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.

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