WEBVTT Kind: captions Language: en 00:00:05.390 --> 00:00:11.880 Welcome to the OAME 2020 virtual conference. I am your host Jolyn Mascarenhas. 00:00:11.880 --> 00:00:17.970 Along with me running the technical side of things is the fantastic, Greg 00:00:17.970 --> 00:00:24.300 Clarke. This is the session: Spatial Thinking in Your Math Program with the 00:00:24.300 --> 00:00:31.500 fabulous Diane Stang and we will get to that in just one second. We wish to 00:00:31.500 --> 00:00:38.879 express gratitude to Mother Earth and for the resources we are using and honor 00:00:38.879 --> 00:00:45.600 all the First Nation. Metis and Inuit who have been living on the land since time 00:00:45.600 --> 00:00:55.289 immemorial. Thank you to all our sponsors. Thank you to Texas Instruments for 00:00:55.289 --> 00:01:00.059 stepping up to help with the infrastructure to put this conference on and 00:01:00.059 --> 00:01:06.479 and the rest of us who have offered door prizes. There these are many of the same 00:01:06.479 --> 00:01:12.270 vendors you would see at our live exhibit and have supported OAME over 00:01:12.270 --> 00:01:17.340 the years. Be sure to wait for instructions at the end of the session 00:01:17.340 --> 00:01:23.280 to learn how you can win one of these door prizes. That being said, please 00:01:23.280 --> 00:01:29.369 welcome Diane Stang to present her session on spatial thinking in your math 00:01:29.369 --> 00:01:31.939 program. 00:01:32.900 --> 00:01:37.820 Okay, just hang on folks, I'm getting, I'm getting there. 00:01:37.820 --> 00:01:42.200 Alright. Here I am. 00:01:43.610 --> 00:01:52.160 So just hang on folks and welcome. Okay and here we go. Like Jolyn said 00:01:52.160 --> 00:01:56.390 please forgive us if anything doesn't go too well. I want to welcome you all. This 00:01:56.390 --> 00:02:02.270 is spatial thinking in your math program and I think it's going to be a lot of 00:02:02.270 --> 00:02:06.110 fun to try this way. It's gonna be new. So it is what it is. So we're just gonna try 00:02:06.110 --> 00:02:08.930 it and have some fun. First of all about me. 00:02:08.930 --> 00:02:14.540 I am, I've been in education 40 years and basically I've taught in 00:02:14.540 --> 00:02:18.730 Ontario and British Columbia. I've taught 00:02:19.140 --> 00:02:23.760 resource teacher. I also worked at the Ontario Ministry of Education. I was 00:02:23.760 --> 00:02:27.030 lucky enough to be in the Capacity Building in Math which really allowed me 00:02:27.030 --> 00:02:31.800 to travel around the province and get into a lot of classrooms. So it's been 00:02:31.800 --> 00:02:37.890 great. Right now what I'm doing is I am working for Scholastic Education and I 00:02:37.890 --> 00:02:42.030 am so blessed to be able to still take do presentations and create resources 00:02:42.030 --> 00:02:45.690 from all the experience that I've been in. So that's me. 00:02:45.690 --> 00:02:49.140 Getting onto that, I'm going to look and tell you I've been reflecting back on 00:02:49.140 --> 00:02:54.450 these 40 years and I would have to say that this pandemic is probably giving us 00:02:54.450 --> 00:02:59.580 the hugest, the biggest challenge we've ever had in education before. And I think 00:02:59.580 --> 00:03:03.510 we're all going to see that, and I think we're all sort of experiencing it, if 00:03:03.510 --> 00:03:07.140 we're doing distance education now, but I think what we're gonna see is going 00:03:07.140 --> 00:03:11.190 future in ahead in the future it's going to be a challenge as well. And I would 00:03:11.190 --> 00:03:17.130 say that the biggest thing I've learned about education in the forty years has 00:03:17.130 --> 00:03:22.470 been to be flexible. And you know that as well as I do that that just doesn't mean 00:03:22.470 --> 00:03:26.040 from year to year, or month to month, that can mean from hour to hour and minute to 00:03:26.040 --> 00:03:28.080 minute. And I think with this whole pandemic 00:03:28.080 --> 00:03:32.250 thing, this is what we're looking at. So as far as I'm concerned, I think you've 00:03:32.250 --> 00:03:36.570 come to the right session because when you go back to your classroom, first and 00:03:36.570 --> 00:03:40.500 foremost, the first thing that you're gonna see is you're gonna have to think 00:03:40.500 --> 00:03:45.540 about the spatial thinking in your classroom. So what I want you to do is, 00:03:45.540 --> 00:03:50.550 and like I said normally if you came to my OAME conference, you would be working 00:03:50.550 --> 00:03:54.150 with these wonderful concrete materials. You'd have your hands going. You'd be 00:03:54.150 --> 00:03:59.280 really working away and testing up your spatial thinking. Well unfortunately, we 00:03:59.280 --> 00:04:01.950 had to be flexible and change that. So you're going to be doing a lot of 00:04:01.950 --> 00:04:06.450 visualizing today. So I want you to visualize first of all, you and your 00:04:06.450 --> 00:04:14.250 classroom on the first day. Here is your visual, your spatial challenge. Okay. What 00:04:14.250 --> 00:04:18.419 do you have to do? You have to think about, oh how am I gonna design a 00:04:18.419 --> 00:04:22.200 classroom that allows physical distancing for everyone in my classroom? 00:04:22.200 --> 00:04:26.100 So just picture that for a minute. You can see this teacher. She's used to being 00:04:26.100 --> 00:04:32.330 close, working in groups, collaborating with kids. And all of a sudden that's not 00:04:32.330 --> 00:04:36.860 happening anymore. So you've got to think about that. Now if you were teaching high 00:04:36.860 --> 00:04:40.669 school, you could set your room up so everybody's six they are two meters 00:04:40.669 --> 00:04:45.680 apart. The problem is we're not. We're teaching primary. How do you keep those 00:04:45.680 --> 00:04:51.500 kids two meters apart? Right. So I'm just, I don't have the answers. I'm just 00:04:51.500 --> 00:04:54.409 telling it. You know what it's like. They haven't seen each other for a couple of 00:04:54.409 --> 00:04:57.919 months. So they're thinking, wow, here's my friend. I want to hug them. And it's gonna 00:04:57.919 --> 00:05:02.060 be really difficult. So when you're thinking about it, let's just add another 00:05:02.060 --> 00:05:07.759 layer to this. What are you gonna do as far as what does two meters look like? 00:05:07.759 --> 00:05:11.030 You know what kids are. They don't know. They need benchmarks. We deal with 00:05:11.030 --> 00:05:16.069 non-standard units. So what are you going to do in order to help them understand 00:05:16.069 --> 00:05:20.300 this. And even why they're doing this without scaring them. So I mean this is 00:05:20.300 --> 00:05:24.349 gonna be a huge challenge. And then we just keep layering things on top because 00:05:24.349 --> 00:05:27.379 I've been reading in some other places, in the States and Europe, and some of the 00:05:27.379 --> 00:05:31.490 the parameters that they're having for schools, how they're going to manage 00:05:31.490 --> 00:05:34.610 everything, and I'm thinking it's just not realistic. I just don't see it yet. 00:05:34.610 --> 00:05:39.020 We're gonna have to be very creative and I think that's where you all come in. 00:05:39.020 --> 00:05:42.620 So let's think about some other things. What about washing hands all day? Not just 00:05:42.620 --> 00:05:46.279 washing hands before lunch, but every time they touch something, and keeping 00:05:46.279 --> 00:05:49.490 their distance apart, and making sure they can all get there. This is another 00:05:49.490 --> 00:05:54.589 spatial kind of dilemma that we have to deal with. And what about cleaning 00:05:54.589 --> 00:05:58.729 surfaces. Look at all the concrete materials that we use in math. Look at 00:05:58.729 --> 00:06:02.599 the books that kids use. What are we supposed to do with all of that now? 00:06:02.599 --> 00:06:08.479 And how are we gonna clean them? And then here's one, wearing masks. This is like 00:06:08.479 --> 00:06:12.409 putting a Halloween costume on a kid and saying don't touch it. You know that's 00:06:12.409 --> 00:06:16.099 not gonna happen. So really what you want to do is you want to think of ways that 00:06:16.099 --> 00:06:19.729 we're going to be able to creatively get around this. And then there's the 00:06:19.729 --> 00:06:23.569 unimaginable that is really hard but I know you can visualize it because you've 00:06:23.569 --> 00:06:28.909 been there before. What about recess? And what about yard 00:06:28.909 --> 00:06:35.240 duty? You know what that's like. So anyways these are some of the 00:06:35.240 --> 00:06:40.449 questions. So as far as I'm concerned, what's happening is, we are basically 00:06:40.449 --> 00:06:45.520 looking at a new spatial world. We're looking at a looking at our 00:06:45.520 --> 00:06:49.750 work space from a brand new perspective. So when we're going into that classroom 00:06:49.750 --> 00:06:52.840 and we're designing, you are doing spatial thinking, and you are doing 00:06:52.840 --> 00:06:57.250 spatial reasoning, and you're going to be doing it continuously. So you will be 00:06:57.250 --> 00:07:04.800 venturing where no educator has gone before. So on that note, let's get started. 