WEBVTT 00:00:11.046 --> 00:00:15.986 I am Bonnie Grossen, Executive Director for the Center for Applied Research in Education, 00:00:16.296 --> 00:00:20.696 also known as CARE, and CARE is affiliated with University of Oregon. 00:00:20.956 --> 00:00:25.576 In weaving together basic skills with algebraic concepts, 00:00:26.076 --> 00:00:32.286 there are some important instructional principles that kind of help guide that process. 00:00:33.506 --> 00:00:41.156 And one is that you don't have to have the same topic occur for the whole lesson. 00:00:41.156 --> 00:00:47.066 It's good to have some tracks so that you might have 10 or 15 minute segments 00:00:47.066 --> 00:00:49.646 where you are working on something you began yesterday. 00:00:49.646 --> 00:00:52.956 For example, well, students who don't know their math facts, 00:00:52.956 --> 00:00:54.746 you don't want to do a whole period on math facts. 00:00:54.746 --> 00:00:58.166 You might do three minutes of a review of multiplication facts. 00:00:58.586 --> 00:01:04.516 Have another little track that is developing an algebraic concept, 00:01:04.516 --> 00:01:09.206 like maybe an algorithm for finding an unknown in a certain position. 00:01:10.706 --> 00:01:16.246 And then as they're learning some of the basic skills, 00:01:16.246 --> 00:01:19.986 you don't want to have the conceptual problems require skills they haven't learned 00:01:19.986 --> 00:01:25.316 because the success is an important part of making them willing to put out the effort. 00:01:25.316 --> 00:01:28.406 As they feel successful, then they put out a lot more effort, 00:01:28.406 --> 00:01:30.406 and everything starts to work together. 00:01:31.016 --> 00:01:37.226 So the curriculum has to be extremely well organized and review built in. 00:01:37.976 --> 00:01:41.516 Review should be massed initially. 00:01:41.876 --> 00:01:44.186 When students are learning a concept, 00:01:44.186 --> 00:01:50.066 they should have enough practice so that they actually can do the algorithm or do the procedure. 00:01:50.546 --> 00:01:54.216 Then after that, the review should be distributed. 00:01:54.426 --> 00:01:57.376 We find that distributed practice leads to retention, 00:01:58.146 --> 00:02:03.966 and that means just a few problems everyday, not a whole page of one type. 00:02:03.966 --> 00:02:08.166 And then it should be cumulative; the different things students have learned 00:02:08.166 --> 00:02:12.406 in the past should be reviewed in this distributed practice. 00:02:12.606 --> 00:02:18.226 And the practice shouldn't take up the whole period. 00:02:18.226 --> 00:02:21.676 It should be another one of those little segments in the instruction. 00:02:21.966 --> 00:02:27.836 One of the issues we have in math education, and all education as a matter of fact, 00:02:27.836 --> 00:02:31.536 is when to use student-centered, or small group, 00:02:31.536 --> 00:02:36.836 instruction and when to have teacher-centered, or explicit, instruction. 00:02:37.466 --> 00:02:41.006 And one thing is quite clear; explicit instruction is more democratic 00:02:41.666 --> 00:02:44.706 than student-centered discovery groups. 00:02:45.236 --> 00:02:53.646 When students have to figure out the concept without any initial presentation from the teacher, 00:02:53.646 --> 00:02:57.206 then some students get the concept and others don't. 00:02:57.206 --> 00:02:59.136 And even if the teachers comes in and ask questions, 00:02:59.136 --> 00:03:02.426 it's hard for the teacher to respond to the kids who are not getting it 00:03:02.426 --> 00:03:03.986 when there are some that are getting it. 00:03:03.986 --> 00:03:08.606 And it just ends up being a focus on those who are getting it and the teacher feeling 00:03:08.606 --> 00:03:13.186 like the class got it when actually there is a large number of them who are still confused. 00:03:13.646 --> 00:03:17.886 So, the most democratic method for initial presentation is, 00:03:18.086 --> 00:03:20.596 we say, make the strategy conspicuous. 00:03:21.186 --> 00:03:22.916 And that can be explicit. 