Why do so many people hate or have trouble with math? Your input is needed!
LearningNerd
college), and I'm planning to write an introduction to learning math on
my blog. To get some ideas, I'd like to hear your answers to any or all
of the following questions:
Why do so many people hate math?
Why do they have trouble understanding it?
What are your experiences with learning math (at school, on your own,
etc.)?
Do you enjoy math? If so, why?
How could teachers and students make math more fun to learn?
Thanks in advance for your feedback! Also, if you have any suggestions
for how I should go about relearning math, please share them. Any
useful websites or books would also be greatly appreciated.
Bart Goddard
> How could teachers and students make math more fun to learn?
It's a huge mistake to assume that "making learning fun" is
the right way to do things. In fact, it's the exact wrong
way to do things, and we have ample evidence.
Bart
--
The man without a .sig
Arturo Magidin
Same reason a lot of people hate spinach or broccoli. They've been
forced to have it because, they are told, "it's good for you", but
they can neither see nor perceive those benefits, and it is being
served by mostly uninspired cooks who don't much care for its taste
either.
Note that the same may be said about reading. A ->lot<- of people hate
reading; the idea of reading a book for fun, or in order to learn
something, is a terrible chore to be avoided if possible. And even
those who may enjoy some reading will often recoil at the idea of
reading Dickens, Tolstoi, Jane Austen, Cervantes, or Milton; let us
not even consider Shakespeare which, granted, was not meant to be read
bu rather seen performed. And let us not even mention Plutarch or the
likes of "Rise and Fall of the Roman Empire".
The difference there, I think, is that while it is considered socially
acceptable to acknowledge, nay, brag about, a hate of math, the idea
of saying that you think reading book is dumb, that people should not
be forced to read quite so much in school, that you "hate books", is
not socially acceptable. So there is less talk about it.
>Why do they have trouble understanding it?
A vast majority of people are taught mathematics by people who do not
like or enjoy mathematics either. That's a very big obstacle to overcome.
Again, the same may be said about reading in general. From what I can
see, there is a very large problem with reading comprehension in
general; let's not even go to reading Dickens or Shakespeare and
making sense of the plot (which far more people have trouble with).
>What are your experiences with learning math (at school, on your own,
>etc.)?
No idea where you are going with here. I've been studying nothing but
math since 1988, barring one summer course of French in 92, and one
semester of introductory japanese in 95. Way too much for me to talk
about in usenet.
>Do you enjoy math?
If I didn't I wouldn't be a mathematician.
> If so, why?
The pleasure of finally solving a problem that once seeemed
unsurmountable is a very big part of it.
>How could teachers and students make math more fun to learn?
Why does it have to be "fun"? I would settle for ensuring more people
learn it properly, just as I would settle for more people being able
to comprehend basic written English. I mean, I just had an exam with
a very big prominent instruction to give extact answers and not
approximations, with explicit examples of what to do and what not to
do (including, explicitly, "Use pi, no 3.14"), only to have about
1/4-th of the students blithely replace every fraction with a one
digit decimal approximation, and e and pi with its decimal
approximation to the hundredths.....
But, first and foremoest, whoever is teaching it has to understand it,
and should probably enjoy it him or herself. When you teach something
you don't like, the students pick up on it.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================
Arturo Magidin
magidin-at-member-ams-org
Gene Ward Smith
Arturo Magidin wrote:
> I mean, I just had an exam with
> a very big prominent instruction to give extact answers and not
> approximations, with explicit examples of what to do and what not to
> do (including, explicitly, "Use pi, no 3.14"), only to have about
> 1/4-th of the students blithely replace every fraction with a one
> digit decimal approximation, and e and pi with its decimal
> approximation to the hundredths.....
How did you grade it?
Ioannis
news:eg4110$umb$1...@agate.berkeley.edu...
[snip]
> >Do you enjoy math?
>
> If I didn't I wouldn't be a mathematician.
>
> > If so, why?
>
> The pleasure of finally solving a problem that once seeemed
> unsurmountable is a very big part of it.
The above pretty much nails it. Note however that this is a quite advanced
view in the eyes of a newbie student who's just learning through pain and toil
and curses every step, not seeing the reason behind it all.
I'd say that this is the gist of being a mathematician, unfortunately
completely "felt" only by an already mature mathematician, so it's kind of
futile to explain to a neophyte.
It's like trying to explain to a kid that chess is going to be fun because at
some later stage, perhaps 20 years from now when he's going to be a good
player, it's going to be fun to win a "strong" opponent.
[snip]
> Arturo Magidin
> magidin-at-member-ams-org
--
Ioannis
-------
The best way to predict reality, is to know exactly what you DON'T want.
David Park
"LearningNerd" <Learni...@gmail.com> wrote in message
news:1160085520.5...@i42g2000cwa.googlegroups.com...
> Thanks in advance for your feedback! Also, if you have any suggestions
> for how I should go about relearning math, please share them. Any
> useful websites or books would also be greatly appreciated.
>
1) Get a book like 'Numbers and Geometry' by John Stillwell. Presupposes
only high school algebra but it is real mathematics.
2) Consider getting a CAS like Mathematica and learn how to use it so that
it can be a powerful tool in your university study. It takes some time to
learn it well so the earlier the better.
Don't worry about having fun or why other people hate mathematics. That's
their problem. There are plenty of people who appreciate and like it.
David Park
dj...@earthlink.net
http://home.earthlink.net/~djmp/
William Elliot
> I'm starting to relearn math on my own (I'm taking a year off before
> college), and I'm planning to write an introduction to learning math on
> my blog. To get some ideas, I'd like to hear your answers to any or all
> of the following questions:
>
> Why do so many people hate math?
>
Fad.
> Why do they have trouble understanding it?
>
Because of the fad.
> What are your experiences with learning math (at school, on your own,
> etc.)?
>
I learned much better on my own than in high school which was a detriment
to my learning.
> Do you enjoy math? If so, why?
>
Yes. It's fun, I've a knack for it.
> How could teachers and students make math more fun to learn?
>
Oh sure make fun of math, make fun of learning.
People make fun of something they disdain.
Make fun of teachers, nay make fun of educational theorists.