00:07:04.800 --> 00:07:10.560 Before beginning, I have one huge message for everybody out there and that is this 00:07:10.560 --> 00:07:15.340 attitudes about math. Doesn't matter what I do a workshop on this is number one. 00:07:15.340 --> 00:07:20.319 Number one because we can't get anywhere unless we get those positive attitudes 00:07:20.319 --> 00:07:25.210 going in math and those growth mindsets. Letting kids know that we they can do it 00:07:25.210 --> 00:07:30.909 and really us believing in ourselves that we can teach. So those to me are 00:07:30.909 --> 00:07:34.659 number one no matter what we're doing. If we don't get through tha,t we're just not 00:07:34.659 --> 00:07:39.789 gonna go very far at all. So I'm really encouraging you because our job really 00:07:39.789 --> 00:07:46.360 is to motivate and inspire. So what we're gonna be doing today is we're also going 00:07:46.360 --> 00:07:51.400 to be looking at your spatial reasoning. Right? A lot of teachers, the research 00:07:51.400 --> 00:07:54.940 says, teachers who aren't comfortable, they tend not to give their kids those 00:07:54.940 --> 00:07:59.020 opportunities. So today you're gonna get a chance to try out some simulations. And 00:07:59.020 --> 00:08:02.050 you're on your own. So it's great. No one else sees how you're doing it. But it 00:08:02.050 --> 00:08:05.469 just gives you a touch. What it feels like and what you can do with your kids. 00:08:05.469 --> 00:08:09.370 So basically, what we're going to be doing is looking at spatial reasoning, 00:08:09.370 --> 00:08:13.330 and first of all here's a quick definition of what it is. Basically my 00:08:13.330 --> 00:08:17.710 description says what it is. It involves the location and movement of objects and 00:08:17.710 --> 00:08:22.389 ourselves, either mentally or physically in space. And this document is a great 00:08:22.389 --> 00:08:26.949 document. We'll put it in the Google Docs. You can get it. It's Paying Attention to 00:08:26.949 --> 00:08:30.009 Spatial Reasoning put out by the Ontario Ministry of Education, if you haven't 00:08:30.009 --> 00:08:33.430 seen it before. Remember that spatial reasoning is not a 00:08:33.430 --> 00:08:39.039 single ability. Why spatial reasoning? I think this is important. I'll be brief on 00:08:39.039 --> 00:08:43.209 this but I want you to know why we are looking at this so carefully. Dehanie 00:08:43.209 --> 00:08:46.959 found over 20 years ago, that spatial reasoning and math are basically the same. 00:08:46.959 --> 00:08:52.779 They're so intertwined that you cannot unravel one without the other. Then there 00:08:52.779 --> 00:08:56.620 is an interesting guy, who's still doing his studies, it's Duncan. He started a 00:08:56.620 --> 00:08:59.280 longitudinal study where he started looking at kindergarten 00:08:59.280 --> 00:09:03.660 kids and just tracking their math ability up throughout the years. And he 00:09:03.660 --> 00:09:08.010 found that math ability when kids enter kindergarten was the best predictor of 00:09:08.010 --> 00:09:13.380 how they do, not just in math, but in reading as well. So this was a really 00:09:13.380 --> 00:09:16.890 important thing but that same year, Wai found something even more interesting, 00:09:16.890 --> 00:09:21.630 that spatial thinking is even a better predictor of math success either verbal 00:09:21.630 --> 00:09:27.780 or math. So this is where you can see that they're intertwined. And then we 00:09:27.780 --> 00:09:32.460 come back to Duncan, five years later, now he's saying the best predictor of math 00:09:32.460 --> 00:09:37.260 performance is the gains made between kindergarten and the end of grade 1. 00:09:37.260 --> 00:09:41.970 So guess what that does? That puts us on the hot seat. It really gives us a great 00:09:41.970 --> 00:09:45.240 opportunity to be able to help those kids and develop their spatial reasoning. 00:09:45.240 --> 00:09:48.990 And I'm going to tell you right now, it has nothing to do with age. There are 00:09:48.990 --> 00:09:53.760 adults that have spatial reasoning skills that are less advanced than some 00:09:53.760 --> 00:09:57.480 kids in grade one. And the truth of the matter is is it all comes from 00:09:57.480 --> 00:10:01.800 experience and being able to challenge your spatial reasoning. And that brings 00:10:01.800 --> 00:10:06.210 me to the last point, is Nora Newcombe, she's a great spatial guru, she says how 00:10:06.210 --> 00:10:10.170 it is malleable and can be improved. And that means all of us have the ability to 00:10:10.170 --> 00:10:15.450 be able to get better at what we're doing. So on that we know it's critical 00:10:15.450 --> 00:10:21.060 to math, and we know it's critical to our lives, and it can be improved. So instead 00:10:21.060 --> 00:10:25.380 of using concrete materials, like I said we would have in my live session, we are 00:10:25.380 --> 00:10:29.700 going to be using visualizing and images. And just so you know this is being 00:10:29.700 --> 00:10:34.170 recorded. So that means any of the images that I show have to be copyrights. So the 00:10:34.170 --> 00:10:40.320 images I'm showing today are from my resource. It's called Math Plays but the 00:10:40.320 --> 00:10:43.800 whole thing is you don't need these images to do it. You can pull up so many 00:10:43.800 --> 00:10:47.190 images on the Internet to be able to carry this out. And the 00:10:47.190 --> 00:10:51.089 other thing I'm really promoting today, are spatial talks. You do number talks in 00:10:51.089 --> 00:10:55.620 your classroom. They're great. They really help. But we can do a lot with spatial 00:10:55.620 --> 00:10:58.950 talks. The same idea except you're throwing up a visual and you're getting 00:10:58.950 --> 00:11:03.170 the kids to talk about it. So that's what we're gonna be looking at today. But 00:11:03.170 --> 00:11:06.480 Diane, there's a couple of things in the chat, 00:11:06.480 --> 00:11:11.720 concerning kindergarten. Teaching spatial reasoning in kindergarten. And 00:11:11.720 --> 00:11:16.520 Katherine Pearson says spatial reasoning reasoning can also being inhibited 00:11:16.520 --> 00:11:23.510 inhibited by certain genetic conditions. Yes it can. In fact, I did a whole, a 00:11:23.510 --> 00:11:27.430 series on supporting students with learning disabilities in math. And we 00:11:27.430 --> 00:11:33.350 found that one of the things we did with kids that had had like the visual 00:11:33.350 --> 00:11:37.100 spatial memory problems or anything like that, what we were really doing was we 00:11:37.100 --> 00:11:41.990 were still trying to, they could still up to their potential develop them. 00:11:41.990 --> 00:11:45.980 We developed a lot of their other strengths in order to support their visualization 00:11:45.980 --> 00:11:50.600 and we found that that really helped. And so what we were doing is we would pair 00:11:50.600 --> 00:11:54.080 visuals with audios or whatever else we were doing, and that really seemed to 00:11:54.080 --> 00:11:56.780 help them because we actually did this in the classroom when we were looking at 00:11:56.780 --> 00:12:02.210 students with learning disabilities. So when we're looking at visualization, what 00:12:02.210 --> 00:12:05.960 we're basically doing is we're thinking with the mind's eye, and we're using our 00:12:05.960 --> 00:12:11.630 imagination to be able to generate, so we want to be able to to pull up, make those 00:12:11.630 --> 00:12:17.420 images in our head, and then retrieve them. And this is the most important part 00:12:17.420 --> 00:12:22.250 is transform them. Right? This is that mental mental rotation and 00:12:22.250 --> 00:12:27.710 we're gonna be talking a bit about that. So what we want kids to do is do this, 00:12:27.710 --> 00:12:32.330 visualize 10. So all of you just sit out there and think, okay visualize 10. Now 00:12:32.330 --> 00:12:37.070 when I do this with my husband he sees the 1 and a 0. Right? That's it. But when 00:12:37.070 --> 00:12:39.500 I'm doing with you, I know your primary teachers, so you're seeing something 00:12:39.500 --> 00:12:47.570 different. So maybe some of you saw this. Right? And that's great because what 00:12:47.570 --> 00:12:50.540 you're doing is you're seeing visually. You can see 10 and you can see how much 00:12:50.540 --> 00:12:56.300 it is, how muchness. Then if I say well what's twice as many? You can see that. 00:12:56.300 --> 00:13:00.800 It's not that twenty is bigger than ten. You know that it is double. It is twice 00:13:00.800 --> 00:13:05.000 that. You can see it in your head. And when we challenge kids to see half as 00:13:05.000 --> 00:13:10.640 many, right, they are able to see that that is half. So you know, so they're 00:13:10.640 --> 00:13:14.330 getting those relationships, the proportional relationships as well. So on 00:13:14.330 --> 00:13:17.660 that note, you're gonna visualize right now. Here is 00:13:17.660 --> 00:13:22.040 a paper folding task for you. So you have to imagine this is a rectangular piece 00:13:22.040 --> 00:13:25.550 of paper. And you can see you have to follow the instructions. 00:13:25.550 --> 00:13:30.140 And what I want you to do is don't do it with paper and pencil. I can't see you. 00:13:30.140 --> 00:13:34.220 Or paper and scissors. I can't see you but I'm trusting you won't. I want you to 00:13:34.220 --> 00:13:39.620 visualize. What will that paper look like when it is opened up? And what I'm gonna 00:13:39.620 --> 00:13:45.830 do is I'm gonna give you some choices. So it's gonna be A, B, C, or D. So I'm going to 00:13:45.830 --> 00:13:48.650 be quiet form you in a few minutes. I'm not going to sing the jeopardy music or 00:13:48.650 --> 00:13:53.300 anything. And then Greg will put up a poll in a couple of seconds and you can 00:13:53.300 --> 00:13:55.264 vote on it. Go ahead. 00:13:55.264 --> 00:14:00.220 And after that Diane there is a question in the chat. 00:14:11.820 --> 00:14:17.480 You may have to move the poll over just so you can still see the screen. 00:14:25.180 --> 00:14:29.180 And don't worry if you're too tired at the end of the day to do this, it's just 00:14:29.180 --> 00:14:34.970 a great opportunity for you to try out your visualization. The votes are coming 00:14:34.970 --> 00:14:40.090 in. Okay we have 50% have voted, have chosen something. Oh good. 00:14:40.090 --> 00:14:43.160 Thanks for letting me know Greg. Yeah no problem. 00:14:43.160 --> 00:14:51.340 There's still 60%. Some are still doing that last fold in their head I think. 00:15:04.000 --> 00:15:18.569 So I'm going to close the poll down in five, four, three, two, one. Closing the poll. 00:15:18.569 --> 00:15:25.620 Alright. So while we're waiting to see how people voted, what I'm gonna say is, 00:15:25.620 --> 00:15:30.399 and this is how I am with all math, I don't care what the answer is. I'm more 00:15:30.399 --> 00:15:32.500 concerned of what you were doing. What were you doing? 