>    Yes, I can do this by using:
>
>              sd=: 4 : '%:  (%<:#y)  * +/ *: y -(+/y)%#y'
>
> but the student is going to ask why we put it in quotes when the
> rest of Mathematics isn't in quotes and doesn't write 4: in the front.
> Seemingly little barriers can actually be big barriers.

Don,

At this point, I must differ with your assumption that modifying tacit  
J, or creating S as another language with different kinds of tacit  
expressions, will make it easier for young learners of mathematics.

As a test case (admittedly a single data point, and with some obvious  
bias :^),  I asked my 13-year old son to evaluate this sequence.  Like  
the proverbial cobbler's kid going unshod, he doesn't have much of a  
computer background, but he does know how to turn it on, play games,  
and has written reports in Word.

He is in 7th grade, but is taking 8th grade math.  He has studied  
algebra, and has learned how to simplify equations.  He has also had  
to deal with multiple equations of multiple variables.

He had no question about the quotes surrounding the statement as part  
of defining the J verb.

He had no problem with the explicit expressions, using "x" and "y".

He did have a problem with tacit expressions, especially when  
converting explicit to tacit, by replacing "x" and "y" with "[" and  
"]".  He said "why do that?"

My son was essentially confirming my own assessment: that young  
learners of math would have more problems with tacit expressions than  
with explicit expressions, using variables.  Most students of any  
algebraic language would prefer to use expressions with variables than  
use expressions with symbols only.

The use of variables in an equation is already an abstraction.  The  
use of symbols to avoid references to variables is either a  
convolution or an abstraction of an abstraction, and thus, more  
challenging, especially to young learners.

In regard to young math learners being able to evaluate math  
expressions, see results, and even possibly plot them, J's use of "x"  
and "y" are easier than using tacit expressions, even if one has to  
use quotes as part of the definition.

I will do some more experiments with both of my sons (11 & 13) to see  
how they fair in using J.

-- 
Alan

----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm

Reply via email to