Gifted Issues Discussion homepage Forums General Discussion Khan Academy - realistically aligned by grade?

I liked Aleks.com for my kids....three in a row correct for mastery but the assessment cycle assured that they really had altered it. They really liked the pie chart and the self determination of what to work on. Both kids used it as a supplemental program...one to our homeschooling work and one who was in second grade working within his classroom using a third grade book.

I am not sure Khan academy is a good way to judge what they know. My ds loves it and the way it introduces new topics that he does not know and videos on how to do them. May not be a great stand alone curriculum but really inspires him to learn new things and use his math. He is 8 too and elementary math can be very repetitive so there might be some test the school can give to see where she is. State sols for future grades is a good way for us.

I think you can do a free trial of ALEKS which includes an assessment, and see if you like it or not. I didn't like it because it moved them on and mastered them way too quickly. I mean, completing 3 problems of long division in a row is not nearly enough to truly learn it and remember it. Plus, it required everything to be copied onto scratch paper, and if this wasn't done my kids would try to solve everything in their heads and make errors. I personally am trying to find a program where they can do things the "correct" way right on the screen without copying. I think IXL changed things around so it's better now, for instance regrouping can be done right on the screen. You can try a certain number of problems on IXL per day for free.

See, my kids were using it along side other instruction....three problems were plenty for how we were using it. And every so often it would retest and if something wasn't really mastered it went back into the mix...I would say maybe one skill each time needed to be recycled through the pie chart to be relearned.

I have the opposite opinion of ALEKS. My son has to use it for precalc, and IMO, 3 correct problems is nowhere near enough to say that he's mastered a given topic. That said, the kids in his class aren't getting any instruction because their teacher has been out since early January, and ALEKS is being used as the primary vehicle for learning the subject.

I think that the larger problem with systems like ALEKS and the Khan Academy is that they don't teach the depth that's there in mathematics. Yes, they teach the basics, and the Khan Academy is good for explanations, but the depth just isn't there in the course sequences.

Val,
Would you have an example of the sort of depths that you see missing?

It seems there is a lot of material that some people can intuit from whatever the presentation. I'd like to figure out if there are real gaps for my DS or if this is a non-issue for him.

Thanks

I'd like to see more exploration of how new concepts in mathematics were discovered and why.

The teaching on the Khan Academy is superb (ALEKS, I'm not so sure about). The site is also incredibly well-organized. I think that the people who run it could turn it into a magnificent piece of work that would survive for a long time if they added in-depth discussions of these kinds of questions:

1. How has mathematics developed over time?

An example would be the appearance of zero in different places in the historical record, the invention of variables and systems used before Descartes started using x and y, the use of negative numbers, etc. Why did zero pop in and out? What finally cemented its use?

2. What has hindered mathematical development?

An example here would be resistance to the use of negative numbers, which were seen as preposterous until relatively recently. Complex/imaginary numbers had the same problem. IMO, probing the reasons for resistance to new ideas is important not only to advancing mathematics, but also for understanding scientific and technical progress as a whole.

3. What unanswered questions or needs drove the development of new mathematical techniques?

An example here would be calculating the volume of a pyramid and a frustum (a pyramid with its top gone). The ancient Egyptians worked out a way to do the very non-trivial frustum calculation without calculus (it's a standard topic in many or most calculus classes today). What are theories about how they did that? Learning about how other people succeeded when you would think they wouldn't have been able to can teach a lot about how to succeed today when confronted with an apparently impossible problem.

IMO, we teach our students how to calculate, but we do a poor job of explaining how to solve fundamental problems. When I say this, I don't mean that we don't teach practical applications like "you can use trig to calculate the height of the cliff." I mean that we need to be teaching patterns of thinking that can help drive major new discoveries. Without this, we can keep calculating (as Richard Feynman advised), but we'll have a lot of trouble making big conceptual leaps. This stuff is part of learning mathematics, not some kind of philosophical tangent, and it's lacking overall today. The KA could fill a big void here.

Sure, very highly motivated people can figure this stuff out for themselves over the course of years or decades, but wouldn't it be, you know, if nothing else, more efficient to put it together up front? This is the kind of stuff that makes an educated population or, looking at it more narrowly, it's something gifted students would eat up.

Thanks, Val, it's been a reoccurring theme in various threads, good to see the details on your perspective. DS roots out a lot of videos with history of mathematics, and he has a couple of grandpas who are keen on that angle. And I've got a soapbox laying around here somewhere labeled metacognition and problem solving.