00:15:32.500 --> 00:15:36.699 First of all, were you stressed by this? Okay look at this. It looks like most 00:15:36.699 --> 00:15:44.259 people thought it was A. Very interesting. We've got some B, C, and D. We've got D in 00:15:44.259 --> 00:15:52.180 second place, C in third, and then B in last place. And very interesting. But 00:15:52.180 --> 00:16:01.779 it's quite quite evenly spaced except for A. Alright so the answer is B. So very 00:16:01.779 --> 00:16:06.699 interesting. And I was going to try and fold it with you with my camera on but 00:16:06.699 --> 00:16:10.990 you'll be able to try it at home and you'll see that it is B. But what's 00:16:10.990 --> 00:16:15.279 interesting about this is, what were you doing when you were thinking about this. First of all 00:16:15.279 --> 00:16:19.389 were you stressed? Because in a lot of cases people just give up. We really want 00:16:19.389 --> 00:16:22.089 to watch kids if they're finding this to be too much to do. 00:16:22.089 --> 00:16:26.920 And this one is. This one's for you. Anyhow the other thing is, were you using 00:16:26.920 --> 00:16:30.910 gestures? Were you taking your hands and moving them down, and folding with 00:16:30.910 --> 00:16:34.720 the paper, and being able to visualize what you're doing? Gestures are really 00:16:34.720 --> 00:16:40.000 important when we're talking about this because we want to use the gestures 00:16:40.000 --> 00:16:43.720 because what they do is they help reinforce a thought. A gesture can take 00:16:43.720 --> 00:16:48.850 on a whole thought. So it really what it does is it relieves a lot of the, a lot 00:16:48.850 --> 00:16:52.629 of the space from the visual memory. So kids don't have to worry so much about that. 00:16:52.629 --> 00:16:57.279 So that's one thing that we want to be able to do is use gestures a lot. But 00:16:57.279 --> 00:17:00.850 we want to be able to give kids opportunities like this. So what would 00:17:00.850 --> 00:17:06.339 this look like in in your classroom? This is what it would look like for instance. 00:17:06.339 --> 00:17:10.569 Okay? You can do this in front of the kids. You can either have them follow the 00:17:10.569 --> 00:17:14.230 instructions or what you can do is you can actually do it in front of them. And 00:17:14.230 --> 00:17:17.860 what you're doing is just taking a piece of paper, folding it, folding 00:17:17.860 --> 00:17:22.240 in different ways. Start with a paper punch because it's a symmetrical figure. 00:17:22.240 --> 00:17:27.400 So it's it's not going to affect, it's gonna affect the location but not 00:17:27.400 --> 00:17:31.390 necessarily how it's gonna look. Ask them how many holes are there gonna be when 00:17:31.390 --> 00:17:35.650 we hold this up? Why do you think so? Right? So you're getting at a lot of these, and 00:17:35.650 --> 00:17:39.790 this is a great spatial talk, and you'll find the kids absolutely love this. And 00:17:39.790 --> 00:17:46.480 then what you can do is you can get on to symmetry and lines of 00:17:46.480 --> 00:17:50.049 symmetry. Right? So you're you're trying in one session, you're saying okay let's 00:17:50.049 --> 00:17:52.840 let's just cut the bottom corner without the fold? What do you think it's gonna 00:17:52.840 --> 00:17:56.470 look like? Okay how is that gonna look like when we're doing this? Again we're 00:17:56.470 --> 00:18:02.320 working with those horizontal lines of symmetry. And then what we can do is we 00:18:02.320 --> 00:18:05.559 can cut out vertical lines of symmetry. We can do them too and this time what 00:18:05.559 --> 00:18:10.240 we're doing is we're making it more of an asymmetrical kind of cut. We cut it on 00:18:10.240 --> 00:18:13.840 the fold. We cut it not on the fold and we see how much changes from picture to 00:18:13.840 --> 00:18:18.280 picture. So as you can see that this kind of thing is great for kids and and 00:18:18.280 --> 00:18:21.309 they love it. And they can be the leaders sometimes and they can do the 00:18:21.309 --> 00:18:25.960 folding. You can get more complex. You can do two cuts and do diagonal lines of 00:18:25.960 --> 00:18:29.890 symmetry. In Ontario here we're doing symmetry in grades one, two, and three 00:18:29.890 --> 00:18:34.090 but we are doing lines of symmetry, all those different kinds in grade three. 00:18:34.090 --> 00:18:38.080 So this is a great opportunity. And then finally you can get as complex as you 00:18:38.080 --> 00:18:41.169 want. I've done this with kindergarten kids and they just love it and they get 00:18:41.169 --> 00:18:45.700 very good at predicting. So just in your head, again just fold this in your head. 00:18:45.700 --> 00:18:50.260 Do your gestures and think where those holes are going to be. How many will 00:18:50.260 --> 00:19:01.750 there be and where will they be? And that's what it would look like. So a lot 00:19:01.750 --> 00:19:07.150 of fun that you can have in the class. How do we develop those visual images? 00:19:07.150 --> 00:19:11.470 This is important and this is where we start with those concrete materials. And 00:19:11.470 --> 00:19:16.240 so in other words your kids are not going to develop those until they it's 00:19:16.240 --> 00:19:19.929 like navigating. One thing I was going to talk about but little bit later. Like 00:19:19.929 --> 00:19:24.490 right now you can sort of visualize where you're going to be going on a map 00:19:24.490 --> 00:19:28.210 if you can if you sort of have a few landmarks. With kids in kindergarten 00:19:28.210 --> 00:19:31.600 especially they can't visualize a path that they're gonna walk 00:19:31.600 --> 00:19:35.799 until they've actually walked it. So this is the same kind of idea. We want kids to 00:19:35.799 --> 00:19:40.419 use those concrete materials first. So I want to tell you about a really 00:19:40.419 --> 00:19:43.990 interesting study that I did called Math for Young Children. It was done it was 00:19:43.990 --> 00:19:48.370 done here in Ontario. I worked with a bunch of researchers including Joan Moss, 00:19:48.370 --> 00:19:53.289 Cathy Bruce, several other people from OISE as well. And what we did was we were 00:19:53.289 --> 00:19:58.809 looking at kids and how they could use their spatial reasoning in math. 00:19:58.809 --> 00:20:02.740 So basically I worked at a school called Blantyre in Toronto District School 00:20:02.740 --> 00:20:07.570 Board and what we did was we gave them a task like this. We said build as many 00:20:07.570 --> 00:20:11.770 unique, this is kindergarten, as many unique configurations as you can 00:20:11.770 --> 00:20:15.880 with for connecting cubes. So I want you to visualize in your head for a minute, 00:20:15.880 --> 00:20:20.980 just think how many different ways could you put those four cubes together? So 00:20:20.980 --> 00:20:24.490 they can't be twisted on their side. They must be flush with each other. But 00:20:24.490 --> 00:20:28.000 how many ways can you put those four cubes together? So just visualize in your 00:20:28.000 --> 00:20:30.210 head. 00:20:38.340 --> 00:20:42.040 So we found that the kids in kindergarten were excellent at this. 00:20:42.040 --> 00:20:44.380 They weren't visualizing. They were building because that's where they 00:20:44.380 --> 00:20:48.460 needed to be. But they easily found the eight configurations that I found at the 00:20:48.460 --> 00:20:52.060 bottom. And what we would ask them was you know, they might come up with the 00:20:52.060 --> 00:20:55.810 l-shape and it might be the mirror shape of it or it might be lying down and we'd 00:20:55.810 --> 00:20:59.230 say are these the same? They had to be able to rotate those in their head. We'd 00:20:59.230 --> 00:21:03.070 ask them before they could touch them. And what they found is that they could 00:21:03.070 --> 00:21:06.280 actually figure out by rotating in their head which were the same in which 00:21:06.280 --> 00:21:10.360 weren't. In fact in a lot of cases, we found that we would give them some very 00:21:10.360 --> 00:21:15.550 complex ones, maybe made of 11 or 12 cubes, and we found they were better than 00:21:15.550 --> 00:21:19.990 the adults of actually being able to rearrange them. So we were amazed at the 00:21:19.990 --> 00:21:23.860 skills that they had. But we didn't finish it there. What we decided to do is 00:21:23.860 --> 00:21:28.630 we give them this challenge, we said well how many can you make with five cubes? 00:21:28.630 --> 00:21:32.470 So we as adults tried it out first. You know thinking were the wonderful researchers 00:21:32.470 --> 00:21:37.930 and we found about 14 configurations which was great. But when we gave it to 00:21:37.930 --> 00:21:43.120 the kids they found 22 configurations. There's 29 altogether. They weren't 00:21:43.120 --> 00:21:46.660 stressed. They worked together. And then we put two pairs together 00:21:46.660 --> 00:21:50.050 and then we'd have to say, well now only put the ones together that are 00:21:50.050 --> 00:21:52.990 different from each other. They'd know right away. They say well that one's the 00:21:52.990 --> 00:21:57.520 same as this one and I can tell just by turning it. So we were absolutely amazed 00:21:57.520 --> 00:22:02.050 and flabbergasted how much these kids had as far as spatial thinking went. So while 00:22:02.050 --> 00:22:05.140 we were doing the lesson study, a grade six teacher said I'm going to do this 00:22:05.140 --> 00:22:08.680 with my class which was the most interesting part because when he did it 00:22:08.680 --> 00:22:13.000 with his group he found that it took them longer. They were stressed. They were 00:22:13.000 --> 00:22:18.910 stressed all out and they found about 21, 22 of the configurations. But it took 00:22:18.910 --> 00:22:23.200 them much longer like I said. And so this is where we really have to question you 00:22:23.200 --> 00:22:27.760 know. What are we doing and what's in our curriculum between the ages of you know 00:22:27.760 --> 00:22:31.840 five and six and when they're older in in grades five and six? What are we doing 00:22:31.840 --> 00:22:35.680 in there to in order to be able to develop it? Like I said earlier it's not 00:22:35.680 --> 00:22:42.460 dependent on, it's not dependent on age. So here are some of the 29 solutions as 00:22:42.460 --> 00:22:45.850 you can see. These are just a few. And the kids found as soon as they could 00:22:45.850 --> 00:22:48.370 start building up, it just opened up a new 00:22:48.370 --> 00:22:52.720 channel of all the different ways they could do it. But it was a great exciting 00:22:52.720 --> 00:22:56.650 test that we learned that kids have a lot more. But they have to start with 00:22:56.650 --> 00:23:02.860 those concrete materials first. That was the most important part. So for instance, 00:23:02.860 --> 00:23:05.470 okay, here's something you can do with the kids too. So I just want you to, 00:23:05.470 --> 00:23:08.920 you're gonna start visualizing again with connecting cubes okay. So just 00:23:08.920 --> 00:23:12.970 listen carefully. I'm gonna give you some verbal instructions and again this would 00:23:12.970 --> 00:23:18.630 be difficult for kids who have any kind of impairment as far as being able to 00:23:18.630 --> 00:23:25.360 audio, so process audio. So anyways we're going to try it with you. So I want you 00:23:25.360 --> 00:23:30.059 to imagine taking three blue cubes. You're going to attach them in a row and 00:23:30.059 --> 00:23:34.450 I want you to lie them flat in front of you so they're straight across from left 00:23:34.450 --> 00:23:36.840 to right. 