Make school funny farms. Kids who don't want to learn, will learn
very little by making fun of the material. The question is wrongthink.
> Thanks in advance for your feedback! Also, if you have any suggestions
> for how I should go about relearning math, please share them. Any
> useful websites or books would also be greatly appreciated.
>
Find what fields of math that you like, that grab your interest, that
enthrall you and study them.
LearningNerd
I said "fun"; I don't mean that learning math should be like playing a
game. Replace "fun" with "interesting". I think math would be
interesting to more students if the teachers taught more about how math
can be applied, why it works, and how it has been and still is
progressing.
I agree that one of the main problems is that so many math teachers
aren't interested in math. Most of them don't even try to make it sound
interesting; they just jump right into what needs to be memorized. In
my experience, math classes were challenging for all the wrong reasons
-- not because the material was a challenge to understand, but because
it was difficult to force myself to memorize everything, do repetitive
worksheets, and stay awake in class.
LearningNerd
problems are too repetitive and not difficult enough? I've only
experienced joy after solving a math problem once or twice, but I think
I can relate to what you're saying.
Jack Maney
Honestly, I think the underlying problem behind all of your questions is a cultural one.
> Why do so many people hate math?
For a variety of reasons. Some have had a math teacher in the past who was either incompetent or who hated math. Also, I personally believe that the "discovery based" and "constructivist" math pedagogical fads may have played a part in why a lot of people hate math.
However, I think the biggest reason why a lot of people hate math is because of a prevailing culture in which it's "cool" not to know any math. Like I said, it's a cultural problem. I wish I had a solution.
> Why do they have trouble understanding it?
One of my favorite professors in grad school once said to me "If any undergraduate doesn't understand a math problem, it's always because he/she hasn't read the problem." Although I'm not so sure about that *always* being the case, I've found that students get tripped up a lot because of reading comprehension. Many of them don't read a problem (or skim over it once) and expect to know exactly what to do immediately. For years, I've been contemplating getting some old-fashioned ink stamps to use while grading; the sentence "Read the problem!" would definitely be on one of those stamps.
> What are your experiences with learning math (at
> school, on your own,
> etc.)?
I remember very little of my early childhood, but I don't particularly remember disliking math...it was something that I wasn't too bad at, but I made my share of mistakes (just like everyone else). Throughout high school, I became a bit more proficient with math (albeit still making plenty of small errors and the occasional bigger error).
When I started college, I had no idea what I wanted to do with the rest of my life. To make a longer story short, I started as a mechanical engineering major, quickly switched to a math education major, and then eventually to a math major. By then, I knew I wanted to enter academia.
That decision forced me to transfer (since the school I was attending at the time didn't have a PhD program in math). Up until this point, I was an A/B student (mostly B's) with a C or two here and there...once I decided I wanted to go to grad school and get a PhD, I became much more serious about my studies.
After getting my B.S., I delved right into grad school. I started as a TA during my last semester as an undergraduate and loved it; I quickly started forging a teaching style.
The transition from being an undergraduate to a graduate student went smoothly (much more so than the transition from high school to college), and I kept up a regular courseload on top of my teaching duties. In the back of my mind, though, I realized that someday, I'd have to write a dissertation; in particular, I'd have to do some research.
Mathematical research scared the hell out of me...I had realized by that time that there were such things as open questions, but I had no idea how they were formulated or answered successfully. With time, however, I managed to gain enough maturity to start asking enough questions so that I (so far) have a somewhat reasonable research program.
> Do you enjoy math?
Absolutely!
> If so, why?
Oh, boy...I could go on for hours and hours answering this question. Instead, I'll give you the reasons off the top of my head.
Mathematical proof is the most rigorous, most incontrovertible method of verification in existence. A mathematical result is as close to certain, unshakable knowledge as we're ever going to get.
And yet, while being highly rigorous, mathematics is, in my opinion, much easier than the sciences. Scientists are (for the most part) constrained to the real world; they have to gather data, do some measurements, form a hypothesis, and then undergo some experiments to gather evidence as to whether or not the hypothesis might be true. As a mathematician, I have the luxury of proof. To be honest, I don't know if I would be smart enough to be a scientist of any stripe.
Also, I love how the concepts in mathematics are so interconnected. From the analytic geometry of Descartes (relating real-valued functions to points on the plane), to the Fundamental Theorem of Calculus (relating differentiation and integration of real valued functions), to Galois theory (relating polynomials, groups, and fields), to groups of divisibility (my specialty, relating divisibility in an integral domain to partially ordered abelian groups)...it's amazing how often two seemingly unrelated topics are related. It's also amazing how one can use new definitions and new "machinery" to view old ideas in a new light.
> How could teachers and students make math more fun to
> learn?
I'm not really sure they should. It may sound harsh, but there are some things that have to be learned that aren't particularly fun to learn. I'm a bit mortified by the "learning has to be all fun, all the time!" attitude so prevalent today. What happens to a kid growing up around nearly endless "edutainment" when she gets a job after college that isn't "all fun, all the time"?
Besides, if everything were to become fun, then...well...everything would cease to be fun. Things that are fun are done in contrast to things that aren't.
Sincerely,
Jack
Lee Rudolph
On a scale of 1 to 0, rounded down to an integer?
Lee Rudolph
eltetot
LearningNerd wrote:
> Thanks for your thoughtful response! I guess I used the wrong word when
> I said "fun"; I don't mean that learning math should be like playing a
> game. Replace "fun" with "interesting". I think math would be
> interesting to more students if the teachers taught more about how math
> can be applied, why it works, and how it has been and still is
> progressing.
I think there is no general answer that we could call "king's way". In
my teaching experience, I always find about 5-10% of the class whose
interest can be raised without mentioning any specific application
(though I am teaching engineers and get this question from time to
time). There is another 10% that cannot be reached at all even if I
tell them the most convincing "application": there will be a task very
much like this in the tests. What the remaining 80% does depends on the
weather, the stars, the previous lessons in that particular day. They
tend to follow the former or the later group.
I have the feeling, that we can do very little against the statistics.
What do you think about that?
BR, Tamas
Arturo Magidin
Those who included exact computations up until the last step, at which
point they had the right exact answer followed by the approximation, I
gave full points and a stern warning. Those who used approximations
throughout got substantial points off.
