High School Math

[Indefinite Integral]

So, you've probably all figured out by now that I teach high school math. There are so many days when I come home frustrated to no end because so many of my students barely put in the bare minimum if that. Just today I was grading tests and some couldn't even do the simple "put it in your calculator" trig functions (e.g. "what is the sin(56)? or if sin(A)=.725, what does A equal?). Why is it that so many students think they can't do math? Where is that disconnect that they don't even try? Is is conditioning? Lack of caring? What was your experience with math in high school? I have a hard time understanding with these kids, since I took all of the courses I am teaching much earlier in my education (middle school). What do you think of the current state of math in public schools?

Here's another link that semi prompted this rant: http://www.ksl.com/?nid=148&sid=14936566&s_cid=rss-148

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p.s. sorry if this seems somewhat disjointed, I have a lot of ideas and frustrations I want to discuss.

[Dragon Lady]

Well, everyone but nerds say math is hard, thus math must be hard.

[Craig Jessop]

As one who is very happy about the fact that he never has to take a math class again, I think I can answer.

I hate math. Hate it. It makes no sense, its logic is beyond me, and even those "enter them into the calculator" questions sometimes seem hard. Granted, I probably could have figured those ones out, even though it's been years since I've even thought about solving something more complex than a basic algebraic equation.

My mind just doesn't work that way. Math isn't real; 2+2=4 only because the paper says so; irrational numbers don't exist; an integral is just moving around of a number. Math isn't real until physics or chemistry, but by then it's too late because those of us who don't delight in formulas and only one answer possible have given up on it. Math has no practical application to the way I live my life, and when teachers give word problems they always seem so contrived and made up. Seriously, who cares where the trains meet? I'm not on those trains -- when they meet, let me know and I can analyze why they got together and what significance that holds, but I'm not in the business of pinpointing the exact time of a fictional train.

[TheAnswerIs42]

I think one problem is that math is a very "teacher heavy" subject. If you had a bad English teacher in 6th grade, that would have little to no effect on your life. As long as you got a couple of good ones in there somewhere, it would be okay. If you got a bad History teacher, you might not know Utah history as well as you know American history (or wherever the good and bad teachers landed), but wouldn't kill anything. But a bad math teacher? I have tutored SO many kids who can point back to the day they decided they hated math - when they had a teacher they didn't understand, who told them their question was stupid, and who didn't have any desire to help them if they asked for help.

The problem is that math builds on previous knowledge. If kids have a bad year, then the next year they have a large disadvantage. So they carry over the "I hate math" attitude, and instead of trying harder just quit. When I taught a high school Algebra 1 class (you had to flunk a few times to make into there), I figured my entire goal was to make them feel like they COULD do it. If they felt like something was attainable, they would go for it. But when they continued to give up before they even walked in the door, it amazed me what they could get wrong on my tests. I think some of them just didn't want to face the hurt again - they had failed before, and it was easier to say you didn't even try anymore than to admit you tried and still failed.

At least, that is one of my observations as a math teacher/tutor. The other one is what Craig hinted at. Some people like math. Some people just don't. And some people are just plain not born with the ability to get "number sense." I have tutored some kids who were honestly doing their best and trying really hard, but it just wasn't the way their brain worked. But hey, that's everything in life. I'm absolutely horrible at foreign languages, singing, and anything that resembles programming. On the other hand, I love math, and could spend all day at my sewing machine if given the chance. Thank heavens for diversity.

[Whistler]

Math as it was taught when I went to high school was either boring or puzzling. Students are taught how to repeat a set of steps in different problems, but I feel like there isn't enough emphasis on the actual problem solving. I think it wasn't until I took the GRE that I found a special glee in finding an elegant solution to a hairy math problem... and I think if students can have that feeling more often they will probably like math more.

[Democritus]

I blame the disconnect between math and application. As Mr. Wilberg suggested, math isn't very interesting until you find out what you can use it for.

I'll be honest, math in high school was really just another series of hoops for me to jump through until I hit calculus and physics simultaneously. Then I was very glad that I did jump those hoops in algebra, geometry, and pre-cal. Even today, I personally hate math classes. I took one just last semester. The only reason I got through it was because I knew exactly where I could apply the concepts that were being taught.

