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Please for the love of maths do not "align" with the common core standards. It would be the saddest, most disheartening thing imaginable* for Khan Academy to be

Please for the love of maths do not "align" with the common core standards. It would be the saddest, most disheartening thing imaginable* for Khan Academy to become a feeder to the American standardized testing system. The author writes: "If one of Khan Academy’s goals is to prepare students for success in Common Core mathematics, they’re emphasizing the wrong set of skills." I would like nothing better than the academy to publicly state this is NOT a goal of theirs. Being good at math and passing math tests are orthogonal* concepts. In my experience teaching to the test is the fastest way to kill the love of any subject because, at the end of the day, the only answer you can give to the question "Why is this important? or "Why should we do it this way?" is "Because the test says so." It's death to independent thought. I don't know who his advisor is but please kill this dissertation before it gets out into the world and he uses it for self promotion on Good Morning America. *intentional hyperbole

spicyj 12y ago
(I work at Khan Academy.) We have no interest in preparing students for tests just for the sake of it, but if you look at the Common Core standards you'll see that they are well thought out (really!) and designing a curriculum around them is a very sensible thing to do. Of course, we won't restrict ourselves to the material covered by the Common Core if/when we feel there are gaps. We're interested in helping students learn to solve problems, not in teaching them how to take tests.
- jacksonaedwards 12y ago
  Khan Academy is obviously a useful tool for learning, and of course it's part of a child's education, not all of it. The point I think Dan is making is that if you 1. say you're aligned to the common core, and 2. provide mastery statistics to suggest a level of comprehension or depth of knowledge tied to those standards then that should predict well a child's performance answering questions aligned to the standards but outside the KA system (e.g. a Smarter Balanced Assessment) That means until that ideal is reached KA could say "Mastery at X depth of knowledge but note, for this standard Y is required" or allow teachers to write free response questions and have them tag the questions by standard, type, depth of knowledge etc. and grade them by hand in the KA system. Including hand graded questions (by a student's teacher)with an adequate tagging system KA mastery statistics might be significantly more accurate.
yummyfajitas 12y ago
Consider a well designed test of an important curriculum. This means the topics are important for $REASONS, and the test is highly correlated with knowledge of the topics. If a student asks "why is this important", you can reply "$REASONS". And you can "teach to the test" secure in the knowledge that you are teaching useful materials. Now, if you believe the curriculum is poorly designed or the test is poorly correlated with it, I encourage you to make that argument. But explaining why "Know relative sizes of measurement units within one system of units including km, m, cm..." should not be part of the curriculum is a lot harder than making emotional pleas about "love of the subject". (I've skimmed parts of the common core on a few occasions. It looks pretty good to me. http://www.corestandards.org/Math/Content/4/MD/ http://www.corestandards.org/Math/Content/4/MD/ )
- VLM 12y ago
  I can't speak for OP, although I basically agree with you and OP simultaneously. However, look at it as an optimization problem. CC testing standards and format may be ideal testing tools for 49 minutes 5th period after lunch 5 days a week in a 40 person classroom, performed in perfect lock step by all 40 students, only failure mode is repeating the entire class or developing a hatred of the topic, aka standard public school experience. However, what does "alignment" WRT KA mean when the educational experience has completely changed? Its analog, you can watch a video 50 times will you get it, jump back and forth, all that. I'd propose the "best" testing technique for that environment probably looks a lot like KA and not so much CC because you need instant feedback and simple questions. Its not quite as good as personal 1 on 1 tutoring, but its better than sitting in class, more importantly the experience is inherently different than sitting in class... The proposal in the linked article seems to be that KA epic fails, solely in "alignment", because it doesn't test like CC, which is trivial to test and prove and analyze statistically. Factually looks like a good study. Maybe it fails the relevance test because "alignment" is fuzzy to me (maybe it has a special jargon meaning among CC teachers?) I think MAYBE OP and I are concerned that KA aligns pretty well to a decent curriculum (CC) WRT topics and order of topics and presentation standards, and I hope KA doesn't ruin the KA assessment portion to better match CC assessments solely to get a checkbox somewhere. Maybe we can abstract out KA from the discussion. I'm tolerably good at math and have tutored people. If you define alignment with CC as slavishly following their assessment technique at all times even though I'm 1 on 1 in an ongoing human conversation, such that everything I speak must statistically match the CC assessment percentages in style, tone, and technique, that's ridiculous. If you defined alignment as I'm talking about sets of linear equations with infinite solution set the same general time, order, and way the CC talks about it, thats OK, even if I assess a tutored student the "wrong way" by asking the wrong type of questions (which may very well be the right question for that kid at that moment while also being on average the wrong way to teach all American Kids in a 40 person classroom) Its seems reasonably non controversial that CC curriculum and assessment are local maxima on society wide averages for teaching math. It seems reasonably non controversial that KAs assessment tools seem to be a local maxima for computerized delivery of help to kids that need extra help. I (and possibly OP) don't think it reasonable to trash talk KA because the local maxima of effectiveness for society as an average whole in a classroom setting doesn't necessarily match KAs local maxima of effectiveness for "kids who need help at home". The danger is screwing up KA enough to make it useless for the kids who need it after school, just to achieve a marketing checkmark.
davmre 12y ago