Arturo Magidin
Don't top-post.
http://www.xs4all.nl/~hanb/documents/quotingguide.html
And edit the message you are quoting when you reply so you only
include relevant portions. Just adding your response on top of the old
message combines most of the bad habits of usenet.
>I guess I used the wrong word when
>I said "fun"; I don't mean that learning math should be like playing a
>game. Replace "fun" with "interesting".
Basic math skills are as important as basic literary skills. Everyone
needs to know how to read and write, basic reading comprehension, and
the basic ability to express simple ideas in written form. We drill
students on reading and writing.
By the same token, there are some basic mathematical skills that
everyone, in today's world, needs. A basic "numeracy" to borrow from
Paulus; you need to drill students in the basic multiplcation tables
as much as you drill them in writing "mama". And in today's they need
to understand the basics of descriptive statistics, at least. Those
skills, we don't need to make them "interesting" any more than we make
learning how to read "interesting". They need to know them, they need
to be second nature to them.
Later on, again, I have to wonder: why does math need to be
"interesting", "fun", "enjoyable"? The basic skills we are supposed to
be learning/being taught in grade school and high school are supposed
to be skills we ->need<-. Not stuff we might enjoy. The basic math
does not need to be interesting. What it needs to be is
->useful<-. Basic statistics and probability to understand the world
we live in (perhaps based on something like the wonderful "How to Lie
With Statistics"); basic arithmetic and algebra skills; basic logic;
how many people do not understand the problem with affirming the
consequent?
Now, granted. We teach students Shakespeare out of a sense that they
need some basic culture, and we do make efforts to make it
interesting; that is as far as mathematical instruction ought to be
taken. The mathematical instruction is the parallel of the basic
language skills instruction. But for some reason it is not looked at
that way.
>I agree that one of the main problems is that so many math teachers
>aren't interested in math. Most of them don't even try to make it sound
>interesting; they just jump right into what needs to be memorized.
Some stuff ->needs<- to be memorized. I'm sorry, but just as you need
to memorize the alphabet, you also need to memorize the basic
multiplication tables. And some things ->do<- require drill. Drill is
not bad per se, and it is not good per se. You do not need to do
drill all the time, but neither should it be avoided like the plague;
sometimes it is necessary. (I know many here disagree; Prof Rubin
definitely disagrees with my view ont his, for example, and he
certainly has more experience to bear than mine).
Halmos, I believe, said that good mathematical teaching stands on a
tripod of understanding, memorization, and drill. You need all
three. Some things you need to memorize, some things you need to drill
on, and some things you need to understand. Take the derivative: it is
important to know ->what<- it is (understanding, and knowing how to
use it to solve certain kinds of problems given what it is); but it is
also important to know certain formulas by heart (product rule, chain
rule), and to drill on them until they become second nature. Short
change any of the three, and you end up with a still that doesn't
stand straight.
Some topics require an emphasizing of one of the legs over the others,
but almost invariable all three are needed. And, for the past 50 years
or so, there's always been one leg that gets ignored. New Math
emphasizing understanding and dropped drill; the reaction to New Math
dropped understanding; New New Math despises memorization, and
essentially ->forbids<- drill, calling it "drill and kill". And so we
have a generation of teachers who were deformed by educational
experiments and cannot teach the subject properly.
[...]
LearningNerd
excuse my newbieness. :)
> Later on, again, I have to wonder: why does math need to be
> "interesting", "fun", "enjoyable"? The basic skills we are supposed to
> be learning/being taught in grade school and high school are supposed
> to be skills we ->need<-. Not stuff we might enjoy. The basic math
> does not need to be interesting. What it needs to be is
> ->useful<-.
I agree with you there. It doesn't need to be interesting or enjoyable;
we do need to have a basic understanding of a number of things, which
is why we send kids to school. That's a given. My point is this:
teachers don't need to make math "fun" or "interesting", but that
doesn't mean they shouldn't try. As long as they still teach what needs
to be taught, there's always room for a little diversion.
> Some stuff ->needs<- to be memorized. I'm sorry, but just as you need
> to memorize the alphabet, you also need to memorize the basic
> multiplication tables. And some things ->do<- require drill.
Again, I agree. I think there's often too much memorization, but I do
understand that there's also such a thing as not enough memorization.
Like you pointed out, there needs to be a balance.
I think one way to make learning math more interesting -- and to make
learning anything more interesting -- would be to incorporate more
group projects, more interaction between the students themselves,
and/or more ways to encourage learning outside the context of school.
I've heard that a growing number of classes are incorporating blogs
into their courses to make everything more interactive. Like someone
else mentioned in this thread, math is culturally "uncool"; one way to
combat that stigma might be to promote math outside of the classroom.
But anyway, that's for an entirely different discussion. I better stop
before I wander too far off topic. Thanks again for your input! Would
you mind if I quoted you in my article (either with your name/website
or anonymously)?
Arturo Magidin
LearningNerd <Learni...@gmail.com> wrote:
[...]
>I think one way to make learning math more interesting -- and to make
>learning anything more interesting -- would be to incorporate more
>group projects,
I've never understood that. I never liked group projects when I was
kid. I never knew anyone who particularly ->liked<- group projects as
opposed to other types of school work, ->except<- those people who
knew they could coast with little or no work, leaning on the other
members of the group.
What is it about "group work" that gets education types so excited,
anyway?
>But anyway, that's for an entirely different discussion. I better stop
>before I wander too far off topic. Thanks again for your input! Would
>you mind if I quoted you in my article (either with your name/website
>or anonymously)?
You are welcome to quote me, though I think you would be better off
trying to take all the comments you've gotten and doing a synthesis. I
would prefer if you do not include my website; there is no point as
nothing there is relevant to this discussion. Since I have no plans to
remove posts from archives, you could always link to the posts you are
quoting from/doing a synthesis from, as opposed to direct attribution
in your page.
