WEBVTT Kind: captions Language: en 00:00:44.060 --> 00:00:50.010 The title of this session by Rudy Neufeld is 'Teach'...don't 'Tell' which means 00:00:50.010 --> 00:00:55.360 teach with understanding. Our objective here in this session is to develop ways 00:00:55.379 --> 00:00:59.309 to achieve deeper conceptual understanding in mathematics for 00:00:59.309 --> 00:01:04.650 teachers parents and students. We will share examples that blend digital 00:01:04.650 --> 00:01:09.020 approaches with related resources to help students develop deeper conceptual 00:01:09.020 --> 00:01:12.979 understanding in mathematics. 00:01:20.490 --> 00:01:25.630 Some educators establish it all. A full-service learning environment that 00:01:25.630 --> 00:01:31.060 supports a growth mindset within a learning pit. Encouraging teachers and 00:01:31.060 --> 00:01:34.950 students to grapple with concepts. 00:01:36.360 --> 00:01:41.049 Grappling is what you do when you do not know the answer. It is more than 00:01:41.049 --> 00:01:49.750 persevering, more than engaging. It is productive struggling. The learning pit 00:01:49.750 --> 00:01:54.490 supports resilient learners. The learning pit supports a learning environment 00:01:54.490 --> 00:01:59.560 where teachers and students address multi dimensional approaches. Build it. 00:01:59.560 --> 00:02:09.869 Draw it. Talk it. Write it and then own it. When you own it then you understand it. 00:02:09.869 --> 00:02:15.849 This is a process where one teaches but does not tell in nurturing a growth 00:02:15.849 --> 00:02:23.800 mindset within a learning pit. 00:02:24.000 --> 00:02:31.209 Were you taught or were you told? Do you teach or 00:02:31.209 --> 00:02:44.049 do you tell? Please encourage them to grapple. It is more than perseverance. 00:02:44.049 --> 00:02:55.480 It is productive struggling. Teach them by helping them learn. Learning is taking 00:02:55.480 --> 00:03:04.480 the plunge into confusion to work our way out into understanding. In concept 00:03:04.480 --> 00:03:09.750 one, we see a picture representing multiplication. We have base ten blocks 00:03:09.750 --> 00:03:19.019 represented on paper. Ones by ones. Ones by tens. Tens by ones and tens by tens. 00:03:19.019 --> 00:03:23.700 Think through this and fill in the spaces. 00:03:28.850 --> 00:03:41.489 This sketch shows 12 x 16. We have 12 ones by ones. 60 ones by tens. 20 tens by 00:03:41.489 --> 00:03:56.340 ones and 100 tens by tens for a total of 192. To understand multiplication by 00:03:56.340 --> 00:04:01.320 partial products use multi dimensional approaches in a three part lesson 00:04:01.320 --> 00:04:11.400 involving, getting started then working at it and then reflect and connect. 00:04:11.400 --> 00:04:21.930 First get started by showing 24 by 37 on paper and with base 10 blocks. Then work at it. 00:04:21.930 --> 00:04:28.430 Let computer with visuals lead you through the interactive lesson. 00:04:33.650 --> 00:04:38.400 Make thinking visible. Use multi-dimensional approaches with base 00:04:38.400 --> 00:04:46.860 10 blocks, paper, and interactive computer lessons. Note the area colored on paper 00:04:46.860 --> 00:04:53.150 and the same area covered with the colorful base 10 blocks. 00:04:54.770 --> 00:05:04.830 Let them grapple. Not all will come out of the learning pit at the same time. 00:05:04.830 --> 00:05:08.870 Let them study this and talk about it. 00:05:11.539 --> 00:05:18.389 In addition with regrouping, do not memorize a process but rather understand it with 00:05:18.389 --> 00:05:22.699 manipulatives on and off the computer. 00:05:24.070 --> 00:05:30.009 Talk to me, tell me what you are doing. The work with base ten blocks on the 00:05:30.009 --> 00:05:35.740 table, drawings on paper, along with the computer animation form the foundation 00:05:35.740 --> 00:05:39.509 for powerful and effective talk. 00:05:43.140 --> 00:05:48.000 In this example the student would be using actual base 10 blocks on the desk 00:05:48.000 --> 00:05:54.390 and follow the model in UMathX. When the number appears the student will 00:05:54.390 --> 00:05:59.250 click and drag the correct tiles to match the number. The student is then 00:05:59.250 --> 00:06:04.470 asked to subtract a certain number and in this case the student must regroup 00:06:04.470 --> 00:06:12.590 since not enough ones are given. Note the concrete and abstract representations. 00:06:13.110 --> 00:06:18.740 In fractions use a multi-dimensional learning environment. Computer. Paper. 00:06:18.740 --> 00:06:28.550 Manipulatives. Build it. Draw it. Talk it. Write it now you own it. 00:06:31.169 --> 00:06:35.990 In this three-part lesson, we use multi-dimensional learning environments. 00:06:35.990 --> 00:06:42.770 Part 1 - Getting started. On computer with manipulatives. 00:06:43.270 --> 00:06:48.969 Part 2 - Working at it. Off computer with manipulatives. 