Results are indeed quite impressive, though just now it took a while to get a “q” (that’s the letter after “p”) recognized as such instead of 9. But I am an old guy not even accustomed to tablets, and only played for about two minutes. Use it heads down for an hour and I imagine it gets dead easy.

Unfortunately I am maybe 20% along in their Algebra I and I had to multiply a binomial times a trinomial. I punted.

“If adaptive software could improve the quality of my feedback, I would be all over it.”

I’m very curious to know more on your dream classroom software:
What professional development or non-software resources have improved the quality of your feedback up to this point?
Would it be useful to see a list of potential misconceptions a particular student may hold? Conversation starters?

On the whole, there is nothing ‘adaptive” about my application. But I suspect you were using ‘adaptive” in a casual sense and just meant “automated”. That’s fine.

If you really want “more effective..software”, you and everyone else in the burgeoning Anti-Feedback Group need to accept one simple idea: different products work different ways.

Happy exploring! Or not. :)

I love when you said, “With immediate feedback, we may find students trying answer after answer, looking for the red x change to a green check mark, learning little more than systematic guessing.” I have found this result whenever I have used adaptive math software in the classroom. Many of my students, particular students who typically struggle with math, go through the motions and end up guessing answers until they get it right. With no human body looking over them or helping them step-by-step through a problem, it becomes a guessing game. This fact only hurts the student’s learning experience and creates more work for the teacher who needs to go back and ensure that students actually understand the concepts.

I also agree with many others on this comment thread that I don’t need more problems as a teacher, I need strong feedback effectiveness, which comes through additional training and resources. Generating a multitude of problems for my students to practice is never an issue and takes very little time with all the resources at hand. The issue is giving strong and consistent feedback to all students in a way that will help them learn and progress. Yes, I would love instant feedback, but it is more important to me that the feedback has quality. If adaptive software could improve the quality of my feedback, I would be all over it. However, that isn’t something I have seen or experienced so far. I feel like I end up cleaning up the mess after my students use adaptive software. Time after time I am explaining the concepts and steps of the problem that they completely skipped when doing problems on adaptive software.

If anyone has insight into more effective feedback systems or software, I am all ears.

@Howard – Interesting! The widely used plugin for LaTeX and MathML on the web is http://www.mathjax.org/ Several LMS’ have this built-in. AFAIK, the best free and open source general Math learning software is: http://www.sagemath.org/

I downloaded the algebra app and made some headway but got stuck on the “Solve” option. I picked “subtract from both sides”, it prompted me for a term, I clicked on a term, then nothing happened.

Shoot me a note at ken at tiltontec dot com if you want to give me a hint on that.

On a more serious matter, I have spent several years (not all the time) developing an algebra program (not “Computer Algebra”) which has the following:
1: Input as text, editable display in algebraic form
2: Numerous algebraic operations
3: Direct, meaningful feedback, explaining why an operation is not going to work, in terms of the algebraic structure, and
4: Useful evaluation and graphing features.

Details via the Software page on my wordpress site.

I would love someone to have a look at it to see if it meets ANY of the desirable aims of “instant feedback” that apparently not possessed by other software.
It is free !

Here’s what I mean. The problem is more or less simple, “How do I create a means of providing instant feedback for the student?” Or is it? As soon as I ask that question, my mind immediately travels to the nuts and bolts. What is the algorithm? What is the most effective feedback? How does guessing fit in to the feedback loop?

Whoops, forgot something, didn’t we? Isn’t the real question “How do I foster the student’s skill and power in mathematical reasoning?” The better question leaves room for better answers. Eventually, you come upon the best answer, which I am pretty sure is that the student learns to create meaning and build understanding through working with the problem, not by watching the red x turn green. When a student experiences this “Aha!” moment, the rewards are instant and lasting.

Still, the operative question it whether to treat ourselves like Pavlov and Skinner, or like Vygotzky and Bruner. I don’t know about you, but I want to see my children and my students grow in math confidence, and to be able to explain their process. Then, if they get the answer wrong, I don’t care! They have gotten the meaning right.

So the best we can manage in the real world are correlations among a variety of influential conditions and activities which in many cases are interdependent. In other words, feedback can only be effective if certain other conditions are met.

In addition, effect sizes naturally correlate with learners’ initial state of performance. It’s much easier to make substantial learning gains (with minimal interventions) with learners who were previously poorly supported than learners who are already working in optimum conditions (AKA “chasing the long tail”).

The role of anecdotal evidence in research is important but should never be taken as conclusive, i.e. don’t base your learning and teaching practice on them. Anecdotes serve as interesting insights that may or may not warrant more thorough and systematic investigation, i.e. research. I certainly wouldn’t base a business model on them.

For your amusement: “Correlation isn’t causation” http://www.fastcodesign.com/3030529/infographic-of-the-day/hilarious-graphs-prove-that-correlation-isnt-causation