When Simple Is Not So Simple

[mmm4444bot]

… I really really dislike these type of vague problem statements … functions, expressions can typically be rewritten in many different forms, and then it becomes an exercise in semantics to determine if one is "more simplified" than the others.

I completely agree! A command to "simplify" ought to be accompanied with an explicit statement of intent.

Last year, I helped a student with an exam question like \(\displaystyle \text{Simplify} \; 3(\frac{x}{5} + 1)\).

As her answer, she had written \(\displaystyle \frac{3}{5}x + 3\), but was marked wrong.

Turns out, the desired answer was \(\displaystyle 3(\frac{x+5}{5})\). Hoo boy… :roll:

 

[ksdhart2]

I completely agree! A command to "simplify" ought to be accompanied with an explicit statement of intent.

Last year, I helped a student with an exam question like \(\displaystyle \text{Simplify} \; 3(\frac{x}{5} + 1)\).

As her answer, she had written \(\displaystyle \frac{3}{5}x + 3\), but was marked wrong.

Turns out, the desired answer was \(\displaystyle 3(\frac{x+5}{5})\). Hoo boy… :roll:

That seems like something an automatic grader would pull. I'd like to think that a real flesh-and-blood teacher would have the intelligence and the flexibility to note that such vaguely worded problems can, and do, have multiple solutions. Recalling my own experiences in grade school though, as well as stories I've heard from others, I suspect that a fair numbers of teachers have the mindset that their answer is absolutely, unequivocally correct. After all, "You're just some snot-nosed little kid, what could you possibly know?!"

Similar to your story, I helped a student with a problem that was marked wrong, despite being a valid answer, simply because it wasn't what the instructor was expecting. The problem was a linear programming exercise, involving buying three different types of books with different costs, and the student had to figure out how many books of each type were bought, given the total cost and total number bought. The student came up with the only possible answer where at least one of each book must be bought. However, the answer the instructor had in mind involved not buying any of the most expensive type of book. Who ever would have thought of that? :-x

 

[stapel]

This is a big part of why I don't much like (that is, I hate) online math courses, where all the grading is automated. Students can be much more creative than a computer (let alone an instructor) might expect. It's so discouraging to students to be told that they're "wrong", when all they did was format differently, or be to clever for the back-end script to handle.