00:06:48.969 --> 00:06:56.499 And part 3 - Reflect and connect. Then at the bottom is the summary reminding 00:06:56.499 --> 00:07:04.019 us to build it, draw it, talk it, write it. Now you own it. 00:07:04.650 --> 00:07:09.380 Here the student is considering equal parts as an introduction to fractions. 00:07:09.380 --> 00:07:14.580 First the student must enter the number three as the number of equal parts and 00:07:14.580 --> 00:07:20.610 one as the number of green parts being considered. Then numerator and 00:07:20.610 --> 00:07:25.919 denominator are pulled over to result in a fraction. The learning takes place from 00:07:25.919 --> 00:07:28.759 concrete to abstract. 00:07:30.910 --> 00:07:35.350 In this slide we see a pattern block being divided up into fractional parts 00:07:35.350 --> 00:07:41.100 as a visual on the computer. The participant is encouraged to repeat 00:07:41.100 --> 00:07:47.930 the action with real pattern blocks then to think and talk about the fraction. 00:07:52.400 --> 00:07:57.650 In this on computer visual component, the learner is given shapes to move and fit 00:07:57.650 --> 00:08:03.220 onto a shape to help in answering questions about fractions. 00:08:03.719 --> 00:08:08.849 At the same time the off computer component with pattern blocks is used to 00:08:08.849 --> 00:08:11.839 see another approach. 00:08:12.090 --> 00:08:17.069 The above examples encourage the learner to use a variety of approaches. 00:08:17.069 --> 00:08:22.509 Using the computer encourages the user to risk. Supporting the pedagogy that a 00:08:22.509 --> 00:08:27.879 mistake is an opportunity to learn. So let them grapple without telling them 00:08:27.879 --> 00:08:30.389 the answer. 00:08:34.060 --> 00:08:38.260 Here we are in the midst of a computer animation along with a corresponding 00:08:38.260 --> 00:08:43.419 activity on paper where one is first shown any rectangle representing any 00:08:43.419 --> 00:08:51.029 group of items. First we will divide the shape into fifths with vertical lines. 00:08:51.220 --> 00:08:56.040 Then show two fifths of the group. 00:08:56.060 --> 00:09:01.360 Then the learner generates 3/4 of 2/5. 00:09:02.030 --> 00:09:08.000 First we see and do a particular case. Then we talk about a more general case 00:09:08.000 --> 00:09:11.080 using colors. 00:09:11.440 --> 00:09:18.880 Again we build it. Draw it. Talk it and write it. We grapple towards owning it. 00:09:18.880 --> 00:09:23.200 We do not get it immediately but through various approaches we get closer and 00:09:23.200 --> 00:09:30.870 closer to owning it. Remember owning means fully understanding. 00:09:33.470 --> 00:09:38.750 This introduction to division leads discussion to the meaning of division. 00:09:38.750 --> 00:09:43.370 To understanding through pictures, through computer animation, through talk. 00:09:43.370 --> 00:09:50.630 To understanding through various approaches. Teaching is not telling a rule. 00:09:50.630 --> 00:09:57.530 Through grappling overtime confusion works its way to understanding. What does 2/3 00:09:57.530 --> 00:10:04.370 divided by 1/6 mean? Can I show that another way? How many sixths are in 00:10:04.370 --> 00:10:09.850 2/3 or how many sixths are in 4/6? 00:10:10.950 --> 00:10:15.870 Now we can see that discussion with more examples leads to a pattern, to understanding. 00:10:15.870 --> 00:10:25.459 Open opportunities leading to understanding. Don't tell. Please teach. 00:10:27.990 --> 00:10:31.830 Here the graphics help in the understanding of the number of 00:10:31.830 --> 00:10:36.870 3/4 in 2 1/2. We click and drag the part of the container 00:10:36.870 --> 00:10:43.529 representing the divisor over each of the other containers. A mistake is an 00:10:43.529 --> 00:10:47.970 opportunity to learn. The program will help the learner to arrive at the 00:10:47.970 --> 00:10:50.630 correct response. 00:11:02.140 --> 00:11:07.450 Some of us have difficulty in seeing patterns. Here we want to find the number 00:11:07.450 --> 00:11:11.620 of blocks in the 30th picture to the right. 00:11:11.620 --> 00:11:19.060 In the first row, all blue. We have three, five, and seven blocks. All blue in the 00:11:19.060 --> 00:11:23.640 first row. In the first three packages. 00:11:24.880 --> 00:11:30.190 We want to find the number of blocks in the 30th package or term. the teaching strategy 00:11:30.190 --> 00:11:35.230 would not involve simply telling a formula. Give them time to grapple. 00:11:35.230 --> 00:11:41.020 To talk. To share strategies with color. we need to give them time so we are pushing 00:11:41.020 --> 00:11:43.530 them here. 00:11:45.360 --> 00:11:50.779 In the second row a colored orange link is added. 00:11:51.340 --> 00:11:58.810 So picture three in row two has one orange plus two times three blue equals 00:11:58.810 --> 00:12:01.440 seven. 00:12:01.889 --> 00:12:08.009 Picture four in row two would then have one orange plus two times four blue 00:12:08.009 --> 00:12:14.579 equals nine. Do you see the pattern? So picture 30 in 00:12:14.579 --> 00:12:17.689 row 2 would have? 00:12:20.420 --> 00:12:27.320 In the third row a white square is added. Now we may notice the pattern. The area 00:12:27.320 --> 00:12:32.080 of the whole square subtract the area of the white square. 