I interpreted the article as making exactly the opposite of your point: because Khan Academy is limited to automated grading, they can only ask standardized-test style questions: solve an equation, select a multiple-choice answer, etc. Meanwhile, the Common Core standards emphasize argumentation (i.e. proofs), formulating equations, and other high-level skills that are harder to test directly but are much more important to actually getting a deep understanding. Common Core is not a set of tests; it's just a curriculum that sets some basic standards for what students ought to learn. It's reasonable to be concerned about standardized testing as a means for assessing whether those standards are being met, but it doesn't sound like you actually have any objection to the Common Core curriculum.
21echoes 12y ago
This response shows a willful ignorance of the stated goals of Common Core, especially with relation to the Common Core math curriculum. Common Core's primary pedagogical shift in math is to remove the historical focus on math as a set of mindless procedures, and instead teach children math as a broader, more holistic approach to logical & numerical reasoning. Common Core teaches children to solve problems many different ways, make arguments about why both tactics work, etc. This is about as far as one can be from the traditional "teaching to the test" downsides.
- kennytilton 12y ago
  Only the worst teachers failed to motivate math procedures. Granted, the curve may have been skewed to worst. :) But CCSS does not suggest a little professional development to get teachers to explain the "why" behind the procedures, it wants kids to invest a ton of time in proving procedures multiple ways before then, well, going ahead and mastering the procedure. CCSS is untested (unless you count its imposition on 40+ states a test) so we'll have to wait and see if it moves the US up the meaningless PISA test rankings.
WalterBright 12y ago
> good at math and passing math tests are orthogonal concepts. What good is being good at math yet being unable to answer any questions about it? Would you get on board an airliner with a pilot who flunked the flight certification tests but assures you that he's really good at flying anyway?
- davmre 12y ago
  There are different ways to be "good" at math. I have a few friends who are very good at contest type math (e.g. well-ranked on the Putnam) and I also have friends doing math PhDs at top schools. They are mostly not the same people. The contest winners are very quick; they know a lot of tricks and general problem-solving strategies and can think very efficiently about how to apply them and come to a clever solution. The researchers are not necessarily as quick, but they're more patient, willing to spend days or weeks focusing on a single problem and learning/developing the machinery necessary to solve it, and they have more of a pure intellectual curiosity about math -- they approach it as a source of new and interesting questions, rather than just a set of techniques to be learned or problems to be solved. Sure they all did well on the usual standardized tests (SAT, etc), but if you were going to use a test like the Putnam to identify who you wanted to hire as a mathematician, you'd make a lot of poor choices. That said I basically agree with you that it's not reasonable to call someone "good" at math if they're unable to do simple calculations (with the caveat that lots of great mathematicians screw up simple calculations on a regular basis -- but they're still at least usually better than the average person). But there are certainly people who memorize enough formulas to pass the test, yet never acquire or don't retain any conceptual understanding. In that sense, passing a test is a necessary but definitely not sufficient condition for being good at math.
- deleted 12y ago
  [deleted]
kennytilton 12y ago
Agreed with your sentiments, but Khan is financed by Bill "Common Core" Gates and in May partnered with the College Board (hard core CCSS folks) so look for KA to get closer to CCSS, not further. Money talks and CCSS, as bad as it is pedagogically, has a surface plausibility that fools folks who have never taught. In this sense it is like the New Math of the Sixties, which tried to improve math learning by starting at the most fundamental concepts (eg, set theory in the first grade) when in fact those concepts were worked out over centuries by the brightest minds working on math. They confused the logical starting point with the pedagogical starting point. The good news is that these catastrophes are dumped even faster than they come into ascendance and CCSS is confirming that trend. We just need to remember this the next time academic geniuses decide we are doing it all wrong and -- instead of offering a little professional development -- decide to offer all new standards, textbooks, and standardized exams. I too have a soft spot in my heart for bold strokes, I just want them to come from folks who know what they are doing. The CCSS authors did not. ps. I do not think thesis says what you think it says.
- jblad 12y ago
  I'm wondering what your pedagogical objections are to the CCSS math standards. From my reading of the CCSS and supporting documents, it sure seems like the designers were research-informed. What did they get wrong, and what would you do differently? It really isn't a rehashing of New Math. They think very carefully about the pedagogical starting point, in fact. Please don't assume that people who think the CCSS are on balance a good thing are people who are inexperienced in the classroom. There is room to disagree about aspects of the CCSS, but the discussion will be more productive if our assertions are supported by evidence, rather than name-calling.
  - kennytilton 12y ago
    (a) my analogy with the New Math was not meant to equate the two, only their conceptual cart before procedural horse qualities (which would also be my pedagogical concern); (b) don't get me wrong: I agree with the "deeper understanding" goal of CCSS, and it was how I taught. The concerns I expressed were with the whole program's implementation, (un)testing, and effectiveness with less than exceptional students -- more of a systems thing than pedagogy. In fact, CCSS would have been great as a professional development "surge", if you will. All this testing, book-rewriting, and saber-rattling over accountability -- well, the proponents get an "F" for change implementation.
jblad 12y ago
What do you oppose in the Common Core? Sure, they might make it easier to develop widely used standardized tests, but the assessment of the Common Core is not the Common Core. Teaching students to be successful with Common Core mathematics doesn't necessarily mean teaching them to pass tests. But the Common Core does ask students to engage with math at a higher level of thinking than did most of the state standards that preceded it. Common Core is actually pretty well thought out--at least the K-8 portion is. Designing a curriculum around a set of standards does not have to be "teaching to the test" and a cursory reading of the CCSS makes it clear that the answer to questions like "Why is this important?" or "Why should we do it this way?" should never be "Because the test says so." Students should "construct viable arguments and critique the reasoning of others." How does this kill independent thought?

