I don't hate math, that is just the title of the post - notice that I put it in quotes.
As you may know, I teach this physics course for elementary education majors (using Physics and Everyday Thinking - which is awesome). The curriculum has very little math in it. That is not necessarily a good thing, but it helps the students understand science and the nature of science without bringing in this mental block they have for math. One of the activities has them look at the energy efficiency of different devices. At the end of the activity, they are asked:
A fluorescent bulb is 25% efficient. A regular 100 Watt bulb produces 8 Watts of light energy. What kind of power would a fluorescent bulb need to have the same light output as a regular 100 Watt bulb?
I like this problem. It is a real problem, uses real math and doesn't just say plug into some equation. There are many students that enjoy problems like this, but for others it causes them to hit a wall.
Here is a typical conversation I have in this class for this activity (this is a very typical conversation - really you could consider it a composite of many student conversations).
Student: "I hate math"
Me:"You hate math? Really?"
Student: "I don't hate math. I just hate this kind of math. If you just give me the formula, I won't hate math."
Me: "Well, if I give you the formula and you plug stuff in, that isn't really math. I guess that would be arithmetic."
Student:"Well, whatever you call it, I hate it."
Me: "Ok. You can't say that. Maybe you think you hate, but you can't say that. You are going to be a teacher, right? As a teacher of young children you have a great power, a great influence on what they think. If you hate math, they are going to hate math. Remember, with a great power comes a greater responsibility."
I hope the students that say stuff like this don't think that I am angry. I am not. I just want them to be careful with kids.
There is another point. Can I change their attitudes towards math? I don't know. Maybe I can change their attitudes by having a positive attitude myself. I don't think I can change the course to work on math - we are busy enough working on ideas about science.
The real question is whether they want to understand the world, or just be led about by someone else who claims to do so. If they can't grasp the simple concepts to understand relative power to light bulbs, how do they hope to think about alternative energy, offshore drilling, tax policies, or anything else of consequence?
But yeah, that kind of consequential prognosis has limited motivational appeal.
I like what you tell them. You might add that you understand they probably got that mental block from their own elementary teachers, and you know they don't want to do that to kids - they want to be great teachers, so you trust they'll find a way to get over their hatred of math. Point them my way if you think it would do any good.
I don't hate math, and overall I like the "fluorescent bulb" problem you used. However, I would have had a problem with this when I was your students' age. I would have had no trouble with the numbers, but I would have gotten bogged down asking, "What is the meaning of the term '25% efficient'?"
Do you cover this before giving them the problem, or do you assume that the kids will understand?
I hate maths as only a person with a degree in it can.
But I still have to use it every freaking day!
"I like this problem. It is a real problem[...]"
It's an improvement over most bizarrely-contrived physics "problems" that I encountered during classes, but it's still sounds a little contrived rather than practical.
The "A regular 100 Watt bulb produces 8 Watts of light energy" sounds almost like some sort of magic number produced by fiat - "never mind where this number comes from, just use it in the calculation". Of course, when you go to the store to actually compare light bulbs, none of the packaging gives "watts of light energy". They usually give "lumens" but that's obviously not very helpful here...
Fluorescent lights seem to usually have the "watt equivalent" (compared to incandescent) already printed right on the box anyway, so in practical terms, from the point of view of the sort of person who doesn't speak mathematics natively (i.e. the "I hate math" population") this ends up seeming like another "math for math's sake" homework question rather than a demonstration of real-world usefulness of mathematics.
(Don't mind me, even all these years later I'm still kind of bitter about all the time wasted in bad math classes all the way up through high school, and not really "getting" much practical application beyond remedial addition/subtraction/multiplaction/division until sometime around college chemistry, when I realized I'd speak mathematics much more naturally now if I'd learned earlier math as a practical subject in my youth. It's NOT actually really a bad example problem, I'm just overly-sensitive about it...)
Yes - they calculate some efficiencies for different devices before this question.