00:12:32.080 --> 00:12:37.930 Let them grapple. The computer animation, real blocks, paper 00:12:37.930 --> 00:12:42.509 and talk will lead to understanding. 00:12:45.980 --> 00:12:53.020 Discussion with time will lead to understanding and finally to a formula. 00:12:57.630 --> 00:13:02.520 In the on computer exercise here learners are asked to find the area on 00:13:02.520 --> 00:13:08.780 paper first then on computer. A STEM activity. 00:13:11.910 --> 00:13:17.700 Learners are not told but encouraged to risk. Then are given more and more 00:13:17.700 --> 00:13:20.510 helpful hints. 00:13:21.080 --> 00:13:26.210 In this elementary example, we are adding vertically but also showing another 00:13:26.210 --> 00:13:32.660 approach horizontal and modelling with the use of cube-A links. The learner would 00:13:32.660 --> 00:13:36.350 work with a real set of cube-a links on their desk as they work through the 00:13:36.350 --> 00:13:39.610 example on the computer. 00:13:41.329 --> 00:13:46.160 Note the number of steps to help the learner with an incorrect answer. 00:13:46.160 --> 00:13:51.940 A correct answer must be given before the student can proceed. 00:14:03.390 --> 00:14:08.550 In this example for middle and high school, we will proceed along the 00:14:08.550 --> 00:14:15.829 following path: graphing; equation of a straight line; word problems; applications; 00:14:15.829 --> 00:14:20.390 the walker; same speed. 00:14:22.339 --> 00:14:27.110 We are asked to click on the starting point for Wendy. 00:14:27.110 --> 00:14:33.050 So we'll start at B and drag a line which represents Wendy's walk at the 00:14:33.050 --> 00:14:39.200 same speed. The slope should be the same as the line representing Walter's walk so 00:14:39.200 --> 00:14:44.600 notice the hint we are given when we make a mistake. this helps guide us to 00:14:44.600 --> 00:14:47.380 the correct answer. 00:14:51.570 --> 00:15:00.269 Towards teaching not telling. Productive math talk moves. Show me another way. 00:15:00.269 --> 00:15:05.790 How are these the same or different? What would you do if...? What else could you have 00:15:05.790 --> 00:15:14.959 done? Why did you...? Say it another way. Repeat it. Reason through. Add on. 00:15:15.500 --> 00:15:21.350 Students articulate their own ideas and consider peer perspectives as a way to 00:15:21.350 --> 00:15:24.610 construct understanding. 00:15:25.830 --> 00:15:31.720 Here is a humorous example of magic over the understanding of math in the life of 00:15:31.720 --> 00:15:40.210 Ma and Pa who considered dividing 25% fairly five ways. I figure 75% to you 00:15:40.210 --> 00:15:47.200 Pa and Ma and 25% divided between the five of us. Yidda. Crowbar. Myself Tom and the baby. 00:15:47.200 --> 00:15:51.670 That makes five percent for each one of us. Ah Billy you're cheating 00:15:51.670 --> 00:15:56.560 yourself. If there's 25% divided among the five of you, 00:15:56.560 --> 00:16:03.490 that's 14% apiece. Oh no listen Pa, I wouldn't cheat you. You know I wouldn't. 00:16:03.490 --> 00:16:11.500 Now look. Look here. I'll show you. Let me rub this out here. 25 divided 00:16:11.500 --> 00:16:19.330 by 5 is 5. You see. 5 won't go into 2 will it? No. But 5 goes into 25 five 00:16:19.330 --> 00:16:33.730 times. You see. You're wrong Billy. Now I'm a pretty good mathematician. Now 5 into 25. 5 won't go into 2, will it? No. But 5 goes 00:16:33.730 --> 00:16:41.440 into 5 once. Now we didn't use the 2 before so we're bring it down here. Now 5 00:16:41.440 --> 00:16:51.250 into 20 goes 4 times. There you are 5 into 25, 14. No. Look Pa, let me prove it to you now 00:16:51.250 --> 00:17:01.600 by multiplication. 5 times 5. 5 times 5 is 25. Really, I'm surprised that you're learning. Huh? 00:17:01.840 --> 00:17:10.960 I'm surprised that you're learning. Now I'll show you. 5 times 14 is 25. 5 times 4 00:17:10.960 --> 00:17:22.720 is 20. 5 times 1 is 5. 25. That's it. No. No. Look Ma. Look you're wrong there because I'll prove it to you. 00:17:22.720 --> 00:17:29.230 We'll put down 5 14s here. 14 14 14... There now. Now I'll prove 00:17:29.230 --> 00:17:35.330 to you by addition that that 5 14s is not 25. 00:17:35.330 --> 00:17:45.529 4 8 12 16 20 21 22 23 24 25. There you are. Better brush up Billy. I don't want to 00:17:45.529 --> 00:17:48.549 to see you boys cheated. 00:17:58.250 --> 00:18:04.780 Coding through robotics models teaching with understanding. 00:18:05.070 --> 00:18:10.340 Coding has become a vital skill for the 21st century. It gives 00:18:10.340 --> 00:18:16.330 learners direct participation in and responsibilities for their own learning. 00:18:16.330 --> 00:18:20.990 The computer language LOGO models a learning environment which encourages 00:18:20.990 --> 00:18:28.310 one to teach rather than to simply tell. Dr. Seymour Papert of MIT developed a 00:18:28.310 --> 00:18:34.490 powerful coding language LOGO which uses code to direct the robot on the floor or 00:18:34.490 --> 00:18:43.000 on the computer screen. It is a model for learning. One learns from mistakes. 