I have a friend who is an architect. It's a good career for him. He is skillful at what he does, he enjoys the work, and he can't see himself in another field. His degrees are all from Ivy League institutions and in almost every way, he's the sort of person that gets held up as a role model for students, especially students who don't like math and need a reason to study the subject.
The irony is that he doesn't particularly like math, doesn't consider himself to be good at the subject, and almost didn't follow through on his dream of becoming an architect because he was alarmed by the frequent declarations of math teachers that architecture is a profession that uses a lot of math.
It turns out that architects do use math regularly, but they don't use very complicated or advanced math in their day-to-day careers. Architects need to be fully fluent in ratios and proportions, comfortable with basic geometry, and have strong spatial skills. They don't routinely use complicated algebra, trigonometry, or calculus. True, those branches of math are used to build major buildings and bridges- but it is the engineers, not the architects who generally do the number crunching.
Similarly, I know a pediatric nurse practitioner who considers her career a calling and is, by any measure, good at her job. She's not afraid of math, but she doesn't exactly like it either. Early in her training she assumed that she'd be using quite a bit of math in her job because people had always told her that math was important for medical professionals. Now, she does use math- and it's incredibly important that she get the math right every time- but the math itself is very simple and repetitive. In essence, she uses proportions to calculate medicine dosage, and that's about it.
I've read many books on personal finance, and a common thread that runs through many of the best ones are vigorous reassurances that it is possible to make good financial choices and even invest intelligently for retirement without doing math. It would appear that many people avoid learning basic skills to take care of their personal finances at least partially because they are afraid that personal finances require too much math for them.
Architecture, medicine, personal finance... all of these are held up as practical fields that require lots of math. When teachers and parents do this, their intentions are pure. After all, what could be better than motivating students to study by connecting the subject matter with the real world? Unfortunately, we often do students a disservice by over-emphasizing the math required for certain endeavors.
Who actually uses advanced math in their everyday lives? Well, students do. This might seem to be obvious, but it is worth pointing out that doing well on the SAT or ACT requires a fair amount of algebra and geometry. (These subjects aren't really advanced math, but they are advanced compared the math that many adults use.) These tests give high school math a certain amount of practical importance, even for people who plan on majoring in liberal arts and entering a mathematics-free profession. Engineers, many kinds of scientist (both pure and applied), computer programmers, and actuaries are a few examples of people that actually do use a great deal of math. There are plenty of other math-intensive careers, but the truth is, most people who don't want to do trigonometry, calculus, or statistics as adults will never be held back by that preference.
So what should teachers and parents tell students who don't like math and want to know why they are being forced to learn it? Well, that depends on the level of math in question.
Elementary and middle school math are in common, everyday use. While there are successful adults who are not comfortable with math through ratios, proportions, and percents these people have limited options. It's analogous to the way that there are successful adults who don't read or write well- while these people exist, they operate with a handicap. Elementary and middle school math has such broad application that it really is fair to tell kids that they will actually use it later in life.
It gets more complicated with high school math. High school math is used by many fewer adults than elementary and middle school math is. From a purely utilitarian point of view, the goal of gaining admission to college is a good reason to study high school algebra. College admission is sometimes (but not always) a good reason to study high school geometry, trigonometry, algebra II, pre-calculus, and calculus. When a student is pretty sure that he or she wants to go into a non-mathematical field, and he or she has enough academic achievements to be appealing to colleges even without advanced math, what (if any) justification is there for pushing these classes on an unwilling teenager?
There is an argument to be made that studying math provides good mental exercise. The analytical, logical skills exercised in math classes may help the brain develop. In essence, learning math may make you smarter. However logical this claim may sound, the actual proof for it is somewhat lacking. (To be fair, it is a devilishly difficult area to research.) There is also an argument to be made that studying challenging subjects that aren't especially enjoyable is important because it helps build discipline and mental toughness in a student. I find this argument to be weak- it seems to me that there are plenty of ways to build discipline that will also result in useful skills or other tangible benefits to the individual.
My proposal is that very practical math, particularly accounting, should be studied more frequently in high schools. Elementary statistics, which is frequently absent from curriculums, should be added because this topic is important for understanding a great many topics. Trigonometry, algebra II, pre-calculus, and calculus should be relegated to elective status. At the same time, analytical skills should be exercised regularly not only in science and math class, but also in history.
From a personal perspective, this change in curriculum would be problematic. As a math tutor, I rely on students being forced into classes that aren't really suitable for them for a significant portion of my living. However, I still think it would be worthwhile. After all, there are no real winners when we force too much math on students and in the process end up with people who are too math-phobic to effectively use the relatively elementary math that they actually do need.
