Let's fast forward a lot of years. I've got my B.A. in English and American Studies but I've ended up as a computer programmer on a university campus. (It's a long distracting story. Let's move on.) I thought that maybe I'd get a degree in computer science because this programming stuff was fascinating. And I took. . .wait for it. . .calculus. Yep. Calculus. Now, I did not do fabulously because I was missing some foundational stuff I hadn't bothered to learn or retain, but I passed. Calculus. There was no great change in my thinking about math except I had a much greater appreciation for it; and it didn't hurt that I felt pretty darned good about passing Calculus, something I never thought I'd be able to say.
Let's fast forward some more years and I'm teaching math. Say what? Yes, I'm teaching math. Mind you, I started with Basic Math for the kids who struggled in high school so it was remedial but it was that foundational stuff that's so important: fractions, decimals, basic algebra, etc. I LOVED it. Why? Because I had stopped fearing it and recognized how freakin' cool math is, and I realized how much math I used every day. Eventually I also taught Discrete Math and Finite Math, and I enjoyed most of it. (Statistics still make me a little itchy.)
Let's fast forward a whole lot more years to the present. I'm a consulting edtech instructional coach and, for the past couple of years, I've found myself teaching a lot of elementary level math. This particular day I was working with second graders who were struggling to do the math of subtracting multi-digit numbers. One little girl threw down her pencil and told me she just couldn't do it because she was "bad at math."
I took her face in my hands and looked her in her sweet brown eyes and said,
Sweetie, you can't do this math yet. And you will be able to do this math when you learn the skills to do this math. You've got to learn the skills before you can do the math. And you can do this.She nodded though I know she wasn't convinced. I'm sure she took that deep breath and tried again only because I wouldn't leave. Could she do multi-digit subtraction by the time I left that day? Well, she was little closer and less frustrated, and, perhaps more importantly, she and her friends were talking and trying to figure it out together. As an aside, I should point out part of their problem was understanding place value and the concept of borrowing, or regrouping.
I read the piece. The writer makes some good points, but I didn't care for the conclusion. I'll summarize: just persevere, take risks, and feel safe making mistakes. ". . .try to have fun and give reassurance that perseverance will yield results. Numbers are always simple, clean, and beautiful--and nothing to be afraid of" (emphasis mine).
I remember looking at math homework when I was in high school and being totally perplexed and frustrated. I knew there was no point in going to my mother, the self-avowed non-math person, and while my dad was a financial analyst and worked with numbers all the time, somehow it never occurred to me to ask him for help. I'm sure that was a big loss on my part. Anyway, I just didn't do the homework. No amount of perseverance was going to help if going back to the textbook and looking at the sample problems and re-reading the information in the textbook didn't help me understand what I was being asked to do. It didn't help that the problems were stupid and uninteresting and boring. The numbers were fine; it was the math skills and the math knowledge I lacked.
A group of authors published "The Myth of 'I'm Bad at Math'" (2013) stated this: "For high-school math, inborn talent is much less important than hard work, preparation, and self-confidence." Note they made the distinction that they were talking about high school math because, by that time, students should have the basics. They should understand place value, they should have strategies for doing basic math operations, etc. They should have foundational skills. They also noted that, in their experiences of teaching math, the students who seemed less prepared, apparently those students whose parents had not "drilled them on math from a young age," thought they were bad at math and gave up. What troubles me is the suggestion that inborn talent is required to do math well before high school, that to do well in math one has to be drilled on math from a young age, and students who are less prepared for whatever reasons just don't try; that is, they are lazy or just don't have a growth mindset.
In another article, "There's no such thing as being "good" or "bad" at math" (2013), we're told that "learning math is hard." Apparently that's the reason some people don't do as well at math: it's too hard and they are, therefore, lazy.
In 2016, Tamar Lichter published a blog post titled "You're Not Bad at Math," and this from someone who is clearly a mathematician. I loved some of her points including an observation that some math classes manage to bury "the things that make math compelling."
She notes that real math is not about "drills, repetition, and memorization." I wonder how many math teachers think that.
Persistence, or perseverance, is part of problem-solving, so if the problem or puzzle piques our curiosity, we will be persistent to find the answer.
First we calibrated Dash to launch a ball into one hoop and then we calibrated the other. I said something like, "What if we try to code Dash to launch into one hoop and then turn to launch into the other?" Kids were keen on that. I asked them, "How do we figure out how to do that?"
Ideas came fast and loud, but they realized they didn't really know how to calculate how far to turn Dash unless they did trial and error over and over again. So I asked if we could find a protractor and a piece of string.
We put an X where we wanted Dash to be and recalibrated for each of the hoops. Then I positioned the protractor and we used string to determine the position for the first hoop and more string to calculate the position for the second hoop so we could do some math based on what the protractor told us. We had to think about degrees and arc and trajectory.
Long story shorter: the first couple of tries were close and we were going back to our calculations with the protractor, but then the teacher realized the kids were about to miss lunch so they had to scramble. One of the boys said while getting in line, "I've never done math like that before. It was fun!" The girl who built one of the hoops nodded and said, "I hope we get to finish figuring this out when we get back from lunch."
What I have also found is that math in context makes more sense to any of us. Kids know they have to learn how to do the rote math--completing a worksheet of multi-digit addition and subtraction. I tell them they are learning the skills of calculation when they identify numbers, are comfortable with the place value, and know how to group and borrow or use whatever techniques help them figure out how to solve the problem. But I have seen teachers make even the most mundane math skills practice into a game.
What I have also found is that for too many kids math is only about completing worksheets, doing drills to practice skills and memorizing their times tables. So Ms. Lichter is correct that math--actual math--isn't about "drills, repetition, and memorization."
Ana Soler Causa Efecto video.
Kids need to learn the skills for doing math, absolutely. But they need to see and hear the math. I remember one of my students was a music major and she hated math class. I asked her to pull out some of her sheet music and asked to her to explain some of the notations--notes and measures. I asked her to help me understand the rhythm as she counted out those notes and measures. We talked about the rest of the composition and its instrumentation and that not all of the instruments were doing the same thing at the same time and yet it all worked. And that's when she realized she'd been talking about fractions and other elements of math all the time she'd been talking about music.
When students can see and hear the math, when they understand its context and how the skills they've learned contribute to how they figure out how to tackle a particular problem, they relate differently to math. When they are invited to do more than plug numbers into formulas, perhaps they will be more engaged in math. When they have a better understanding of why they are being asked to know how to solve quadratic equations, well, you might refer to parabolas, but you might also refer to how to helps in the analysis of the sales and cost of a product. There are plenty of real-world examples that will help quadratic equations or any other math make sense. Because that's what us non-mathy types need: we need to understand how and why it makes sense because we need more or other than the beauty of the numbers themselves. We need to see and hear the beauty of math; we need to see its art.