Molecular Manipulations
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Math and science taught together?
One thing I've noticed is how much easier math gets when I use it in science.
It's impossible to learn science, especially physics and chemistry without using a lot of math. If math and science where taught in the same class, at
the right levels of difficult, linked together with logic, wouldn't learning both would be easier?
“Mathematics is the language of science.” -Galileo Galilei.
Why aren't they taught together? I haven't seen any good books like this.
-The manipulator
We are all here on earth to help others; what on earth the others are here for I don't know. -W. H. Auden
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mayko
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Hm. My impression (of US public schools) was somewhat different: especially at the college level, physics (and to a lesser extent chemistry) are
heavily mathematical, often requiring prerequisites in calculus and differential equations. Books like Hewitt's Conceptual Physics, which use no more than high school algebra, which is introduced on the fly, are rather exceptional.
In my experience/observation, algebra became 'mainstream' in ~6th grade. That means grades K-5 has to teach science within a fairly rudimentary
language for making quantitative statements. Realistically, even if you introduce algebra at grade 6, people won't necessarily learn
it on any particular schedule, especially if it is taught without any physical context to give it meaning (I was in remedial algebra in 8th grade,
lulz). So, the ability to teach science quantitatively remains somewhat delayed.
Most of the rest of the time is spent on teaching 'the scientific method' (*vomits everywhere*) or requiring the memorization of facts without explaining underlying, unifying principles and giving only perfunctory hands-on
time.
This is sad, because I think it could be different; I've seen a few of really interesting books which try to bridge that gap between math and
science, and might be the base of a creative science/math program:
* Geometry, relativity, and the fourth dimension by Rudy v. B. Rucker
* Chaos Under Control by David Peak and Michael Frame
* Who Is Fourier? A Mathematical Adventure
Don't forget the Zoombinis, either!
[Edited on 6-3-2015 by mayko]
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Zombie
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I agree that a qualifier is really need in most of the way classes are taught.
math would be easier to understand if it had an application.
Science would be easier to understand it it were attached to say social studies.
The only way I learned anything was to have something to equate to. Remembering random formulas with nothing to use them on was not something I was
fond of.
I'm back re'learning everything now!
They tried to have me "put to sleep" so I came back to return the favor.
Zom.
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Magpie
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Quote: Originally posted by mayko  |
Realistically, even if you introduce algebra at grade 6, people won't necessarily learn it on any particular schedule, especially if
it is taught without any physical context to give it meaning (I was in remedial algebra in 8th grade, lulz). So, the ability to teach science
quantitatively remains somewhat delayed.
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In my day (the '50s) algebra 1 was not taught until the 9th grade. When I first saw it presented my mind rebelled saying "you can't do math with
letters of the alphabet!" Within a few days (or weeks?), however, I was doing the work and understanding it. My point is that I think abstract
concepts can be introduced too early. The brain must be sufficiently mature/experienced to handle them. I hear that some high schools teach
chemistry and calculus at the 9th grade level or earlier even. I seriously doubt that the students are mature enough at that age.
Ideally math can be learned without real examples, or as we called them, "word problems." I have always enjoyed math so this was not a problem for me
to learn it in the abstract. I understand that many people cannot see the point of math until they have to use it for a practical purpose.
[Edited on 6-3-2015 by Magpie]
The single most important condition for a successful synthesis is good mixing - Nicodem
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Molecular Manipulations
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Good point mayko. But I was thinking more for at least high school level math and science. My idea is more of using science to make
it easier to understand math, not necessarily the other way around. I've always loved science, but disliked math. I still got decent grades in it, but
never liked it until high school because of how it was tied with logic and science, I loved the theorems in geometry for example.
Why social studies?
| Quote: Originally posted by Zombie |
The only way I learned anything was to have something to equate to. Remembering random formulas with nothing to use them on was not something I was
fond of. |
Yup, I was so bad in math, but liked logic so much, that instead of memorizing the formulas like everyone else (except the idiots), I just thought
about every problem logically until I figured out how it worked. This actually worked fine for quite a while, but eventually I couldn't keep up once
the problem where to big to wrap my head around. Then I had no fallback, and had to go back and memorize tons of formulas.
| Quote: Originally posted by Magpie |
The brain must be sufficiently mature/experienced to handle them. I hear that some high schools teach chemistry and calculus at the 9th grade level
or earlier even. I seriously doubt that the students are mature enough at that age. |
Agreed. Ninth graders
can't do that.