spicyj 12y ago

(I work at Khan Academy.) We have no interest in preparing students for tests just for the sake of it, but if you look at the Common Core standards you'll see that they are well thought out (really!) and designing a curriculum around them is a very sensible thing to do. Of course, we won't restrict ourselves to the material covered by the Common Core if/when we feel there are gaps. We're interested in helping students learn to solve problems, not in teaching them how to take tests.

jacksonaedwards 12y ago
Khan Academy is obviously a useful tool for learning, and of course it's part of a child's education, not all of it. The point I think Dan is making is that if you 1. say you're aligned to the common core, and 2. provide mastery statistics to suggest a level of comprehension or depth of knowledge tied to those standards then that should predict well a child's performance answering questions aligned to the standards but outside the KA system (e.g. a Smarter Balanced Assessment) That means until that ideal is reached KA could say "Mastery at X depth of knowledge but note, for this standard Y is required" or allow teachers to write free response questions and have them tag the questions by standard, type, depth of knowledge etc. and grade them by hand in the KA system. Including hand graded questions (by a student's teacher)with an adequate tagging system KA mastery statistics might be significantly more accurate.

yummyfajitas 12y ago

Consider a well designed test of an important curriculum. This means the topics are important for $REASONS, and the test is highly correlated with knowledge of the topics. If a student asks "why is this important", you can reply "$REASONS". And you can "teach to the test" secure in the knowledge that you are teaching useful materials. Now, if you believe the curriculum is poorly designed or the test is poorly correlated with it, I encourage you to make that argument. But explaining why "Know relative sizes of measurement units within one system of units including km, m, cm..." should not be part of the curriculum is a lot harder than making emotional pleas about "love of the subject". (I've skimmed parts of the common core on a few occasions. It looks pretty good to me. http://www.corestandards.org/Math/Content/4/MD/ http://www.corestandards.org/Math/Content/4/MD/ )

