WEBVTT Kind: captions Language: en 00:00:00.560 --> 00:00:06.089 All right. Hello everyone. Welcome. Where we going here? Okay 00:00:06.089 --> 00:00:15.089 Welcome to OAME 2020 online version. Okay. Very exciting. My name as you can see 00:00:15.089 --> 00:00:23.850 right here is Kieran Flahive. Okay and my my presentation today, my my pre-recorded 00:00:23.850 --> 00:00:27.269 session today is called "I failed my math test - 00:00:27.269 --> 00:00:32.040 now what? Right so pretty exciting there. You know it happens. Right our students do 00:00:32.040 --> 00:00:37.380 worse on their tests and then we would like and they would like to do. And and 00:00:37.380 --> 00:00:42.000 you know and your may be like oh alright this is frustrating. You know I wish they'd 00:00:42.000 --> 00:00:45.539 learned this. But you know what do you do now? How can you help them make sense of 00:00:45.539 --> 00:00:49.710 their mistakes and and and learn not just the previous content that was on 00:00:49.710 --> 00:00:55.020 the test but the better the correct way or the correct ways to learn math going 00:00:55.020 --> 00:00:58.500 forward? All right so that's I'm going to talk about for about 30 minutes. All 00:00:58.500 --> 00:01:02.300 right. So I just like I said my name is Kieran. 00:01:02.300 --> 00:01:09.360 This is me. I teach math at Loyola University Chicago. Obviously in Chicago. 00:01:09.360 --> 00:01:12.630 In the States. Okay we have a junior college called a 00:01:12.630 --> 00:01:17.130 Arrupe. In fact let's go over here, this is me right here. Okay. This is where I 00:01:17.130 --> 00:01:22.560 work. Arrupe College. Okay it is a two-year Community College. Junior 00:01:22.560 --> 00:01:25.979 college. We use those words interchangeably to the best of my 00:01:25.979 --> 00:01:32.490 understanding. And I've been there for four years. Right been there for four 00:01:32.490 --> 00:01:35.850 years. I'm from New York City. I taught New York City middle school and high 00:01:35.850 --> 00:01:38.850 school for five years before that. So that's a total of nine years teaching. 00:01:38.850 --> 00:01:46.920 Right and I put, what have I put here, I put that this session was or is for 00:01:46.920 --> 00:01:51.540 grades 7 through 14. Right 13, 14 being the first two years of college because 00:01:51.540 --> 00:01:55.380 that's what I taught. And I and I've used tests corrections for all of those 00:01:55.380 --> 00:01:59.820 grades because I think they're really valuable. All right so so yeah that's a 00:01:59.820 --> 00:02:04.890 little bit about me. Right I teach so at Arruppe. Students 00:02:04.890 --> 00:02:09.780 need to take stats before they leave and graduate with their associates, their 00:02:09.780 --> 00:02:12.960 two-year degree but I also teach some fundamentals 00:02:12.960 --> 00:02:18.570 of math, fundamentals of math course, a couple precalculus courses that they 00:02:18.570 --> 00:02:22.050 don't put the other one down there, hasn't been updated and then a stats class we 00:02:22.050 --> 00:02:24.510 have offered now which is really exciting. The students seem to really be 00:02:24.510 --> 00:02:29.790 liking math. Arrupe's a wonderful place. I encourage you to look it up. And as 00:02:29.790 --> 00:02:36.210 always you know please feel free to contact me. It's my email address here if 00:02:36.210 --> 00:02:40.530 you have any questions or comments or like to see the test correction template. 00:02:40.530 --> 00:02:44.130 Want me to send it to you. Don't hesitate to reach out 00:02:44.130 --> 00:02:48.690 please. Alright so yeah so so that's the name of the session right. There it is. 00:02:48.690 --> 00:02:53.610 And then normally I don't find reading off a slide to be very helpful but I will 00:02:53.610 --> 00:02:57.300 in this case. I think this description is a good description of what I am going to for the next 00:02:57.300 --> 00:03:03.690 you know half hour or so. Alright so let me read it. Students fail math tests. It 00:03:03.690 --> 00:03:09.810 happens. How can we as instructors help them master the content after the test 00:03:09.810 --> 00:03:14.400 has been given so they don't fall further behind? Right. In my classroom I 00:03:14.400 --> 00:03:19.760 ask students to do test corrections with a keen eye on finding their mistakes and 00:03:19.760 --> 00:03:23.670 mathematically explaining why their work is wrong. That's a really important thing. 00:03:23.670 --> 00:03:27.600 We're gonna get to that okay. It can be a frustrating activity for all parties 00:03:27.600 --> 00:03:32.490 involved. I can assure you of that but an extremely worthwhile one if done well. 00:03:32.490 --> 00:03:39.390 And I can definitely assure you of that. Right it is frustrating for students. You 00:03:39.390 --> 00:03:45.750 know who already have done poorly on the test to then have to you know look back 00:03:45.750 --> 00:03:48.480 at the work that they've done before in terms of their homework and their 00:03:48.480 --> 00:03:53.490 classwork and their notes. Go back to the answer key that I send them and then 00:03:53.490 --> 00:03:58.170 find out mathematically what is it they did wrong. You know it's a frustrating 00:03:58.170 --> 00:04:02.490 activity but it's really worthwhile in my opinion. Okay so I'll be showing some 00:04:02.490 --> 00:04:06.510 examples of student work. I actually have the work from one student. I'm in a 00:04:06.510 --> 00:04:10.410 stats class. I don't have any my pre calc stuff with me unfortunately because of 00:04:10.410 --> 00:04:14.820 you know the quarantine obviously a lot of my stuff is on my computer at work 00:04:14.820 --> 00:04:19.170 not on my home computer. So it's too bad but the stats stuff is great. I got a lot 00:04:19.170 --> 00:04:23.970 of good examples here. And then the test correction template itself that I use in 00:04:23.970 --> 00:04:26.430 the hopes that you might adapt it for your classroom. 