WEBVTT Kind: captions Language: en 00:00:00.640 --> 00:00:07.279 Hello everyone welcome to OAME 2020. It is a pleasure to be here. 00:00:07.279 --> 00:00:11.759 I'm Heidi Allum and I am an educational technology coach with the Durham 00:00:11.759 --> 00:00:15.839 District School Board and I'm here to talk about Midpoint Math Thinking. 00:00:15.839 --> 00:00:20.000 Before we start I want to take time to thank you so much 00:00:20.000 --> 00:00:24.800 for attending the session on your own time and especially during 00:00:24.800 --> 00:00:28.240 these very unprecedented times. I appreciate 00:00:28.240 --> 00:00:33.840 your time, your thinking, and being here with me today. 00:00:33.840 --> 00:00:37.360 I am accessible by my email which you can see right here up on the screen. 00:00:37.360 --> 00:00:39.200 Please email me if you have any questions 00:00:39.200 --> 00:00:46.800 or thoughts. I would love to hear your thinking. You can reach me on twitter and I have a blog that you are more than 00:00:46.800 --> 00:00:50.559 welcome to check out. During the presentation I 00:00:50.559 --> 00:00:53.600 might point out some blogs that match what I'm 00:00:53.600 --> 00:00:57.520 talking about today I also want to take the time to point 00:00:57.520 --> 00:01:01.120 out that if you visit my blog you will find that I blog about many 00:01:01.120 --> 00:01:05.600 things math but also many things to do with trauma and 00:01:05.600 --> 00:01:08.799 trauma informed learning which is another lens that I am 00:01:08.799 --> 00:01:11.920 very interested in and would love to chat with you about 00:01:11.920 --> 00:01:16.479 and in fact was going to do a trauma informed math session with 00:01:16.479 --> 00:01:19.520 another presenter. We just decided that would be better 00:01:19.520 --> 00:01:22.479 done in person so hopefully that's something that 00:01:22.479 --> 00:01:27.680 we can work on in a future date. Before we get into the math I would like 00:01:27.680 --> 00:01:30.799 to take the time to acknowledge the land that we are on. 00:01:30.799 --> 00:01:34.960 I am in the Durham region and I am going to go with the Durham District School 00:01:34.960 --> 00:01:38.640 Board land acknowledgement. I would like to acknowledge that many 00:01:38.640 --> 00:01:41.840 Indigenous Nations have long-standing relationships both 00:01:41.840 --> 00:01:45.520 historic and modern with the territories upon which our school board and schools 00:01:45.520 --> 00:01:48.399 are located. Today this area is home to many 00:01:48.399 --> 00:01:50.799 Indigenous peoples from across Turtle Island. 00:01:50.799 --> 00:01:53.920 We acknowledge that the Durham Region forms a part of the traditional and 00:01:53.920 --> 00:01:57.840 treaty territory of the Mississaugas of Scugog Island First Nation, 00:01:57.840 --> 00:02:01.600 the Mississauga Peoples and the treaty territory of the Chippewas of Georgina 00:02:01.600 --> 00:02:06.159 Island First Nation. It is on these ancestral and treaty 00:02:06.159 --> 00:02:11.360 lands that we teach, learn and live. 00:02:11.360 --> 00:02:14.560 This to me is the most important part of the acknowledgement and I really 00:02:14.560 --> 00:02:17.920 want to think a lot about how are we having students specifically 00:02:17.920 --> 00:02:21.200 become really active with that. How do they honor 00:02:21.200 --> 00:02:24.400 these treaty lands that they're on? Do they fully understand 00:02:24.400 --> 00:02:29.120 the treaties and especially maybe we could look at mathematics as a window 00:02:29.120 --> 00:02:32.800 into Indigenous culture and Indigenous histories right 00:02:32.800 --> 00:02:38.400 that we are right in so perhaps something to consider. 00:02:40.560 --> 00:02:44.879 I would like to start with a quote. "Of course I want them to know their times 00:02:44.879 --> 00:02:49.519 tables and be able to add, etc. but that is not even close enough for me 00:02:49.519 --> 00:02:54.319 in a world looking for thinkers." In my mind 00:02:54.319 --> 00:02:58.560 math proves and opens a door to my students thinking. 00:02:58.560 --> 00:03:01.840 I can really get in and see where perhaps 00:03:01.840 --> 00:03:05.760 their thinking becomes muddled, their thinking becomes really clear, 00:03:05.760 --> 00:03:10.400 and it really gives me an insight into those processes a student might go into 00:03:10.400 --> 00:03:14.319 in everything is just going to come out in math. 00:03:14.319 --> 00:03:17.440 I would like to take the time to thank Marian Small for that great quote 00:03:17.440 --> 00:03:21.040 and it's something that I'm thinking a lot about. How do we get our students 00:03:21.040 --> 00:03:24.400 to really demonstrate to show their thinking? How do we get 00:03:24.400 --> 00:03:27.920 into that math mess brain of theirs as we are 00:03:27.920 --> 00:03:35.599 teachers navigating a classroom? I'm especially wondering about the 00:03:35.599 --> 00:03:38.319 process of encouraging math talk