Thursday, September 30, 2010

Apple's sexy new iPad now has a bit of an Algebra experiment underway: HMH Fuse: Algebra 1 is being tried out in a number of California schools, with the iPads being provided by Houghton-Mifflin.

Much of Fuse: Algebra 1 (F:A1) is old news. Kids already have access to Algebra on the Web, including on-demand video instruction on specific topics and step-by-step solutions to sample problems. But google this story enough and one discovers that the educational model will also change to make the teacher more of a mentor while kids themselves will determine their own path to Algebra mastery. Good things happen by letting folks decide their own course, so why do I not think this product will help much?

One simple reason, in one compound word: multiple-choice. With F:A1, problems are presented in multiple-choice form and no successful math tutor can be built atop multiple-choice.What is wrong with multiple-choice? It means the only tutorial intervention while the student is working is answer-checking. That is not enough.

What about the video lessons and solved examples? All good, which is why F:A1 will help a little, but true learning begins only when we ourselves attempt a new task. Confucius was more eloquent:
I hear and I forget. I see and I believe. I do and I understand.
Students can listen in class or watch problems solved by the teacher and think they understand, but only when they themselves tackle a problem do they:
  • realize they are not quite sure what to do; and
  • make mistakes involving prerequisite skills (a big problem for many students).
But most software Algebra tutors are nowhere to be found at this critical juncture. They are simply waiting for the student to finish working on paper and to come back and type in A, B, C, or D. As an experienced private Algebra tutor, I know students have trouble at every step of a solution, with the first step usually being the toughest since that is most often where the key new transformation introduced by the day's lesson must be applied. Any software Algebra tutor that wants to make more than a marginal improvement in how kids experience Algebra must be involved in every step they do.

Yes, multiple-choice is the nearly universal standard for computer Algebra tutors, but as these notes reveal, computer Algebra tutors are also largely ineffective. (Or we would not be talking about an Algebra crisis.)

So why does most software work this way? Two reasons, both having to do with development cost. First, to check intermediate steps, one has to let the student type mathematics the way you can here. But that kind of math editor is quite hard to write. Second, checking intermediate steps means creating a software Algebra expert that can recognize any possible approach the student might take to a solution, and there can be many. Again, quite hard to develop. So instead students end up with multiple-choice.

This page includes a link to a video (look for "Watch Fuse: Algebra 1 in action") where in the opening scene you can get a feel for how students do Algebra with F:A1. The bit where she uses the scratchpad to enter "6 - 2 = 4" as if she could not do it in her head tips us off that this is a major shortcoming of the product. Imagine her using that to simplify algebraic fractions involving parentheses and exponents. Even if it were feasible, the F:A1 software still would not be checking her work or offering hints -- it does not see the scratchpad work.I

t does not have to be this way. The software here lets students type readable math and work on problems step-by-step, asking for hints or seeing random examples solved and explained, having every step of every problem checked as soon as it is entered. That is where F:A1 needs to go next if it wants to transform Algebra instruction to any interesting degree.

Trouble in Monterey

A blow-by-blow replay of a disappointing
on-line Algebra experience at

[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.