00:04:26.430 --> 00:04:29.460 Right because that's the goal. You want to come out of this and say alright well 00:04:29.460 --> 00:04:33.240 I listened to this guy you know talk for a little while but you know what can I do? 00:04:33.240 --> 00:04:37.590 How can this help me? So unfortunately, obviously this activity 00:04:37.590 --> 00:04:43.169 of tests corrections is is an intensive one. I always encourage students to come 00:04:43.169 --> 00:04:47.490 see me during my office hours. I actually give them partners in the class that 00:04:47.490 --> 00:04:50.639 they work together with when I gave him a little bit of class time. But there 00:04:50.639 --> 00:04:53.400 isn't that much time in class in the lectures. You know between 00:04:53.400 --> 00:04:56.970 lectures and the class work to be doing this. So I encourage them come see me. 00:04:56.970 --> 00:05:01.919 They have math fellows. So they'll do that. So it's a little bit harder for 00:05:01.919 --> 00:05:06.240 sure when everything is online. So obviously we can't fix the timing but I 00:05:06.240 --> 00:05:11.130 hope that's something that you decide to use you know once we're back, once we're 00:05:11.130 --> 00:05:17.070 back in you know in person. Hopefully in the fall my gosh. Okay so that's what I'm 00:05:17.070 --> 00:05:21.479 doing. So the test correction template is right here. Okay it's just a Word 00:05:21.479 --> 00:05:24.330 document. All right in fact actually shout out to 00:05:24.330 --> 00:05:27.810 an old, an old co-worker, I've been teaching for nine years. I taught with her for a 00:05:27.810 --> 00:05:32.909 couple of the first years. She taught algebra with me. Amal is her name. I stole 00:05:32.909 --> 00:05:38.010 this from her. S props to her. You know I really liked her idea of having 00:05:38.010 --> 00:05:43.020 students learn from their mistakes not just in class. You know not just in their more 00:05:43.020 --> 00:05:47.639 informal stuff but also in their formal stuff like exams. And I think that you 00:05:47.639 --> 00:05:53.490 know I've gotten a lot better about being clear to students on what I'm looking for 00:05:53.490 --> 00:05:58.349 because it's it's definitely challenging for some of them as I said. But it's still 00:05:58.349 --> 00:06:01.830 I still have some work to do. I still definitely find myself being like I 00:06:01.830 --> 00:06:05.039 could have explained this better to these students even when I'm you know I'm 00:06:05.039 --> 00:06:10.590 doing it for nine years now. So yeah so this is it. So my test usually have 20 00:06:10.590 --> 00:06:17.310 questions. Right usually three or four chapter or unit tests in every class. And 00:06:17.310 --> 00:06:20.310 I ask them right here just to write down their incorrect answer with the work. 00:06:20.310 --> 00:06:23.669 Okay if there are multiple parts to the question I asked him to just to write 00:06:23.669 --> 00:06:28.590 down the part they got wrong. If they actually did it because this is a stats 00:06:28.590 --> 00:06:32.610 class as not as much algebraic manipulation happening in a lot of 00:06:32.610 --> 00:06:37.139 these questions so we won't be able to see that today. But for some of the 00:06:37.139 --> 00:06:40.410 precalc you know, algebra, trigonometry based 00:06:40.410 --> 00:06:45.510 courses, there is a lot more. And so I say you know write down the part that's 00:06:45.510 --> 00:06:50.070 wrong. Write down the part where you went wrong there okay. And find that incorrect 00:06:50.070 --> 00:06:54.180 work and write that down. Then obviously I give them the answer 00:06:54.180 --> 00:06:58.740 key. In fact I have where is it where is it I have the answer key here 00:06:58.740 --> 00:07:06.540 for the test we are going to looking at. Okay stats 101 is your typical college intro to stats 00:07:06.540 --> 00:07:10.590 class. Kind of like the AP stats curriculum that we have in the States. 00:07:10.590 --> 00:07:15.480 I think that's in Canada. I don't know. Maybe not. Sorry I don't know. But yeah so 00:07:15.480 --> 00:07:20.010 so write down the correct answer. Give that to them and usually I put the work 00:07:20.010 --> 00:07:23.490 down as well. Sometimes I won't if it's a very similar to what they've done in 00:07:23.490 --> 00:07:30.090 their notes before then I don't bother. But usually I do. Okay but then the real 00:07:30.090 --> 00:07:34.860 key, once they've written this stuff down is this part. Okay this part right here 00:07:34.860 --> 00:07:39.570 is really what's important okay. It's the explanation. It's the saying my answer is 00:07:39.570 --> 00:07:44.550 wrong because what. And as you can see I don't want them to be overly verbose and 00:07:44.550 --> 00:07:49.080 I'm not looking for paragraphs. I'm looking for one, two, maybe three sentences 00:07:49.080 --> 00:07:53.910 but really one or two sentences that get to that get to the main idea of what 00:07:53.910 --> 00:07:58.680 they did wrong. You know and as you'll see a lot of students despite me saying 00:07:58.680 --> 00:08:02.520 you know this not I'm looking for will write down oh because I didn't I didn't 00:08:02.520 --> 00:08:07.919 I didn't know how to do it or I wasn't there that day or or I just didn't know 00:08:07.919 --> 00:08:11.280 you know. And it's like I understand that and I appreciate you understanding that 00:08:11.280 --> 00:08:14.880 and thinking about that as well but that's not I'm looking for here. What I'm 00:08:14.880 --> 00:08:19.500 looking for is mathematically what where did you go wrong here? Did you use the 00:08:19.500 --> 00:08:24.510 wrong word? Did you misread you know did you misread the question? 