00:23:37.090 --> 00:23:42.920 Now you're going to take one orange cube and you're going to put a yellow cube, so 00:23:42.920 --> 00:23:46.490 you're gonna take an orange and yellow cube, put them together, and you're going 00:23:46.490 --> 00:23:51.200 to put them on top of your row of blue cubes. And you're going to make it so the 00:23:51.200 --> 00:23:56.390 orange cube is on the right. 00:23:56.450 --> 00:24:00.810 Now you're gonna take a green cube and you're gonna put it on top of the orange 00:24:00.810 --> 00:24:04.170 cube. Again your working memory is going. I know but we did this with 00:24:04.170 --> 00:24:08.490 kindergartens and it does work. We didn't make them this complex. So we now put an 00:24:08.490 --> 00:24:13.800 or a green cube on top of the orange cube. And finally you're gonna put a red 00:24:13.800 --> 00:24:18.810 cube and it's gonna go right in front of that first blue cube that also has the 00:24:18.810 --> 00:24:23.820 orange cube. So you've got your three blue cubes on the bottom.Your orange and 00:24:23.820 --> 00:24:28.020 yellow cube on the next layer. Then there's a green cube and then the very 00:24:28.020 --> 00:24:35.070 front of it all is going to be the red cube. So here's my question. Is this what 00:24:35.070 --> 00:24:44.460 you imagined? As you can see, and kids were great at this. We did this a 00:24:44.460 --> 00:24:48.750 lot with them and the more we made them complex the more they could do this. 00:24:48.750 --> 00:24:52.410 So once they've worked with the concrete materials, they were able to make these 00:24:52.410 --> 00:24:56.460 visualizations which was fabulous. Then we do things like this, we'd say well I 00:24:56.460 --> 00:25:02.640 want you to turn it upside down. Is this what you imagined? So we didn't keep it 00:25:02.640 --> 00:25:08.970 just static. We also made it dynamic as far as being able to see what it was. 00:25:08.970 --> 00:25:12.540 So here's another spatial talk okay. This is a great thing. They've worked with 00:25:12.540 --> 00:25:15.930 concrete materials. So what you can do with this spatial talk is say okay which 00:25:15.930 --> 00:25:21.510 one of these will stand? Have them think about it. Choose one yourself. Which one 00:25:21.510 --> 00:25:26.120 will stand? Which one won't stand? 00:25:26.120 --> 00:25:27.450 Diane, we have a question here saying 00:25:27.450 --> 00:25:31.860 where can I find those types of exercises? And then another one about 00:25:31.860 --> 00:25:36.810 spatial reasoning, saying I wonder how much spatial reasoning and visual 00:25:36.810 --> 00:25:42.180 spatial intelligence according to the theory of multiple intelligences are 00:25:42.180 --> 00:25:48.000 connected. Are they the same? What if visual spatial intelligence is 00:25:48.000 --> 00:25:51.440 one weak spot? 00:25:51.440 --> 00:25:55.170 Are they the same? I'd say that they, I think they're 00:25:55.170 --> 00:25:58.560 related. I think what happens is we're sort of giving different names to the 00:25:58.560 --> 00:26:02.640 sort of, the sort of the the same things. I think in a lot of, in a lot of ways, if 00:26:02.640 --> 00:26:09.330 you're looking at spatial reasoning and visual spatial intelligence yeah there's 00:26:09.330 --> 00:26:13.130 so much related. I would have to say. And like I said 00:26:13.130 --> 00:26:16.370 before if it is a weakness, what you're gonna do is you're going to pair it with 00:26:16.370 --> 00:26:20.960 what their strengths are right? Whatever it, whatever they're going to be. But we 00:26:20.960 --> 00:26:24.800 found that when we were working with kids that had difficulties in like 00:26:24.800 --> 00:26:28.730 learning disabilities, like true learning disabilities, in visualizing and 00:26:28.730 --> 00:26:32.900 spatial, we found that as long as we paired them with other things they they 00:26:32.900 --> 00:26:40.970 actually develop their visualizations so it could help. So you see that's it it's 00:26:40.970 --> 00:26:45.170 um it's a it's a tricky one, but we found even if they were exposed to the things 00:26:45.170 --> 00:26:48.830 and giving them the concrete materials as much as possible was even a better 00:26:48.830 --> 00:26:52.730 idea than the visualization. So I would really go to the concrete materials as 00:26:52.730 --> 00:26:58.400 much as possible and then you pair it with verbal. In this case you may decide, 00:26:58.400 --> 00:27:02.960 okay I see, and this here's your spatial talk, you're saying okay I can see that A 00:27:02.960 --> 00:27:06.350 is gonna work, and then this is when you go back to and you say to them okay 00:27:06.350 --> 00:27:09.440 build it. Build it with the concrete materials. So they've now had a chance to 00:27:09.440 --> 00:27:14.180 visualize. They're now building with a concrete to see if it'll work. Then you 00:27:14.180 --> 00:27:19.370 may come to one like F and you see oh dear, this isn't this isn't standing and 00:27:19.370 --> 00:27:23.060 they prove it by making it. So you say okay use those materials. Visualize in 00:27:23.060 --> 00:27:26.930 your head how you could organize them so they will stand. Oh I was going to answer 00:27:26.930 --> 00:27:30.080 the other question in a minute. I can only do one at a time. 00:27:30.080 --> 00:27:33.710 These are from my resource that I've developed called Mathplace. But like I 00:27:33.710 --> 00:27:37.070 said you can find things if you look on the internet. What you can do is build 00:27:37.070 --> 00:27:43.610 them yourselves or in a lot of cases we just built them or I often just 00:27:43.610 --> 00:27:47.410 built them and took pictures of what I wanted. 00:27:47.690 --> 00:27:51.410 So anyways then, what you're doing is you're saying, okay how can I make this 00:27:51.410 --> 00:27:54.170 so it will stand? And so you're really getting those kids to think and 00:27:54.170 --> 00:27:58.220 visualize. Like I said there's a lot of different aspects to spatial reasoning. 00:27:58.220 --> 00:28:01.880 I'm just picking the visual because this is the best I can do with our virtual 00:28:01.880 --> 00:28:06.740 presentation here. So another thing you can do is you can go and try pentominoes. 00:28:06.740 --> 00:28:11.360 So in other words you're doing the five cube challenge but you're doing it with 00:28:11.360 --> 00:28:15.260 colored tiles this time. And I'm going to show you how you can do that live in 00:28:15.260 --> 00:28:20.150 just a minute. Again kids are working and now we're going from three dimensions 00:28:20.150 --> 00:28:23.030 which is really important to start with because that's the world they live in 00:28:23.030 --> 00:28:26.150 and going down to two dimensions. They can find the different 00:28:26.150 --> 00:28:30.320 unique solutions here. And then you can build on that and say, okay which ones 00:28:30.320 --> 00:28:34.490 will fold into open boxes? And then what you could do is you can give them these 00:28:34.490 --> 00:28:38.750 nets and then have them experiment to find out which ones will fold and which 00:28:38.750 --> 00:28:44.720 ones won't. So again it's just getting giving these kids these opportunities. 00:28:44.720 --> 00:28:48.650 Also if you can make spatial talks dynamic again, this is one from my 00:28:48.650 --> 00:28:52.700 resource again, but it's looking at these and I just, you can do this live, you can 00:28:52.700 --> 00:28:56.300 build this in front of them. Just build the one on the right and the left and 00:28:56.300 --> 00:29:01.460 then just say okay, how can you move the green on the left so it looks like the 00:29:01.460 --> 00:29:05.390 one on the right? So you can do it live. You don't have to do it virtually. 00:29:05.390 --> 00:29:08.780 So basically you're showing them that okay, they're discussing it. They're 00:29:08.780 --> 00:29:11.510 turning and talking to their neighbor and then you're talking about the 00:29:11.510 --> 00:29:14.960 different ways that this can happen. But it's really great if they're having 00:29:14.960 --> 00:29:18.410 difficulty with the visualization you give them those concrete materials so 00:29:18.410 --> 00:29:23.900 they can try it out. Something that's really important, and you're gonna see as 00:29:23.900 --> 00:29:27.800 we go through, is composing and decomposing shapes because it really 00:29:27.800 --> 00:29:31.280 affects everything they do in math. So this is one of the little books that I 00:29:31.280 --> 00:29:36.650 developed but it's basically covering an outline with pattern blocks. And this 00:29:36.650 --> 00:29:41.360 follows the developmental trajectory of Doug Clements and he's fabulous to read 00:29:41.360 --> 00:29:45.140 if you don't have any of his stuff. He talks about kids in the early years. But you 00:29:45.140 --> 00:29:48.170 can see what I've done in this case is, the kids are building, they have those 00:29:48.170 --> 00:29:53.300 inner lines. They can see what they're building on. And it's great. They can they 00:29:53.300 --> 00:29:57.350 can cover the page and they can make them work. Then what you can see is, in 00:29:57.350 --> 00:30:01.670 the next page, some of those lines aren't there anymore. And now in order to build 00:30:01.670 --> 00:30:06.320 that caterpillar, kids have to go back to where they were before and remember the 00:30:06.320 --> 00:30:11.900 pattern that they had, right here, so they can see the caterpillar, they can see the 00:30:11.900 --> 00:30:15.650 pattern that started, and they have to extend it into the other one. So now 00:30:15.650 --> 00:30:19.580 we're relying a little bit on their memory. What they visualized, what 00:30:19.580 --> 00:30:24.530 they've retained in their brains in order to be able to put it here. So then 00:30:24.530 --> 00:30:28.790 what we do is we build it even more and now we're saying okay don't just cover 00:30:28.790 --> 00:30:32.330 it, cover it in more than one way. So I want you to look at the caterpillar on 00:30:32.330 --> 00:30:36.400 the right. Visualize it yellow. 