00:18:43.920 --> 00:18:49.650 In these two diagrams we are learning by teaching a robot. In the first example 00:18:49.650 --> 00:18:59.550 in 1990, working with a hearing-impaired class. In 2020, working with a blue bot. 00:18:59.550 --> 00:19:05.100 LOGO is referred to as the language of learning. 00:19:05.100 --> 00:19:13.170 I met Dr. Papert at MIT some years ago. The meeting determined my future 00:19:13.170 --> 00:19:18.620 direction in education. Let me show you briefly and let you try it. 00:19:18.620 --> 00:19:26.430 LOGO is available in both a free and a licensed version. We will first click on 00:19:26.430 --> 00:19:32.630 the link to result in three options. 00:19:40.490 --> 00:19:47.580 My examples will demonstrate the LOGO learning environment to you. I will now 00:19:47.580 --> 00:19:55.410 click on the LOGO link and proceed. Here you have our three options. If you click 00:19:55.410 --> 00:20:01.020 here you need to pay. If you click here it's for a classroom. If you click here 00:20:01.020 --> 00:20:08.610 we get the free trial. I'm going to click on this one. The LOGO learning 00:20:08.610 --> 00:20:14.130 environment comes up. I'm just going to try a few commands here. The code, I 00:20:14.130 --> 00:20:18.540 realize you do not know the code but I'll just use some simple examples, some 00:20:18.540 --> 00:20:32.730 simple commands. First of all I am going to enter home clear screen set width 3. 00:20:32.730 --> 00:20:38.520 That will set the width of the path quite wide so that you can see what's 00:20:38.520 --> 00:20:43.980 going on. I want a slow turtle. I want a slow 00:20:43.980 --> 00:20:51.270 turtle. So again you can see what's going on and I want to set the pen color of 00:20:51.270 --> 00:20:58.410 the turtle, has many pen colors, I want to send it to 4. When I press the enter 00:20:58.410 --> 00:21:05.010 button here it'll do all that at once. You will only see the final command set 00:21:05.010 --> 00:21:11.640 pen color 4 which is red because it hasn't moved. Now I'm going to go ahead 00:21:11.640 --> 00:21:17.600 and I'm going to do a little test here. Let's go home. Let's clear the screen. 00:21:17.600 --> 00:21:26.929 Let's go forward 67. And let's turn right 90 and let's go 00:21:26.929 --> 00:21:33.850 back, oh let's go back 67. I enter that. 00:21:33.850 --> 00:21:40.270 Good. So I got a command there, a code that gave me action and I could predict 00:21:40.270 --> 00:21:44.410 what might happen if I put a similar similar command in there. 00:21:44.410 --> 00:21:52.450 So now let's clear the screen good. And I want to chunk. That's a process 00:21:52.450 --> 00:21:57.700 where I can break a line into parts and see one step at a time what's 00:21:57.700 --> 00:22:03.180 happening. So that's a good tool for problem-solving. So let's go forward 00:22:03.180 --> 00:22:15.430 67 and enter. Then let's turn right 90. Enter. And let's go back 67 and 00:22:15.430 --> 00:22:23.290 enter. Good. Now let's go ahead and clear the screen. And let's clear the text as 00:22:23.290 --> 00:22:30.990 well so that you can see what's happening. Now I'd like to try, repeat 00:22:30.990 --> 00:22:42.570 4 times, square brackets, go forward 60, turn right 90. So if I look at that, I 00:22:42.570 --> 00:22:49.470 would go forward 60, right 90 and I'll do that four times. Let's see what happens 00:22:49.470 --> 00:22:55.370 here. So I'm going to say do it by pressing the enter button. 00:22:57.770 --> 00:23:04.370 Good. That's what I expected. So let's add a bit here. I'm going to say let's repeat, 00:23:04.370 --> 00:23:09.650 let's, first of all, let's clear the screen. I'll do that. And then let's go 00:23:09.650 --> 00:23:17.900 ahead and say let's repeat 4 times, square brackets, let's repeat again 4 00:23:17.900 --> 00:23:30.530 times, and do a forward 60, right 90. So I already, if I've done enough of these 00:23:30.530 --> 00:23:36.890 I'll realize what this does. And then after that I would like to at the end of 00:23:36.890 --> 00:23:46.030 that, I would like to put in a turn right, turn right 90. 00:23:46.440 --> 00:23:51.570 So I would discuss this with my partner. What would I get here? After making a 00:23:51.570 --> 00:23:56.519 square, turns right 90. Does it four times. Let's see what happens here. 00:23:56.519 --> 00:24:01.970 So I am going to enter that. So here we go. 00:24:07.230 --> 00:24:12.000 Many more commands I could use but I just want to give you an idea of the 00:24:12.000 --> 00:24:17.760 learning. I'm going to clear the screen and let's go home 00:24:17.760 --> 00:24:24.180 and then also we might as well clear the text there. So it does that in order. Then 00:24:24.180 --> 00:24:31.080 I'm going to go ahead and let's do a repeat again, repeat four times. Let's go 00:24:31.080 --> 00:24:42.450 forward. I'm sorry. The repeat again four times. Let's go forward 60, right 90, 00:24:42.450 --> 00:24:50.250 and then within that, let's turn a right 90. We did that before but now let's go 00:24:50.250 --> 00:24:58.800 forward 60 as well. So I would think of what what might happen there and I might 00:24:58.800 --> 00:25:05.190 use a color on here which is a square. I've learned that and that might help me. 00:25:05.190 --> 00:25:08.660 But let's see what happens here. 00:25:09.389 --> 00:25:14.399 We added that forward 60. 