Is there value in learning algebra, geometry and calculus?
Most students would agree that learning how to do arithmetic — how to add and multiply, subtract and even use fractions and percentages — is a useful skill. How else can we keep track of money, budgets and such? But what about higher-level math, like algebra, geometry and calculus? Do you see the value in learning these math topics that are such a core part of middle and high school curriculums? In the guest essay “Math Is the Great Secret,” Alec Wilkinson writes: Do we appreciate math enough?
As a boy in the first weeks of algebra class, I felt confused and then I went sort of numb. Adolescents order the world from fragments of information. In its way, adolescence is a kind of algebra. The unknowns can be determined but doing so requires a special aptitude, not to mention a comfort with having things withheld. Straightforward, logical thinking is required, and a willingness to follow rules, which aren’t evenly distributed adolescent capabilities.
When I thought about mathematics at all as a boy it was to speculate about why I was being made to learn it, since it seemed plainly obvious that there was no need for it in adult life. Balancing a checkbook or drawing up a budget was the answer we were given for how math would prove necessary later, but you don’t need algebra or geometry or calculus to do either of those things. But if I had understood how deeply mathematics is embedded in the world, how it figures in every gesture we make, whether crossing a crowded street or catching a ball, how it figures in painting and perspective and in architecture and in the natural world and so on, then perhaps I might have seen it the way the ancients had seen it, as a fundamental part of the world’s design, perhaps even the design itself. If I had felt that the world was connected in its parts, I might have been provoked to a kind of wonder and enthusiasm. I might have wanted to learn. Five years ago, when I was 65, I decided to see if I could learn adolescent mathematics — algebra, geometry and calculus — because I had done poorly at algebra and geometry and I hadn’t taken calculus at all. I didn’t do well at it the second time, either, but I have become a kind of math evangelist.
Mathematics, I now see, is important because it expands the world. It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention. To be made to consider a problem carefully discourages scattershot and slovenly thinking and encourages systematic thought, an advantage, so far as I can tell, in all endeavors.
Students, read the entire article, then tell us:
Mr. Wilkinson writes, “When I thought about mathematics at all as a boy it was to speculate about why I was being made to learn it, since it seemed plainly obvious that there was no need for it in adult life.” Does his experience resonate with your own? Do you see the value in learning math, beyond balancing a checkbook or drawing up a budget?
At age 65, Mr. Wilkinson decided to see if he could learn adolescent mathematics — algebra, geometry and calculus. He said he struggled with it, but that, nonetheless, he still became “a kind of math evangelist.” Can you imagine wanting to study math later in life, just for the sake of learning (and not because you have to)? Why?
He discusses many benefits of learning math, beyond the concepts themselves. Things like: math teaches reverence; it requires that a person pay close attention; and it discourages scattershot and slovenly thinking and encourages systematic thought. Do any of these benefits, or others that he doesn’t mention, come to mind when you think of the value of learning math? Mr. Wilkinson explains how deeply mathematics is embedded in the world and discusses the mysteries of math, including “whether mathematics is created by human beings or exists independently of us in a territory adjacent to the actual world.” He writes that as a boy, he couldn’t see any of this. Now, however, math fascinates him — even if he still finds it difficult to learn. Are you fascinated by math? In what ways? At the end of his essay, the author offers one of his favorite definitions of math: “Mathematics is a story that has been being written for thousands of years, is always being added to and might never be finished.” Are you familiar with that perspective on math? Do you find it appealing? Why, or why not?
Does Mr. Wilkinson’s essay get you more excited about learning math? Why or why not?
As a boy in the first weeks of algebra class, I felt confused and then I went sort of numb. Adolescents order the world from fragments of information. In its way, adolescence is a kind of algebra. The unknowns can be determined but doing so requires a special aptitude, not to mention a comfort with having things withheld. Straightforward, logical thinking is required, and a willingness to follow rules, which aren’t evenly distributed adolescent capabilities.
When I thought about mathematics at all as a boy it was to speculate about why I was being made to learn it, since it seemed plainly obvious that there was no need for it in adult life. Balancing a checkbook or drawing up a budget was the answer we were given for how math would prove necessary later, but you don’t need algebra or geometry or calculus to do either of those things. But if I had understood how deeply mathematics is embedded in the world, how it figures in every gesture we make, whether crossing a crowded street or catching a ball, how it figures in painting and perspective and in architecture and in the natural world and so on, then perhaps I might have seen it the way the ancients had seen it, as a fundamental part of the world’s design, perhaps even the design itself. If I had felt that the world was connected in its parts, I might have been provoked to a kind of wonder and enthusiasm. I might have wanted to learn. Five years ago, when I was 65, I decided to see if I could learn adolescent mathematics — algebra, geometry and calculus — because I had done poorly at algebra and geometry and I hadn’t taken calculus at all. I didn’t do well at it the second time, either, but I have become a kind of math evangelist.
Mathematics, I now see, is important because it expands the world. It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention. To be made to consider a problem carefully discourages scattershot and slovenly thinking and encourages systematic thought, an advantage, so far as I can tell, in all endeavors.
Students, read the entire article, then tell us:
Mr. Wilkinson writes, “When I thought about mathematics at all as a boy it was to speculate about why I was being made to learn it, since it seemed plainly obvious that there was no need for it in adult life.” Does his experience resonate with your own? Do you see the value in learning math, beyond balancing a checkbook or drawing up a budget?
At age 65, Mr. Wilkinson decided to see if he could learn adolescent mathematics — algebra, geometry and calculus. He said he struggled with it, but that, nonetheless, he still became “a kind of math evangelist.” Can you imagine wanting to study math later in life, just for the sake of learning (and not because you have to)? Why?
He discusses many benefits of learning math, beyond the concepts themselves. Things like: math teaches reverence; it requires that a person pay close attention; and it discourages scattershot and slovenly thinking and encourages systematic thought. Do any of these benefits, or others that he doesn’t mention, come to mind when you think of the value of learning math? Mr. Wilkinson explains how deeply mathematics is embedded in the world and discusses the mysteries of math, including “whether mathematics is created by human beings or exists independently of us in a territory adjacent to the actual world.” He writes that as a boy, he couldn’t see any of this. Now, however, math fascinates him — even if he still finds it difficult to learn. Are you fascinated by math? In what ways? At the end of his essay, the author offers one of his favorite definitions of math: “Mathematics is a story that has been being written for thousands of years, is always being added to and might never be finished.” Are you familiar with that perspective on math? Do you find it appealing? Why, or why not?
Does Mr. Wilkinson’s essay get you more excited about learning math? Why or why not?
