We started using Khan Academy a few weeks ago, and my daughter, age 8, just loves it. I hadn't been paying much attention until today when I looked at her level of accomplishments. I had put her in the 3rd grade level to see what she had accomplished, but it showed that she had "mastered" from 10% - 20% of 4th, 5th, 6th, and 7th grade work (she was just randomly picking activities). She has even "mastered" 9% of 8th grade work. Now, this makes me doubt that Khan Academy is accurate grade-wise. What are these "masteries" really showing us?
I was using this to assess her skill sets in 3rd and 4th grade as she has been nominated by the AG teacher for single subject acceleration, and I want to know if she really knows her math work. She is currently in third grade.
Thanks!!
I haven't looked at Khan's grade reporting, but I know with my ds8 he'll follow threads of topics how they make sense to him. It seems a pretty natural way to learn. If he has a strong interest in statistics one day he may watch videos and work on math problems through to calculating standard deviations which threaded as subjects are could show as a percent blip through to somewhere in high school.
What are these "masteries" really showing us?
Honestly?
I've looked at this as DD has attempted to use Khan as a supplemental instructional tool.
IMO, most of the "mastery" doesn't necessarily represent actual "mastery" the way that I think about it because of the way that assessments are structured and offered via Khan.
So that's strike one, IMO, in terms of using the software itself to evaluate what a student truly has mastery over...
secondly, recognize that the way that math is taught now, there is spiraling. I'd expect that a 2nd grader with complete mastery of 2nd grade WILL have mastered about 10% of what is on offer through 6th grade-- meaning, in each year's topics-- because of that spiraling.
I noticed this in jumping around and playing with it to see how good the software was; I could "relearn" things that I probably never really "learned" the way Khan apparently "teaches" them-- trig topics, for example, or those in stats that use different notation-- in a VERY short amount of time simply through trial and error on those assessments. That is so not to say that I have "mastery" over those topics, however. I couldn't tell you HOW to use the equation of a parabola to determine what its graph should look like to save my life-- truly-- but that topic shows that I've "mastered" it, because I was able to "pass" five questions in a row through raw trial and error discovery.
Now, I don't know whether that is entirely relevant here, since I'm an adult, and my LOG is similar to most of the kids around here, plus I've obviously had all of those topics previously-- it's just been 35+ years or so in that particular case...
but still, it makes me think that being able to USE the concepts isn't what Khan is actually measuring, even if they think that they are. KWIM?
I wouldn't really worry too much about this at the K-6 level, though. Not with an HG+ kiddo-- they'll learn to fill in whatever gaps they have in a hurry, IMO, up until high school level at least.
@ greenlotus — Interesting, thanks for sharing your experience.
We have some thoughts about Khan Academy here (
http://info.cognitomentoring.org/wiki/Khan_Academy), but they're geared toward high school students rather than elementary school students (in particular, we don't know as much about better resources for elementary school students
). We agree with HowlerKarma that it's easy to learn to answer questions on Khan Academy correctly without understanding the material. ALEKS seems to test for mastery better than Khan Academy does, because the questions are more heterogeneous.
Feel free to be in touch if you'd like – I have experience teaching gifted elementary school students math, and earned a PhD in math as well, and so may be able to offer helpful pointers.
Email: cognitomentoring@gmail.com
Thank you for the links. Khan Academy certainly stirs up a lot of emotion. Reading the Huffington Post comments was interesting!
As I stated, I am trying to get a handle on my child's knowledge of Common Core standards so I can have some ammo when I face the principal and ask for a more challenging education. I know my child's IQ, Cogat scores, and Iowa scores, but schools are all about Common Core. I did find a website, IXL, which seems to have a test that a child can take which would assess a child's knowledge of CC math standards by grade. I am going to check that out when I have the chance.
I think with Khan Academy, if a kid answers about 2 questions correctly on a topic, it considers them "mastered". I would take it with a grain of salt. DD has done it a few times and took the placement test, and then started doing the lessons in the order that it gave her. It was jumping around all over the place. One question would be "find the perimeter of this square" and then the next question would be something from high school alegebra. Since the placement test she took had a total of about 20 questions, I don't think it is a good instrument to use to find out what level they are at or what they should be working on. ALEKS is probably better in terms of having an "assessment" but you have to pay for it and I don't think it has any instructional videos like Khan Academy does (someone correct me if I'm wrong). With Khan Academy, I told DD that the next time she does it she should go into the fourth grade level and do things in order (skipping things she already knows), rather than skipping around all over the place from one grade level to the next randomly or doing it in the order that they throw things at her.
Programs like this have a lot of limitations but the fact of the matter is that when it comes down to it, I have a choice between trying to teach DD these concepts myself, or allowing Mr. Khan to do it for me. Her teacher isn't teaching math above a third grade level and she already has the third grade math curriculum mastered. He is much better than I am. If she gets stuck then I am there to try to help, but with the higher level math I am pretty useless and have to scream for Dh to come help (he majored in math).
We have a subscription to IXL but I have never seen a placement test on it. It does give info about what skills the child is proficient in as they do the lessons but that's pretty much it, as far as I know. So if a child masters 2 digit multiplication with regrouping, as an example, and they finish the lesson or get enough correct, it will consider that skill mastered. I think this is what they mean by the program assessing or monitoring progress.
http://www.ixl.com/standards/common-core/math/grade-3This is the page I saw. I have not checked it closely at all so if anyone has experience with it, I would love to hear about it!
The skills that they have are aligned to common core (or possibly the specific state standards as some states did not adopt common core), but I don't think there's a placement test or assessment. It's pretty much up to the parent or kid to decide what the kid should work on.
sorry, i haven't read the entire thread but wonder if this view would be helpful to you;
https://www.khanacademy.org/commoncore/mapalso, it is 5 correct in a row to 'master' a topic last a saw...
We used ixl for awhile. It's kind of like a big on-line workbook. You can flip page by page in perpetuity and work on exercises, but I never felt like anything was ever mastered. You can also easily get out of "learning sequence". I found it was best as additional practice on skills or a way to differentiate homework. It didn't work for us as a stand alone curriculum.
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.