Mitch
Arturo Magidin wrote:
> LearningNerd <Learni...@gmail.com> wrote:
>
> >I think one way to make learning math more interesting -- and to make
> >learning anything more interesting -- would be to incorporate more
> >group projects,
>
> I've never understood that. I never liked group projects when I was
> kid. I never knew anyone who particularly ->liked<- group projects as
> opposed to other types of school work, ->except<- those people who
> knew they could coast with little or no work, leaning on the other
> members of the group.
>
> What is it about "group work" that gets education types so excited,
> anyway?
I'm totally with you there... but...
I think the use of group work in a classroom setting (that is, having
the students work in small groups on problems, and having the
instructor be an asynchronous advisor), is that slower students will
benefit from hearing the quicker students work out the problems out
loud (learn to emulate their problem solving skills), and the quicker
students will benefit from the usual 'you-learn-from-teaching'. I
suppose another educationalism is that different students have
different learning strategies and one of those strategies is bouncing
ideas off each other (in addition to prolonged concentrated reasoning
usually associated with mathematics).
However, when such group work is intended for grades, my feeling is
that every side is being venal (slow students can prey on the pride of
the quicker ones, it is simply a labor saving device for the
instructor/grader, administrators can then increase teaching load). But
that's just being cynical.
Mitch
P.S. I did experience one class in grad school (intro mathematical
logic) that had some small group in-class problem solving sessions. I
think this worked well in the setting because everybody was extremely
motivated.
Arturo Magidin
Mitch <mah...@gmail.com> wrote:
>
>Arturo Magidin wrote:
>> LearningNerd <Learni...@gmail.com> wrote:
>>
>> >I think one way to make learning math more interesting -- and to make
>> >learning anything more interesting -- would be to incorporate more
>> >group projects,
>>
>> I've never understood that. I never liked group projects when I was
>> kid. I never knew anyone who particularly ->liked<- group projects as
>> opposed to other types of school work, ->except<- those people who
>> knew they could coast with little or no work, leaning on the other
>> members of the group.
>>
>> What is it about "group work" that gets education types so excited,
>> anyway?
>
>I'm totally with you there... but...
>
>I think the use of group work in a classroom setting (that is, having
>the students work in small groups on problems, and having the
>instructor be an asynchronous advisor), is that slower students will
>benefit from hearing the quicker students work out the problems out
>loud (learn to emulate their problem solving skills), and the quicker
>students will benefit from the usual 'you-learn-from-teaching'.
I have no objection to students workinging in groups. I find, however,
that forcing them to work in groups in the classroom setting is seldom
productive as the theories you describe assure me. In theory it may
sound useful, but I just don't see it happening.
I don't know of any studies that may have been done to test the
efficacy of the method; though I confess I have never searched for
any. The ones reported to me were pretty bad. I was told very
excitedly about the "great research" done on group work, in which the
researcher compared the work done by two groups of students. One group
attended class and each student worked on its own however long it
decided to work on it. The other group attended class, met regularly
during the week to go over the material in class and to work out
homework problems together, and had a very full schedule for studying
the material as it went along; they were spending about two or three
hours outside of class for every hour of classroom instruction going
over, studying the material, and working on homework problems. They
worked in a group, sure. But the conclusion of that study was "working
in groups helps students learn more than working by themselves". Which
seems like a rather silly (or at best highly unsupported)
conclusion. It seems far clearer that "spending a lot of time outside
of class working rather than the more obvious "spending more time
studying the material will help students learn more than spending less
time."
I tell my students that they should be spending about 2 hours outside
of class for every hour of classroom, throughout the week, studying
the material, going over it, and doing homework. How they spend those
hours (working in groups, by themselves, etc), is up to them, but they
should really figure out that that is at ->least<- how long they
should be working.
>I suppose another educationalism is that different students have
>different learning strategies and one of those strategies is bouncing
>ideas off each other (in addition to prolonged concentrated reasoning
>usually associated with mathematics).
->Some<- people have that strategy. In my experience, people who learn
better by bouncing ideas off each other tend to congregate and
->do that<-. That's great. But if "different students have different
learning strategies", then forcing them to work in groups, a
particular kind of strategy, does not seem to foster that.
In my particular experience I find that the success of the multiple
"alternate teaching methods" (working in groups, workshop-style,
self-discovery, and the like) is extremely sensitive to the actual
composition of the class. Some methods work well for some groups, or
some particular mix of students, but fare dismally with others.
While lecturing tends not to achieve the high level of success that
some of those methods ->may<- achieve in ideal circumstances (both in
terms of the student mix and composition, and the ability of the
instructor), it is far less sensitive to such conditions, and it
almost invariably achieves a minimum level of success which tends to
be much higher than the level of success those methods achieve under
less-than-ideal circumstances. Not to say that it cannot go dismally,
mind you, but rather that it is far less sensitive to particular
conditions than the other methods I have tried from time to time.
There is nothing wrong with experimenting with those methods; I tend
to base my courses on lecturing, with alternate activities sprinkled
throughout the semester tailored to the topics. If some of them seem to
work well with that particular class, then I try to incorporate more
of them that semester. If they don't, I drop them. But well over 70%
of my time in class is spend in an "interactive lecture" mode, where I
lecture but encourage the students to stop me with questions if they
have any, and where I frequently stop mid-sentence and ask the
students to prompt for what follows, reinforcing definitions, methods,
and the like. Seems to work pretty well.
>P.S. I did experience one class in grad school (intro mathematical
>logic) that had some small group in-class problem solving sessions. I
>think this worked well in the setting because everybody was extremely
>motivated.
Grad school is very different. For one thing, you have a self-selected
group of individuals who have already demonstrated success in
learning, and who are very likely to have identified the learning
strategies that work for them and know how to exploit them. The same
certainly cannot be said of mandatory education (say levels K-12); or
of undergraduate education, in which we seem to be trying to put more
and more people who may not be ready (or may never be ready) for it.
William Elliot
> LearningNerd <Learni...@gmail.com> wrote:
>
> >I think one way to make learning math more interesting -- and to make
> >learning anything more interesting -- would be to incorporate more
> >group projects,
>
> I've never understood that. I never liked group projects when I was
> kid. I never knew anyone who particularly ->liked<- group projects as
> opposed to other types of school work, ->except<- those people who
> knew they could coast with little or no work, leaning on the other
> members of the group.