00:25:16.440 --> 00:25:22.420 If that was a mistake I would learn from it and possibly change, adapt it, whatever. 00:25:22.420 --> 00:25:29.800 A mistake is an opportunity to learn. So I'm going to go ahead and say, well I 00:25:29.800 --> 00:25:36.340 like that. But in in this particular coding language and in most you would 00:25:36.340 --> 00:25:43.930 build progress on progress. I want to build knowledge on knowledge. So suppose 00:25:43.930 --> 00:25:52.960 I teach a lesson, call it, let's be a call it box. So I say To Box and see what 00:25:52.960 --> 00:25:59.800 happens. To box and I enter that. then It goes into a screen over here. The To 00:25:59.800 --> 00:26:05.380 tells me a lesson is coming and I'm going to teach it To Box. Its repeat 00:26:05.380 --> 00:26:17.170 four times, go forward 60, right 90. Good and I remember that lesson. Why I know 00:26:17.170 --> 00:26:23.950 that, by hitting the run key. Run and it'll say over here box is defined. 00:26:23.950 --> 00:26:30.070 So it's like you go to school. You learn a lesson based on certain concepts and you 00:26:30.070 --> 00:26:36.010 build next day on what you already know. So I built a lesson Box based on 00:26:36.010 --> 00:26:41.710 commands that ideally we have would have spent a lot of time with. So now after 00:26:41.710 --> 00:26:46.900 you've taught a lesson, I clear the screen and that box becomes a new 00:26:46.900 --> 00:26:52.900 command. A new concept that I know. But as a teacher I would test that concept and 00:26:52.900 --> 00:26:59.350 so let's put in Box and see if we get what we thought we would get and so it's 00:26:59.350 --> 00:27:04.660 really I like the positive approach. We're really testing if the teacher has 00:27:04.660 --> 00:27:08.380 taught it correctly. Are we going to get what we expect? 00:27:08.380 --> 00:27:15.010 So Box. I enter it and it gives me this item. I could have called it whatever I 00:27:15.010 --> 00:27:18.850 wanted to but it might as well call it that's something that is something that 00:27:18.850 --> 00:27:26.830 I remember. So now I can say, okay let's so clear screen and let's go a repeat. 00:27:26.830 --> 00:27:36.039 I can get much more efficient now. Four times. Let's go let's go forward 60 00:27:36.039 --> 00:27:46.659 and let's put in right 90. I'm gonna change this around. Let's say I go repeat 00:27:46.659 --> 00:27:52.830 4 times, make a box and then turn right 90. 00:27:53.440 --> 00:28:00.890 And I enter that. Makes the box. Turns right 90. 00:28:12.679 --> 00:28:18.659 So we have taught a new lesson based on present knowledge as you do in school. 00:28:18.659 --> 00:28:23.850 We taught it to box. Then we tested that lesson to see if you the teacher have 00:28:23.850 --> 00:28:31.049 taught it correctly. Use the new lesson to build knowledge on knowledge. We could 00:28:31.049 --> 00:28:37.140 now build a lesson manybox which makes use of a lot of boxes if we want to do 00:28:37.140 --> 00:28:43.110 that. That's just the tip of what could happen here but you can see that we 00:28:43.110 --> 00:28:50.990 showed coding through robotics models teaching with understanding. 00:28:52.530 --> 00:28:58.110 This written resource including a blue bot robot and LOGO license will be 00:28:58.110 --> 00:29:02.420 available in June 2020. 00:29:06.870 --> 00:29:11.730 Examples in this video presentation have been taken from UMathX the 10th 00:29:11.730 --> 00:29:16.530 version of Understanding Math. This learning environment supports a growth 00:29:16.530 --> 00:29:20.730 mindset within a learning pit. Encouraging students and teachers to 00:29:20.730 --> 00:29:24.260 grapple with concepts. 00:29:24.490 --> 00:29:31.630 Learners worldwide have free access to UMathX. For a glimpse of growth 00:29:31.630 --> 00:29:41.700 mindsets, use any browser and enter the URL www.umathx.com. 00:29:44.039 --> 00:29:51.770 Login with the username: count and password: umathx 00:29:51.770 --> 00:29:57.560 And please note, the new UMathXi for all devices will be available to educators 00:29:57.560 --> 00:30:02.590 and parents in June 2020. 00:30:04.930 --> 00:30:09.700 This has been a video on productive struggling within a learning pit through 00:30:09.700 --> 00:30:15.700 teaching not telling. Once you have shared your new teach not tell 00:30:15.700 --> 00:30:20.590 techniques with your class, we suggest that you see and discuss the following 00:30:20.590 --> 00:30:24.940 excellent video by the originator of the learning pit concept, 00:30:24.940 --> 00:30:30.460 James Nottingham of Challenging Learning - the learning pit. Have a great time 00:30:30.460 --> 00:30:35.250 teaching. Thank you for watching. 