00:30:38.370 --> 00:30:43.200 And once you've done that, then I want you to say okay, how could it be all red 00:30:43.200 --> 00:30:48.900 and blue? And you give those kids those challenges. So now what they're doing is 00:30:48.900 --> 00:30:54.120 they're having to be able to figure out how they can cover them. Finally you can 00:30:54.120 --> 00:30:57.539 build in the whole symmetrical idea where they're building one side and then 00:30:57.539 --> 00:31:05.370 what they're doing is they're being able to recreate the symmetrical side. So the 00:31:05.370 --> 00:31:10.470 here's being able to build it. There's a great site called mathies tools. It's 00:31:10.470 --> 00:31:14.880 out by the Ontario Ministry of Education. This is mathies learning tools. They're 00:31:14.880 --> 00:31:18.240 free from the Ministry of Education and I'm going to tell you right now they are 00:31:18.240 --> 00:31:21.750 great. If you're distance learning or you're doing this in the classroom, this 00:31:21.750 --> 00:31:24.840 is a great way for those kids to do the activities that we just did. I'm going to 00:31:24.840 --> 00:31:30.140 show you how to do them. If you're just patient with me for a second here. 00:31:32.420 --> 00:31:37.530 Okay so when you go to mathies tools, you can see that there are there are 00:31:37.530 --> 00:31:42.270 your pattern blocks. And the kids, it's so simple and like I said it's free. It's 00:31:42.270 --> 00:31:47.040 just online. And you can see what I'm doing right here. I am being able to 00:31:47.040 --> 00:31:53.900 build. I can take as many of these shapes that I want. I can rotate the shapes. 00:31:53.900 --> 00:31:59.700 I can make them fit. I can build that little duck and I did this by memory. I'm 00:31:59.700 --> 00:32:02.670 pretty proud of myself because I don't have the best spatial memory myself 00:32:02.670 --> 00:32:06.810 which I'm really working on. And then you can challenge them and say well how can 00:32:06.810 --> 00:32:10.770 you make this it's duck so it's blue? So they have to be able to figure out, okay 00:32:10.770 --> 00:32:13.920 how am I gonna do this? Well this piece isn't working. How can I 00:32:13.920 --> 00:32:17.280 move it around? Look at that. I've got to be able to fit it right into that spot 00:32:17.280 --> 00:32:21.450 there. There we go. And what's nice about mathies tools, you 00:32:21.450 --> 00:32:25.890 have a magnet up here that you can turn on and off which is great because they 00:32:25.890 --> 00:32:29.760 don't have to be exact. So if they have fine motor difficulties, this really 00:32:29.760 --> 00:32:33.900 helps them be exact. I just have to sort of turn it where I want it. Get it close 00:32:33.900 --> 00:32:38.760 and then it'll just snap into place. So it's a great tool for you to use. Like I 00:32:38.760 --> 00:32:42.300 said you can make these challenges. If they're working, there's also, there's 00:32:42.300 --> 00:32:46.020 lots of different tools. These are just a couple of them. These are the colored 00:32:46.020 --> 00:32:49.590 tiles. So if I'm doing the pentominoes, you can see what I'm doing. I can make 00:32:49.590 --> 00:32:55.650 them all in different colors if I want. So I heartily encourage you to use them 00:32:55.650 --> 00:33:01.530 and explore the other tools there at mathies tools. But we found them really 00:33:01.530 --> 00:33:10.320 helpful in what we've been doing. So check it out. Okay visualizing. It's your 00:33:10.320 --> 00:33:13.890 chance again. This is really important. It's gonna connect with what we just did. 00:33:13.890 --> 00:33:19.080 So this is a balance right. Right now you can see that's the fulcrum in the middle 00:33:19.080 --> 00:33:25.080 and what we have is we have a sphere or sorry cylinder that is balanced by two 00:33:25.080 --> 00:33:31.290 cubes. So that's a balanced scale. You can see it. They're equal. Okay look at the 00:33:31.290 --> 00:33:33.390 next one. This time it's a completely different 00:33:33.390 --> 00:33:41.750 scale. On this scale we see two cylinders balanced by four spheres. Your job is 00:33:41.750 --> 00:33:46.179 what will balance two spheres? 00:33:48.030 --> 00:33:52.230 Think of more than one solution. 00:33:59.570 --> 00:34:01.380 Okay. Diane, you are getting a few responses. 00:34:01.380 --> 00:34:02.520 Good. 00:34:02.520 --> 00:34:04.889 Lots. 00:34:04.889 --> 00:34:10.710 Oh good. So you may have said one cylinder which makes sense because we're 00:34:10.710 --> 00:34:14.010 looking at that proportional reasoning up here. We see that if we just cut all 00:34:14.010 --> 00:34:18.059 of these both of these sides in half we can see that relationship right there. 00:34:18.059 --> 00:34:23.220 And then if you're transferring it over to the other side, you may see that it's 00:34:23.220 --> 00:34:30.000 going to be, it could be also two cubes. So this is really important. You can do 00:34:30.000 --> 00:34:33.629 you can you can make a lot of these things with the kids getting them to do 00:34:33.629 --> 00:34:36.720 the balance thing and I'm going to show you a couple examples later on. But I 00:34:36.720 --> 00:34:40.859 really want to show you why this is important because this is about the 00:34:40.859 --> 00:34:46.799 equal sign. This was um what does it mean? We found out that kids do not know what 00:34:46.799 --> 00:34:51.599 the equal sign means. This is a huge deal. This was a study that was done by 00:34:51.599 --> 00:34:55.889 carpenter in 2003 and I think this really changed the way I looked at so 00:34:55.889 --> 00:35:00.420 much of what I was teaching and doing. First of all kids were given the 00:35:00.420 --> 00:35:04.410 question eight plus four equals something plus five. Okay great. 00:35:04.410 --> 00:35:11.039 So it was given to kids in grades three and four and five and six. And as you can 00:35:11.039 --> 00:35:15.150 see not too many kids got the right answer. Only nine percent in grade four 00:35:15.150 --> 00:35:17.519 and only two percent in grade five and six which is scary. 00:35:17.519 --> 00:35:23.009 What is really scary is that almost half of the kids thought it was 12 in grade 00:35:23.009 --> 00:35:29.339 three and four and in grade five and six three-quarters thought it was twelve. 00:35:29.339 --> 00:35:32.369 We even had some say it was seventeen and then some other state was twelve and 00:35:32.369 --> 00:35:37.950 seventeen. So they interviewed the kids and this is what they got. Student 00:35:37.950 --> 00:35:42.329 Teacher: how do you...oh the student said 12. Well how do you know 00:35:42.329 --> 00:35:48.569 it's twelve? Ah because that's the answer. Right eight and four twelve. What about the five 00:35:48.569 --> 00:35:52.170 over there? That's just there. It doesn't have anything to do with the 8 or the 00:35:52.170 --> 00:35:56.940 12. Well what do you think it means? Maybe they just put it there to confuse 00:35:56.940 --> 00:35:58.970 us. 00:35:59.269 --> 00:36:04.140 What about seventeen? Well how do you figure its 17? Well because I know 00:36:04.140 --> 00:36:08.849 that 8 and 4 are 12 and 5 more is 17. Well why did you add? Because 00:36:08.849 --> 00:36:13.320 it's said to add. See? But these two numbers are over here and the 00:36:13.320 --> 00:36:16.890 five is on the other side of the equal sign. Yeah but you have to add. That's 00:36:16.890 --> 00:36:23.340 what all the numbers. That's what it says to do. Then there is this one .Can you 00:36:23.340 --> 00:36:28.020 tell me what you did? Sure I did 8 plus 4 and that's 12. And 00:36:28.020 --> 00:36:35.280 then I had to add 5 so that made 17. So in this case they had two answers. so a 00:36:35.280 --> 00:36:38.580 little bit scary. We finally they interviewed the 00:36:38.580 --> 00:36:43.110 student who thought it was 7. How did you know what 7? Well I saw that the 5 00:36:43.110 --> 00:36:49.470 over there was one more than the 4 over here so the number in the box had to be 00:36:49.470 --> 00:36:58.110 one less than the 8 so it's 7. So what did this kid see? This. This kid, when you 00:36:58.110 --> 00:37:01.350 think about it, look at the two sides like our balance scale that we were just 00:37:01.350 --> 00:37:06.030 looking at. If you move that one little dot with a 5 over to the other side, you 00:37:06.030 --> 00:37:10.140 can see how they balance over. Right? So you can see that that's one heavier than 00:37:10.140 --> 00:37:15.090 the other side. So that means that in order to compensate for that, that 8 over 00:37:15.090 --> 00:37:19.530 there has to be 1 less, so it's 7. Notice they never even figured out what each 00:37:19.530 --> 00:37:24.540 side equaled. What they were doing is they were looking at it as a balance. 00:37:24.540 --> 00:37:28.260 So they had the whole idea and they really understood what the balance or the equal 00:37:28.260 --> 00:37:33.420 sign is. This was what we want kids to understand. And believe it or not spatial 00:37:33.420 --> 00:37:37.350 reasoning really helps with this. So what when we were doing all that composing 00:37:37.350 --> 00:37:41.370 and decomposing and rearranging things in our head, this is where it pays off. 00:37:41.370 --> 00:37:46.350 This was done by Cheng and Mix in 2013. They did a study with 6 to 8 year olds 00:37:46.350 --> 00:37:50.970 and then they found even doing one single 20-minute session on mental 00:37:50.970 --> 00:37:56.640 rotation resulted in higher scores on a math test. They found that the kids did 00:37:56.640 --> 00:38:02.070 so much better on questions where they were a change unknown wasn't a question 00:38:02.070 --> 00:38:06.810 like 3 plus something equals 9. Think about how they can visualize. They can 00:38:06.810 --> 00:38:11.670 see the 3 over there. They can see that 3 in the array on the on the right of 9 00:38:11.670 --> 00:38:17.820 and they can see that there's the 6 left. Excuse me. So as you can see, this is 00:38:17.820 --> 00:38:21.510 why we're doing all of this because all of these visualizations turn into the 00:38:21.510 --> 00:38:26.760 symbolic forms for the numbers. And they had the ability to visually and 00:38:26.760 --> 00:38:31.799 rearrange, visualize and rearrange and that's what got them through. So when 00:38:31.799 --> 00:38:34.680 we're looking at this kind of thing what we're always doing is trying to go for 00:38:34.680 --> 00:38:39.809 the concrete to the pictorial. This is like the balance that we were doing. What 00:38:39.809 --> 00:38:43.770 I did when I created this was just put animals into them. And the kids can look 00:38:43.770 --> 00:38:47.210 at the proportional relationships and they love doing this kind of thing. And 00:38:47.210 --> 00:38:51.779 then we can go to the symbolic where then we're putting the numbers to them 00:38:51.779 --> 00:38:56.160 and what they're doing is they're being able to see how the numbers are 00:38:56.160 --> 00:38:59.490 proportionately related to each other. So that's what we're looking at in the 00:38:59.490 --> 00:39:03.480 early years, in our primary grades. So when we're doing space talks in number 00:39:03.480 --> 00:39:07.230 sense, here's another example. Find a picture on the Internet of anything. 