>
I like the mural we did. Though was a group project, each person did a
single thing by themselves.
> What is it about "group work" that gets education types so excited,
> anyway?
>
Get's them get off the hook, having to teach, to hold the attention of the
class for the whole class period. Instead of teaching, wouldn'd it give
them time for some individual tutoring, which would otherwise have to be
done after class when the teacher is otherwise too busy paper working?
In addition, doesn't that cut down on the amount of class planning paper
work that needs to be done?
The poster formerly known as Colleyville Alan
news:eg4110$umb$1...@agate.berkeley.edu...
snip
>>Do you enjoy math?
>
> If I didn't I wouldn't be a mathematician.
>
>> If so, why?
>
> The pleasure of finally solving a problem that once seeemed
> unsurmountable is a very big part of it.
>
>>How could teachers and students make math more fun to learn?
>
> Why does it have to be "fun"?
Because students who enjoy the subject will learn it more thoroughly than
those who hope that once the final exam is over they never have to see
another math book. If the subject is worth knowing, it is worth knowing it
thoroughly, not superficially.
Perhaps a better question still is "how could teachers present the subject
matter in such a way that students will experience '...the pleasure of
finally solving a problem that once seeemed unsurmountable...'"? Heck, that
gets you going, it oughta work for the students as well!
mensa...@aol.com
LearningNerd wrote:
> I'm starting to relearn math on my own (I'm taking a year off before
> college), and I'm planning to write an introduction to learning math on
> my blog. To get some ideas, I'd like to hear your answers to any or all
> of the following questions:
>
> Why do so many people hate math?
Because it's hard.
>
> Why do they have trouble understanding it?
Because it's not trivia like History.
When the teacher says "open book test" it means the answers
aren't in the book. The methods to find the answers are, but you
have to figure out how to apply them.
>
> What are your experiences with learning math (at school, on your own,
> etc.)?
I almost didn't pass Algebra as a HS freshman, had to study all
summer and take a test to get a grade.
Then, as a sophmore, I took Geometry and discovered I
was better at deriving answers than memorizing them
and got straight A's. And suddenly, the Algebra that I
couldn't previously fathom suddenly became clear and
I got A's in all subsequent math classes.
>
> Do you enjoy math?
You should see the looks I get when I tell people that
math is a hobby of mine.
> If so, why?
It's enjoyable because you WANT to do it, not because
you have to. There is nothing I want to do that involves
Calculus. If I had to do it (say, for work) I wouldn't enjoy
it. Yet I plan to spend a good portion of my vacation
doing further research on the Collatz Conjecture. My sister
thinks I'm nuts.
>
> How could teachers and students make math more fun to learn?
You can't make it fun. The fun only comes from a person's
internal motivations. Want to learn MS-Access? It helps
greatly if you have something to motivate you, such as a desire
to do baseball statistics.
But not everyone is into baseball and many who are don't care
about statistics. Those are the problems you face when you
want to make math "fun".
>
> Thanks in advance for your feedback! Also, if you have any suggestions
> for how I should go about relearning math, please share them.
You need a hobby where math is applicable.
The poster formerly known as Colleyville Alan
news:1160184075.8...@i42g2000cwa.googlegroups.com...
>
>snip
>
> I almost didn't pass Algebra as a HS freshman, had to study all
> summer and take a test to get a grade.
>
> Then, as a sophmore, I took Geometry and discovered I
> was better at deriving answers than memorizing them
> and got straight A's. And suddenly, the Algebra that I
> couldn't previously fathom suddenly became clear and
> I got A's in all subsequent math classes.
>
>> How could teachers and students make math more fun to learn?
>
> You can't make it fun. The fun only comes from a person's
> internal motivations.
Ah, but I would be willing to bet that you did not find Algebra fun when you
were a HS freshman. Geometry made math fun for you because you could derive
the answers and not just memorize them. Teaching the subject so that
students can use their minds would be a step in the right direction.
It is true that many students do not want to take math, and for them there
may be no way to make it interesting or fun or whatever, but there are ways
of teaching that can make it unbearable even to those who like the subject.
So at least learning to avoid those methods and find better methods can
allow people who enjoy the subject to look forward to the class rather than
count the days until the semester ends.
William Elliot
> <mensa...@aol.com> wrote in message
> >
> > You can't make it fun. The fun only comes from a person's
> > internal motivations.
>
> Ah, but I would be willing to bet that you did not find Algebra fun when you
> were a HS freshman. Geometry made math fun for you because you could derive
> the answers and not just memorize them. Teaching the subject so that
> students can use their minds would be a step in the right direction.
>
They have been know to wrongthink about Vietnam, but that can't be allowed
anymore. No wrongthink about Iraqnam, no wrongthink about Bushbrat. You
all memorize what you're supposed to think.
> It is true that many students do not want to take math, and for them there
> may be no way to make it interesting or fun or whatever, but there are ways
> of teaching that can make it unbearable even to those who like the subject.
I didn't want to take history for the same reason, memorizing names of
stupid people and when they were stupid. However once beyond school, I
found history was ultimately fascinating. More enthralling than any novel
for in soothe, truth is stranger than fiction.
> So at least learning to avoid those methods and find better methods can
> allow people who enjoy the subject to look forward to the class rather
> than count the days until the semester ends.
>
Memorize newthink truth and you better get it right.
--
Formerly no one was allowed to think freely; now it is permitted, but
no one is capable of it any more. Now people want to think only what
they are supposed to think, and this they consider freedom.
-- Oswald Spengler (1880-1936) from The Decline of the West, 1926
----
The poster formerly known as Colleyville Alan
news:Pine.BSI.4.58.06...@vista.hevanet.com...
> The poster formerly known as Colleyville Alan wrote:
>> <mensa...@aol.com> wrote in message
>> >
>> > You can't make it fun. The fun only comes from a person's
>> > internal motivations.
>>
>> Ah, but I would be willing to bet that you did not find Algebra fun when
>> you
>> were a HS freshman. Geometry made math fun for you because you could
>> derive
>> the answers and not just memorize them. Teaching the subject so that
>> students can use their minds would be a step in the right direction.
>>
> That is gross wrongthink, to teach students to think.