I teach middle school math (primarily Algebra I) and I inherit many of those students who have typically decided that they hate math before they leave elementary school...
I sat in a math curriculum meeting TODAY where a first grade teacher beside me said "I'm not good at math." How many teachers would be willing to say "I'm not good at reading" and still expect their peers to respect them?
That is EXACTLY my response when people say they are no good at math (or I am not a math person). It drives me crazy.
Where was it that I read (maybe it was Neil deGrasse Tyson) that said "oh, I was never good at nouns and verbs" as a reply to that statement.
If I had a child I would not want someone who disliked learning about the world or was unable to address such a simple problem teaching them at all.
You don't need advanced calculus to teach elementary school but if you are unable to complete that problem you are not qualified to understand the world never mind teach others about it.
I know! 32 watts!
I really wish I could remember the source, but not terribly long ago a science/skeptical blogger posted something about how they really really hate the phrase "I just don't understand math" and its variants.
Imagine you're at a party. Someone says, "I just don't get math." Several people around them laugh and agree, providing anecdotes of their struggles with math. This is ok and accepted.
Now imagine someone at the same party says, "I just don't understand music/art/reading/etc." In most educated groups everyone would stare at them and wonder what was wrong with them.
How is the first ok, but not the second? It shouldn't be, but it frequently is. You can substitute science for math in the first one and it's still accepted. Why?
Ah, nevermind, found it, here on Sb: The Innumeracy of Intellectual by Chad Orzel.
The most math-phobic group of students I ever taught was a summer class of "math for elementary school teachers". I like to think I won them over by the end, but it's a hard, hard road....
Best of luck compadre.
I don't hate math...as long as I get the problems right. =)
Many students find physics challenging as well. Although physics is cool because of its real world applications, it can be quite challenging for students. But I guess practice will definitely help mitigate the pain...
@Peter - When I was in grad school, I had a professor who taught the undergrad "math for elementary school teachers" course. At the start of the semester, she would announce (actually, I assume that she still does) that all of the arithmetic that they'd do that semester would be in Base 8, not Base 10. That way they would have to basically start from scratch with learning how to "do math" with simple operations! It was to help put them in their students' shoes.
That's not necessarily a direct response to Rhett's posting today, but it certainly could be intimidating to a lot of folks!
Peter: The most math-phobic group of students I ever taught was a summer class of "math for elementary school teachers"
It's all part of the vicious circle of life: people going for grammar school credentials have the thinnest math requirements of any college program. The math-phobic get herded in this direction, after which they take their disdain of math into the elementary schools and raise up several more crops of math-averse students. (But we can't raise the math requirements because that would devastate enrollments in a historically math-challenged field -- and we need the teachers too much! Ow.)
The more I think about it, the more awesomer that idea is. The idea of using base 8 instead of base 10. Not only would the students see what kids think things like - but you would have to understand _the idea_ of math rather than some procedure for math.
I actually would suggest base 16 (hexadecimal) as it does have use if you get deep into computers. (Plus it introduces new numbers like a,b,c,d,e,f.
Dear trainee teachers,
If you hate math so much you have trouble not expressing with regard to the sample problem posted above, I don't want you anywhere near my kid's education.
Even if you're teaching music or physical education or what, I don't want to risk that attitude to learning and effort rubbing off on them.
If teachers expressed the same feelings about reading and reading comprehension that they do about mathematics, people would be horrified.
I get that you don't see the beauty and power of mathematics.
Nevertheless, while you chat and text your friends on your cellphone about how much you hate mathematics, you might like to take a look at how that cellphone actually works.
At heart, it's mathematics, mathematics, mathematics, and some more mathematics. Same with pretty much every other piece of technology. That your pampered, comfortable life works at all is in a fairly large part down to mathematics.
Deal with it. Some things in life take a fair bit of effort.
Anything really good does.
I hope your students get the even bigger message here - that words matter. Everything we say to our students (and plenty we don't say) is soaked in. I teach first grade and I work really hard to make everything seem exciting, no matter how much it may bore me. Fortunately, I find most of it exciting myself!