00:39:07.230 --> 00:39:11.010 I just threw these pictures together for my resource. You can see what we're doing. 00:39:11.010 --> 00:39:14.789 We're looking at license plates. We're looking at concert tickets. What did the 00:39:14.789 --> 00:39:18.450 concert ticket numbers mean? Who do you think would be sitting beside these 00:39:18.450 --> 00:39:21.869 people? Who do you think sitting behind them? Why do you think they have that bar 00:39:21.869 --> 00:39:26.720 tag on there? What are the numbers of the day telling you? Right? Look at the the 00:39:26.720 --> 00:39:32.339 what numbers could be on the scoreboard? What game are we playing? How big can the 00:39:32.339 --> 00:39:36.559 numbers be? Right? You're getting at all of these different kinds of things 00:39:36.559 --> 00:39:41.490 all through by having them look at pictures. So this is really important 00:39:41.490 --> 00:39:45.210 being able to do that. The calendar. What month could that be? What month couldn't 00:39:45.210 --> 00:39:48.930 it be? Right? You're asking a lot of these questions. You're getting them to really 00:39:48.930 --> 00:39:53.279 think and wonder. So again it's those spatial talks. One thing I'm huge into 00:39:53.279 --> 00:39:58.230 are quick images. Quick images and and subitizing. A lot of you probably already 00:39:58.230 --> 00:40:02.720 do this. And you can make them on dot plates but again it's what do you see. 00:40:02.720 --> 00:40:07.559 Right? That's five. That's perceptual subitizing. Being able to see a quantity 00:40:07.559 --> 00:40:12.839 without being able to have to count. Then we move over to conceptual subitizing. 00:40:12.839 --> 00:40:17.940 You saw the five. So you saw the part and then you saw the whole. So we're moving 00:40:17.940 --> 00:40:21.299 kids in grade one from perceptual to conceptual subitizing. 00:40:21.299 --> 00:40:25.230 You may find that kids in grade three still need to do that. But that's okay, 00:40:25.230 --> 00:40:29.849 Showing these visuals and kids love doing these are really important. 00:40:29.849 --> 00:40:33.779 You build them. So you can do them throughout the year and they take so little time to 00:40:33.779 --> 00:40:39.210 do. What do they see? What do they see? In both of these cases 00:40:39.210 --> 00:40:43.859 what we've done is now anchoring 5 and 10. Right? And believe it or not 7 or 8 00:40:43.859 --> 00:40:48.930 are the hardest to be able to subitize because they're either missing 2 or 00:40:48.930 --> 00:40:54.210 missing 3. So that's just for your interest. What else can we do? We can 00:40:54.210 --> 00:40:57.599 visualize patterns. And this pattern is gonna be important for what we're gonna be 00:40:57.599 --> 00:41:01.589 looking at in just a few minutes. Here's an example of a pattern. It's consecutive 00:41:01.589 --> 00:41:05.549 numbers and yes, I've done this with grade ones and they get it. They can see that 00:41:05.549 --> 00:41:09.210 that's gonna be one, and two. They counted up. They see that in their mind. That is 00:41:09.210 --> 00:41:15.720 10 which helps them see more than 10. They can see 20. And they can see when 00:41:15.720 --> 00:41:18.390 they put them together like that, they can see that they're actually making 00:41:18.390 --> 00:41:22.920 equal rows of five. So to hold that in your head because will could be coming 00:41:22.920 --> 00:41:27.240 up with some more of those in a minute. You can do quick images with other 00:41:27.240 --> 00:41:32.130 patterns. You can do it with arrays. As kids getting into repeated addition when 00:41:32.130 --> 00:41:35.549 they're getting into multiplication. Show them. Show them as many times as they 00:41:35.549 --> 00:41:39.510 need to keep adding those visual images to them especially for students that are 00:41:39.510 --> 00:41:43.950 having difficulty holding that in their working memory. Show the images as many 00:41:43.950 --> 00:41:48.480 times as they need to for as long as they need. But every time you show it and 00:41:48.480 --> 00:41:51.180 they give it a little bit more information, they'll put it into their 00:41:51.180 --> 00:41:56.880 their brains. You can do it with fractions. Right? You show it you say 00:41:56.880 --> 00:42:01.260 which fraction, what fraction is blue? Is it closer to one or is it 00:42:01.260 --> 00:42:06.089 closer to zero? What fraction is not blue? I know in other parts of, I know in 00:42:06.089 --> 00:42:09.539 Alberta is starting to do fractions much earlier but I know in some places 00:42:09.539 --> 00:42:14.220 they're not doing them yet but in Ontario, we start early. So it's really 00:42:14.220 --> 00:42:18.359 important that they get that holistic approach to fractions. Not about using 00:42:18.359 --> 00:42:23.160 3/4 represented in symbolic notation. We want them to understand. That's what it is. 00:42:23.160 --> 00:42:28.829 Is it closer to 1/2? Is it closer to a full amount? Is it is it closer to, is it 00:42:28.829 --> 00:42:34.580 closer to 0? And then I'm gonna tell you right now, I use 00:42:34.580 --> 00:42:38.210 literature so much. Look at the illustrations in books. There's so many 00:42:38.210 --> 00:42:42.140 illustrations you can use for your math talks. This one is, the ones I'm going to 00:42:42.140 --> 00:42:48.320 show you from Math Appeal by Greg Tang. Great. There every there's sixteen pages. 00:42:48.320 --> 00:42:53.150 I've got them in my resource and like I said every page is a math talk. How many 00:42:53.150 --> 00:42:57.730 sea horses? Figure it out in a few ways. Just take a look. 00:43:21.340 --> 00:43:25.790 Okay, so here's some ways that you may have come up with. First of all we 00:43:25.790 --> 00:43:29.900 want kids to look to things in different ways. So do they see that this 00:43:29.900 --> 00:43:37.040 is like an array? It's just on the diagonal. Can they see the six times six? The six 00:43:37.040 --> 00:43:42.350 groups of six. Or this way. Do they see those? And be able to work from that and 00:43:42.350 --> 00:43:45.680 then subtract the ones that are there. Think of the math talk that you can have. 00:43:45.680 --> 00:43:50.690 Think of how many ways they can discover this and talk about this. Let's take a 00:43:50.690 --> 00:43:53.630 look at this. Remember that consecutive pattern that I 00:43:53.630 --> 00:43:57.470 told you to keep in your head? The one, two, three, four, that makes 10. Well they 00:43:57.470 --> 00:44:00.890 can see those top four rows and those bottom four rows right away and say 00:44:00.890 --> 00:44:04.820 those are two groups of ten. And then I know those two middle rows on either 00:44:04.820 --> 00:44:09.680 side of the six, those would be another group of ten. So I got 10, 20, 30, 36, and 00:44:09.680 --> 00:44:15.830 get rid of the count. I can count backwards. 35, 34, 33, 32, 31. Lots of 00:44:15.830 --> 00:44:19.370 different things you can do with them. And then what you do is you translate 00:44:19.370 --> 00:44:25.130 these into these sentences for them. Right? Or they may say that the five 00:44:25.130 --> 00:44:28.640 objects that are not seahorses cancel out one row five. So there's going to be 00:44:28.640 --> 00:44:32.240 lots of different ways they're gonna look at it. What I love about it is, you 00:44:32.240 --> 00:44:37.940 can do so much with consecutive numbers. How many apples? Again you can see the 00:44:37.940 --> 00:44:41.780 consecutive pattern going here. But this time we're not starting at one which 00:44:41.780 --> 00:44:46.070 gets me into the whole point of conjectures. For instance, kids may come 00:44:46.070 --> 00:44:50.000 up with, does this work every time? Well if you pair up the first and the last, 00:44:50.000 --> 00:44:54.500 and the second last and the second, and the second first and the second last, 00:44:54.500 --> 00:44:59.990 you'll see they all equal 11. Very nice and handy. How do you show that to grade 00:44:59.990 --> 00:45:02.540 ones? How do you prove that it works every time? Well I've done it. 00:45:02.540 --> 00:45:06.500 You get one kid stand at one end of the number line, at any number, let's say 00:45:06.500 --> 00:45:10.310 number two. And you get the other one to stand at number 11. And you say okay, if 00:45:10.310 --> 00:45:16.310 we add two and 11, what are they? That's 13. Okay, each of those students move in 00:45:16.310 --> 00:45:21.650 one space. So one goes to 3 and one goes to 10. Look at us - 13 again. They keep 00:45:21.650 --> 00:45:25.670 moving in. How come? Well because as one number gets bigger the other number gets 00:45:25.670 --> 00:45:30.530 smaller. So we're giving one number over there to the other one. So there's lots 00:45:30.530 --> 00:45:33.470 of things that you can do with coming up with different ways to look at it 00:45:33.470 --> 00:45:36.340 besides ten frames. 00:45:36.990 --> 00:45:42.490 Spatial number talks. Takes some die, dice, and just come up and say, okay what do 00:45:42.490 --> 00:45:45.610 you see? How are these dots the same? How are they different? There's lots of 00:45:45.610 --> 00:45:50.110 things you can do. I want to make sure there's time for questions at the end. 00:45:50.110 --> 00:45:53.320 So I just want to make sure that I'm just going through and showing you some ideas. 00:45:53.320 --> 00:45:58.570 I want to talk about this. This is a document that came out in Ontario about 00:45:58.570 --> 00:46:04.300 Focusing on Fundamentals in 2018. And I know this is big across the country. 00:46:04.300 --> 00:46:09.760 It's getting down to those math facts. And yes we really are encouraging, this 00:46:09.760 --> 00:46:13.030 document encourages that. The kids have to know their math facts but they should 00:46:13.030 --> 00:46:16.870 be learning them through strategies. And like I said visualization for this is 00:46:16.870 --> 00:46:21.730 critical. So for instance visualize a number string. Create those number 00:46:21.730 --> 00:46:28.120 strings where they can see 4. What's that? 4 plus 0. Yep. 5. What's this? 4 plus 4. 