Re: [Phys-l] What are your answers for this teacher?

[William Robertson <wrobert9@ix.netcom.com>]

Using triangles for various math operations is quite popular in  
elementary schools. I don't mind it much when it's used as "flash  
cards," where students learn that 2x5=10, 10/5=2, and 10/2=5, all on  
the same triangle. I can see an argument for these that is similar to  
knowing your multiplication tables by heart. It helps you concentrate  
on higher-level thinking if you don't have to stop and figure out a  
multiplication or division result.

When used for basic algebraic manipulations, though, I think it's a  
huge mistake. The world, and this includes students of physics, is  
full of people who do not understand basic algebra. It's amazing how  
many teachers, for example, still "take something to the other side  
and make it negative" when dealing with equations. When I taught  
college physics, many incoming students did not understand how to  
solve an equation for a particular variable. When I sat in on graduate  
education courses in statistics, I was amazed at how many education  
GRADUATE students freaked out at the sight of something as simple as  
V=IR and solving for R.

For these students to rely on triangle "crutches" (agree with  
everything in JD's recent post) alone, and not understand the process,  
is wrong. And if they do understand the process, wouldn't it be better  
for them to be able to simply look at V=IR and be able to mentally  
solve for each variable? Wouldn't it actually take longer to use the  
triangle? So the question is, if the students truly understand the  
basic algebraic manipulation involved with V=IR, why in the world  
would they need the triangle?

Bill



On Apr 9, 2011, at 9:19 AM, Bernard Cleyet wrote:

> Today's first PTSOS post:
>
> My 9th grade physics students were taught a method for solving speed  
> problems in middle school that does not require algebra. The  
> variables are separated in a diagram of a triangle (or a circle).  
> When you cover up the variable you are solving for, the diagram  
> shows you the recipe on how to solve the problem. If you're not  
> familiar with what I'm talking about, here's a link to an example  
> using Ohm's Law: http://www.electronics-tutorials.ws/dccircuits/dcp_2.html
>
> I have avoided use of this device for a variety of reasons. First of  
> all, it has zero meaning. I feel that it is important to reinforce  
> my students' algebra skills, which this method completely skips. I  
> also prefer Hewitt's method on using equations as "guides to  
> thinking" which these triangles/circles avoid. Finally, I have found  
> in the past that various memory devices in math (e.g. FOIL, cross  
> multiplication, etc.) have limited function and students tend to use  
> them incorrectly much of the time.
>
> However, I am wondering if I should reconsider my stubborn position.  
> I have had many students approach me this year showing me the  
> triangle and claiming "here's an easier way to solve the problems!"  
> In addition, at the NSTA conference I was introduced to a text  
> entitled "Active Physics" by Arthur Eisenkraft which uses the circle  
> for every equation given in the book.
>
> Again, these are 9th graders I am teaching, so maybe I should not be  
> such a stickler on going through all the algebra. This device is  
> primarily used for "plug and chug" problems anyway, which have  
> little meaning themselves.
>
> Do any of you use this method with your students? Have you found it  
> useful? Do you have any tips to make it more meaningful and  
> universal? Do you see it as a hindrance?
>
> Thanks in advance for your collective knowledge and wisdom!
>
> bc thinks the picture is not a model.
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