WEBVTT 00:00:00.506 --> 00:00:08.576 [Music] 00:00:09.076 --> 00:00:15.436 Charles Willems: I incorporate review into my class by having daily warm-ups, 00:00:15.626 --> 00:00:21.176 and the first thing the students do in class when they come in is work on two or three problems, 00:00:21.676 --> 00:00:24.786 and that allows me some time to walk around and check their homework assignment 00:00:24.786 --> 00:00:29.466 from the previous night, and those problems deal with the variety of topics. 00:00:29.466 --> 00:00:33.536 So right now, we are studying quadratics, graphically parabolas. 00:00:33.976 --> 00:00:39.236 But the review topics might go back to finding equations for lines or finding the point 00:00:39.236 --> 00:00:42.716 of intersection of two lines, things we did in the previous two chapters. 00:00:43.296 --> 00:00:45.946 And they also might just go back to what we did let's say the day before, 00:00:45.946 --> 00:00:50.966 so it is very much related, but just to kind of build up to what's coming that day itself. 00:00:51.056 --> 00:00:55.076 Mike Comiskey: One of the ways that I incorporate into my Geometry class, say, 00:00:55.416 --> 00:00:57.516 which is the course after Algebra, 00:00:57.776 --> 00:01:00.936 is to bring in a lot of Algebra topics into the Geometry problem. 00:01:00.936 --> 00:01:04.075 So you might have a triangle and you are trying to find the measure of all 00:01:04.075 --> 00:01:07.996 of the different angles, and there will be algebraic expressions in each of the corners 00:01:07.996 --> 00:01:11.826 of the triangle, and students should know that those add up to 180 degrees. 00:01:11.826 --> 00:01:17.076 So, it becomes a simple linear Algebra problem to solve for X; at the same time, 00:01:17.076 --> 00:01:20.176 they are reviewing the Geometry idea. 00:01:20.176 --> 00:01:24.786 And this happens quite a bit also in their homework, where they're expected to know things 00:01:24.786 --> 00:01:26.786 from previous courses or previous chapters 00:01:26.786 --> 00:01:30.716 as you incorporate new material, especially true in Geometry. 00:01:30.716 --> 00:01:34.926 Willems: So, we've all set up, every math teacher set up in their homework 00:01:35.426 --> 00:01:37.356 that most every question is reviewed. 00:01:37.656 --> 00:01:41.126 There might be just one question or two that's from the day's topic. 00:01:41.626 --> 00:01:45.636 Most everything goes back to what we learned a day before or a week before 00:01:45.636 --> 00:01:48.156 or three months before, so they are constantly reviewing. 00:01:48.156 --> 00:01:50.986 And then, that builds into all of the tests that we write. 00:01:50.986 --> 00:01:56.146 And as teachers, we sit down; all the teachers sit down together and write the test. 00:01:56.446 --> 00:01:59.116 Geometry teachers do the same things for their courses. 00:01:59.466 --> 00:02:03.076 And the review part of that is that at least half the test is going back 00:02:03.076 --> 00:02:04.496 to covering previous chapters. 00:02:05.256 --> 00:02:07.616 And so, we are constantly reviewing in there as well. 00:02:07.616 --> 00:02:11.716 Comiskey: And we find that at the end of the semester, whereas in a typical traditional class, 00:02:11.716 --> 00:02:15.126 you have to sort of have a week and a half of cram for semester time. 00:02:15.396 --> 00:02:18.146 We can spend a couple of days to just kind of give them an outline 00:02:18.146 --> 00:02:19.776 of "Look, this is where we have been." 00:02:20.046 --> 00:02:22.936 Now, you had homework and different review topics on this. 00:02:23.226 --> 00:02:24.936 We've been talking about all these things all the time. 00:02:25.236 --> 00:02:29.556 And we don't find that we have to play catch-up a lot and remind them "Oh, 00:02:29.556 --> 00:02:31.356 in February, remember we did that thing." 00:02:31.806 --> 00:02:37.316 In May and June, it's still fairly fresh because we have been cycling it around and around. 00:02:37.736 --> 00:02:42.776 And what we find is that the risk of them not getting it at the end of the chapter 00:02:42.776 --> 00:02:46.516 when it was first introduced is decreased for students then. 00:02:46.516 --> 00:02:50.286 They don't have to necessarily get it in an eight-day span. 00:02:50.286 --> 00:02:52.536 They might blow it the first time they take that question 00:02:52.536 --> 00:02:55.346 on that new topic eight days after it was introduced. 00:02:55.346 --> 00:02:59.476 But, then, another 20 days later, they are going to see a similar question on that topic 00:02:59.476 --> 00:03:02.836 and now we hope because we have been reviewing, because it's been in the homework, 00:03:03.136 --> 00:03:04.566 that now they have got that concept. 00:03:04.566 --> 00:03:07.716 Willems: And what I really like about the homework, the way we have it set up, 00:03:08.096 --> 00:03:13.706 the fact that almost every question is reviewed, is that students don't fall in this trap 00:03:13.706 --> 00:03:18.976 where in class, they understood everything I was saying and then got home to work on 40 problems 00:03:18.976 --> 00:03:21.676 of the exact same type and they forgot and couldn't do anything. 