and math thinking 00:03:38.319 --> 00:03:42.319 especially while students are doing the math - actively engage in the math that's 00:03:42.319 --> 00:03:47.840 happening in front of them right now. 00:03:48.239 --> 00:03:53.200 So let's talk about that. When do you have your students actively think about 00:03:53.200 --> 00:03:56.400 the math they are working on. 00:03:59.200 --> 00:04:02.720 I think before we do the math, we do this pretty well. 00:04:02.720 --> 00:04:06.720 We might pre-read the problem and give our students plenty of strategies in 00:04:06.720 --> 00:04:09.040 order to attack the problem before they even 00:04:09.040 --> 00:04:12.560 get to the problem. The concept of numberless math problems comes to me 00:04:12.560 --> 00:04:16.079 there or chunking the math problem. 00:04:16.079 --> 00:04:19.199 We follow the four-step problem-solving model here in Ontario 00:04:19.199 --> 00:04:23.280 and you know making a plan is a huge one. We teach the students to go through to 00:04:23.280 --> 00:04:27.440 highlight keywords. We're good about having students talk 00:04:27.440 --> 00:04:29.440 before the problem. We might model a think pair 00:04:29.440 --> 00:04:34.479 share. Sarah VanDerWerf has a great strategy called stand & talks 00:04:34.479 --> 00:04:38.639 which I do have live links in this presentation. You're going to notice the 00:04:38.639 --> 00:04:42.479 bitly at the bottom here which is rolling on that you can access the slide 00:04:42.479 --> 00:04:46.880 and see all the live links. Another time we're really good at 00:04:46.880 --> 00:04:49.680 capturing student math thinking is at the end 00:04:49.680 --> 00:04:52.800 and I say at the end of quotation marks. Generally when we're done 00:04:52.800 --> 00:04:57.360 with a math problem or it's the next day, we're embarking in a three-part lesson 00:04:57.360 --> 00:05:00.400 plan and our students are reflecting and consolidating, 00:05:00.400 --> 00:05:03.840 we might do math congress, a bansho, a math gallery walk 00:05:03.840 --> 00:05:09.039 or an exit ticket. What happens in the middle? And this is 00:05:09.039 --> 00:05:13.360 where I'm personally very interested. Now i have a 00:05:13.360 --> 00:05:16.880 lot of question marks on the screen here and it's not to say that we don't do 00:05:16.880 --> 00:05:20.479 anything in the middle as educators. We're really good at walking around and 00:05:20.479 --> 00:05:24.400 listening to students talk about math. Many of us might be doing small group 00:05:24.400 --> 00:05:30.000 and our guided instruction at this point. I think at this point it becomes really 00:05:30.000 --> 00:05:34.880 easy to jump in and to help when maybe our help isn't needed 00:05:34.880 --> 00:05:38.960 rather than sit back and really actually listen. And that becomes hard when there 00:05:38.960 --> 00:05:42.000 are many students in the classroom and we're trying to listen. 00:05:42.000 --> 00:05:48.000 So I'm hoping today, I'm hoping today that we can talk about 00:05:48.000 --> 00:05:51.520 some ways to help us document that learning, that 00:05:51.520 --> 00:05:53.919 thinking, as students are working the math problem 00:05:53.919 --> 00:05:57.840 and maybe some ways to really engage making students become more aware of 00:05:57.840 --> 00:06:00.240 what they're thinking while they're doing the math. 00:06:00.240 --> 00:06:03.840 I guess what I'm trying to say is we don't often give students a chance to 00:06:03.840 --> 00:06:07.520 reflect on their thinking while they're solving a problem. What I'm 00:06:07.520 --> 00:06:10.319 really looking for is students changing their minds. 00:06:10.319 --> 00:06:16.800 Stopping asking themselves questions or changing their strategy. 00:06:16.800 --> 00:06:19.840 That can happen through a couple of different ways. They might change their 00:06:19.840 --> 00:06:22.639 mind based on new information. That new information might come from 00:06:22.639 --> 00:06:26.319 them realizing a different part of the problem that they missed the first time. 00:06:26.319 --> 00:06:29.919 That realization might come from them talking to a peer. 00:06:29.919 --> 00:06:33.600 That realization might come from them by using a tool or by looking at the 00:06:33.600 --> 00:06:36.160 problem a different way. All those problem-solving strategies sort of that 00:06:36.160 --> 00:06:39.759 we embody as math educators and I'm just wondering if we're really 00:06:39.759 --> 00:06:43.759 letting them dig into that. 00:06:44.160 --> 00:06:47.440 I think a lot of that comes from the process expectations actually. 00:06:47.440 --> 00:06:50.479 And the process expectations are verbs. They're actions. 