00:30:36.039 --> 00:30:45.279 I was working with a group of students recently and they were studying tourism. 00:30:45.279 --> 00:30:49.450 So I asked them well what is a tourist? And they said a tourist is someone who 00:30:49.450 --> 00:30:53.440 visits another place. I said does that make me a tourist today then. I'm 00:30:53.440 --> 00:30:57.909 visiting another place, your school. And they said, no you have to be having fun. 00:30:57.909 --> 00:31:02.169 I said I am having fun. I overheard one of them saying he's weird him, isn't he? I said 00:31:02.169 --> 00:31:06.100 what is a tourist if its not just visiting another place then? And they 00:31:06.100 --> 00:31:10.090 said well it's somebody who takes photographs when they visit that other 00:31:10.090 --> 00:31:13.570 place. And I said I've been taking photographs of your school as I've been 00:31:13.570 --> 00:31:17.889 walking around. They said okay but you have to spend money. I said I've spent 00:31:17.889 --> 00:31:22.869 money coming here today and I'm going to spend money on my lunch. They said you've 00:31:22.869 --> 00:31:26.229 got an answer for everything. I said I'm not trying to give that 00:31:26.229 --> 00:31:30.729 impression. What I'm trying to do is find out what you think a tourist is. How could 00:31:30.729 --> 00:31:34.239 we find out more? They said well we can go and look in the books. We can look 00:31:34.239 --> 00:31:38.440 online. I said great. I'll give you twenty minutes. Go and do your research. Come 00:31:38.440 --> 00:31:42.399 back and we'll see where we go from there. The teachers who were watching 00:31:42.399 --> 00:31:47.259 that lesson said their children were far more animated than normal particularly 00:31:47.259 --> 00:31:51.759 when it came to the research. The students were in groups. One child would 00:31:51.759 --> 00:31:56.320 say see I told you a tourist is someone who goes on tour. Another one says yes 00:31:56.320 --> 00:32:00.429 but we could go on tour and not be tourists. For example go on a tour of our 00:32:00.429 --> 00:32:06.399 school. And somebody else said ah yes but it's about being on holiday. And I 00:32:06.399 --> 00:32:10.389 said but I've been on holiday. We were all on holiday in the summer holidays. It 00:32:10.389 --> 00:32:14.169 doesn't mean that we were tourists for that whole summer holiday. One girl said 00:32:14.169 --> 00:32:19.570 I know, you're a tourist if you think you're a tourist. And she was very smug 00:32:19.570 --> 00:32:23.739 about her answer. But another girl said hang on a minute. I've just been on 00:32:23.739 --> 00:32:27.789 holiday. My baby sister didn't think of herself as a tourist and yet probably 00:32:27.789 --> 00:32:32.400 she was. And it's about this idea of getting students 00:32:32.400 --> 00:32:38.570 to question, to challenge. to wonder together. I want to create that sense of 00:32:38.570 --> 00:32:45.180 cognitive wobble. That sense of intellectual dilemma so that the 00:32:45.180 --> 00:32:50.730 students think more. And the metaphor I use for this is a learning pit. 00:32:50.730 --> 00:32:55.470 I developed this idea in the early 90s when I was teaching and using philosophy 00:32:55.470 --> 00:33:01.020 for children a lot. And it's a really nice way to think through concepts. Stage 00:33:01.020 --> 00:33:07.140 one of the pit is to identify a key concept. For example tourism. Lots and 00:33:07.140 --> 00:33:11.760 lots of other examples from right across the curriculum. Fair test. Justice. 00:33:11.760 --> 00:33:20.070 Knowledge. Shape. Toys. Names. Real. Telling lies. Tragedy. Culture. Every subject has 00:33:20.070 --> 00:33:26.900 lots and lots of concepts. And by concept I mean more than facts. We could say 00:33:26.900 --> 00:33:33.210 Paris is the capital of France. That's a fact. We can't really challenge that very 00:33:33.210 --> 00:33:38.270 well. Are you sure? The kids say yes, we are sure. Paris is the capital of France. 00:33:38.270 --> 00:33:43.980 But what is a capital city? Now we're getting into looking at the concept. 00:33:43.980 --> 00:33:49.140 Capital cities. What is a capital city? Is it always the most important city? Is it 00:33:49.140 --> 00:33:54.270 always the biggest city? And so on. It's identifying the key concept because then 00:33:54.270 --> 00:34:01.110 we've got the opportunity to begin to think and to question. Stage two then is 00:34:01.110 --> 00:34:07.260 creating the cognitive conflict. Cognitive conflict is where students 00:34:07.260 --> 00:34:12.629 have got two or more ideas in their mind at the same time and they agree with 00:34:12.629 --> 00:34:18.020 both of those ideas but those ideas conflict with each other. For example a 00:34:18.020 --> 00:34:23.129 student who's the victim of bullying. We might say to them if you are bullied, 00:34:23.129 --> 00:34:28.050 tell the teacher. That's idea number one. But they might say to us, yes but my dad 00:34:28.050 --> 00:34:31.850 says I have to hit back twice as hard. There's idea number two. 00:34:31.850 --> 00:34:36.590 Those two ideas they agree with but they're in conflict with each other. 