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Re: [Phys-L] just for fun

I've never been brave enough to try, but one of my faculty taught the intro course not allowing calculators on exams and didn't get much in the of push-back. I've met others who have done this as well. Personally I think it’s a good idea. One obviously has to be careful with how you ask questions, but you may get fewer complaints about algebraic problems with symbolic answers.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Bill Nettles
Sent: Thursday, December 19, 2013 10:07 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] just for fun

I think it's important to teach the art of estimation. I agree with JD that learning to solve problems as a general system is important, powerful, and artful. Estimation another "coin of the realm" that every (serious?) student should have. Don't be afraid to use convenient fractional numbers, but get students to realize and remember such numerical relationships that g_Earth~ pi^2 (SI units), sqrt(2), ln(2), squares of integers from 1 to 20. Trinity, Little Boy, Fatman, and the Nautilus were developed primarily with slide rules by people who were trained to be numerate (is that a word, parallel to literate?)

That's why I favor ditching calculators until absolutely needed for precise numerical work. I think calculators are being used to enable "math" teachers who don't want the hard work of forcing students to work hard. And calculators are being forced on the good math teachers who see the destruction they are causing.

Do it, Anthony...teach at least one 6-8 week period without the calculator. Yes, the students will whine. If the admin complains tell them you will allow calculators when the football and basketball teams quit running wind sprints and having 3-hour practices. (Easier for me to say than for you to do.)

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Anthony Lapinski
Sent: Thursday, December 19, 2013 9:36 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] just for fun

This is all very nice and interesting, but kids don't think like this.
They're not taught
to deal with fractions like this. Kids these days seem weaker than those in the past.
They can't do basic fractions/decimals/estimations in their head (3/4, 2/5, 1/20, etc.).
They are literally lost without a calculator (or a cell phone). This is the big downfall of technology, which we are slowly seeing -- taking the thinking out of learning. Much easier to "click" than think.

Over the years I have thought about teaching physics without a calculator.
I could
essentially make up math problems where the numbers would come out as simple, non-repeating decimals. Might be difficult for the circular motion/universal gravitation topic, but I could always uses rounded numbers for the masses of the Sun, Earth, etc.
And for projectile motion with trig, I could always use simple angles (30, 45, 60). The inverse trig problems would be an issue. Maybe eliminate them? Still, kids would have to do basic algebra/fractions in their head. I've often wondered what the results would be like and how my students would handle this. I imagine not well at all, so this is why I have hesitated.

Anybody else thought about something like this?



Phys-L@Phys-L.org writes:

Surendranath

keep going
and now compare
1/6 with 1/8.5
and clearly 1/6 is bigger

faster for me

Richard




On Dec 19, 2013, at 9:56 AM, Surendranath <surendranath.b@gmail.com>
wrote:

how about 25/28 = (28-3)/28 = 1-3/28

and 15/17 = (17-2)/17 = 1-2/17

and compare 3/18 and 2/17


Best Wishes,

Surendranath

www.surendranath.org
www.youtube.com/user/Surendranath1954
https://play.google.com/store/search?q=pub:Surendranath.B.


On Thu, Dec 19, 2013 at 7:34 PM, John Denker <jsd@av8n.com> wrote:

The question was:

Which is bigger: 25/28 or 15/17? [1]

Here's my take: Write it as

a b
------- ¿>? ------- [2]
a + 3 b + 2

We know the value of a and b, so we don't need to solve for them,
but for now let's leave them as symbolic rather than numeric.

Cross multiply. Throw away the "ab" term from both sides.
This leaves us with

2a ¿>? 3b

Now plug in the numeric values and do the multiplication.

I can do all of the above in my head, in less time than it takes to
find a pencil and paper.

=================

The larger point here is that sometimes it is /easier/ to do the
general case rather than the specific case. It's just plain easier,
even if only one specific case is of interest.
-- The advantage is even greater if there are multiple specific
cases on the agenda.
-- The advantage is even greater if the generalization provides
some insight into the structure of the problem, into the nature of
the problem.

There is artistry involved in finding a "good" generalization.
Equation [2] is not the only possible generalization of equation
[1].

The artistry is not however a shot in the dark. Experience suggests
patterns that are worth looking at. In this case there is an
analogy to differential-mode signaling. On the LHS "a" is the
common-mode signal, common to both numerator and denominator, while
"3" is the differential-mode signal.
Rewriting it so as to focus attention on what's common and what's
different is a technique that you can use in lots of situations.
There is no chance that HS students will have the experience and
expertise to do something like this, which is why this is not a
placement-test question but rather a just-for-fun question.

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_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l



_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l