Whether your thing is statistics, accounting, or engineering, everyone needs math to some extent. If more emphasis was placed on direct application of mathematical concepts, i.e., those dreaded WORD PROBLEMS, I think students would be a little more engaged. Math needs to be able to give students a glimpse into what they can do with it. I would also say that it would be great to get science teachers involved in using more quantitative thinking in their curriculum.

[Dragon Lady]

I'm gonna agree with the teacher bit. I only had two math teachers through all of middle and high school. (Small town, remember?) The one was my teacher from 7-10th grade. The other was for 11-12th grade. The first, Mrs. P, was amazing. She cared about us. She was firm, but kind. She did a bunch of extracurricular activities that I joined. She knew me and was an excellent teacher. The second, Mr. C taught me Pre-Cal and Calculus. Pre-Cal was pretty good. He was funny. He cared. He taught well. But my senior year was his last year teaching. He stopped caring. He coached the golf team and spent more time prepping for his matches than teaching us. It wasn't uncommon for him to come to class, give us our assignment, then leave. We taught ourselves out of the textbook (which we all know is a ridiculous way to learn math) then did the assignment. Then we checked the answers to the odd questions in the back, and found the answer manual for the even questions in Mr. C's desk. Both sets of answers walked through the problems, so the answers helped us learn as much as the book. Though, the problem was sometimes we concluded rules that were just flat out wrong, but worked 96% of the time. On tests he made us write out our work and he often came back completely befuddled when the entire class did a problem the exact same way, which was completely wrong, and got the right answer. And he knew we weren't cheating cuz he'd (usually) stay in the class room for the tests. I had to take Calculus twice in college before I finally got the hang of it.

[Marduk]

I don't know a lot about math. I DO, however, know a great deal about teaching.

In this limited scope (i.e., in a class of I'm assuming 30+ students with an hour, give or take 20 minutes, every other day) there's a lot of really good teaching advice that just frankly can't apply here. But what you CAN do is ensure that you focus on approaching problems in different ways. You ask why they can't (or really, won't) do something as simple as putting an equation into a calculator; I am suggesting precisely BECAUSE there is exactly one way to do it. Those things are necessary, sure, and in math it happens more often than in other subjects, as Craig pointed out, but focus on those areas where different methods can be applied. Do group work, and organize groups so that people who think differently work together, and can see that different ways apply. Have students do problems on the board, especially ones that approach things differently than you do. Utilize humor in your class; studies show that we learn much better from people we like, regardless of the subject. As much as possible show your students that you are personally invested in their success (I'm sure you are very invested, but how obvious is that to your students?) Try to encourage participation with open-ended questions, and try to avoid questions that have specific answers (i.e., no 5+2 is ____ questions.) Since math is foundational, as 42 pointed out, you'll have much of the class frustrated and struggling to keep up, while the rest are bored because you are going too slow. I myself don't mind math; it is easy to understand since all the rules are internally consistent, but it never attracted me because most teachers could not do the things I suggest.

And at the end of the day, realize that you are only there to facilitate their learning, and you are not in charge of it. No matter what you do, there will be some who simply do not want to learn. That happens in every subject everywhere, and you can't beat yourself up about it.

[Defy V]

I might have a slightly different perspective because I absolutely love math. I taught myself Algebra 2 over the summer one year to fit in more math classes in high school. I learned Calc BC from an AP cram book (and then TAed Math 113 in the math lab, so I actually did learn the stuff pretty well). Right now I'm in 3 upper level math classes and 2 of them I am absolutely loving (with the remaining one being one I put off til the end of my undergrad because I dreaded it [and with good reason]).

So I can't answer why students hate math. But I can answer why someone might love math. To me math is like a beautiful piece of music or a well written novel. Every time I go back to the unit circle something new and exciting pops out. Every time I see the time on the microwave I try to factor the numbers and see interesting patterns.