See word
problems I like, they use logic! Same with science, it's like thousands of huge word problems.
-The manipulator
We are all here on earth to help others; what on earth the others are here for I don't know. -W. H. Auden
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blogfast25
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In my secondary education math and science teaching were roughly coordinated. My daughter, whose sec. educ. I closely followed, had the same
experience.
But in math teaching there has to be an element of 'pure math', things that an 'ordinary' scientist may never have to apply to real world problems.
I'm for that.
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MrHomeScientist
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I think that's a common cry of the average math student: "I'll never use this!"
I did that plenty of times myself.
The way to think about stuff like that is that it's brain exercise. Thinking about and solving these abstract problems you'll never run across in real
life actually helps you think through the problems you do face. Just like exercising your muscles at the gym - most people will never need to bench
press hundreds of pounds in daily life, but we do it because it builds overall strength.
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blogfast25
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MrHS:
I've always been opposed to that kind of 'utilitarianism'. There are things that are simply beautiful without being useful.
But, perhaps more importantly, it is simply impossible to predict whether or not a particular a particular mathematical insight, concept or discovery
will find actual later use or not.
Outside of math for instance, 'spin offs' have come from the most unexpected corners.
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Zombie
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I definitely fall into the "logic" side of this... I have to see the flow chart in my mind for it to become real, and therefore learned.
Everything has a mechanical way of becoming what it is. I need to know the entire process or I have no interest in the item.
Telling me that (3) is three because it is... You might as well tell me to leap off a cliff. I'm not accepting either one.
(3) is three because (1), and (2) made it. What made (1)?
Thus my dilemma in life. The brain can do some amazing things. The amount of data strings that can be learned, and processed are staggering to
realize. Most of us could NEVER put to paper everything we understand, yet I keep it all in there. The more times I have to begin at (0) the more
ingrained the process becomes, until I could solve a problem in my sleep.
I was equating Science to Social studies as a way to maintain a flow chart...
Take the invention of "gun powder"... I don't know when that was nor exactly who is credited. If the two fields were combined I would have a
mechanical method to follow human development based on the "tools" developed.
A good yardstick for history is the scientific advances that occur (IMHO).
I had perhaps 97% of my teachers spewing random facts in some apparent order (to them) but perhaps (3%) actually gave a real world qualification to
what they were teaching.
97% of what I was listening to was... Leap off a cliff! I've fought my entire life to fill in that missing group of "data strings" starting with the
3% that stuck.
That's why I am so prolific on forums. I'm fighting to learn.
They tried to have me "put to sleep" so I came back to return the favor.
Zom.
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Etaoin Shrdlu
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I think I would have hated it and myself. Every other subject I had in highschool was tied into social studies for no reason whatsoever. Kindly leave
science out of the mess. 
I have to wonder if I would have done better in mandatory college Spanish if it hadn't been half language, half
why-the-hell-are-we-studying-the-Day-of-the-Dead.
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Bright Spark
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I love maths, its what I live and breathe and becoming an electronics engineer allows me to apply it and I do use the vast majority of what I have
studied at some point
My job requires lots of advanced maths, ODE's, PDE's, FFT's fourier series state space modelling the list is long
Anyone who says its easy is a liar, being hard is what makes it intereesting
I am particularly interested in the limitations of math, of the things it can't handle like turbulance for example the none mathematician thinks maths
is complete but its as lacking as all the other subjects
I think the reason science and math isn't taught as one is because its its own subject, maths is the science of numbers and the field is enormous,
arguably one of the biggest fields you can study wso it needs to be delivered on its own because it is its own thing, you can use maths all on its own
without science but it doesn't work the other way
Maths is the foundations for almost everything so it needs to be delivered as such
my 2p
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Aria
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In science, geometric principles such as symmetry, reflection, shape, and structure reach down to the atomic levels. In science, algebraic balance is
required in chemical formulas, growth ratios, and genetic matrices. In science, math is used to analyze nature, discover its secrets and explain its
existence and this is the big problem. Science is so complex and getting more so each day.