00:46:28.120 --> 00:46:32.950 They're learning their doubles. Then you're saying well what's that? 4 plus 5. 00:46:32.950 --> 00:46:37.780 We're learning our strategy doubles plus 1 but we're doing it with visuals. Then 00:46:37.780 --> 00:46:42.910 we're saying what's this one? 5 plus 4. Ah, look at I can turn that around. 00:46:42.910 --> 00:46:48.070 There's the commutative property right there. So as you can see we can really 00:46:48.070 --> 00:46:51.520 build on these visual number strings and then what you do is the next time you 00:46:51.520 --> 00:46:54.520 show them with numbers. So what you're doing is you're building those 00:46:54.520 --> 00:47:00.070 strategies by starting with the visualizations first. You can also, this 00:47:00.070 --> 00:47:05.350 is a really neat thing, build math facts with with two colors of snap cubes. 00:47:05.350 --> 00:47:10.330 Snap them together like that. So that's 4 plus 4. There's 4 plus 5. And then kids can use 00:47:10.330 --> 00:47:14.800 those as another way of visualizing to practice their math facts. Just a couple 00:47:14.800 --> 00:47:18.370 of things I wanted to put in there. I also wanted to mention estimation. 00:47:18.370 --> 00:47:23.140 Estimation is huge for kids. Have an estimation jar in your class all the 00:47:23.140 --> 00:47:27.370 time. Different size jars. Different size things that go into it. As you can 00:47:27.370 --> 00:47:31.000 see on the left, they have the circle around the little jelly beans. You can 00:47:31.000 --> 00:47:33.910 see a group of five. And what you're doing is you're using that group of five 00:47:33.910 --> 00:47:37.810 to be able to estimate how many more there are. We're moving on to the right. 00:47:37.810 --> 00:47:41.590 We can see now we're organizing our stuff. How much easier is it for them to 00:47:41.590 --> 00:47:45.520 do that? So again these spatial talks are really helpful and they can be live 00:47:45.520 --> 00:47:48.760 objects. Just pour something out on the on the carpet and say 00:47:48.760 --> 00:47:56.080 how many are there? Right. Mental rotation. Okay, this is another big thing that I 00:47:56.080 --> 00:48:00.340 wanted to just touch on briefly. So this is where you were taking the object on 00:48:00.340 --> 00:48:06.040 the left and you are rotating it and it will match up with two of those objects 00:48:06.040 --> 00:48:08.730 on the right. 00:48:10.110 --> 00:48:14.070 So even if you can think of one that will do that, just take a look and try it 00:48:14.070 --> 00:48:17.750 out. 00:48:18.849 --> 00:48:24.529 Just so you know it ends up being one and four. And don't worry if you can't do 00:48:24.529 --> 00:48:28.369 this. This takes time. This is where you build that thing and you rotate it 00:48:28.369 --> 00:48:31.789 in your mind. So for instance if you feel like you're visually spatially 00:48:31.789 --> 00:48:36.140 challenged, that's where you build it. You go back to those concrete materials. 00:48:36.140 --> 00:48:40.249 What do you do with kids with this? You give them something like this. Make squares. 00:48:40.249 --> 00:48:43.939 How can you rotate those in their head so you can turn those around to make 00:48:43.939 --> 00:48:49.640 different kinds of squares? Right? Again, you can actually have them, 00:48:49.640 --> 00:48:53.450 give them a black line master of that. They can cut them out. They can put them 00:48:53.450 --> 00:48:59.960 together. But again you're getting them to visualize first. Mental rotation. These 00:48:59.960 --> 00:49:03.680 are really great. These are optical illusions. I use them a lot. How many 00:49:03.680 --> 00:49:07.970 squares? How many blocks do you see? How many are you gonna see when it's upside 00:49:07.970 --> 00:49:12.500 down? Have them try to visualize. And then they can see. You can turn it for them 00:49:12.500 --> 00:49:18.170 and they can see that there's actually more now. And they love, I can't talk 00:49:18.170 --> 00:49:23.000 enough about perspective. Taking that is where we use our optical illusions. Right? 00:49:23.000 --> 00:49:27.880 This is how we're perspective taking on differently in our classrooms right now. 00:49:27.880 --> 00:49:32.750 So like I said I do use optical illusions a lot and kids love it. 00:49:32.750 --> 00:49:37.130 I've used them from kindergarten right up to grade 10. And what is fascinating is, you 00:49:37.130 --> 00:49:41.360 look, you say what shapes do you see in that first shape there? Right. And if 00:49:41.360 --> 00:49:45.560 they really look closely at it, there are no triangles. There are none. There's no 00:49:45.560 --> 00:49:50.810 squares. They're just shapes that are there that have been cleverly put there 00:49:50.810 --> 00:49:55.340 so you would see them in a different way. What I love for measurement is the ruler. 00:49:55.340 --> 00:50:00.170 Which is longer between the two arrows at the left or the two arrows on the 00:50:00.170 --> 00:50:04.460 right? It's an optical illusion. Kids got to get the rulers out and check it out 00:50:04.460 --> 00:50:09.500 because and they just love doing these kinds of things. Again this is really 00:50:09.500 --> 00:50:14.840 cool too. You say to them how many blocks are in this tower? And that means the 00:50:14.840 --> 00:50:21.550 ones that are hidden. Just take a minute to think about it. Picture it in your head. 00:50:24.309 --> 00:50:29.569 Diane, there is a question about where do you find these? Okay I'm just gonna 00:50:29.569 --> 00:50:32.959 talk about that. Again like I said these are in my resource book. For this I would 00:50:32.959 --> 00:50:37.430 build it and take a picture. I would literally and I found one like this 00:50:37.430 --> 00:50:43.039 on the just on the internet. I went to perspective-taking I think and I found 00:50:43.039 --> 00:50:46.430 one and I built it myself because for copyright reasons but I found one right 00:50:46.430 --> 00:50:50.390 on the internet exactly like this. But like I said just build it in your 00:50:50.390 --> 00:50:55.430 classroom because that was my next thing to say is, you build this, you have take a 00:50:55.430 --> 00:50:59.539 picture of it or you just show kids one side. Then what you do is you build it 00:50:59.539 --> 00:51:03.559 and have them walk around to the other side. Let them see it from all different 00:51:03.559 --> 00:51:08.359 perspectives. So I'm always getting to this visualizing to the concrete. But 00:51:08.359 --> 00:51:12.469 seriously if you go on, you're gonna be able to find on the internet, you'll find 00:51:12.469 --> 00:51:16.039 that there are quite a few resources and there are some that you can get. I've 00:51:16.039 --> 00:51:22.180 incorporated my own into my resource but anyways there they are online. 00:51:22.180 --> 00:51:28.160 For instance, have kids visualize. If we put these two shapes together, what's it 00:51:28.160 --> 00:51:34.430 gonna look like? And this one isn't too hard for us. We can see that it's going 00:51:34.430 --> 00:51:40.130 to be the first one. But it really gets a good conversation going. This is great. 00:51:40.130 --> 00:51:44.390 Which one doesn't belong? You put out four things and what you do is you 00:51:44.390 --> 00:51:47.989 selectively choose them so there's one reason that one of them doesn't belong 00:51:47.989 --> 00:51:52.400 for some reason. And kids will come up with crazy reasons. These are the ones 00:51:52.400 --> 00:51:55.009 I've made but I'm gonna tell you right now, and we'll put it there, there's a 00:51:55.009 --> 00:52:01.519 site called Which One Doesn't Belong? So it's wobd.ca. And if you go there 00:52:01.519 --> 00:52:05.539 there's tons of these Which One Doesn't Belong? You will have a math conversation 00:52:05.539 --> 00:52:09.319 going about everything. You're talking about 3D properties here. You're talking 00:52:09.319 --> 00:52:13.160 about everything. So much comes out because for some reason they can come up 00:52:13.160 --> 00:52:19.239 with reason for for one of them not belonging. And like I said do it with 00:52:19.239 --> 00:52:23.869 2D attributes. But to make it interesting for kids. Like I said you can go to that 00:52:23.869 --> 00:52:27.890 site. There's tons of them. But I did it so I thought let's do it with real 00:52:27.890 --> 00:52:32.089 objects. These are things they see in their lives. Here they can see the 00:52:32.089 --> 00:52:37.479 shapes. Which one doesn't belong? And you can come up with the reasons for them. 00:52:37.780 --> 00:52:42.680 Again another thing I really try to do is I try to use art. Here what I've done 00:52:42.680 --> 00:52:46.460 is I've taken a lot of different and these were I found them on the internet 00:52:46.460 --> 00:52:49.280 and got permission from all of the artists to use them. So they're on the 00:52:49.280 --> 00:52:51.770 internet. But what great pictures to use because 00:52:51.770 --> 00:52:56.420 look at the different geometric shapes we're talking about here. Here in a lot 00:52:56.420 --> 00:53:00.020 of cases they use all ovoids. So you talk about the importance of them and how 00:53:00.020 --> 00:53:04.280 they're using them. How they build the symmetry. And these are from 00:53:04.280 --> 00:53:07.820 different these are from all across the country. So this is what kind of makes it 00:53:07.820 --> 00:53:11.840 interesting. That you can really get into a lot of great discussions about just 00:53:11.840 --> 00:53:14.810 artwork. And these I just got off the internet. Like I said though in order to 00:53:14.810 --> 00:53:19.220 do this, I did get permission from all of the artists to show them. Which are 00:53:19.220 --> 00:53:22.340 three-dimensional? Which are two-dimensional? Right? Kids don't know 00:53:22.340 --> 00:53:25.160 the difference between three dimensional and two dimensional until you actually 00:53:25.160 --> 00:53:30.590 do it with them. Here's another one. Very easy. I got off the internet. I made it 00:53:30.590 --> 00:53:33.650 myself. But how many triangles do you see? It's that composing and decomposing 00:53:33.650 --> 00:53:45.109 shapes. And in fact there are seven. And here you're getting at the different 00:53:45.109 --> 00:53:48.980 kind. So you're not always showing