00:34:36.590 --> 00:34:41.840 That's what I mean by cognitive conflict. Another example, students will tell us 00:34:41.840 --> 00:34:47.540 stealing is wrong. But they will also say that Robin Hood was a good man. Those two 00:34:47.540 --> 00:34:52.280 ideas are in conflict with each other. Food is something I eat. 00:34:52.280 --> 00:34:57.050 There's my idea number one. Idea number two just think of all the disgusting 00:34:57.050 --> 00:35:03.710 things children eat. For example their bogies or nails or hair. That's idea 00:35:03.710 --> 00:35:08.720 number two. Food is something I eat. Lots of things I eat are not food. That's a 00:35:08.720 --> 00:35:12.470 conflict. I was working with a group of students. They were seven or eight years 00:35:12.470 --> 00:35:14.510 old and I asked them what are you studying. 00:35:14.510 --> 00:35:19.160 They said odd numbers. I said oh wow what's an odd number? They said an odd 00:35:19.160 --> 00:35:24.320 number cannot be divided by two. I said okay so if I've got five cakes and I 00:35:24.320 --> 00:35:29.450 share five cakes with your teacher, how many would we get each? And they said she 00:35:29.450 --> 00:35:35.420 would get three and you would get two. I said well why? And they said because 00:35:35.420 --> 00:35:40.370 you're a gentleman. I said no. I want my fair share. They said okay she'll get two, 00:35:40.370 --> 00:35:44.720 you'll get two, and you'll leave one for a friend. I said come on what would you 00:35:44.720 --> 00:35:49.220 really do? And they turned round as if to apologize to their teachers for what 00:35:49.220 --> 00:35:52.640 they were about to say, they leaned forward and they said we've cut the 00:35:52.640 --> 00:35:57.860 cakes really. I said so you can divide five by two can you? They said yes. I said 00:35:57.860 --> 00:36:02.360 so does that make five an even number then? And they said yes. Lots of the 00:36:02.360 --> 00:36:07.730 teachers sat at the back going awww. Spent weeks teaching this. My purpose is not to 00:36:07.730 --> 00:36:12.440 confuse them and then leave them there. My purpose is to get them to think more. 00:36:12.440 --> 00:36:17.150 If for example I had said what is an odd number? They had said an odd number 00:36:17.150 --> 00:36:21.620 cannot be divided by two. And I said very good well done. How much thinking would 00:36:21.620 --> 00:36:26.630 there have been. But by challenging them and questioning them they then had to use 00:36:26.630 --> 00:36:32.080 more skills of thinking. And by skills of thinking I mean for example defining, 00:36:32.080 --> 00:36:36.770 evaluating, generalizing, interpreting, predicting, questioning, 00:36:36.770 --> 00:36:41.990 testing, verifying. These are important life skills. They're important study 00:36:41.990 --> 00:36:47.780 skills. They're important exam skills. Think of the exams where the students 00:36:47.780 --> 00:36:51.770 are asked to predict what would happen if or summarize what the author is trying 00:36:51.770 --> 00:36:57.619 to say, to verify the following statement or to interpret this diagram. Of course 00:36:57.619 --> 00:37:01.640 it's not just about exams. It's about those life skills. There's 00:37:01.640 --> 00:37:06.740 also a collaborative element to the pit as well because students work together. 00:37:06.740 --> 00:37:13.010 They come together to support each other, to help each other and to build on each 00:37:13.010 --> 00:37:18.170 other's ideas. After a while of being in the pit some of the students come out of 00:37:18.170 --> 00:37:21.950 the pit. And notice I say some because they don't all come out of the pit at 00:37:21.950 --> 00:37:27.110 the same time. When I was working with those children on odd numbers, it was 00:37:27.110 --> 00:37:31.250 halfway through the lesson when one of the boys said I know it's like odd socks. 00:37:31.250 --> 00:37:35.510 I said what do you mean? That well my mum and dad say no matter how many socks 00:37:35.510 --> 00:37:40.190 they put in the washing machine, they always get an odd number out. So can you 00:37:40.190 --> 00:37:43.730 tell me a bit more about that? And he said well socks come in pairs don't they? 00:37:43.730 --> 00:37:47.480 And when you get the socks out you have to pair them up and there's always one 00:37:47.480 --> 00:37:55.270 left over without another sock. iIt's like that isn't it? That caused a sense of 00:37:55.270 --> 00:38:00.440 eureka for children because they said oh yes that's right. And then they started to build on 00:38:00.440 --> 00:38:06.140 his answers. One of the first times I use this metaphor at