So, a valid issue remains, how do you engage the under-performers? Far more difficult as they typically lack motivation. Also, high achievers almost always get instant rewards, under-performers tend to struggle along behind, often with negative reinforcement more than offsetting ‘rewards’.

With regards to the latter, I also dislike the apparent need for the ‘gamification’ of these things. Yes, I understand incentives for achievement, but is this what we are really deriving here? I fully understand comments from teachers who say that students race through the tests racking up their badges without really absorbing very much. The game tokens thus become more important than the real objective.

Much remains to be done in the field of online tuition, therefore.

To learn something new from it, or ANY OTHER VIDEO/ON-LINE INDEPENDENT STUDY TOOL… we start the video (or text or multimedia whatever), run until the problem is posted, then stop the video and THINK. Maybe for a minute, maybe for a day, maybe for a week. Once we appreciate the problem (and probably have some understanding of the solution) listening to a clean top-down description is kind of cool and helpful.

So yeah, helpful. Transformational? Not so much but, really, that doesn’t stop us from using it. It is better than what we were using before. (Not as good as AoPS, ST Math, or Wuzzit Trouble though)

Those few adept at algebra are practicing in a different way, I posit, than those many just struggling to get through math without failing. It is of course possible to have students productively practice solving thousands of problems per year, many of them very challenging, with quality instructional design of the digital learning environment and content. On ST Math, we saw thousands of students firing up their school-based digital math homework on new iPads on Dec 25th to ‘play’.

Software can be good for good math practice. I agree that lots of good math practice is a requirement for math literacy. As @Dan Meyer notes in his comment above, digital math content also extends beyond practice, of course. And that i.m.o. is a very interesting place to look for how digital content can help bring about transformative outcomes in student learning.

Wow, “practice” sure is taking a beating in this blog post and thread. :) And it sounds like it is being equated with memorization. If I see (a^2-b^2) and without thinking also see its factorzation, that is a math skill built up over long practice. That is not recall from memory.

Anyone adept at algebra is not sitting there summoning up rules to apply from some memorized lookup table, they are simply recognizing patterns and applying the rule for transforming that pattern.

How is the right rule associated with the right pattern? How are patterns even recognized as the concrete terms vary? The same way one gets to Carnegie Hall: practice, practice, practice.

Prior to that we need an engaging teacher who loves math for itself, and instruction that goes deep, deriving rules from more fundamental rules. But then we need practice, at anything we wish to learn which does not yield to simple rote learning.

If my horse does not fare well in the practice derby I’ll live. What concerns me here is the prospect of our long-suffering young (beginning with me and others enduring the Sputnik-inspired New Math) being short-changed by educators who would eschew practice thinking practice must be unpleasant.

In fact, again, anyone who did well in Algebra enjoyed every problem for what it was: a transformation puzzle.

Kids do not need less practice, they need better instruction and, as the study noted, immediate feedback when they do the practice. Looks like Khan understands that now so I better get back to work. :)

Andrew Coulson:

Not all digital math content is just for practice: parsing sentences, recognizing a problem type from lecture or book, and then recalling and repeating memorized standard procedures, again as shown by lecture and book.

Not what I said. I’m specifically referring to “math practice software” here, not “all digital math content.”