Week 5: What do YOU think should be the kind of math competence we require students to learn? And, is it important for students to see the relevance of math to jobs and everyday life?
At COMAP (Consortium for Mathematics and Its Applications) we work with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world. In our 2009 paper, Math to Work we argued for offering curricular alternatives in math that would emphasize how discrete ideas taken from high school math courses apply to a variety of careers and your everyday lives. These alternatives would help students like you make connections between what they are learning and how you would use those skills in future jobs.
COMAP further argued that too many people have accepted a false argument that continuous mathematics is essential for all students. Continuous mathematics are highly technical subjects that teach a good deal of symbol manipulation (like using “x” and “y” in Algebra II) and typically lead up to calculus and analysis. This kind of math learning is necessary for future engineers and epidemiologists, but for the large majority of students it won’t be needed. The false argument goes like this: All students need to learn mathematics (so far so good). We shouldn’t discriminate against any group of students (still hard to argue). All students must be given the opportunity to reach some basic level of mathematical competence. That basic level of mathematical competence can be defined by the content of Algebra II (as exhibited on a particular test). Criminal!
In the name of giving everyone an equal chance to succeed, we merely give them an equal chance to fail. The simple truth is that there is an enormous choice of mathematical topics we could (and should) be teaching. If you read the short paper, you’ll learn some examples of good, well-paying jobs where Algebra II is simply not required but other math concepts are used to some extent. In other words, we could say, as a nation, that the “basic level of math competence” is not about being well-along in the path toward calculus and more about having math skills for work and life. This would not mean that anyone who wants to pursue continuous mathematics necessary for their own future careers would be prevented from doing so (but even exposing such students to how what they’re learning will apply to their careers and lives would be a good idea.)
Failing to see the point of math--partiucalrly what Sol has termed continuous math-- is a longtime hobby of mine, so I've asked every math teacher I've had from seventh grade on to explain its relevance and justify its continued existence in secondary school curricula. They all open with a vague insistence that "we use math all the time, we just don't realize it." When I pressed them further, (Isn't it a problem that I don't realize the practical applications of what I'm learning? What are they, anyway?) one forced me to watch the CBS procedural Numb3rs (their spelling, not mine), one admitted that I would only need enough algebra to calculate interest and enough geometry to grasp basic measurements, and everything else wouldn't come up again unless I pursued a career in mathematics/engineering/hard sciences etc. All the others pointed out that the continuous math sequence was a college entrance requirement.
I find that last one bizarre. My teachers were right: most state universities explicitly require at least three years of math. (Colorado universities require four.) More often than not, they also mandate that those three years consist of Algebra I, Geometry, and Algebra II and specifically indicate that other math courses, such as finances and statistics, will not count towards the three year total. This seems backwards to me. Wouldn't those last two be more applicable to and useful in many more careers and fields of study, to say nothing of day-to-day life?
It appears to me that our obsession with teaching the calculus sequence has already hurt our nation. I realize, of course, that our current economic climate is the result of a perfect storm of any number of factors, but I would venture to say that at least one of those was consumers who didn't quite grasp the economic realities of exotic mortgages and predatory lending practices. Would so many have agreed to adjustable-rate mortgages and NINA loans had they received an education that empowered them to detect a too-good-to-be-true financial product?
To that end, I would be inclined to believe that proficieny standards should be geared less towards AP calculus and more towards financial independence. Can you do basic arithmetic? Can you balance a checkbook? Calculate interest? Keep a budget? These are the sorts of things that keep a person afloat in Grown-Up Land, not y=mx+b. Most of my teachers in subjects other than math , by their own admission, would have trouble breaking 400 on the math section of the SAT. But despite what some of my past math teachers would have me believe, they are all still happy, succesful people who can, to the best of my knowledge, put their pants on without bruising themselves.
As for the question of motivation, what I've just said more or less illustrates my interest in continuous math and my opinion of its worth, and I'd wager that my attitude is widespread. And it isn't just young people who are skeptical about the very idea of staying in school anymore. If I had a dollar for every op-ed I read that declared college degrees worthless, bemoaned the ever-shrinking job market, and urged would-be college students into vocational schools instead (to receive training in a job sector said to be "growing"), I'd be tempted to drop out of high school myself, in order to live full time on the island (Corsica) I bought with the money.
And only now do I notice my glaring typos. What a "succesful" demonstration of my "proficieny" in spelling. Sorry everyone..."partiucalrly" indeed.
I have certainly been told continous mathematics is a good idea for anyone possibly pursuing a career in an engineering, science, etc. field. However, for those not interested in a future with mathematics, I don't think it's very stressed. Honestly, I think Algebra II was an important class for me, and while every student will not directly benefit in their career from this class, I felt more confident in my algebra skills and thought it was a good basic class to have. As for students' motivation to learn math, I think if their not interested, they're not interested. Students understand why we take classes, and even if they realize it will benefit them later, I think its hard to get excited about math when that's not your passion. While clear connections between work/school might motivate many students to continue with their education, I think a lot of the motivation for a higher education comes from a love of learning. And while a guidance and knowledge of jobs that are possible with/without a college education would be helpful, I'm not sure how effective it would be in impacting dropout rates. For mathematical competence, I think Algebra II is sufficient right now. An integrated approach might be more effective though, combining Algebra I/Geometry/Algebra II. As I haven't taken anything beyond Algebra II yet, I do not yet see the advantages of taking a Calculus class.