00:03:22.916 --> 00:03:24.796 That can be the teacher illustrating on the board, 00:03:24.796 --> 00:03:29.526 but there are other ways also to make math strategies conspicuous. 00:03:30.206 --> 00:03:38.016 The appropriate place for students to do group work is in applications 00:03:38.016 --> 00:03:41.196 or in making the review more interesting. 00:03:41.686 --> 00:03:45.916 Structured activities where the students work together to monitor each other's practice 00:03:45.916 --> 00:03:52.636 and have little challenges, and that makes the review and practice interesting. 00:03:53.326 --> 00:03:57.106 And then having students work together in groups 00:03:57.106 --> 00:04:01.126 where they're applying the concepts they learned to maybe more complex applications 00:04:01.126 --> 00:04:03.616 where they can put their heads together to figure 00:04:03.616 --> 00:04:07.936 out how the things they've learned might apply to this new situation. 00:04:08.326 --> 00:04:12.616 A real important tactic for teachers to use is scaffolding, 00:04:13.746 --> 00:04:18.065 and however strategies are made conspicuous, 00:04:18.216 --> 00:04:25.066 the students may often need continuous scaffolding or some guided prompting. 00:04:25.366 --> 00:04:31.346 So if teachers are completely involved with students while they're working, 00:04:31.426 --> 00:04:35.796 after they have finished working, looking at their work all the time and responding to that, 00:04:35.796 --> 00:04:37.876 they're doing a kind of formative assessment. 00:04:37.946 --> 00:04:42.036 One of the things we've done with students who are weak with their multiplication facts, 00:04:42.286 --> 00:04:48.936 we've put little tables in the back of their book that they could refer to that have the factors 00:04:48.936 --> 00:04:53.326 across the top and bottom and the multiples in a little grid sheet, 00:04:54.036 --> 00:04:55.776 rather than giving them calculators. 00:04:56.006 --> 00:04:58.326 Calculators are more opaque. 00:04:58.596 --> 00:05:02.416 One of the things that's become very popular in high schools is, 00:05:03.416 --> 00:05:06.006 for students who are not quite ready for algebra, 00:05:06.286 --> 00:05:10.716 the school will take the regular algebra course that's taught over a year 00:05:11.336 --> 00:05:14.596 and divide it into four pieces and take the first piece, 00:05:14.596 --> 00:05:19.536 the first quarter and then teach it in a full semester to students who are behind 00:05:20.216 --> 00:05:23.386 and thereby taking two years to get through algebra. 00:05:25.026 --> 00:05:30.186 Now when you do that, you don't have anything engineered into that textbook 00:05:30.186 --> 00:05:33.876 that helps the teacher teach those missing basic skills. 00:05:33.876 --> 00:05:37.306 You're just going more slowly through the same algebra course. 00:05:38.696 --> 00:05:42.826 And we have found that if you really spend sometime engineering the instruction, 00:05:42.826 --> 00:05:52.116 planning the examples, and building in some of that pre-skill instruction into the textbook, 00:05:52.116 --> 00:05:53.866 it can be very helpful for the teacher. 00:05:54.346 --> 00:05:58.946 A well-engineered text is going to help the teacher make progress more efficiently 00:05:58.946 --> 00:06:00.566 and effectively. 00:06:00.566 --> 00:06:04.366 High schools need to provide, for students who don't have the pre-skills for algebra, 00:06:04.776 --> 00:06:08.326 a course that's designed specifically for them, 00:06:08.636 --> 00:06:13.956 that is engineered to teach the pre-skills they are missing, the concepts of proportions 00:06:13.956 --> 00:06:18.186 and ratios and the relationship between decimals, fractions, and percents. 00:06:18.186 --> 00:06:23.066 Those kinds of things are built-in as they are being led into algebra, 00:06:23.316 --> 00:06:27.826 rather than just taking the standard algebra course and dividing it into chunks 00:06:27.826 --> 00:06:30.456 and taking two years to teach that same content. 00:06:30.456 --> 00:06:37.116 There has to be a smarter design to the curriculum to catch those kids up, and it can be done. 00:06:37.116 --> 00:06:38.426 We know it can be done.