> They have been know to wrongthink about Vietnam, but that can't be allowed
> anymore.
Absolutely. Remember, Oceania has always been at war with Eastasia.
Michael Press
mag...@math.berkeley.edu (Arturo Magidin) wrote:
> Note that the same may be said about reading. A ->lot<- of people hate
> reading; the idea of reading a book for fun, or in order to learn
> something, is a terrible chore to be avoided if possible. And even
> those who may enjoy some reading will often recoil at the idea of
> reading Dickens, Tolstoi, Jane Austen, Cervantes, or Milton; let us
> not even consider Shakespeare which, granted, was not meant to be read
> bu rather seen performed. And let us not even mention Plutarch or the
> likes of "Rise and Fall of the Roman Empire".
Or Edward Gibbon's
Decline_and_Fall_of_the_Roman_Empire.
--
Michael Press
LauLuna
it is all about; it seems like a game whose initial rules are
completely arbitrary and have no meaning at all. Teaching mathematics
should be something else than showing how to use pure formalisms with
no understandable purpose.
Learning mathematics requires intense and continuous attention, the
capability of dealing with details (analytical rather than synthetic
intelligence) and with abstract objects; it requires memory to retain
all the steps in intricate proofs or constructions, as well as previous
results. It also requires the sense of ordered and methodic proceeding.
In a nutshell, mathematics is entirely ruled by the Freudian 'principle
of reality' and seems to leave no room for the 'principle of pleasure',
for free creativity.
The crucial factor to break through all these difficulties is getting
to the point where one says: 'I can do it': the possibility of exerting
one's own abilities to get exact results is highly rewarding.
Regards
William Elliot
> In a nutshell, mathematics is entirely ruled by the Freudian 'principle
> of reality' and seems to leave no room for the 'principle of pleasure',
> for free creativity.
>
> The crucial factor to break through all these difficulties is getting
> to the point where one says: 'I can do it': the possibility of exerting
> one's own abilities to get exact results is highly rewarding.
>
What about sports? How come no difficulty teaching that?
Because current culture is sports minded and not science minded?
How come so many business majors? Because that's where the money is?
How come so few math majors? Because other careers pay better?
As for meeting ladies, don't take a math class, take an art class
or a business class. As for meeting men, take math and physics classes.
Arturo Magidin
The poster formerly known as Colleyville Alan <nos...@nospam.net> wrote:
>"Arturo Magidin" <mag...@math.berkeley.edu> wrote in message
>news:eg4110$umb$1...@agate.berkeley.edu...
>
>snip
>>>Do you enjoy math?
>>
>> If I didn't I wouldn't be a mathematician.
>>
>>> If so, why?
>>
>> The pleasure of finally solving a problem that once seeemed
>> unsurmountable is a very big part of it.
>>
>>>How could teachers and students make math more fun to learn?
>>
>> Why does it have to be "fun"?
>
>Because students who enjoy the subject will learn it more thoroughly than
>those who hope that once the final exam is over they never have to see
>another math book. If the subject is worth knowing, it is worth knowing it
>thoroughly, not superficially.
The first question is: WHY do we teach mathematics in K-12?
Is it because "math is worth knowing", or is it because basic math
skills are as necessary as basic literate skills (reading and
writing)?
In my opinion, it is the latter. Math is not taught because "it is
worth knowing". It is taught because you need to know it to function.
The second question is: what does "knowing thoroughly" mean?
Is basic arithmetic "worth knowing"? Certainly; everyone needs to know
addition, subtraction, multiplication, and division of rational
numbers, at the very least. Butis it worth knowing "thoroughly"?
Should they know that the natural numbers are categorically determined
by the Peano axioms? Should they know how to construct integers out of
naturals, rationals out of integers? Should they know a number of
nuances that we all know and appreciate here? If they don't, can we
really say they "know it thoroughly"?
I simply disagree. There are things that are worth knowing
superficially by everyone, and that only those truly interested in
going beyond should be expected or required to know "thoroughly". In
fact, there are things that it is a waste of time to teach
"thoroughly", for most understandings of "thoroughly".
As to making the subject "enjoyable"... That is such a subjective
thing; certainly certain teaching methods are more or less likely to
make it so. But in any case, I simply do not see why "making it
enjoyable" should be our goal. The goal should be, pure and simple, to
have students that learn the material and are able to use them for the
purposes that they need them (which is presumably the reason they are
being taught the material in the first place).
>Perhaps a better question still is "how could teachers present the subject
>matter in such a way that students will experience '...the pleasure of
>finally solving a problem that once seeemed unsurmountable...'"? Heck, that
>gets you going, it oughta work for the students as well!
Why? Some people derive NO pleasure in solving problems, whether easy
or hard. Isaac Asimov once wrote that he ->hated<- problems; unless he
saw the solution immediately, in which case he felt they were boring,
they were only a source of frustration that was not paid for by
solving them. There was no pleasure whatsoever for him. Was he an
ignoramus? Was he someone who simply was not taught math properly?
No. He simply did not feel the same way I do. Why should I expect my
students to get going for the same reasons I get going?
Arturo Magidin
Michael Press <ja...@abc.net> wrote:
>In article <eg4110$umb$1...@agate.berkeley.edu>,
> mag...@math.berkeley.edu (Arturo Magidin) wrote:
[...]
>> And let us not even mention Plutarch or the
>> likes of "Rise and Fall of the Roman Empire".
>
>Or Edward Gibbon's
>Decline_and_Fall_of_the_Roman_Empire.
Well, sorry; I read it in Spanish and misremembered the ttle.
The poster formerly known as Colleyville Alan
>>>>How could teachers and students make math more fun to learn?
>>>
>>> Why does it have to be "fun"?
>>
>>Because students who enjoy the subject will learn it more thoroughly than
>>those who hope that once the final exam is over they never have to see
>>another math book. If the subject is worth knowing, it is worth knowing
>>it
>>thoroughly, not superficially.
>
> The first question is: WHY do we teach mathematics in K-12?
>
> Is it because "math is worth knowing", or is it because basic math
> skills are as necessary as basic literate skills (reading and
> writing)?
Basic math skills such as "addition, subtraction, multiplication, and
division of rational numbers" are taught well before the 12th grade, so
asking about K-12 lumps too many years into the "basic math" learning phase.