I also agree with Miriam, having pre-calculus as the requirement could be beneficial because it gives students the option to pursue calculus in college, if during their junior/senior years in high school and freshmen year in college, they choose to go into a different career path. Why spend money taking pre calculus and more advanced classes when you can get it for free in high school?
In general, I don't like math much. But I feel like the thing I like the least about math (especially algebra) is that I struggle to find a real-world connection to the subject. I don't see how taking classes like Algebra I and II really apply to a wide variety of future professions. No one has really mentioned to me the need to take Algebra II to be successful later in life, but I have always somewhat assumed that I would have to take these classes no matter what, and not thought about the reasons why. Right now I am taking, Geometry, and I find I can enjoy it much more because I can find many more connections between the class and the real world. It's not that I don't consider algebra important, it's just that I think it needs to be taught in a way that students can connect with real-world issues. For me, there is definately a connection between my motivation to learn math and my understanding of how it connects to the real world. In Algebra I, I found that I didn't care about the work, didn't treat it with reverance, mostly because I couldn't see its importance. I also found it much harder to understand for this reason. In Geometry, I feel like I try much harder to do well because I can see more connections to how it might help me in the future.
i have almost been told by all my teachers that taking or learning mathematics is good for you because you use it everywhere and you will keep on using it in the future. They say its very imortant to learn and use mathematics. My mom says math is very important and my math teacher of course, and my science teacher because even though physics isnt math i still do problems in physics with math in it. I think every student should take Algebra II beacuse you never know that you are going to use it in your job. I dont think there is a relationship when students are motivated to learn math because if thats something they dont like they wont really care. But later on they will realize that math is important for all types of jobs and then they might be motivated.Yes giving more guidance to students about well-pay jobs and weather they have to attend college or not, will help their self awareness to choose their destiny. (hopefully not dropping out of school). I think it should be pre-caculus because their they have the choice to further study math but still stop while functioning in society.
Continuous mathematics at my public high school, Harry D. Jacobs, is recommended for most students however, some choose not to do so. Entering high school, all freshmen are required to take an Algebra I course. Depending on what track you take (general, advanced, or honors) determines the course length throughout the year. For example, a general class is all four terms and an honors class is only first and second term. As the year progresses, an honors student moves on to honors geometry for term three and four while a general student is still behind in algebra I. A general student would begin with geometry the following year as an honors student would advance to Algebra II. As you can see, a general student is hindered from the start and by their senior year may only reach Trigonometry, if they choose to do so. Many general students do not continue past Algebra II as it is the minimum math requirement to graduate at Jacobs. I am currently in the honors track and my honors friends agree continuous mathematics is beneficial to our future. The higher the math level course, the more it is likely for one to test out of math courses in college. My general class-level friends do not have the desire to continue math throughout their high school career and typically stop at algebra II. I think that every student should take algebra II and BEYOND in order to be successful in a well-paying job. The standards are being raised for this generation and students should take the courses offered to them, despite the challenge, in order to be prepared for their future.
I believe there is a correlation between a student’s desire to learn math and their knowledge of how it will pertain to them in the future. If students aren’t provided with the motivation to learn in high school, it’s most likely they will not pursue higher level careers that require beyond algebra II math skills. I see how this may lead to the increase of drop-out rates. If motivation is not instilled in high school, it is likely this will carry on to the professional world.
I believe there should not be a basic level of math for students, I think math should be REQUIRED for all students, all four years of high school. This way students have the knowledge from the beginning of high school on the importance of math throughout their educational experience.
1. Math to me is the subject I find is most hotly debated on importance. I have heard equally throughout my life that math is one of the most important subjects and one of the least important. While I feel one would probably expect to mostly hear students say math is not important, I find I hear a fair amount of disregard for math from adults (even educators) as well as praise for math by a lot of students. I personally don't believe one needs to have taken courses in any particular subject to be succesful since often times success is not determine by skill but by luck, ( such as being born into an already "succesful" family).
2. I believe that it's the way math is taught in school that sways the way students feel about it I also feel there is this idea in society that being good at math makes one intelligent beyond all else and somehow more capable than anyone else. I' not sure I'm expressing it right here and if I need to explain again please ask.
3. Yes I do believe that high school students would benefit from understanding there is a wide range of career options, as for attending college, I am honestly unsure. I feel students dropout for all kinds of reasons, but mostly probably due to stress of college work and the feeling that pay-off my be minimal in comparison, at least this is a complaint I hear from fiends I have in college.
4.I feel one should know at least basic arithmetic and basic algebra.
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