned that he was a very smart kid and fascinated with building things. To him, a 2 was just a symbol. Initially, he had no idea that it represented an assortment of objects that could be seen in almost everything he had built.
But as we visually drew math together, his interest began to grow. In short, I showed Matthew the power of counting numbers. I allowed him to visualize how basic – and absolutely essential – this skill is to mathematicians. And in doing so, I started to help him draw a “mind map” that he could rely on whenever he became lost in a jungle of abstract symbols.
I felt very confident is using this approach. So do many other educators. Arthur J. Baroody, professor of math at the University of Illinois, explains it this way:
“Counting puts abstract numbers and basic arithmetic within the reach of the child.”
Matthew’s scale topped 10 on the first day. Since then, over a three-month period, we’ve spent many hours doing addition, subtraction, and multi-digit multiplication. His age notwithstanding, I can honestly say that the conversations we have about math are deep and meaningful. Best of all, it’s evident to me that he looks forward to our sessions.
The simple concept of counting to solve problems has changed the way that Matthew views math. And to think that he was so very close to giving up on math completely – and on his ability to handle the subject on even the most basic level.
I can only wonder how many more children like Matthew are out there in today’s schools – kids who are disheartened, defeated, and convinced they’re simply not smart enough to understand anything that has to do with numbers. This is very sad to me, but it’s not as if we can’t help them. My experience informs me that we can come alongside these children – and in doing so change the way they view their own potential.
That’s why I think that this is about more than just numbers.