00:08:24.510 --> 00:08:27.630 Where exactly did you misread the question? Did you do a small calculation 00:08:27.630 --> 00:08:32.339 error? Try to find that mistake right. And then of course not just why the wrong 00:08:32.339 --> 00:08:37.140 answer is wrong but why is the correct answer correct right? What you know what 00:08:37.140 --> 00:08:41.339 were the steps you had to do now to get that correct answer and can you explain 00:08:41.339 --> 00:08:44.960 that mathematically right? And so this is the key word here and I'm fairly 00:08:44.960 --> 00:08:50.370 nitpicky about this. I give students till the next test to complete these. They 00:08:50.370 --> 00:08:52.720 have about three weeks or so and they're welcome to hand 00:08:52.720 --> 00:08:58.990 it in multiple times. Encouraged to come see me. I'll make sure they proofread it. 00:08:58.990 --> 00:09:01.960 I'm very nitpicky about that. I want there you know I want them to make sense 00:09:01.960 --> 00:09:08.830 when they write. So yeah so you know it's it's not you know just kind of like oh 00:09:08.830 --> 00:09:11.290 it's right cuz that's the right answer. It's right because we did this in class. 00:09:11.290 --> 00:09:15.010 No no no. I want you to explain mathematically why especially because 00:09:15.010 --> 00:09:19.420 that kind of thinking, that kind of focus on the why is gonna help you make sense of 00:09:19.420 --> 00:09:23.020 the material down the road. That's kind of saying, these aren't just processes we're 00:09:23.020 --> 00:09:28.150 doing. There's a reason why we do these processes. Okay so this is a test 00:09:28.150 --> 00:09:33.070 correction template and I got two per page. Some other teachers and professors 00:09:33.070 --> 00:09:36.550 I've seen do this will put one on the page just because it gives a little more 00:09:36.550 --> 00:09:40.570 space right. It's a balance. And I put on the other side as well you know. So four 00:09:40.570 --> 00:09:45.430 on each page. Yeah obviously I asked them not to hand it in right. And on 00:09:45.430 --> 00:09:48.460 actually an updated version that I have at work, that I don't have my personal 00:09:48.460 --> 00:09:54.580 computer, it clarifies again you know explain mathematically right. Which is 00:09:54.580 --> 00:09:58.240 really the challenge today right. Especially because like I was saying 00:09:58.240 --> 00:10:02.980 earlier you're working with students who may have gotten a 50 or 60 or even 00:10:02.980 --> 00:10:06.160 lower on their test. They're already stressed about, they're already annoyed 00:10:06.160 --> 00:10:10.810 at themselves or whoever. Then you're asking them to think deeply about what 00:10:10.810 --> 00:10:14.410 they did wrong which is not something that may be necessarily used to you know. 00:10:14.410 --> 00:10:18.610 And so it can be frustrating but it's really valuable and it helps the 00:10:18.610 --> 00:10:25.450 students do the right kind of thinking going forward okay. So yeah so so here's 00:10:25.450 --> 00:10:30.730 a test correction template. Let's look at some student work here. Okay so I have 00:10:30.730 --> 00:10:37.240 some student work here from a student of mine. It's okay and then the test itself 00:10:37.240 --> 00:10:41.470 that we have it, this is our unit test that I've done in years past. I changed it 00:10:41.470 --> 00:10:45.040 up a little bit every year but you know the first unit, the first couple chapters 00:10:45.040 --> 00:10:49.360 in your intro stats classes pretty straightforward. Lot of the terminology. We 00:10:49.360 --> 00:10:55.480 have a population, sample, quantitative, qualitative. Some basic probability. Some 00:10:55.480 --> 00:10:59.170 more definitions about different sampling techniques. It's cool to do it 00:10:59.170 --> 00:11:03.820 to teach this class and around 2020 because in the States we do our we do 00:11:03.820 --> 00:11:08.700 our census every year which is one of the few things that anyone really does 00:11:08.700 --> 00:11:13.480 that counts the whole population. And we have some just more frequency 00:11:13.480 --> 00:11:19.810 distribution tables. Some more definitions here. Histograms. More 00:11:19.810 --> 00:11:24.010 definitions. And stuff in the TI-83 calculators that students will 00:11:24.010 --> 00:11:28.240 use where you know we're reviewing things that they've seen sometimes in 00:11:28.240 --> 00:11:32.560 middle school. Mean, median, mode they get into. Well what about some things that 00:11:32.560 --> 00:11:35.020 are more descriptive. Some things that we can use a little more advanced like 00:11:35.020 --> 00:11:42.820 standard deviation. Quartiles rather than just medians right. Some ogives which 00:11:42.820 --> 00:11:47.589 are kind of interesting idea that's always in stats. Dot plots. Just different 00:11:47.589 --> 00:11:52.570 ways of showing data. Probability here as well. This is a great question. We'll get to 00:11:52.570 --> 00:11:55.360 this one in a moment. You know just kind of getting students to think about not 00:11:55.360 --> 00:11:59.140 just the multiplication rule that we have in stats but also like how does 00:11:59.140 --> 00:12:02.320 that make sense with the pass code with like an iPhone something that students 00:12:02.320 --> 00:12:06.970 have a lot of familiarity with. Okay so that's the general idea. Gets a little 00:12:06.970 --> 00:12:09.670 bit tougher towards the end here. We have to get some conditional probabilities. 00:12:09.670 --> 00:12:14.650 Some "and" "ors" at the end there okay. But let's take a look. All right let's take a 00:12:14.650 --> 00:12:19.890 look. All right so, let's start. Where do I want to start here. I don't like to start 00:12:19.890 --> 00:12:26.050 here okay. The student I think submitted six of these. So I want to look at maybe all 00:12:26.050 --> 00:12:29.830 six. Maybe not. But we're gonna see what we think about the students the 00:12:29.830 --> 00:12:40.630 students work here. Okay so number 12. Number 12. Let's look at it. Use the three 00:12:40.630 --> 00:12:47.290 dot plots below to fill in the blanks. All right you got three dot plots. I don't 00:12:47.290 --> 00:12:54.520 know they're ages of students perhaps. And you can see that they they all have the 00:12:54.520 --> 00:12:59.709 same mean and median. They're both 16.5 right. Right this is 00:12:59.709 --> 00:13:03.910 something we looked at in class a little bit as well. But and two of them have the 00:13:03.910 --> 00:13:08.980 same range right. One and two, the same range of 19 minus 14 which is 5. 