Peter Johnston's book, Choice Words, is fabulous for this issue.
They don't hate math, per se; they hate translating problems in the English language into problems in an arithmetic language. This is somewhat understandable; the general problem of finding conformities from one language to another is Halting Problem hard, due to Rice's Theorem... another bit of math. =)
Once again, the biggest problem in teaching introductory physics at the college level is how to deal with the students who get to college without being able to do algebra.
Efrique, and others who share this sentiment, I wholeheartedly agree with you. It is one thing to specialize, and we all understand that in doing so, a person has weak areas. But to express those weak areas, in almost any way, undermines the efforts of teachers specializing in other areas.
I am 40 years old, and I still remember a Phys Ed teacher I had in high school who made the claim that Germany had a population of 60,000 people. I had an epiphany that day. The pedestal was torn down.
I wish our educational system would treat innumeracy as seriously as it does illiteracy. The cynic in me thinks that one makes it near impossible to be a consumer, the other only makes it impossible to be a wise consumer.
I don't really think it's their fault. For TWELVE years they have only been taught that type of "math". Their creativity has been sucked right out of them. They haven't really been taught how to think through problems, and they're probably afraid to try because they're afraid of failure-of doing something they haven't really ever done before, like creating their own little equations. Thinking should be encouraged right from the start, not just starting from the college level.
Of course it's their fault. At some point, we all have to take responsibility for ourselves and what we do with our lives. Why do we give people a pass on what they do with their brains?
I might have problems with social situations, but that doesn't mean I get a free pass because nobody taught me the rules. I have to work, now, to figure them out on my own.
My point is not that "They must suffer like I do!", but that part of being an adult is overcoming the limitations imposed on you by your childhood, whether it's a problem recognizing and internalizing social rules, or a lack of training in rigorous thought. And saying "Oh, it's not their fault" is nothing short of babying them.
I hate(d) math. That's why I majored in Physics.
Nowdays my friends and I do math puzzles and some recreational math, and I can catch glimmers of the beauty and elegance. I still don't find it as satisfying and understandable as, say, the derivation of General Relativity in a given metric.
Of all the math teachers from grades 1 - 12 that I recall, I hated all but one. Unfortunately, Calculus in the senior year of high school is too late to make up for 11 formative years of hating math teachers who hated math.
There was a talk on TED about this too:
I love math, and I actually have fun during a good math test or physics test. However, it is extremely tedious to memorize 50+ or 100+ equations over the course of a semester before being able to use them.
The best tests are those that give you a list of all equations that you will use, and perhaps even a few extra. As you read through the word problems, you will have to know which one is the right to use for this problem, and that means you have to know what the equation does.
These tests/assignments allow the student to use their knowledge to choose the right equation for a problem without having to rote memorize it. And after using the equations enough, they'll eventually start to memorize them.
Every bit of information you could need is easily accessible online these days, so you're really wasting time memorizing equations that you don't use enough to memorize with use. You just need the concepts, and need to know what to do without having to know where ever parenthesis and square root sign goes. That all gets ingrained through repeated use.
In case you weren't aware, this excellent post has another comment thread going on Reddit:
See the essay "Mathematics, the most misunderstood subject" by Prof. Robert H. Lewis.
I believe that mathematics should be taught, not collaboratively explored; algebra and geometry are better than a vague course of Integrated Math; spiraling doesn't work nearly as well as learning it properly the first time; "I don't DO math" should be an incentive rather than an excuse. "I don't DO English" should be treated the same way.
Oddly, I have consistently had the opposite problems in math classes. I remember being in an elementary geometry class and given a picture of a circle and the radius. We were told to calculate the area of the circle. So, I took out some string and ran it around the perimeter of the circle, closed it off in a loop and then moved the string so that it became a square then measured one side of the square and calculated area as if it was a square. I remember being penalized (receiving no credit) for this.