00:03:21.676 --> 00:03:25.186 They're always going to have some success by going back and doing some of the problems 00:03:25.186 --> 00:03:29.636 that we've discussed in previous days because that's what they are seeing in their homework. 00:03:29.636 --> 00:03:31.226 Really makes them feel a lot more confident, too. 00:03:31.856 --> 00:03:36.926 I think of parent/teacher conferences that we've just had last week and a comment from a parent, 00:03:37.656 --> 00:03:45.456 and her daughter actually had Algebra last year at our middle school, and it didn't go so well. 00:03:46.386 --> 00:03:51.236 And so she took it again this year, which is a wise thing to do, and the mother's comment was, 00:03:52.226 --> 00:03:55.796 it's all making sense this year, it's all the visuals that you are doing, 00:03:56.846 --> 00:04:02.336 the hands-on manipulatives, and all the reviews spiraled in is really helping her 00:04:02.336 --> 00:04:05.436 to actually understand all the things that we are doing, 00:04:05.436 --> 00:04:08.006 all the concepts, and she is acing it right now. 00:04:08.006 --> 00:04:10.376 Comiskey: And I am finding that in my Geometry class, 00:04:10.376 --> 00:04:15.296 I have some of those freshmen that succeeded reasonably well in Algebra and, yet, 00:04:15.296 --> 00:04:22.106 they are into Geometry now, still struggling a little bit with some of those Algebra topics. 00:04:22.106 --> 00:04:26.146 And by hitting it with some frequency, they are strengthening those skills. 00:04:26.146 --> 00:04:30.026 So when they go to the next course, it won't be such a cold shower of "Oh, 00:04:30.026 --> 00:04:32.446 what's all this stuff I don't remember from my 8th grade year." 00:04:32.586 --> 00:04:35.706 It will be a two-year gap there between Algebra courses. 00:04:36.256 --> 00:04:39.696 So, yeah, we are fairly confident that that's something 00:04:39.696 --> 00:04:42.046 that will help them move on to the next course. 00:04:42.756 --> 00:04:47.776 Their constant review and quizzing is important because of this mastery over time idea. 00:04:48.206 --> 00:04:52.756 Traditionally, math courses assume that you are going to again need sort of that two-week window 00:04:52.756 --> 00:04:55.366 in which you are going to presumably learn everything. 00:04:55.626 --> 00:04:58.826 And for those of us who are math teachers, we probably were able to succeed in that world. 00:04:58.826 --> 00:05:01.446 You know, we liked math, we did it, and we succeeded and in two weeks, 00:05:01.446 --> 00:05:02.716 we could learn it and take a good test. 00:05:03.236 --> 00:05:10.216 But for many students who don't get it right away, but that successive review 00:05:10.216 --> 00:05:15.056 and even successive tests will help them sort of master it over time, 00:05:15.056 --> 00:05:17.686 and I think that review builds into that. 00:05:17.826 --> 00:05:25.006 One of the beauties of the spiraling curriculum is that it really requires students to not give 00:05:25.006 --> 00:05:29.286 up on a topic that traditionally they might have been able to work their way 00:05:29.286 --> 00:05:32.156 through as best they could and then it would fall away 00:05:32.656 --> 00:05:35.586 and never to be seen again-maybe one question on the final exam, 00:05:35.586 --> 00:05:37.726 but I will blow that one and that will be okay, too. 00:05:38.386 --> 00:05:43.596 And with the spiraling and with the review that's built into the new material all the time, 00:05:44.086 --> 00:05:50.566 students who never really master a topic that will come up again and again, and in some ways, 00:05:50.566 --> 00:05:55.666 it will require them to really work through their struggles with it, 00:05:56.146 --> 00:05:59.386 or it will prevent them from really getting onto the next topic. 00:05:59.836 --> 00:06:04.936 Compared to other text that I have taught out of our other approaches, 00:06:05.516 --> 00:06:11.086 you could let topics fall away and still end up with a B in the class or a B plus, I mean, 00:06:11.086 --> 00:06:15.346 you could still be a successful student never really having learned how to do that one thing, 00:06:15.866 --> 00:06:18.266 and that's pretty hard to do in this setting. 00:06:18.586 --> 00:06:20.796 Willems: And I think we really believe here at the school 00:06:20.796 --> 00:06:23.546 that mastery will take place over time. 00:06:24.336 --> 00:06:26.096 It's not going to happen in the one-day lesson. 00:06:26.876 --> 00:06:28.926 And for some students, it might; but for most, 00:06:28.926 --> 00:06:33.016 it is not going to and it might take some students a month or two to finally master something. 00:06:33.016 --> 00:06:36.956 But they get these chances over and over in practice, in homework, 00:06:37.266 --> 00:06:40.306 then again in test to eventually, nail the material. 00:06:40.846 --> 00:06:46.870 [Music]