00:13:08.980 --> 00:13:14.709 Three is a little bit more tighter. A little closer together. But it's asking which 00:13:14.709 --> 00:13:18.320 one has the greatest sample standard deviation. They have to 00:13:18.320 --> 00:13:23.240 know what the word means. Standard deviation - how spread out the data is and 00:13:23.240 --> 00:13:26.390 then they have to kind of look at it. Sometimes students will put all these 00:13:26.390 --> 00:13:30.440 numbers in a calculator which is kind of ridiculous but you can do that. So 14 14 00:13:30.440 --> 00:13:35.690 14 14 15 15 15 16 17 and so on. All right they can do that and then they get their 00:13:35.690 --> 00:13:39.800 answers and compare but it's not necessary. But you have to look at this 00:13:39.800 --> 00:13:45.200 and say well which one is the most spread out because that's what the greatest 00:13:45.200 --> 00:13:48.440 sample standard deviation means. You have to look at them closely. 00:13:48.440 --> 00:13:53.840 So two is spread out. Way more than three but one is the most right, that has the most 00:13:53.840 --> 00:13:59.480 data points furthest from the middle. So boom and then vice-versa dataset three has 00:13:59.480 --> 00:14:03.710 the smallest or the least sample standard deviation because they're 00:14:03.710 --> 00:14:08.600 closest together. Okay nothing too crazy just definitions there. Let's see what 00:14:08.600 --> 00:14:14.270 our student did. Okay so she wrote down her work boom. 00:14:14.270 --> 00:14:19.370 First on the correct work right she only got one part of the question wrong okay. 00:14:19.370 --> 00:14:24.650 But then there's some real some stuff really lacking in this explanation here. 00:14:24.650 --> 00:14:29.240 So my answer is wrong because I was looking at my notes and just copying 00:14:29.240 --> 00:14:34.970 whatever I had answered in the packet. So I appreciate her understanding of what 00:14:34.970 --> 00:14:39.890 she did there. That you know the students get to use notes and a lot of the stuff 00:14:39.890 --> 00:14:45.050 I give them, not everything, but not a lot its a way for me to help them see the value 00:14:45.050 --> 00:14:48.590 of taking, being neat and taking good notes. But you know I appreciate that 00:14:48.590 --> 00:14:51.410 she's like oh I just looked at a similar problem we've done before and just kind 00:14:51.410 --> 00:14:54.710 of run through it. And like that's good but that's not what I'm looking for here. 00:14:54.710 --> 00:14:59.450 I wanted to explain mathematically why this is wrong. I mean a good 00:14:59.450 --> 00:15:06.110 good answer I'd want would be well 2 is wrong because if you look it's got four 00:15:06.110 --> 00:15:11.210 data points at 16, four at 17 and they get smaller as it goes out while it's the opposite 00:15:11.210 --> 00:15:16.190 in number 1 right. That shows me that you not only know what the definition means 00:15:16.190 --> 00:15:19.880 but you're saying I know what that means it terms of the way that dots are 00:15:19.880 --> 00:15:26.750 located on the in the problem okay. So not great. I'd ask the student to redo 00:15:26.750 --> 00:15:31.360 this one. And a similar issue with the correct answer okay. Yes it's actually answering 00:15:31.360 --> 00:15:36.459 the question yes but that's not that's not helpful here okay. This is getting 00:15:36.459 --> 00:15:39.880 somewhere. Looking at the evidence given on the test but that's still not clear 00:15:39.880 --> 00:15:45.730 enough. It's too vague. You'd have to say you know. What am I looking for here. I'm 00:15:45.730 --> 00:15:50.920 sorry. I should have said, I made a mistake before. Two is wrong right but 00:15:50.920 --> 00:15:53.230 three, I shouldn't have talked about one sorry about that, 00:15:53.230 --> 00:15:57.250 three has a lot more, it has six of them that are within sixteen and 00:15:57.250 --> 00:15:59.290 seventeen rather than the four. Sorry about that. 00:15:59.290 --> 00:16:03.640 And she would say, you look at it, you can say even I eyeballed it. They all 00:16:03.640 --> 00:16:06.790 kind of have these bell curve shape which we get to later in the course. 00:16:06.790 --> 00:16:11.560 Maybe even just say there's sixteen, seventeen has way more data points and 00:16:11.560 --> 00:16:16.269 that's where the middle is rather than sixteen seventeen in number two okay. 00:16:16.269 --> 00:16:21.070 So I do like mathematical words but just showing understanding even without the 00:16:21.070 --> 00:16:25.510 terminology is definitely acceptable for me at this point in the course okay. 00:16:25.510 --> 00:16:29.170 Sorry keep going the wrong way there. See my Spotify. Okay so this one I asked the 00:16:29.170 --> 00:16:34.630 student to redo. But this one number fourteen is a lot better. Here the 00:16:34.630 --> 00:16:37.810 student she's showing a clear understanding of what I'm looking for 00:16:37.810 --> 00:16:47.020 here. So let's look at number fourteen. Okay how many different codes of four 00:16:47.020 --> 00:16:52.839 digits, like an iPhone passcode, are possible if the first digit must be 00:16:52.839 --> 00:17:02.160 three, four, or five and if the code cannot end in zero? Alright so because 00:17:02.160 --> 00:17:08.740 because each digit is not dependent on another one, these are all independent, so 00:17:08.740 --> 00:17:11.740 therefore when you're calculating a probability or a total number of codes 00:17:11.740 --> 00:17:16.209 which is just the denominator for a probability, you can just multiply all 00:17:16.209 --> 00:17:20.919 the options together right. We'll get to some we in this course, where you can't 00:17:20.919 --> 00:17:25.600 just do it, you can't just multiply. You have to, you have to do some some more nuanced 00:17:25.600 --> 00:17:29.590 stuff there. There are different rules right. But for this, they're independent so 00:17:29.590 --> 00:17:33.669 you say how many options do I have for the first digit? Three, four, or five. 00:17:33.669 --> 00:17:40.070 That's three numbers boom. Second digit. Well there are 10 digits 0 through 9 00:17:40.070 --> 00:17:44.870 right? It could be any of those, so times 10, times 10, and the last one can't end 00:17:44.870 --> 00:17:51.890 in a zero, so it's one through nine which is only nine digits. Multiply them together. 