Ironically, I've never been a fan of word problems. I really don't think they're the answer to making kids love math. I'm with Craig -- I don't care when the trains meet. But throw a Galois group at me and I'll eagerly poke and prod it to see what comes out. When it comes down to it, objects that mathematicians create are like characters in a novel. Some are more boring than others, at least on the surface (think trigonometric functions, especially on the calculator). Some you want to avoid at all costs (think "what is the domain and range of this function?") But some are just fascinating, and it is worth wading through all those painful years to get there.

But how to get there? I think that teachers should try and make numbers interesting from the getgo. Go ahead and introduce Fibonacci numbers in elementary school and explain that it's a model for how trees grow. They don't need to understand the calculus and limit theory and all that junk. Some people suggest teaching math by having kids play more strategy games, or even card games. I wouldn't go for that but a lot of kids would. It's not like you personally can change the curriculum but maybe you could incorporate things like that a bit more into math classes, so kids (even in high school) would actually look forward to it.

Okay, I've rambled long enough and racked up a bazillion nerd points, so I'll stop. Thanks for reading my somewhat related soapbox.

[Dead Cat]

I wasn't like it in high school, but almost all of the students (especially me) in my math class like messing with the professor, but that probably has to do with the fact that we're all engineering majors in there. Today (or yesterday by now) we got an irrational number of Smart Alec points from him.

[Katya]

Why is it that so many students think they can't do math? Where is that disconnect that they don't even try?

I think we have a mindset in the American school system that math is something you either "get" or you don't. And if you don't, there's no use trying, because you can't force your brain to be a math brain. To add to the problem, I think a lot of students who feel like they don't get math have had math teachers who did "get it" and don't know how to explain it to a student who's struggling.

What was your experience with math in high school?

Math was my easy A until I hit calculus and then I really struggled because the mindset and approach were so different. When I had to take calculus again in college (because I'd decided to minor in physics), I asked around for recommendations for a really good calculus teacher because I'd had such a hard time with the subject, previously.

[thebigcheese]

I agree with the multitude of opinions expressed above. Most people give up on math at an early age. Also, since math builds upon itself, it becomes increasingly more difficult to learn the advanced levels if you haven't mastered the easier ones.

Also, a word about math being interesting and applicable. I was one who always excelled at math but never particularly enjoyed it. To me, math class was basically watching the teacher do something and then repeating that like 50 times for homework. There was nothing insightful, awe-inspiring, or creative about it. The tougher problems were more interesting in that regard -- you have to think a little and really apply the skills to figure out the answer. But even still, math just never excited me very much. Now, given that, I have to wonder how interesting a basic (or possibly even remedial) math class could possibly be? If the kids are still trying to master the rudimentary skills, they probably never get to touch the tough problems that actually require some element of creative thinking. And that sounds horribly boring to me.

[Katya]

Also, a word about math being interesting and applicable. I was one who always excelled at math but never particularly enjoyed it. To me, math class was basically watching the teacher do something and then repeating that like 50 times for homework. There was nothing insightful, awe-inspiring, or creative about it. The tougher problems were more interesting in that regard -- you have to think a little and really apply the skills to figure out the answer. But even still, math just never excited me very much. Now, given that, I have to wonder how interesting a basic (or possibly even remedial) math class could possibly be? If the kids are still trying to master the rudimentary skills, they probably never get to touch the tough problems that actually require some element of creative thinking. And that sounds horribly boring to me.

I've always loved patterns, especially highly quantifiable ones, so I liked math as a means to the end of being able to understand and articulate the patterns I see in life. But the patterns I think about don't necessarily require advanced mathematics to understand them. (Of course, those patterns may not be interesting to everyone, either.)

[thebigcheese]

Hmm...the only patterns I remember caring about were in calculus class. Algebra made the most sense to me, geometry was generally easy but annoying, trigonometry was friggin hard, and calculus seemed to have the most interesting real-world applications. So I would say that algebra and calculus were my favorites, by level of understanding and level of interest.

And then there was my dad who tried to tutor me for my physics homework. Gosh, that was a mess. At my school, they taught physics using advanced algebra and I didn't take calculus until the next year. So my dad, with his master's in physics, was trying to tutor me in physics using calculus even though we learned it using algebra. I think that was a form of intellectual suffering.