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DrP
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| Quote: Originally posted by Molecular Manipulations | One thing I've noticed is how much easier math gets when I use it in science.
It's impossible to learn science, especially physics and chemistry without using a lot of math. If math and science where taught in the same class, at
the right levels of difficult, linked together with logic, wouldn't learning both would be easier? |
Same for me - I did 2 maths A-Levels, Pure and Applied maths. I found applied maths easy and pure maths one of the most boring subjects ever. I did
find some of the integration useful later in life and at uni, but it was so boring to me that I had a hard time putting in the effort to understand
it. Later, at uni, when I had need to integrate by parts and things I found that I understood it a lot better due to the application and it didn't
take long to relearn the equations and rules you needed to be able to do it. Some just have a gift for it I think - I do not know how/why people get
excited about pure maths. lol. Good for them.
Our A-level physics teacher first introduced us to calculus (and our chem teacher a bit) as we hadn't done it in maths yet and he needed us to know
about it for him to explain the physics we needed to learn. He actually asked us to ask our maths teachers to get on with the calculus so that we
could progress in our science class. When this didn't happen fast enough he taught us himself in our physics class.
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woelen
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Math and science could be taught together, but only to a certain extent. Mathematics is more than what is just needed for science. If you only teach
mathematics in this way, then it just becomes a toolbox and people pick out those tools which they need for their particular job.
Mathematics on its own is a science as well. Not about natural phenomena, nor about economics or social structures, but something really on its own.
The beautiful thing is that mathematics, developed at a certain time as something on its own can become a useful and nearly essential tool, to be used
in some other science. E.g. think of complex numbers, with the first ideas developed in the 17th century. Description of modern linear electronics is
very awkward and hard to understand without complex numbers.
When mathematics only is taught as a toolbox for other sciences, then I expect that true developments soon will come to a halt.
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sodium_stearate
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When I was in school during the 1960s and 70s, math
and science were, essentially taught together.
In math class we were always told to pay attention
because this stuff will be used in your science class.
In science class we were reminded that the stuff we were
being taught uses the math from the math class.
Yes, they were two separate classes that we had during
different hours of each day. But the teachers at the schools
reminded us almost daily of the great importance of each,
and drummed it into our heads that these two subjects
depend upon each other.
We were told that these things are tools that enable
man to do things that no other living creatures on earth
can do. We were told to use our brain.
"Opportunity is missed by most people
because it is dressed in overalls and it
looks like work" T.A. Edison
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JJay
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I think that math is much more interesting when I can see a use for it, but so much of it does not have a use that can be immediately connected to
anything practical. To some extent, it makes sense to teach them together, but that's only practical less than half the time.
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j_sum1
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Pedagogically, Mathematics is very different from Science.
It does not follow that they should be taught simultaneously.
Of course, the two disciplines ought to support one another and it is sensible to use some scientific contexts when teaching Mathematics. But the
beauty of Mathematics is that it transcends any given context. That abstraction needs to be taught. Therefore pinning it to the tangible world of
Science is counterproductive.
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sodium_stearate
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| Quote: Originally posted by j_sum1 |
But the beauty of Mathematics is that it transcends any given context. That abstraction needs to be taught. Therefore pinning it to the tangible world
of Science is counterproductive. |
I will add that, to me, the most interesting portion of
the interrelationship of math and science is how math
(being totally abstract), can be used so effectively to
model how things behave in the real world.
I find that fact very remarkable! 
"Opportunity is missed by most people
because it is dressed in overalls and it
looks like work" T.A. Edison
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Panda
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I personally like to keep the two subjects separate. For me it works better that way. However, I do realize what you mean. What about 3 different
classes? One that does science and math together and then the ones which separate them. This can let the student decide which way is better for their
learning.
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