2700. 00:17:51.890 --> 00:17:56.800 Cool. All right. Well this student she got it wrong. No big deal. 00:17:56.800 --> 00:18:01.790 Three times nine times nine times eight. Cool. It is very clear what her what her 00:18:01.790 --> 00:18:06.110 mistake is. She only thought there were nine she thought there were only 00:18:06.110 --> 00:18:10.550 nine digits but there aren't. There are ten okay. 00:18:10.550 --> 00:18:14.060 And that's her mistake. In fact the correct there's not too much more to say 00:18:14.060 --> 00:18:17.030 for this. She could have you know annotated it you know but you don't have 00:18:17.030 --> 00:18:20.270 to. This would be sufficient work for the question if that was the right 00:18:20.270 --> 00:18:24.830 answer. This was sufficient work. And her explanation is very clear here. My 00:18:24.830 --> 00:18:29.210 answer is wrong because I forgot to include zero as a possibility right. Would 00:18:29.210 --> 00:18:32.990 I have liked a little bit more, a little bit more? Yeah but that's acceptable you know. 00:18:32.990 --> 00:18:37.610 You could say I didn't include zero as a possible digit. Or you could say I 00:18:37.610 --> 00:18:43.250 you know I included I said there were nine digits instead of ten total and 00:18:43.250 --> 00:18:48.380 that's wrong. But yeah I mean she has it all down here. The correct answer is 00:18:48.380 --> 00:18:52.760 correct because when you include zero that gives you ten digits rather than 00:18:52.760 --> 00:18:57.320 nine. Okay so that's really nice. Not a crazy big mistake there so a little bit 00:18:57.320 --> 00:19:02.230 easier to explain which is definitely one of the tricky part of test corrections 00:19:02.230 --> 00:19:10.040 because the the smaller the mistake you made the easier to explain your explain 00:19:10.040 --> 00:19:15.830 your work right. But yeah that's a nice job by her there. So there you go. We 00:19:15.830 --> 00:19:19.130 got two right there. Let's keep going. Okay some more work here. This is pretty 00:19:19.130 --> 00:19:22.430 typical you know. You got some really nice things and some that need work and 00:19:22.430 --> 00:19:27.220 you know you improve on it. No big deal. Okay number 17. 00:19:27.220 --> 00:19:33.530 That's a nice question. Here we go. So this is our compound probability, independent 00:19:33.530 --> 00:19:38.360 probability here. Okay. You toss a coin and select a number from 00:19:38.360 --> 00:19:45.140 0 to 9. Are they independent or dependent? And explain. Right well they don't have 00:19:45.140 --> 00:19:47.630 any relationship to each other. They don't affect each other. 00:19:47.630 --> 00:19:51.020 So therefore they're independent. That's a definition right. We got a little bit of 00:19:51.020 --> 00:19:53.370 a math problem here. A little bit of a calculation problem. 00:19:53.370 --> 00:19:57.990 I'm a probability, excuse me, find the probability of tossing tails in the coin, 00:19:57.990 --> 00:20:02.399 excuse me on the coin and selecting and no selecting, oh my god, 00:20:02.399 --> 00:20:05.700 that's a typo there, selecting an odd number. Cool. 00:20:05.700 --> 00:20:11.909 Or select a number that is odd. Either way. Okay so well tails, 00:20:11.909 --> 00:20:19.620 one out of two. Odd five out of ten. One, three, five, seven, nine. Okay you could 00:20:19.620 --> 00:20:24.090 reduce that to one half. Either way you know you multiply them. Reduce. Students 00:20:24.090 --> 00:20:27.749 have calculators. They can do math. Enter, enter on their TI-83s to reduce it. 00:20:27.749 --> 00:20:32.129 You get one-fourth. That's the chance of tossing a tails and selecting a number, 00:20:32.129 --> 00:20:38.840 and odd number. Selecting an odd number okay. So let's see what the student did here. 00:20:38.840 --> 00:20:42.749 So it looks like, I'd have to look back at their work here, but it looks like they 00:20:42.749 --> 00:20:47.820 just didn't answer the first part of the question. So they wrote my answer is wrong 00:20:47.820 --> 00:20:52.019 because the variables are independent. They have no relationship with each 00:20:52.019 --> 00:20:57.299 other. All right that is a period there. I certainly hope. I think so. That isn't 00:20:57.299 --> 00:20:59.970 exactly what I'm looking for because that's the answer. 00:20:59.970 --> 00:21:05.909 I asked them to explain in the answer. What she could have said is you know 00:21:05.909 --> 00:21:11.759 they had no relationship because flipping a coin and tossing a sorry and 00:21:11.759 --> 00:21:16.019 selecting a number from 0 to 9 don't have any effect or are unrelated. Just to 00:21:16.019 --> 00:21:19.259 get a little bit more detail there would have been nice. But that's fine what she 00:21:19.259 --> 00:21:22.799 put. Ok then period. The second reason why it's wrong because it was wrong for two 00:21:22.799 --> 00:21:27.299 reasons. The denominator needs to be a 10. All right now the 00:21:27.299 --> 00:21:30.990 reason for that is obviously there are 10 digits from 0 to 9. It would have been 00:21:30.990 --> 00:21:38.690 nice for her to say and but that's all right. That's it's kinda in the middle there. 00:21:38.690 --> 00:21:43.289 And then the correct answer is correct because the denominator in my equation was 00:21:43.289 --> 00:21:46.860 nine when it needed to be 10. Well that should be more about why the 00:21:46.860 --> 00:21:51.360 answer is wrong. The answers right because now I have a denominator. 10 total digits. 