VLM 12y ago
I can't speak for OP, although I basically agree with you and OP simultaneously. However, look at it as an optimization problem. CC testing standards and format may be ideal testing tools for 49 minutes 5th period after lunch 5 days a week in a 40 person classroom, performed in perfect lock step by all 40 students, only failure mode is repeating the entire class or developing a hatred of the topic, aka standard public school experience. However, what does "alignment" WRT KA mean when the educational experience has completely changed? Its analog, you can watch a video 50 times will you get it, jump back and forth, all that. I'd propose the "best" testing technique for that environment probably looks a lot like KA and not so much CC because you need instant feedback and simple questions. Its not quite as good as personal 1 on 1 tutoring, but its better than sitting in class, more importantly the experience is inherently different than sitting in class... The proposal in the linked article seems to be that KA epic fails, solely in "alignment", because it doesn't test like CC, which is trivial to test and prove and analyze statistically. Factually looks like a good study. Maybe it fails the relevance test because "alignment" is fuzzy to me (maybe it has a special jargon meaning among CC teachers?) I think MAYBE OP and I are concerned that KA aligns pretty well to a decent curriculum (CC) WRT topics and order of topics and presentation standards, and I hope KA doesn't ruin the KA assessment portion to better match CC assessments solely to get a checkbox somewhere. Maybe we can abstract out KA from the discussion. I'm tolerably good at math and have tutored people. If you define alignment with CC as slavishly following their assessment technique at all times even though I'm 1 on 1 in an ongoing human conversation, such that everything I speak must statistically match the CC assessment percentages in style, tone, and technique, that's ridiculous. If you defined alignment as I'm talking about sets of linear equations with infinite solution set the same general time, order, and way the CC talks about it, thats OK, even if I assess a tutored student the "wrong way" by asking the wrong type of questions (which may very well be the right question for that kid at that moment while also being on average the wrong way to teach all American Kids in a 40 person classroom) Its seems reasonably non controversial that CC curriculum and assessment are local maxima on society wide averages for teaching math. It seems reasonably non controversial that KAs assessment tools seem to be a local maxima for computerized delivery of help to kids that need extra help. I (and possibly OP) don't think it reasonable to trash talk KA because the local maxima of effectiveness for society as an average whole in a classroom setting doesn't necessarily match KAs local maxima of effectiveness for "kids who need help at home". The danger is screwing up KA enough to make it useless for the kids who need it after school, just to achieve a marketing checkmark.

davmre 12y ago

I interpreted the article as making exactly the opposite of your point: because Khan Academy is limited to automated grading, they can only ask standardized-test style questions: solve an equation, select a multiple-choice answer, etc. Meanwhile, the Common Core standards emphasize argumentation (i.e. proofs), formulating equations, and other high-level skills that are harder to test directly but are much more important to actually getting a deep understanding. Common Core is not a set of tests; it's just a curriculum that sets some basic standards for what students ought to learn. It's reasonable to be concerned about standardized testing as a means for assessing whether those standards are being met, but it doesn't sound like you actually have any objection to the Common Core curriculum.

21echoes 12y ago

This response shows a willful ignorance of the stated goals of Common Core, especially with relation to the Common Core math curriculum. Common Core's primary pedagogical shift in math is to remove the historical focus on math as a set of mindless procedures, and instead teach children math as a broader, more holistic approach to logical & numerical reasoning. Common Core teaches children to solve problems many different ways, make arguments about why both tactics work, etc. This is about as far as one can be from the traditional "teaching to the test" downsides.

kennytilton 12y ago
Only the worst teachers failed to motivate math procedures. Granted, the curve may have been skewed to worst. :) But CCSS does not suggest a little professional development to get teachers to explain the "why" behind the procedures, it wants kids to invest a ton of time in proving procedures multiple ways before then, well, going ahead and mastering the procedure. CCSS is untested (unless you count its imposition on 40+ states a test) so we'll have to wait and see if it moves the US up the meaningless PISA test rankings.

