A blow-by-blow replay of a disappointing
on-line Algebra experience at
the Monterey Institute.
[Originally posted here. Everything below will make a lot more sense if you open the lesson being discussed in a second window and follow along. The lesson is here.]
We start with a word problem, the kind one would never have to solve in life. Super.
The answer is 2n so I choose n/2 to see what happens. The software says "Incorrect" in red, does not offer the correct answer, and simply encourages me to go on to the next slide. Very helpful. I guess the idea is to throw in an interaction so we do not fall asleep reading the material, but not to try teaching at this point since that will come later. I guess, but then they should say "Incorrect. Not to worry, we'll work on this more later." But then I am reminded of the teacher who will not take a question that occurs to me now because they pre-planned a presentation that answered it some other time. Well excuuuse me.
Having no choice, I hit "Next". The material continues like this until eventually I get to play with two helicopters to solve x/2 - 3 = 1. I found myself wondering where the two expressions came from and why a helicopter would be doing hovering at x/2 - 3, but I was always a troublemaker in school.
Nowhere does the software talk about even needing to keep the two choppers at the same altitude, let alone why we would have to in terms of what the choppers were doing (which was nothing).
Me, I like see-saws which are level when the two sides are the same, just as we want to preserve an equation's truth as we transform it. Anyway...
Clicking +3 (we are offered only adding or multiplying plus or minus 1 thru 3) on the first chopper moves it up but leaves the expression as x/2 - 3. It should have changed to x/2. In case you think I did not understand the task, the other chopper's expression indeed changed from 1 to 4 when I clicked +3. Total bug there.
Clicking x2 (meaning multiply, not the variable "x") finally changes the first chopper's expression to x. The other chopper continues to work and becomes 8. Yeah!!!!!!
Now the accompanying text simply goes wrong, saying we have to add before we multiply. No, that just makes it easier.
It gets worse: the text says that if we multiply by 2 first we will end up with the wrong answer, x=5. Nonsense, as the graphic shows: we end up with x - 3 = 5, what it calls "an incomplete solution".
Thought one: an incomplete solution is not a solution! Add 3 to both sides!!
Second thought: how on Earth did we get to x-3=5? By going x/2-3=1 to 2(x/2-3)=2*1 to x-6=2 to x-6+3=2+3 to x-3=5. ie, Right, they accepted as inevitable the two operations of adding at most 3 and multiplying by at most 3, with nothing else permitted. Hunh? Math is done with pushbuttons, and only certain ones?
Just this little bit of material is wrong in one place, inconsistent with itself, confusing, unmotivating, and plain leaves out the fundamental concept of preserving the truth of the equation as necessary, ie, never mentions that we need to keep the choppers at the same altitude.
On-line and interactive is only as good as the underlying fundamental material, and in that regard Monterey comes up short. They made a brave effort and they have my sympathy over the bugs (software validation is a pain) and they mean well, but this site is worse than no site at all.