In the movie "Oh, God" John Denver could not believe the unprepossessing George Burns was God, but he at least believed God existed.
I do not have that edge: no one believes Algebra failure rates can be reduced from 60% to 10%.
God did not win John over by levitating a sugar bowl in the diner, but He got him later when they were driving in the car and He made it rain. Inside the car.
All I can do is quote letters like this (with Margaret's kind permission):
Dear Ken,
Back in the '90s I used your Homework Tutor program successfully with my Algebra I students who were behind. I was excited about the efficient progress they made and how quickly they got to the same level as my better students after using the program.
Now I have some new teachers in my school who need help with their poor algebra students. Do you know where I could purchase your software?
Of all of the software I have used in the evolution of school math and computers, your Algebra I Homework Tutor was the most elegant and practical.
Sincerely,Margaret LekseRoundup High School, MTNice, but no rain.Or so I thought. Maybe you missed it, too.
When I reached out to Margaret (I was already resurrecting the app) and asked her to say more about her experience. She made clearer what her letter said: a half-dozen kids had fallen so far behind in Algebra that they no longer could follow her class presentations. She put all the kids on my software so the strugglers would not be embarrassed, then each kid worked at their own level. In one month the strugglers got up to speed and they put the software aside until new material proved challenging.
Wow. Same (exclellent, btw) teacher, same content, same kids. They fell behind under the traditional chalk talk/homework approach, then overtook the class when left to their own devices on my software.
But still, no one believes me, even long enough to let me show them the software. In this case my audience has definite information that what I am saying is impossible: we already tried software -- AlgeBlaster, Algebra Solved!, Cognitive Tutor, MyMathLab, MyMathLabPlus, ALEKS, Khan Academy, Mathspace, LearnBop -- and the Algebra failure rate is unchanged.
So what makes my software different? We will look at the details next, but the bottom line is that it was designed for real, struggling, unhappy, unenthusiastic students with shaky basic skills -- for the kids I worked with as a math teacher and private Algebra tutor.
Let's break that down by looking at my personal check list when assessing competitors:
Does the software check intermediate steps on multi-step problems?
I like to say that students do not do problems, they do steps of problems. Even if they do them in their head, they solve 3x-2 = 13 in two or more steps. Likewise, they do not get stuck on problems, they get stuck on steps of problems. Or make careless errors or reveal weak prerequisite skill on steps of problems.
If software is not checking steps, it cannot deeply engage the student. Sure, having the answer checked immediately instead of the next day is a big win, but it is not enough to create an immersive environment in which students are free to interact with Algebra the way a beginning programmer can interact with certain computer languages.
The ed theory buzzword for this is "active learning". With highly granular (step-by-step) feedback and hints and even videos, we enter a zone where even an indifferent student can apply native intelligence to sorting out the Algebra beast. They can try this, try that -- Algebra is talking to them saying "Fine" or "Not so much" or "Watch me", in detail.
Checking intermediate steps is hard because kids can type anything, and correct work can come in many forms -- the only way to do it is to create an artifical intellignece expert system that can parse and understand Algebra -- so most software checks only answers, explaining why come up short in research.
I was a private tutor, and worked problems in the classroom with the students. Step by step. I knew that students can have trouble with any step, but most often the first step is where the new topic had to be applied.
Looking back at 3x-2=13, that would come after students could handle 3x=15 and x-2 = 13. So the first step presents the new challenge: which of the two familiar balancing transformations do I apply first?
Where is the vast majority of Algebra tutorial software while the student is contemplating that new concern? Nowhere to be found: "Come see me when you have the answer." followed by "Sorry, wrong."
Note that this is not so bad for the strong student, who then gamely rechecks all their steps looking for their mistake and usually finds it without much trouble. Great, but those are not the students failing Algebra.
Does the student generate answers, or is it multiple-choice?
Multiple choice just does not work. My French teacher liked to say (in French) that there is all the difference in the world between recognition and recall. She said this after we all came up empty on a bit of vocabulary but as soon as she started the word we all finished it with her.
Think about it. Multiple choice always provides the answer! It tries to challenge us by providing three or four other choices, but it still provides the answer. As for the several other choices, well, students have twenty ways to go wrong in Algebra. Providing just three silently corrects seventeen of those mistakes.
By contrast, let students enter their own answers and ironically we help them learn by making success harder. That blank piece of paper, be it of pixels or tree, forces them to generate the mathematics. Yes, help is available, but there again they must do the heavy lifting of asking for and analyzing the help.
The current buzzword for this is "active learning", but I prefer Confucius's "I do and I understand".
Whatever the term, multiple-choice makes this impossible.
OK, the student supplies all work. How? By typing (x^2 -1)/(x+1)?
My target students are strugglers. They will not get far trying to type or read stuff like
(x^2 -1)/(x+1), known as "ASCII math".
(x^2 -1)/(x+1), known as "ASCII math".
And if the software can render maths nicely (as would TeX), does it include a slick maths editor? Or does it have a graphical keypad with icons for different operations forcing strugglers to build equations click by click?
A slick editor is hard, btw, which is one reason software does multiple choice.
Fail on either of these and the struggle with composing or reading math will prevent immersion in the maths.