Around the 7th grade students are introduced to pre-algebra or algebra.
Many of them ask a similar question to the one you just asked "WHY do we
have to study this". They also provide a reason why they should not have to
study it: "I'll never use it".
So, why teach algebra? Many people do go through life without using it and
they do not "need it to function". IMHO, we teach algebra to middle school
and high school students for the same reason that we teach them history,
because we feel that it is part of what an educated person should know.
As to "knowing thoroughly", it is as subjective as the word "enjoyable".
You mention that some things are worth knowing superficially. Ok, many
students know basic arithmetic skills superficially and that seems to work
for them. But again, consider algebra. Many students memorize stuff for an
exam and promptly forget it. That stuff they do not know even superficially
six weeks after the exam. In that case, why bother teaching it? Shouldn't
you want them to learn it well enough that they don't forget the vast
majority of it? Many adults who hated math as kids still possess basic
arithmetic skills but not basic algebra skills. Would it not be worthwhile
to try and find ways of teaching algebra so that they had basic algebra
skills years later?
James Dolan
the poster formerly known as colleyville alan <nos...@nospam.net> wrote:
|"Arturo Magidin" <mag...@math.berkeley.edu> wrote in message
|news:eg4110$umb$1...@agate.berkeley.edu...
|
|snip
|>>Do you enjoy math?
|>
|> If I didn't I wouldn't be a mathematician.
|>
|>> If so, why?
|>
|> The pleasure of finally solving a problem that once seeemed
|> unsurmountable is a very big part of it.
|>
|>>How could teachers and students make math more fun to learn?
|>
|> Why does it have to be "fun"?
|
|Because students who enjoy the subject will learn it more thoroughly
|than those who hope that once the final exam is over they never have
|to see another math book. If the subject is worth knowing, it is
|worth knowing it thoroughly, not superficially.
the main reason to "make" math fun is that it _is_ fun. when it's not
fun that's generally a tip-off that you're not actually doing math but
are instead wasting your time on worthless crap.
--
Arturo Magidin
> "Arturo Magidin" <mag...@math.berkeley.edu> wrote in message
> news:eg8vg2$1frl$1...@agate.berkeley.edu...
> >>>>How could teachers and students make math more fun to learn?
> >>>
> >>> Why does it have to be "fun"?
> >>
> >>Because students who enjoy the subject will learn it more thoroughly than
> >>those who hope that once the final exam is over they never have to see
> >>another math book. If the subject is worth knowing, it is worth knowing
> >>it
> >>thoroughly, not superficially.
> >
> > The first question is: WHY do we teach mathematics in K-12?
> >
> > Is it because "math is worth knowing", or is it because basic math
> > skills are as necessary as basic literate skills (reading and
> > writing)?
>
> Basic math skills such as "addition, subtraction, multiplication, and
> division of rational numbers" are taught well before the 12th grade, so
> asking about K-12 lumps too many years into the "basic math" learning phase.
> Around the 7th grade students are introduced to pre-algebra or algebra.
> Many of them ask a similar question to the one you just asked "WHY do we
> have to study this". They also provide a reason why they should not have to
> study it: "I'll never use it".
And they have no idea. Certainly if they don't know it then they'll
never use it. Which, of course, is the same one might say about reading
and writing. It is possible to go through life with a 3rd grade reading
and writing level. You don't really "need to learn to read" any better
than that. If they say "I'll never use" any better reading skill, are
they right?
I disagree with your assertion that algebra is taught for the same
reason we teach history, as part of general educational background. The
most basic notions of algebra are somethng which people should be using
just as they use arithmetic. From figuring out that 15% tip without
having to use a little card, to figuring out that getting a 10%
discount on the 25% discounted item is not a 35% discount. Of course, I
certainly agree that algebra is not ->being<- taught in a way that
makes this clear. ->I<- think this is in part because it is often
misguidedly thought of as something which we teach because we think any
educated person should know some algebra the same way he should know
some history and some geography. I think that is simply not the case.
I also think teaching trig and geometry should be replaced with basic
probability and statistics, but maybe that's just me.
> So, why teach algebra? Many people do go through life without using it and
> they do not "need it to function".
And many people go through life without knowing how to read and write,
and they do not need it to function (i.e., earn a wage and be able to
buy food and pay for shelter).
>IMHO, we teach algebra to middle school
> and high school students for the same reason that we teach them history,
> because we feel that it is part of what an educated person should know.
That I do not agree with.
> As to "knowing thoroughly", it is as subjective as the word "enjoyable".
I certainly agree. But then, what does it mean to try to teach things
so that people "know them thoroughly"? It's like trying to teach music
so that people will learn to "enjoy Stravinsky".
> You mention that some things are worth knowing superficially. Ok, many
> students know basic arithmetic skills superficially and that seems to work
> for them. But again, consider algebra. Many students memorize stuff for an
> exam and promptly forget it.
I certainly agree with you that algebra is not taught in a good way.
But I do not think the solution is to make it "fun" or "enjoyable." I
think the solution is to figure out ->why<- we teach it in the first
place; I think that teaching algebra as "exercise for the mind" (not
what you say, but something I've heard often enough from other
sources), or as you put it as an analog to history, "a part of what an
educated person should know", i.e., as 'general culture', is misguided.
For that matter, if we teach algebra for the same reason we teach
history, then it is hardly a suprrise that the results are the same:
many students memorize the dates and names for the exam and promptly
forget them, do they not?
> That stuff they do not know even superficially
> six weeks after the exam.
Same for history. Then perhaps we should not be taking the teaaching of
history as a model to be followed?
> In that case, why bother teaching it? Shouldn't
> you want them to learn it well enough that they don't forget the vast
> majority of it?
I would want them to learn it the same way I would want them to learn
arithmetic, basic statistics, and basic logic; the same way I would
want them to learn to read and write. I certainly don't want them to
learn the basics of algebra the way we deal with history or geoegraphy.
I do not think algebra is (or rather, should be) taught for that
reason.
> Many adults who hated math as kids still possess basic
> arithmetic skills but not basic algebra skills. Would it not be worthwhile
> to try and find ways of teaching algebra so that they had basic algebra
> skills years later?