[Katya]

Here's an example of a pattern I was thinking about a few months ago:

The ceiling of my bedroom is divided into square tiles. Each row of tiles is offset from the last, like the pattern of a brick wall (if that makes any sense). I got to wondering what the pattern would be like if I could inscribe a circle in every square tile. Would the pattern be the same as inscribing a circle in hexagonal tiles? (Like the lower half of this pattern?)

As it turns out, the answer is no. (The rows of squares are too far apart.) But it's interesting to think about, and it doesn't require more than geometry to grasp the problem and play with it.

[thebigcheese]

Hmm...yeah, I probably wouldn't think about that stuff too much. Geometry wasn't exactly my cup of tea.

But I would think of this: real-world applications for graphed integrals and derivatives. That stuff was like a revelation to me. There's a way to graph things that aren't linear or exponential? OF COURSE!

[TheAnswerIs42]

I think it is an interesting quandary that students always hate word problems and whine about "none of this applies to my life". You'd care about when two trains met if you were on one of them and trying to get onto the other one, for example. I tried to give students problems that they would actually see in their lives - use grocery ads for a project in Algebra, house measurements to buy paint or tile in Geometry class, etc. But the honest truth is sometimes you just need practice trying to apply very specific topics in odd ways that you won't see often in your life.

Oh, and Whistler- you just described the entire logic behind a method of math instruction that is called "Investigations" in the Alpine School District. It is more like how Japanese students are taught. They aren't directed how to do things by the teacher, generally, but given a difficult problem on the board to try and figure out on their own. After some time on their own or in groups, then the have to present their ideas and the teacher guides them until they see how the problem should be solved. American students, unfortunately, just sit back and try to force the teacher to do all the work anyway, but it can be a good program when used properly. (I did my undergrad research on it, so obsviously this is a topic I have lots to say about this.)

[Whistler]

Oh, and Whistler- you just described the entire logic behind a method of math instruction that is called "Investigations" in the Alpine School District. It is more like how Japanese students are taught. They aren't directed how to do things by the teacher, generally, but given a difficult problem on the board to try and figure out on their own. After some time on their own or in groups, then the have to present their ideas and the teacher guides them until they see how the problem should be solved. American students, unfortunately, just sit back and try to force the teacher to do all the work anyway, but it can be a good program when used properly. (I did my undergrad research on it, so obsviously this is a topic I have lots to say about this.)

That sounds really interesting! I wonder why American students aren't receptive to the method...

[Dragon Lady]

Oh, and Whistler- you just described the entire logic behind a method of math instruction that is called "Investigations" in the Alpine School District. It is more like how Japanese students are taught. They aren't directed how to do things by the teacher, generally, but given a difficult problem on the board to try and figure out on their own. After some time on their own or in groups, then the have to present their ideas and the teacher guides them until they see how the problem should be solved. American students, unfortunately, just sit back and try to force the teacher to do all the work anyway, but it can be a good program when used properly. (I did my undergrad research on it, so obsviously this is a topic I have lots to say about this.)

That sounds really interesting! I wonder why American students aren't receptive to the method...

Because we're lazy and would rather have someone else do the work for us? I mean, really, why do you think the Board exists?

[Marduk]

I don't know that it is that simple, DL. I think that we don't necessarily value hard work, which is certainly part of it, and I don't think that's necessarily the same thing as being lazy. I remember, for example, my Japanese friend instructing me on some of the differences; in the U.S., getting something without trying is a win, "I didn't study at all for that test and I still aced it!" whereas, in Japan, one would never brag about getting something without trying. But I think it really is much more involved than simply not wanting to work for things.

Our educational system as a whole devalues independent thought. Our form of teaching is far less Socratic than just about any eastern method; when we do ask questions, they are overly simplistic and closed. Since the system is so institutionalized, we judge based on regurgitated answers and pre-programmed rhetoric, rather than analysis and problem-solving skills. Should we really be so surprised when students are reticent to do it?