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so this is Sal Khan founder of the Khan Academy and this is a very exciting Skype call that we're on I'm with Ben Hedrick who's the lead for AP Calculus what do you do at the College Board really anything with AP Calculus NAEYC ap statistics just something that I have a little bit of control over so for example freaky calculus anything with the curriculum anything with the assessment is something that I work with and I'm sure that you're as excited as I am and and you know several hundred thousands of students are around the country for the AP exams that are coming up in roughly a little less a little less than a week and I thought a fun place to start would be when you guys write the test what are you trying to assess what's kind of the the spirit of the questions both on the multiple-choice and the free response section so what we're looking for from students is evidence of good conceptual understanding and calculus now we have some things that are going to test procedures but really we want students to understand what's going on with the calculus rather than just calculating things or putting numbers on paper a lot of thinking questions a lot of insight to make sure that whatever good calculus those students have learned in their courses we're assessing it on the AP exam and you know I've done a bunch of example problems for for the AP exam and yeah my sense of it is you sometimes will do some of the the minutia work or you'll give the formula and you're really trying to understand whether students understand the essence of what an integral is or the essence of you know derivative is a rate of change or the slope of a tangent line so if you were preparing for this exam if you were these students what would you suggest to them you know obviously we have a little less than a week for this current test so what advice would you have for those students and then just generally as students go through the year what should they think about it yeah the advice I would give is depending on how much time students how to prepare so the advice that I give at the beginning of the year is different from the advice that I get now several days before the exam getting ready for it first relax you know this is a calculus exam we're not going to be throwing anything at you from left field it's calculus you need to know limits you need to know derivatives you need to know integrals in term of preparation make sure you're taking the time to review the basics every question that they see is going to hit one of those big topics so make sure you know your derivative rules make sure you know your integral rules take a look at the old exams and see how we're asking questions and you look at the pattern instances that we're always asking about understanding what a derivative means understanding integration of the idea of accumulation there are no secrets on the exam so really stick with what we've done make sure that you're thinking of ways to apply your good knowledge and just review your basics in my experience with the exam is there's a lot of as you just said the really the mainstream media topics you know a chain rule fundamental theorem or theorems of calculus things like that what's your sense of the the more what I would consider maybe a little bit more than minutiae is some of the more special case derivatives or special case integrals you know arctangent debate how much does that play into the exam you know I think so you've actually answered your own question and asking that is it is the minutia so really at this point in time if you're getting ready for the exam spending time on the minutia is not where you're going to be best served with your time should be hitting the major things and you said Arendt the beginning chain rule in any kind of question we do with derivatives you know if you're doing in Max's or mins if you doing tangent lines if you're doing a related rates problem they're all derivatives derivatives derivatives and if you're having trouble with a chain rule it doesn't matter how much my new sheet you spend your time with the chain rule is going to come up so I would say don't sweat the minutia there might be something on the exam that you haven't reviewed as much as you want to but it's going to be one single solitary question basic derivatives are going to form the basis for all those problems so that's where your time is best about yeah I definitely get that sense especially you know how do you interpret the first second you know derivatives concavity things like that those seem to show up a lot but once again that's the D that's a conceptual idea of derivatives and on the integration side I've been doing a bunch of the free response it just seems like I mean you know what happens if you swap the bounds of integration or if you add integrals if they so a lot of the properties and the conceptual understanding would an integral is but you know not necessarily like the fancy tricks at least at this point if you're studying absolute there's there's nothing that we go after the fancy tricks we're not trying to ask your questions or playing gotcha moments on it it's really assessment of calculus and for the students who have been going through these great courses all year this is a wonderful opportunity to show us everything that you know and get a really great score on the exam and and what about calculator I mean I was doing some of the free response that first part of the free response to knowing your calculator well helps oh absolutely the the calculator is a tool and like any tool you want to make sure that you're applying it appropriately and strategically which sometimes means using your calculator and using it well incorrectly but other times not using your calculator I mean even the free response section where the calculator is being used we expect students to show their work if you're taking an integral we want to see that you've actually taken that integral now the calculator will do the work of it we want to see the notation that says this is the integral you calculated and this is the answer you obtained and then do whatever you will with that answer as required by the question but good communication through writing even on the calculator sections necessary and for students taking the the BC exam above and beyond the the core differentiation integration you know a lot of what you learn about parametric equations is actually just an extension of what you learn in differentiation integration but probably some of the the convergence tests are something to become pretty familiar with that would be correct yes and in terms of grading of the exam you know some people it to get a to get a five or a high my understanding is you don't need to answer absolutely every question perfectly well like any test if you want to date it well you don't have to have perfection on it and this you know this is a test where students are coming in and it's a three-hour time thethe little over three hour time test and you know you can do a lot of really good work in earn I pretty easily so I wouldn't I wouldn't tell anyone to go in there worrying about trying to figure out what magical numbers they need to get in order to get a perfect score on the test or to get a five on the tester whatever it is they're going for just go in like you would on any test do your best on every question get every point that you can and hopefully it'll work out fine for you what advice would you have for students especially on the free response where there's multiple sections and if you know in part a they say well that that's I don't I don't get with that what what you know should they skip to the next what should they do I actually have very very common base on that one is that's to make sure that students are trying every part of every response question one of the misconceptions students have is exactly what you said if you hit Part A and you're freaking out a little bit because you don't know what Part A is about that's okay move on to Part B there are some questions where the answer for Part B depends on Part A but for the majority of the questions they're separate pieces so Part A Part B Part C if there's a Part D they may all be asking very different things and if you have probably even with Part C that doesn't mean you know the question gets progressively more difficult give Part D a try and a lot of the things that we do get points for our good solid calculus work so if you can set up a problem maybe you don't have time to finish it maybe you make some mistakes along the way the answer point is only one little point out of enough iron there are other points for the setup and the conceptual understanding of the problem and a lot of students have good conceptual understanding that they could set up pick up a point here and have a point there but they panic a little bit and they move on to another question and never come back and that's okay if you want to move on to another question but absolutely I would say if you're having trouble with Part A that's alright take a look at Part B and one thing that I've observed is a lot of these questions at first when you look I'm like oh wow this looks like some really you know super deep thing but it really is some core basic calculus ideas and that if you're on the right track it's actually quite simple so if you know would you say it's fair if a student finds themselves doing a very hairy calculation that they might question whether they need to go beyond might they should question what they're doing if if you've done something where you feel like you need to prove a new calculus theorem in order to answer it something has gone terribly terribly wrong and also if you feel like you need to bring in some sort of mathematics you've never seen before in calculus I mean I as much as I hate to say it you know this is oculus is limits its derivatives its integrals even though there's a lot of wealth in that one if you're doing something beyond that probably something is going wrong yeah yeah well thanks I think you know thousands of AP students are going to really appreciate that any other kind of parting words for the company test you know it's the the same thing that I used to tell my students when I was teaching AP calculus this is just another test and the beauty of AP is the teachers have been prepping their students since the beginning of the year it's one of the few tests where everyone knows what's coming so when you sit down and you've got free response questions you've got multiple choice questions you know there really shouldn't be any surprises this is the stuff they've seen all year they know what to do take a moment take a breath take a look at the problem get all the points that you can show us that good councils awesome and I'll throw in a plug we have tons of resources for the students as well and we're going to have our office hours on on Monday so super exciting thanks a bunch of ed know thanks for having me

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