kids equilateral triangles and they're not 00:53:48.980 --> 00:53:53.240 always in the same position. And you're being able to discuss what really makes 00:53:53.240 --> 00:53:59.900 a triangle. What are the actual properties? And this one I love. This is 00:53:59.900 --> 00:54:03.530 where you just take paper. Just use, cut these paper shapes out and say 00:54:03.530 --> 00:54:07.970 how can you get from that rectangle to that chevron on the bottom? What are you 00:54:07.970 --> 00:54:12.410 doing to it? So you're getting kids to be able to visualize first and then use the 00:54:12.410 --> 00:54:16.420 paper to be able to cut them out and be able to make the new shapes out of it. 00:54:16.420 --> 00:54:21.200 A lot of fun and kids love doing this. Like I said they're motivating. And I just 00:54:21.200 --> 00:54:24.770 want to talk briefly about location and movement. I talked earlier about the 00:54:24.770 --> 00:54:30.470 kindergarten kid who cannot find their way until they've walked the path. Then 00:54:30.470 --> 00:54:34.340 you build concrete maps right with them in the classroom. And then finally you 00:54:34.340 --> 00:54:38.290 get down to maps where they have to discuss the relative positions of 00:54:38.290 --> 00:54:43.580 objects on the maps. This is a lot of fun. Give them something like this, a road map. 00:54:43.580 --> 00:54:46.400 You can find them on the internet. I found, this is where I get a lot of my 00:54:46.400 --> 00:54:50.299 ideas. But have them sit there pretending they're driving a car. Where 00:54:50.299 --> 00:54:54.619 they're gonna put those signs to make that street safe to go? Have them follow 00:54:54.619 --> 00:54:58.999 the street and actually turn as they're going through. A lot of fun for them to 00:54:58.999 --> 00:55:02.359 do but also very good for their visualization skills. And here we're 00:55:02.359 --> 00:55:10.519 connecting the visual with the symbolic. Again, go to your literature. This is a 00:55:10.519 --> 00:55:13.549 great book you're probably familiar with. We're going on 00:55:13.549 --> 00:55:18.289 a lion hunt. You can't go over it, can't go under it, can't go around it. So we're 00:55:18.289 --> 00:55:22.699 gonna have to go through that grass. And you do the gestures with them. So you're 00:55:22.699 --> 00:55:27.369 putting those gestures that I talked about earlier and hanging them on there. 00:55:27.369 --> 00:55:31.819 Oh this is really important too. Coding is all the biggest thing. I know 00:55:31.819 --> 00:55:37.819 there's one going on now at OAME. Well you know what, you can code on paper. Coding 00:55:37.819 --> 00:55:42.589 is just being able to give instructions. So how do you get, kids have can have 00:55:42.589 --> 00:55:45.499 fun with this. You can do it as a barrier game. But how do you get from, create a 00:55:45.499 --> 00:55:50.150 code, so you're creating the code there. And then the other student is following 00:55:50.150 --> 00:55:55.189 the code. So you're really getting this whole idea of this whole spatial 00:55:55.189 --> 00:55:58.969 navigation. But this is what coding is. Its being making sure that the 00:55:58.969 --> 00:56:04.789 instructions that you're creating work and do what you want it to do. Build some 00:56:04.789 --> 00:56:09.319 barriers in. But there's lots of things that you can do very quickly. I'm just 00:56:09.319 --> 00:56:15.529 gonna finish up with two little things here. I love gathering data. If I were you 00:56:15.529 --> 00:56:20.059 on distance learning, I would do a survey every day. I would create them because 00:56:20.059 --> 00:56:24.229 and and you get them to vote. You come up with something. I do this in September. Every 00:56:24.229 --> 00:56:27.890 day we have a vote. We get to know each other. But we also get to really compare 00:56:27.890 --> 00:56:31.579 data. Throw something like this. Just build this in your class with 00:56:31.579 --> 00:56:36.499 snap cubes. Say what is this? What's this a graph of? Right. They may say it's about 00:56:36.499 --> 00:56:39.619 strawberries and it's about limes and lemons and blueberries. They may come up 00:56:39.619 --> 00:56:44.179 with a million reasons but you want to ask them, what might it represent? What 00:56:44.179 --> 00:56:49.069 titles might you see? What can you tell from this graph? What might be important 00:56:49.069 --> 00:56:53.599 to know? Lots of fun there. You can just build it in your class. But here they're 00:56:53.599 --> 00:56:57.410 comparing numbers. They're comparing quantities. You can then put numbers to 00:56:57.410 --> 00:57:01.429 them. They're doing more or less. They can figure out there's 17 altogether. Lots 00:57:01.429 --> 00:57:06.440 they can do. Probability - the same thing. Throw it up there. Have a 00:57:06.440 --> 00:57:11.810 conversation. In the next case, what I'm showing you is, just get a jar. Put some 00:57:11.810 --> 00:57:15.920 stuff in there. What are the chances that I'm gonna, put things in a jar and 00:57:15.920 --> 00:57:19.190 or in a bag, and say what are the chances I'm gonna pull out something that's 00:57:19.190 --> 00:57:23.030 yellow? What's the chance when you saw what I put in there, what's gonna pull out 00:57:23.030 --> 00:57:27.650 that something black? Right? Getting at all of that different language. So a lot 00:57:27.650 --> 00:57:32.690 of fun to do as well. Anyhow that's as much as I'm gonna say. I know I went a 00:57:32.690 --> 00:57:36.680 little quickly there at the end because I wanted to get everything in. The final 00:57:36.680 --> 00:57:40.940 thoughts that I have basically are basically, look at everything and think 00:57:40.940 --> 00:57:46.430 how you can spatialize it. How can I get kids to visualize? Before they you ask 00:57:46.430 --> 00:57:50.930 them to do something, have them visualize it in their head. How can I use a spatial 00:57:50.930 --> 00:57:55.340 talk to encourage spatial thinking. I encourage you to grow your own spatial 00:57:55.340 --> 00:57:58.550 thinking. I do that every day because I lose my car in the parking lot all the 00:57:58.550 --> 00:58:08.240 time. And just have fun. So those would be the things. Yes. You can find a lot of 00:58:08.240 --> 00:58:11.510 these resources. I'm going to tell you that too. A lot of this comes from a book 00:58:11.510 --> 00:58:16.160 called "Taking Shape". The resources, the research that I work with are Joan Moss 00:58:16.160 --> 00:58:24.770 and Bev Caswell, Tara Flynn, Kathy Bruce and Zack Hawes. And I worked with 00:58:24.770 --> 00:58:27.500 all of them on these projects and they're the ones that wrote the book. 00:58:27.500 --> 00:58:32.060 I was just involved in some of them. So if you go to the book by Joan Moss called 00:58:32.060 --> 00:58:38.060 "Taking Shape", you'll find a lot of the ideas there. How do you promote spatial 00:58:38.060 --> 00:58:42.560 reasoning among preschoolers to encourage them to be more ready for K? Listen just 00:58:42.560 --> 00:58:46.760 give them a lot of get them build. Build everything. Build with them. That's 00:58:46.760 --> 00:58:50.660 another thing they say with preschoolers. Don't just give them free build. Give 00:58:50.660 --> 00:58:55.550 them instructions and build along with them. If you give them the language, they 00:58:55.550 --> 00:59:01.100 found that the kids who are given the language, the spatial language, if their 00:59:01.100 --> 00:59:04.430 parents use it more, they actually have better spatial 00:59:04.430 --> 00:59:08.270 thinking. So when you're telling them to get something, if for instance, don't say 00:59:08.270 --> 00:59:12.350 get the ball over there, say get the ball that's on the middle shelf. That's really 00:59:12.350 --> 00:59:17.570 important to do. Right? I have a daily check with a Google Form of questions. 00:59:17.570 --> 00:59:21.170 That's a good idea to ask them what they see. That's excellent. 00:59:21.170 --> 00:59:28.550 So those are the the questions. Yes and I would I would check out the 00:59:28.550 --> 00:59:31.730 research on spatial reasoning, spatial thinking. There's lots of it. But I'm 00:59:31.730 --> 00:59:36.260 telling you we did we did so much research with the little kids, but also 00:59:36.260 --> 00:59:39.920 we found with the older kids they needed a lot of the same stuff that we were 00:59:39.920 --> 00:59:46.130 doing now. So I would really encourage you, and I and like I said it's fun. Kids 00:59:46.130 --> 00:59:50.660 love it. It's motivating and you'll really start seeing the benefits. So I 00:59:50.660 --> 00:59:54.890 hope that you can find some of these things. You can take them away with you 00:59:54.890 --> 00:59:59.090 and try some of them on your class. And listen, I wish you the very best moving 00:59:59.090 --> 01:00:04.610 forward with this pandemic. I really do. And I'll be thinking of you. And I know 01:00:04.610 --> 01:00:09.280 you're all very innovative and creative and you'll get through it. 01:00:09.370 --> 01:00:19.940 Awesome. So that's it. I don't know if, is that Jolyn? 01:00:19.940 --> 01:00:22.900 Yes. I'm coming. 01:00:35.430 --> 01:00:41.800 Hi everyone. Thank You Diane for that awesome presentation. It was awesome. 01:00:41.800 --> 01:00:45.910 I loved it and I think everyone else did too. 01:00:45.910 --> 01:00:51.910 So if you, attendees, if you have any more questions, the Google Doc for this 01:00:51.910 --> 01:00:56.980 session is open to you and add your questions in there and Diane will try to 01:00:56.980 --> 01:01:03.550 answer them in the upcoming days. Also in the Google Doc are the links. Any links 01:01:03.550 --> 01:01:09.970 that Diane wishes to share and and a link to the entry for the door prizes. 01:01:09.970 --> 01:01:14.830 Be sure that you get that one. The entry form is also posted in the chat. 01:01:14.830 --> 01:01:20.710 You may enter once per session per session attended and prizes will be 01:01:20.710 --> 01:01:27.250 drawn at the end of the conference. This form will be available today. You can 01:01:27.250 --> 01:01:31.690 get to Google Doc and the recording of this session once it is posted on the 01:01:31.690 --> 01:01:39.160 OAME website. We ask that you please do not share this link publicly. To access 01:01:39.160 --> 01:01:44.050 to access the recordings after Monday, please consider becoming a member of 01:01:44.050 --> 01:01:52.200 this fabulous organization OAME. Thank you so much to everyone and stay safe.