00:21:51.360 --> 00:21:57.869 5 of them are odd. You multiply and you get, oh 1/4. That's actually wrong because 00:21:57.869 --> 00:22:01.200 didn't put 1.4 which is obviously not the same as 1/4. 00:22:01.200 --> 00:22:05.070 So actually this wouldn't be acceptable right. When you look look closely here. 00:22:05.070 --> 00:22:08.309 In this case student is getting there right. Some small mistakes. Just you know 00:22:08.309 --> 00:22:12.299 they can take their time. You know make sure their proofreading their work. But as 00:22:12.299 --> 00:22:15.330 you can see this is kinda what it looks like you know. You know students don't 00:22:15.330 --> 00:22:19.409 always make sense of it totally even second time. That's fine. They go back and 00:22:19.409 --> 00:22:24.750 they proofread them. They can always do these again. Cool. All right number 00:22:24.750 --> 00:22:34.559 eleven here. This one is not great. All right this one is with the ogive here. 00:22:34.559 --> 00:22:39.570 We have the leisure time of college students. This is a cumulative line graph 00:22:39.570 --> 00:22:44.639 meaning we have our 9.5 is the lowest, 39.5 hours 00:22:44.639 --> 00:22:49.679 a lot of time, the number of students who fit into the total categories up to that. 00:22:49.679 --> 00:22:54.330 So for example what I mean is the number of students who have up to 29 00:22:54.330 --> 00:22:59.669 point sorry 24.5 leisure hours is what would that be. that 00:22:59.669 --> 00:23:05.639 would be about I guess I would say like 65. This is be about 65 there. 00:23:05.639 --> 00:23:11.549 That means that includes all the students below. That means zero students 00:23:11.549 --> 00:23:19.470 had 9.5 hours of leisure. Ten students had 14.5. What is 00:23:19.470 --> 00:23:23.429 that. We got, what is that, about thirty five students had 19.5. 00:23:23.429 --> 00:23:28.529 That means, sorry, had up to 19.5. That means twenty five of 00:23:28.529 --> 00:23:32.549 them had somewhere between 14.5 and 19.5. 00:23:32.549 --> 00:23:37.679 The way you find what's in the middle of these or in this category would be by 00:23:37.679 --> 00:23:42.299 subtracting consecutive ones and that's tricky there okay because it's uh that's 00:23:42.299 --> 00:23:45.960 because it's cumulative cumulative excuse me. All right also cuz it's 00:23:45.960 --> 00:23:49.440 cumulative, the sample size is just the highest bar on the right because it 00:23:49.440 --> 00:23:53.389 tallies up all the previous ones. It already includes all the previous ones. 00:23:53.389 --> 00:23:57.980 The greatest increase in frequency is just where the the jump is the biggest. 00:23:57.980 --> 00:24:03.000 Okay and then more than, one kind of way students enjoy leisure time for more than 00:24:03.000 --> 00:24:07.559 29.5 hours, you'd have to see the jump from that point to the 00:24:07.559 --> 00:24:12.960 top which would be five or ten, you can see it's kind of hard to tell here 00:24:12.960 --> 00:24:18.600 and so I gave students some leeway about that answer. Now unfortunately our 00:24:18.600 --> 00:24:24.440 our student didn't really do too much to explain why it was wrong right. 00:24:24.440 --> 00:24:30.240 Some students are able to say I know why I got 333. For example there's a chance 00:24:30.240 --> 00:24:36.330 they added it up maybe all of these numbers. That might be it. Maybe some of these too right. 00:24:36.330 --> 00:24:40.680 And sometimes they don't know that and that's okay. What they can say 00:24:40.680 --> 00:24:46.380 to me is that that sample size is way too large because in a cumulative line 00:24:46.380 --> 00:24:52.680 graph or in an ogive the the previous frequencies are already included and it 00:24:52.680 --> 00:24:57.660 goes up to the highest number is 80 here. So like somehow just saying that 00:24:57.660 --> 00:25:01.590 number does making sense to me or showing you an understanding would be 00:25:01.590 --> 00:25:06.630 helpful if they're not exactly sure why you got that number. Okay same here. 00:25:06.630 --> 00:25:11.370 An increase in frequency has to be between two, between two categories, between two 00:25:11.370 --> 00:25:17.400 classes and it shows only one class. Okay looks like the student maybe got this 00:25:17.400 --> 00:25:22.260 right maybe. Well I would have accepted nine as a right answer. I don't 00:25:22.260 --> 00:25:25.830 know if her work was correct,. I didn't ask for work here but they could have left that 00:25:25.830 --> 00:25:29.370 out because nine is valid. I mean I put five or ten. Anything in between that is 00:25:29.370 --> 00:25:32.640 valid but this one just isn't enough. You have to be really clear with these. 00:25:32.640 --> 00:25:37.560 It's a three-part question right. They have to really go through it and say ABC and that 00:25:37.560 --> 00:25:41.880 didn't happen here. But no problem. Room for improvement. 00:25:41.880 --> 00:25:53.070 Okay last couple ones here. All right last couple ones. Okay number four. 00:25:53.070 --> 00:25:56.070 All right so these are the sampling techniques and I give them some 00:25:56.070 --> 00:26:00.180 definitions on this and we look at some pictures and there are just different ways 00:26:00.180 --> 00:26:04.920 of collecting information from a group that isn't the whole population. I've got 00:26:04.920 --> 00:26:08.850 simple random sampling and some kind of randomization maybe like random 00:26:08.850 --> 00:26:14.280 number drawing or a lottery or like an Excel random function right. Stratified 00:26:14.280 --> 00:26:18.960 sampling. We break things into strata or groups based on some level like income 00:26:18.960 --> 00:26:23.550 levels. Strata groups. Cluster sampling is usually geographic but its based on 00:26:23.550 --> 00:26:27.150 breaking things into clusters. They're supposed to be the same like zip codes. 