WalterBright 12y ago

> good at math and passing math tests are orthogonal concepts. What good is being good at math yet being unable to answer any questions about it? Would you get on board an airliner with a pilot who flunked the flight certification tests but assures you that he's really good at flying anyway?

davmre 12y ago
There are different ways to be "good" at math. I have a few friends who are very good at contest type math (e.g. well-ranked on the Putnam) and I also have friends doing math PhDs at top schools. They are mostly not the same people. The contest winners are very quick; they know a lot of tricks and general problem-solving strategies and can think very efficiently about how to apply them and come to a clever solution. The researchers are not necessarily as quick, but they're more patient, willing to spend days or weeks focusing on a single problem and learning/developing the machinery necessary to solve it, and they have more of a pure intellectual curiosity about math -- they approach it as a source of new and interesting questions, rather than just a set of techniques to be learned or problems to be solved. Sure they all did well on the usual standardized tests (SAT, etc), but if you were going to use a test like the Putnam to identify who you wanted to hire as a mathematician, you'd make a lot of poor choices. That said I basically agree with you that it's not reasonable to call someone "good" at math if they're unable to do simple calculations (with the caveat that lots of great mathematicians screw up simple calculations on a regular basis -- but they're still at least usually better than the average person). But there are certainly people who memorize enough formulas to pass the test, yet never acquire or don't retain any conceptual understanding. In that sense, passing a test is a necessary but definitely not sufficient condition for being good at math.
deleted 12y ago
[deleted]

kennytilton 12y ago

Agreed with your sentiments, but Khan is financed by Bill "Common Core" Gates and in May partnered with the College Board (hard core CCSS folks) so look for KA to get closer to CCSS, not further. Money talks and CCSS, as bad as it is pedagogically, has a surface plausibility that fools folks who have never taught. In this sense it is like the New Math of the Sixties, which tried to improve math learning by starting at the most fundamental concepts (eg, set theory in the first grade) when in fact those concepts were worked out over centuries by the brightest minds working on math. They confused the logical starting point with the pedagogical starting point. The good news is that these catastrophes are dumped even faster than they come into ascendance and CCSS is confirming that trend. We just need to remember this the next time academic geniuses decide we are doing it all wrong and -- instead of offering a little professional development -- decide to offer all new standards, textbooks, and standardized exams. I too have a soft spot in my heart for bold strokes, I just want them to come from folks who know what they are doing. The CCSS authors did not. ps. I do not think thesis says what you think it says.

jblad 12y ago
I'm wondering what your pedagogical objections are to the CCSS math standards. From my reading of the CCSS and supporting documents, it sure seems like the designers were research-informed. What did they get wrong, and what would you do differently? It really isn't a rehashing of New Math. They think very carefully about the pedagogical starting point, in fact. Please don't assume that people who think the CCSS are on balance a good thing are people who are inexperienced in the classroom. There is room to disagree about aspects of the CCSS, but the discussion will be more productive if our assertions are supported by evidence, rather than name-calling.
- kennytilton 12y ago
  (a) my analogy with the New Math was not meant to equate the two, only their conceptual cart before procedural horse qualities (which would also be my pedagogical concern); (b) don't get me wrong: I agree with the "deeper understanding" goal of CCSS, and it was how I taught. The concerns I expressed were with the whole program's implementation, (un)testing, and effectiveness with less than exceptional students -- more of a systems thing than pedagogy. In fact, CCSS would have been great as a professional development "surge", if you will. All this testing, book-rewriting, and saber-rattling over accountability -- well, the proponents get an "F" for change implementation.

jblad 12y ago

What do you oppose in the Common Core? Sure, they might make it easier to develop widely used standardized tests, but the assessment of the Common Core is not the Common Core. Teaching students to be successful with Common Core mathematics doesn't necessarily mean teaching them to pass tests. But the Common Core does ask students to engage with math at a higher level of thinking than did most of the state standards that preceded it. Common Core is actually pretty well thought out--at least the K-8 portion is. Designing a curriculum around a set of standards does not have to be "teaching to the test" and a cursory reading of the CCSS makes it clear that the answer to questions like "Why is this important?" or "Why should we do it this way?" should never be "Because the test says so." Students should "construct viable arguments and critique the reasoning of others." How does this kill independent thought?