Certainly. I just don't think that this is possible so long as algebra
is being viewed the way Latin and Greek were once upon a time, a sign
of education or a part of what "any educated person should know." If
they knew what algebra is for (if the people teaching it knew what
algebra was for) and used it on a regular basis, their algebraic skills
would no doubt be about the same as their arithmetic ones. Then perhaps
they could figure out what the gas mileage on their car actually is,
how many gallons they can buy if they only have 20%, how much to leave
for a tip when the service was good and you'd like to leave 18% instead
of the usual 15%, and the like.
I am certainly not saying math is being taught ->well<- now. But I
think part of the problem is an erroneous view of ->why<- math is being
taught in the first place, and what the objective of that instruction
should be.
But again, it could very well just be me.
Arturo Magidin
Arturo Magidin
James Dolan wrote:
> the main reason to "make" math fun is that it _is_ fun.
Many people assure me that hunting is fun. I just don't see it. I think
the games of Diplomacy and Cosmic Encounter are great fun; but there
are plenty of people who think they are boring, annoying, a waste of
time and effort, and any other number of things.
Sure, ->I<- like math. I also like soccer, for which I can also produce
several million people who will swear up and down that it is not a fun
sport.
> when it's not
> fun that's generally a tip-off that you're not actually doing math but
> are instead wasting your time on worthless crap.
Did I fail to enjoy hunting because I was not actually doing hunting?
Did my friends who failed to find Diplomacy "fun" do so because they
were not actually playing Diplomacy, and were instead doing some
worthless crap?
I enjoy math; I also enjoy a lot of classical compositions, and are
bored to death by requirems and masses. Other people find math boring,
think classical music is boring, and think Punk is fun. Are they wrong?
Or am I?
Arturo Magidin, sans s.ig
The poster formerly known as Colleyville Alan
>> arithmetic skills but not basic algebra skills. Would it not be
>> worthwhile
>> to try and find ways of teaching algebra so that they had basic algebra
>> skills years later?
>
> Certainly. I just don't think that this is possible so long as algebra
> is being viewed the way Latin and Greek were once upon a time, a sign
> of education or a part of what "any educated person should know." If
> they knew what algebra is for (if the people teaching it knew what
> algebra was for) and used it on a regular basis, their algebraic skills
> would no doubt be about the same as their arithmetic ones. Then perhaps
> they could figure out what the gas mileage on their car actually is,
> how many gallons they can buy if they only have 20%, how much to leave
> for a tip when the service was good and you'd like to leave 18% instead
> of the usual 15%, and the like.
>
> I am certainly not saying math is being taught ->well<- now. But I
> think part of the problem is an erroneous view of ->why<- math is being
> taught in the first place, and what the objective of that instruction
> should be.
I think we are tripping over each other in the use of "is" vs. "should be".
I think algebra "is" being taught as part of a general education "this is
what an educated person should know" philosophy. If you say that is should
not be taught because of that, then you have one argument, but you have a
very different argument if you are saying that it *is* not being taught for
that reason. I think, for the most part, that algebra *is* taught for
"educational" rather than practical reasons.
I agree that basic probability and stats would serve most people well. In
my intro stats book some 30 years ago, I read that "...the average person
uses statistics like a drunk uses a lamppost, for support rather than
illumination".
Arturo Magidin
The poster formerly known as Colleyville Alan wrote:
I agree with you. And part of my argument is that the problem is that
this is how it is being taught. Yes, I think it should not be taught
because of that.
The problem I find with "we should make math fun" is partly because of
that. If you begin with the premise that this is something they
"should" know, for "educational" reasons, then certainly you want to
motivate them to want to learn it, and perhaps making it "fun" is the
way to go. I'm all for making Shakespeare "fun" if that makes people
more eager to read (or watch) the plays.
The math that is taught, at least up to grade 9, though, should be math
that is taught for practical reasons, the same way we teach reading and
writing and comprehension for practical reasons at those levels. The
goal of teaching them algebra should not be to make them better
educated people, but rather to give them tools to use.
Yes, the world can go on without algebra. The world got along with the
vast majority of the population not knowing how to read and write, even
in "advanced" countries. In one major civilization, reading and writing
were so uncommon that the notion of cryptography never arose because
simply writing something down made it almost unintelligible to pretty
much eveyrone (China). And yet it "functioned". Surely the world
doesn't ->need<- people to know algebra to get along. And people don't
->need<- to know algebra to survive. But anyway, that's a different
argument, I think.
We are still teaching trig as a "basic skill". Why? Honestly, why? One
could perhaps excuse it when the farmer needed to be able to do some
measuring and surveying; but today, why do we spend a year teaching
everyone trig (at least, we spent a year teaching trig in Mexico in 8th
grade, if I recall the grade correctly; if not, it was 9th)? That time
would definitely be better spent ignoring trig completely and teaching
basic descriptive stats and basic probability. Instead of hoping for
every high school graduate to remember "SohCahToa", how about having
them remember that the odds of rolling a 6 with a single die, having
just rolled a six, is still just 1 in 6?
> I agree that basic probability and stats would serve most people well. In
> my intro stats book some 30 years ago, I read that "...the average person
> uses statistics like a drunk uses a lamppost, for support rather than
> illumination".
That's very good! I'm afraid I'm going to have to steal it. (-:
Arturo Magidin
David Marcus
> I'm starting to relearn math on my own (I'm taking a year off before
> college), and I'm planning to write an introduction to learning math on
> my blog. To get some ideas, I'd like to hear your answers to any or all
> of the following questions:
>
> Why do so many people hate math?
> Why do they have trouble understanding it?
Most (98%?) of people can't (or haven't learned to) think conceptually.
Since in math, all we do is teach concepts, these people never really
learn what the teacher is trying to teach. Instead they pass their math
classes by trying to memorize the solution to every problem the teacher
might ask on an exam. This disconnect between what is being taught and
what they are learning results in them hating math and not understanding
it.
I recommend reading the book review by Peter Ungar in the March 1986
American Mathematical Monthly pp. 221-230. In particular, see his "Point
of view" section on page 222.
--
David Marcus