00:26:27.150 --> 00:26:30.270 I would say zip codes don't really have a lot of the same attributes but that's 00:26:30.270 --> 00:26:33.010 one of the the possibilities for bias in the 00:26:33.010 --> 00:26:38.260 cluster sampling. Systematic rating system like in this case every 5th phone 00:26:38.260 --> 00:26:42.010 call is a system right. Or asking every third person who who walks through the 00:26:42.010 --> 00:26:45.910 door is a systematic sampling. And convenience is kind of anything else 00:26:45.910 --> 00:26:52.360 that you just do because it's easier and it forms bias okay. So we have A here. 00:26:52.360 --> 00:26:56.170 To ensure customer satisfaction every fifth phone call received will be monitored. 00:26:56.170 --> 00:27:02.170 Systematic right. Pretty typical. Kind of like a TSA PreCheck stuff you know. Every 00:27:02.170 --> 00:27:09.160 you know X number of people who comes through gets gets targeted. Gets 00:27:09.160 --> 00:27:13.420 asked for additional screening. Whatever it is right. Okay letter B is a little 00:27:13.420 --> 00:27:18.970 tricky. It should be cluster right. We're interviewing all the 00:27:18.970 --> 00:27:22.540 passengers on some flights. Obviously there are way more than five flights that 00:27:22.540 --> 00:27:27.700 happen per airline or per day or whatever it is. And so the cluster means 00:27:27.700 --> 00:27:32.410 you breaking things into, you take a subset right, breaking things into subsets, in this 00:27:32.410 --> 00:27:36.280 case subsets of five and then you ask all for one of those subsets. 00:27:36.280 --> 00:27:40.480 While in stratified you ask which is this next one you ask some from all of 00:27:40.480 --> 00:27:44.290 the subsets which is a difference I should have said earlier okay. I started 00:27:44.290 --> 00:27:48.700 accepting last year simple random sampling here because I found that word 00:27:48.700 --> 00:27:52.200 to be tricky. Five randomly selected flights. 00:27:52.200 --> 00:27:57.190 You know cluster is really the answer there but I've become a pushover as 00:27:57.190 --> 00:28:00.490 I've gotten older I guess and said you know maybe random isn't totally 00:28:00.490 --> 00:28:05.530 wrong there. But that's cluster. And stratified. You broke the upper class, 00:28:05.530 --> 00:28:08.880 the sophomore, junior, seniors into 00:28:08.880 --> 00:28:15.520 into the groups by their classes and you took some from all. 35 from 388, 24 from 00:28:15.520 --> 00:28:21.820 418, 25 from 573. Okay you broke them into strata and you took some from all the 00:28:21.820 --> 00:28:27.370 strata. Okay so let's see what the student wrote. So they're telling me that 00:28:27.370 --> 00:28:33.040 they only got C wrong. Okay. You don't to write my incorrect answer but simple random 00:28:33.040 --> 00:28:36.130 sampling. There is no other work to be shown so they could have just wrote 00:28:36.130 --> 00:28:40.690 simple random sampling. The correct answer is stratified. Okay my answers wrong because 00:28:40.690 --> 00:28:44.110 there is no equal probability of being selected. 00:28:44.110 --> 00:28:51.850 I really like this answer because in in random samples, in random samples there 00:28:51.850 --> 00:28:55.360 is, by definition that they want to be equal. Like drawing something from a lottery 00:28:55.360 --> 00:28:58.270 or picking a number at random out of a hat. Everything as an equal 00:28:58.270 --> 00:29:01.150 chance. While in here, you're still creating you know you're 00:29:01.150 --> 00:29:04.840 still creating something that is random but it's not necessarily equal 00:29:04.840 --> 00:29:08.890 probability and that's that's okay. In fact you're purposely trying to make 00:29:08.890 --> 00:29:13.090 sure you get some from all those. Some sophomores. Some juniors. Some seniors. 00:29:13.090 --> 00:29:16.809 Okay and they're not equal. These proportions are not equal. This case it 00:29:16.809 --> 00:29:22.150 looks like the sophomores are being over over-represented a little bit. But such is life. 00:29:22.150 --> 00:29:27.520 Okay so that's good. And then here, this is a correct because, so they'd 00:29:27.520 --> 00:29:31.780 have to write this, but because they are breaking up groups into smaller groups 00:29:31.780 --> 00:29:37.770 and only asking some of them. It's a little vague here. They're breaking up 00:29:37.770 --> 00:29:44.110 students into groups by class and asking some from all of the groups would be a 00:29:44.110 --> 00:29:48.429 little bit more accurate. Just some touch up here would be great because it needs 00:29:48.429 --> 00:29:51.910 to be a little bit more clear there. Okay but that's pretty close. It's pretty nice. 00:29:51.910 --> 00:29:58.960 Okay last one. Question number six. All right where we going here. Okay so this 00:29:58.960 --> 00:30:03.760 one is based on this frequency distribution table that I have there. 00:30:03.760 --> 00:30:06.940 I just gave them some different information. It's weight of, I don't know 00:30:06.940 --> 00:30:10.900 maybe they're like, I don't know like a middle school baseball team or something. 00:30:10.900 --> 00:30:16.660 Who knows right. And these are all the players. Here are the weight in pounds. The 00:30:16.660 --> 00:30:21.040 midpoints of each class. We've got one, two, three, four, five classes. Relative 00:30:21.040 --> 00:30:23.650 frequency. I said it was fine I left it as a fraction. 00:30:23.650 --> 00:30:28.000 Cumulative frequency which means the frequency and everything above it. So 4 00:30:28.000 --> 00:30:34.809 plus 6 is 10. 11 plus 4 plus 6 is 21. So so so so. Ok the class width though is 00:30:34.809 --> 00:30:39.040 really is asking what's the space between each class. Okay and notice how 00:30:39.040 --> 00:30:43.870 we're doing these, you're really working really with whole numbers. And so in this 00:30:43.870 --> 00:30:48.520 case the way to find class width is to subtract consecutive lower class bounds. 00:30:48.520 --> 00:30:56.110 So 140 minus 135 5. 144 minus 139 5. You could even subtract consecutive midpoints. 00:30:56.110 --> 00:31:00.360 You got a lot of options there okay. But what you don't do is subtract 00:31:00.360 --> 00:31:04.590 the upper minus the lower. That's just not the way we do it. Those are really five 00:31:04.590 --> 00:31:10.410 numbers. 