Actually, I remember being consistently penalized in math classes for showing a real-life perspective to math problems. Plugging in values into a formula - the standard f(x) mindset is how math is taught. If you are changing the rules on the students now after years of math education (or conditioning - however you want to look at it), it is unfair. They have been taught a way of thinking needed to pass tests and you are trying to make them critically think about it - that will actually lower your test scores.
If you have taken the GMAT or GRE style tests you will often see multiple choice questions like:
Here is a sequence:
2, 3, 4, 5
Please choose the next number from the numbers below
However, anyone sufficiently brilliant will be able to find sequences where all the numbers fit. Yet, the test wants you to only find one answer.
I think even the question that you posed is somewhat misleading if you approach it from a real-life perspective. How is one defining one's terms? What "light energy" - do you mean only the spectrum of visible light? What about the conversion that happens within the tube from UV that reradiates to visible light? What is "light output"? Are we discussing the human perception of light output? Or are we calculating in absolute terms?
Real life problems have real life solutions. I see that often in math classes that the teachers come up with a half-baked simplified version of real-life problems that ignores real-life.
This is a great bit of advice and as kids are our future, I would say important too.
I think the best way to handle it is not to argue with people about why they hate math, but totally ignore their hatred of math, always presume that they love math, and believe that math is the greatest thing in the universe. Your enthusiasm for math will be contagious. Love needs to be demonstrated, never, ever explained. Ever!
Nobody hates math. They hate failure.
Despite what you say @6, the problem here is that they HATE FRACTIONS, not "math".
The 'forward' problem of calculating efficiencies is not as bad as the 'backward' problem of using a fraction to figure out the whole. The teachers (your students) don't get it, and it will only get worse as guessing methods (like Everyday Math) do to arithmetic what "look say" did to reading a generation or so ago.
Do your students know that 25% is 0.25 (so they can use their calculator)? Do they know that 25% is 1/4, and do they know how to invert and multiply? Can they solve A/B = C for B? You might be surprised.
One of the great losses in the blogosphere is that a memorable post, wherein two students are overheard talking about how awful it was that there was some math on an exam in a math-for-teachers math class, has been lost forever. They hated math, and couldn't wait to get out of college and into the K-5 classroom where they would never use it again. Want to guess why students can't deal with fractions?
You can make math fun like this game:
Ask your students how is made. It is not super hard to figure it out.
The reason that many folks hate math is that it is so poorly taught. Yup it may have less to do with students and more to do with how its taught. I attend Oregon State University major Physics and a few years back they changed the curriculum. They have every term an intense 4 week course in one subject, waves for instance. We meet everyday, a tenured experience prof will teach, often two profs will be tandem teaching, and no one assumes that because you've taken a multiple variable calculus course that a student knows how to apply it to physics. They SHOW you how it works and why it supposed to work, so that you don't spend hours trying to tie both courses together, rather you can apply the math to the physics.
But the real point is why they needed to do that change. Because when the department surveyed their students, they had no idea what was going on, and these were responses from their best students. As was told to me by the Dept Chair, they were completely confused re: concepts and applications, and this was just a couple of weeks after the course. They realized that the way physics was being taught made their graduates functioning illiterates in the subject. Unless a solid, functioning connection is made between physical concepts and the math tools to supplement that understanding, then physics and math will make little sense. That is all on the teaching profession and has little to do with students.
notice they said: "this kind of math."
i hate physics. that's because i fail at it quite miserably. i know that if i practiced enough problems however, it would eventually click- but that means hours upon hours of days and weeks of doing nothing but physics problems. i don't have the time for that.
the only reason why i would spend time doing physics is to understand the concepts well enough that i'd know when to apply them, under any type of problem with an object undergoing any type of conditions.
so it isn't the math...it's the physics, and how it affects the math. i'm sure they'll like physics more if they were more successful w/it...
i hate maths because it goes like wind over the head i have write a post 'i hate mathematics' please read it.