a conference. I talked 00:38:06.140 --> 00:38:10.880 about stage 3 being the eureka moment. And there's a woman on the front row jumped 00:38:10.880 --> 00:38:14.570 up and she said I've just got married. So I'm thinking I'm very happy for you but 00:38:14.570 --> 00:38:18.350 please sit down. She said I just got married to a Greek man and so I'm 00:38:18.350 --> 00:38:23.690 learning Greek and Eureka is Greek for I found it. And I thought isn't that 00:38:23.690 --> 00:38:29.359 interesting. Eureka means I found it. It doesn't mean my teacher gave me the 00:38:29.359 --> 00:38:35.150 answer. It doesn't mean my friend showed me. It means I found it. 00:38:35.150 --> 00:38:38.510 And when you get that sense of eureka what you want to do with it? You want to 00:38:38.510 --> 00:38:43.040 share it. You want to talk to people and you want to repeat it. How many times 00:38:43.040 --> 00:38:48.710 have parents picked up children and said what did you do at school today? And our 00:38:48.710 --> 00:38:53.810 children say nothing. Try shutting them up if they've had that eureka moment. 00:38:53.810 --> 00:38:57.200 They will bl bl bl bl and when they come back to school the next day, 00:38:57.200 --> 00:39:03.800 what will they want? More of the same. And here's the key about the pit. Do you get 00:39:03.800 --> 00:39:08.300 that sense of eureka if you haven't first struggled? If I had said what is a 00:39:08.300 --> 00:39:10.970 tourist? They had said someone who visits another 00:39:10.970 --> 00:39:16.340 place. And I had said very good well done. Is that the sense of eureka? No. They 00:39:16.340 --> 00:39:22.310 necessarily have to struggle first to then have a chance of getting that sense 00:39:22.310 --> 00:39:28.760 of elation. That sense of eureka. That sense of I found an answer. At the end of 00:39:28.760 --> 00:39:35.020 the pit stage four is to look back over the learning journey and ask a series of 00:39:35.020 --> 00:39:40.070 metacognitive questions. For example, what did you think a tourist was at the 00:39:40.070 --> 00:39:44.720 beginning? What caused you to think again? What got you into the pit? What 00:39:44.720 --> 00:39:49.070 strategies did you use when you're in the pit? How did you come out of the pit? 00:39:49.070 --> 00:39:54.140 What do you think your answer is now compared to what it was before? The 00:39:54.140 --> 00:39:58.960 learning pit helps students to develop a deeper understanding of concepts. 00:39:58.960 --> 00:40:04.280 At stage one that's where they've got surface level knowledge. They know the 00:40:04.280 --> 00:40:09.770 basics. They have a reasonable grasp of the facts. And then stage two which is 00:40:09.770 --> 00:40:13.490 down at the bottom of the pit. This is where they're getting into some deeper 00:40:13.490 --> 00:40:18.320 thinking. They're questioning their own and others assumptions. They're looking 00:40:18.320 --> 00:40:22.820 at exceptions to a general rule and they're exploring concepts in greater 00:40:22.820 --> 00:40:28.820 detail. Very often it's at this stage two that the desire for enhanced learning 00:40:28.820 --> 00:40:34.160 strategies and collaboration increases. That's when they say please help us. Help 00:40:34.160 --> 00:40:38.900 us to develop the strategies we need. And it's also when they realize that 00:40:38.900 --> 00:40:44.210 they can overcome conundrums and dilemmas. If they apply effort. If they're 00:40:44.210 --> 00:40:49.700 determined. If they're resilient. In other words being in the pit helps us get into 00:40:49.700 --> 00:40:55.069 what Carol Dweck would called a growth mindset. Stage three is where 00:40:55.069 --> 00:41:00.829 they've got their constructed, their deep, their thoughtful answer. That idea 00:41:00.829 --> 00:41:06.619 exactly what it is and what is not to take with them into the future. The pit 00:41:06.619 --> 00:41:09.230 is a metaphor that you can share with your students. 00:41:09.230 --> 00:41:13.849 So for example you can say how many of you are out of the pit now? They put 00:41:13.849 --> 00:41:17.690 their hands up. And how many of you are still in the pit? They put their hands up. 00:41:17.690 --> 00:41:23.150 Pair them up. So if you are out of the pit, it's your job to help those who are 00:41:23.150 --> 00:41:28.279 still in the pit to come out. Mind you if you are still in the pit, it's your job 00:41:28.279 --> 00:41:32.480 to try and drag those who are out of the pit back down into it. Don't let them get 00:41:32.480 --> 00:41:37.730 away with easy answers. And what is wonderful is those students who often 00:41:37.730 --> 00:41:42.740 struggle in the lessons where memory is king, that if I can memorize this I can 00:41:42.740 --> 00:41:48.289 do well in a test and exams and the tasks that I'm asked. This is changing that 00:41:48.289 --> 00:41:52.970 and saying, we've got a think it through. We've got to get into the complexity and 00:41:52.970 --> 00:41:59.170 we've got to really work together.