135, 136, 137, 138, 139 and counting and subtraction don't work the 00:31:10.410 --> 00:31:16.080 same way. They're off by one right. So this explanation here needs some some 00:31:16.080 --> 00:31:21.690 focus on using the right words. She said I didn't include the last class. She 00:31:21.690 --> 00:31:27.030 means the last possibility in the class, the last weight in the class. Or you can 00:31:27.030 --> 00:31:30.900 say I subtracted the class max minus the class min. The class upper bound minus the 00:31:30.900 --> 00:31:33.210 class lower bound right. And that's not what you do. 00:31:33.210 --> 00:31:38.120 It's not that definition. And here she did that. I included the last 00:31:38.120 --> 00:31:45.330 well, no this is wrong because 139 is the last option in that class. You would say 00:31:45.330 --> 00:31:50.940 I subtracted consecutive lower class limits to find the five. Okay this one 00:31:50.940 --> 00:31:53.700 needs a little work here. All right but as you can see you know there's some 00:31:53.700 --> 00:31:57.780 really good stuff there that we saw and some that need some improvement but it's 00:31:57.780 --> 00:32:03.360 not a big deal. You know one of the one of things I'm constantly working on with 00:32:03.360 --> 00:32:08.720 these test corrections is helping students who didn't do as well to really 00:32:08.720 --> 00:32:12.299 be clear at their work right because oftentimes the students who did do well 00:32:12.299 --> 00:32:15.720 they're still able to do test corrections, so I'm happy to let them do them and I 00:32:15.720 --> 00:32:20.070 gave them half the points they lost back. I don't give partial credit on these 00:32:20.070 --> 00:32:23.490 tests so I let them get half points back by doing these. Think they're really 00:32:23.490 --> 00:32:28.830 valuable and those points are worthwhile. So my challenge isn't with those 00:32:28.830 --> 00:32:32.130 students who already kind of made small mistakes and can find them very easily 00:32:32.130 --> 00:32:36.240 and have the organized notes. But it's kind of with the students who didn't do 00:32:36.240 --> 00:32:41.250 that. How do we say alright on one hand you know let's not stress about it, we 00:32:41.250 --> 00:32:44.610 can figure this out you know, we can learn it but what are the 00:32:44.610 --> 00:32:47.790 mathematical habits you should be developing to do that you know. That's 00:32:47.790 --> 00:32:50.940 you know obviously coming to class of course but taking those good notes, being 00:32:50.940 --> 00:32:53.910 organized, referencing your notes when doing the classwork, referencing your 00:32:53.910 --> 00:32:57.299 classwork when you're doing the homework right. You know with that structure of learning 00:32:57.299 --> 00:33:00.299 math you know. Sometimes a little sometimes with me you start out with me 00:33:00.299 --> 00:33:03.450 there and then have students work together in class but then at home 00:33:03.450 --> 00:33:07.500 you're doing homework usually by yourself. So just getting more 00:33:07.500 --> 00:33:11.399 autonomy there but still using what you've done before to help you. 00:33:11.399 --> 00:33:15.239 Right those mathematical habits are really important but also getting students to think 00:33:15.239 --> 00:33:20.789 the right way about like yes, I'm doing these processes but like why. Yes, this is 00:33:20.789 --> 00:33:23.669 definition. Does this definition make sense? Is it related to any words that I 00:33:23.669 --> 00:33:27.089 already know. Especially for a lot of students I have English is not 00:33:27.089 --> 00:33:31.049 necessarily their first language and even if it is, it is not spoken at home. So just 00:33:31.049 --> 00:33:34.529 kind of like getting used to using words you know. Words they may not know in 00:33:34.529 --> 00:33:37.049 Spanish or whatever it is because they're because they're math words 00:33:37.049 --> 00:33:41.369 really. There are math words in every language. Some are right. Some aren't. But 00:33:41.369 --> 00:33:44.999 yeah just kind of building that habit but also like getting them to fix their 00:33:44.999 --> 00:33:47.789 mistakes. Getting them to find their mistakes and part of it is giving them 00:33:47.789 --> 00:33:52.229 the answer key. Part of it is pairing them up with other people. But also 00:33:52.229 --> 00:33:55.349 part of it is me working with them and saying hey you know look for it you know. 00:33:55.349 --> 00:33:58.499 Like let's try to find this. Don't just say I don't know where the mistake is. 00:33:58.499 --> 00:34:03.359 I got it wrong cuz it's wrong. But you know looking back at the work. And it's 00:34:03.359 --> 00:34:08.399 definitely, as the classes become more algebra, working with more 00:34:08.399 --> 00:34:13.349 algebra heavy classes like pre calc, that that's even more important because there 00:34:13.349 --> 00:34:19.020 are more steps and more places to go wrong, And yeah but it's also a little 00:34:19.020 --> 00:34:23.089 bit easier to find the mistakes because students can kind of work a little more 00:34:23.089 --> 00:34:27.059 down a process as long as I understand how that process might change if the 00:34:27.059 --> 00:34:32.700 question changes. But that is all I have for you today. I hope I hope you enjoyed 00:34:32.700 --> 00:34:36.450 me talking at you for 30 minutes or so whatever that was. I hope you learned 00:34:36.450 --> 00:34:41.520 something from it. Right please email me if you'd like the test correction template or just 00:34:41.520 --> 00:34:47.789 want to say hello or want to reach out. Yeah so that is it. This is me again 00:34:47.789 --> 00:34:52.500 right. This is us. OAME 2020. Very cool. First time. Wish it could have been in 00:34:52.500 --> 00:34:58.079 person but this is very cool too. Thanks to them. Alright email me. Reach 00:34:58.079 --> 00:35:05.089 out. Say hi but that is all. Alright thanks guys. Enjoy.