The irony is that he doesn't particularly like math, doesn't consider himself to be good at the subject, and almost didn't follow through on his dream of becoming an architect because he was alarmed by the frequent declarations of math teachers that architecture is a profession that uses a lot of math.
It turns out that architects do use math regularly, but they don't use very complicated or advanced math in their day-to-day careers. Architects need to be fully fluent in ratios and proportions, comfortable with basic geometry, and have strong spatial skills. They don't routinely use complicated algebra, trigonometry, or calculus. True, those branches of math are used to build major buildings and bridges- but it is the engineers, not the architects who generally do the number crunching.
Similarly, I know a pediatric nurse practitioner who considers her career a calling and is, by any measure, good at her job. She's not afraid of math, but she doesn't exactly like it either. Early in her training she assumed that she'd be using quite a bit of math in her job because people had always told her that math was important for medical professionals. Now, she does use math- and it's incredibly important that she get the math right every time- but the math itself is very simple and repetitive. In essence, she uses proportions to calculate medicine dosage, and that's about it.
I've read many books on personal finance, and a common thread that runs through many of the best ones are vigorous reassurances that it is possible to make good financial choices and even invest intelligently for retirement without doing math. It would appear that many people avoid learning basic skills to take care of their personal finances at least partially because they are afraid that personal finances require too much math for them.
Architecture, medicine, personal finance... all of these are held up as practical fields that require lots of math. When teachers and parents do this, their intentions are pure. After all, what could be better than motivating students to study by connecting the subject matter with the real world? Unfortunately, we often do students a disservice by over-emphasizing the math required for certain endeavors.
Who actually uses advanced math in their everyday lives? Well, students do. This might seem to be obvious, but it is worth pointing out that doing well on the SAT or ACT requires a fair amount of algebra and geometry. (These subjects aren't really advanced math, but they are advanced compared the math that many adults use.) These tests give high school math a certain amount of practical importance, even for people who plan on majoring in liberal arts and entering a mathematics-free profession. Engineers, many kinds of scientist (both pure and applied), computer programmers, and actuaries are a few examples of people that actually do use a great deal of math. There are plenty of other math-intensive careers, but the truth is, most people who don't want to do trigonometry, calculus, or statistics as adults will never be held back by that preference.
So what should teachers and parents tell students who don't like math and want to know why they are being forced to learn it? Well, that depends on the level of math in question.
Elementary and middle school math are in common, everyday use. While there are successful adults who are not comfortable with math through ratios, proportions, and percents these people have limited options. It's analogous to the way that there are successful adults who don't read or write well- while these people exist, they operate with a handicap. Elementary and middle school math has such broad application that it really is fair to tell kids that they will actually use it later in life.
It gets more complicated with high school math. High school math is used by many fewer adults than elementary and middle school math is. From a purely utilitarian point of view, the goal of gaining admission to college is a good reason to study high school algebra. College admission is sometimes (but not always) a good reason to study high school geometry, trigonometry, algebra II, pre-calculus, and calculus. When a student is pretty sure that he or she wants to go into a non-mathematical field, and he or she has enough academic achievements to be appealing to colleges even without advanced math, what (if any) justification is there for pushing these classes on an unwilling teenager?
There is an argument to be made that studying math provides good mental exercise. The analytical, logical skills exercised in math classes may help the brain develop. In essence, learning math may make you smarter. However logical this claim may sound, the actual proof for it is somewhat lacking. (To be fair, it is a devilishly difficult area to research.) There is also an argument to be made that studying challenging subjects that aren't especially enjoyable is important because it helps build discipline and mental toughness in a student. I find this argument to be weak- it seems to me that there are plenty of ways to build discipline that will also result in useful skills or other tangible benefits to the individual.
My proposal is that very practical math, particularly accounting, should be studied more frequently in high schools. Elementary statistics, which is frequently absent from curriculums, should be added because this topic is important for understanding a great many topics. Trigonometry, algebra II, pre-calculus, and calculus should be relegated to elective status. At the same time, analytical skills should be exercised regularly not only in science and math class, but also in history.
From a personal perspective, this change in curriculum would be problematic. As a math tutor, I rely on students being forced into classes that aren't really suitable for them for a significant portion of my living. However, I still think it would be worthwhile. After all, there are no real winners when we force too much math on students and in the process end up with people who are too math-phobic to effectively use the relatively elementary math that they actually do need.
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