00:06:50.479 --> 00:06:55.440 They're things that we are doing all the time while we're engaged in that math. 00:06:55.440 --> 00:06:58.160 I know we know what the process expectations are but just humor me for a 00:06:58.160 --> 00:07:01.520 minute - problem solving, reasoning and proving, 00:07:01.520 --> 00:07:05.039 reflecting, communication, selecting tools and 00:07:05.039 --> 00:07:09.360 computational strategies, connecting, representing. Any of us 00:07:09.360 --> 00:07:13.280 probably have a favorite uh process expectation or one 00:07:13.280 --> 00:07:17.440 that we weigh on. Generally speaking I find that 00:07:17.440 --> 00:07:20.479 communication is one that we generally like to work on or think 00:07:20.479 --> 00:07:25.039 about. And obviously the math content, deep rich 00:07:25.039 --> 00:07:27.919 math content, is what we're wanting here and that's part 00:07:27.919 --> 00:07:31.199 of the conversation we're going to have too and the way that I have this graphic 00:07:31.199 --> 00:07:34.400 sort of set up is the math content is sort of sitting on 00:07:34.400 --> 00:07:37.680 the process expectations. The process expectations sort of take the math 00:07:37.680 --> 00:07:41.280 content along on a journey. I know there's that 00:07:41.280 --> 00:07:46.080 famous quote "Literacy floats on a sea of talk." I feel 00:07:46.080 --> 00:07:49.199 like math can float on all of these processes. 00:07:49.199 --> 00:07:52.639 I don't think they happen linearly. I don't think they happen in any sort of 00:07:52.639 --> 00:07:57.360 order. I think they all work together and let's investigate that a little bit 00:07:57.360 --> 00:08:00.400 further through this today. 00:08:01.840 --> 00:08:04.960 So I'm going to start by maybe getting us 00:08:04.960 --> 00:08:10.840 into a math thinking stance. So when I think of my thinking I think 00:08:10.840 --> 00:08:15.039 of places or tasks or problems that are going to 00:08:15.039 --> 00:08:19.680 come and elicit thinking in a very very open way. They're going to 00:08:19.680 --> 00:08:24.160 get kids thinking and then talking and then doing the math, 00:08:24.160 --> 00:08:28.960 feeling invited in and open into the math space. 00:08:29.440 --> 00:08:33.039 So this link will take you to this Google sheet that I've created 00:08:33.039 --> 00:08:37.279 that I'm always adding on with tons of places to go 00:08:37.279 --> 00:08:43.440 to get math thinking ideas. Really open ways to make math engaging 00:08:43.440 --> 00:08:47.279 to students and to get them really thinking and 00:08:47.279 --> 00:08:50.880 having them use those process expectations to demonstrate their 00:08:50.880 --> 00:08:54.000 thinking. Many of these websites are very familiar 00:08:54.000 --> 00:08:58.800 to all of you. Estimate 180. Which one doesn't belong. 00:08:58.800 --> 00:09:03.279 I'm trying to add as I go. The live link in this slide deck when 00:09:03.279 --> 00:09:06.399 you go to that bitly will take you here and please feel free 00:09:06.399 --> 00:09:10.480 to suggest to me any that you know get your students 00:09:10.480 --> 00:09:15.519 motivated to talk that are not here right now. 00:09:16.240 --> 00:09:20.399 Math is play. We really want to have a playful 00:09:20.399 --> 00:09:25.120 classroom, a playful disposition and have students grapple and play with different 00:09:25.120 --> 00:09:29.839 math ideas. This will get students thinking talking 00:09:29.839 --> 00:09:34.320 and therefore the natural want to discuss what they're doing while they're 00:09:34.320 --> 00:09:39.120 doing it might become even more evident. 00:09:40.080 --> 00:09:44.480 So we want high engagement tasks that promote play. 00:09:45.839 --> 00:09:50.720 We kind of want to leave them alone. Maybe we want to stand back a little bit. 00:09:50.720 --> 00:09:54.720 In my blog, I do have a blog and it's called exactly that 00:09:54.720 --> 00:09:57.920 exactly that. If you want better math students then leave them alone. 00:09:57.920 --> 00:10:01.920 If you're interested please feel free to check it out. 00:10:02.800 --> 00:10:06.399 When we're playing we're we're creating a community. We're sharing. We're 00:10:06.399 --> 00:10:08.640 engagement and we're helping create a sense of 00:10:08.640 --> 00:10:12.160 wonder with students especially within each other. 00:10:12.160 --> 00:10:16.240 Sarah VanDerWerf who you probably have seen on Twitter before and again 00:10:16.240 --> 00:10:19.600 in the presenter notes of this slide deck you will see her links there 00:10:19.600 --> 00:10:21.839 has a great blog about creating a math table. 00:10:21.839 --> 00:10:26.160 And I tried it out and you can see an image from my math table from a couple 00:10:26.160 --> 00:10:28.480 of years ago when I was in a grade 6 classroom 00:10:28.480 --> 00:10:32.240 and honestly my students went to it all the time. 00:10:32.240 --> 00:10:35.519 As a place for math for sure i would leave them prompts like the one you see on 00:10:35.519 --> 00:10:38.720 the screen but also I noticed they would go there as a place 00:10:38.720 --> 00:10:42.560 to sort of relax. Many students would use it as a way to 00:10:42.560 --> 00:10:48.160 transition from inside to outside or to transition from me doing a mini 00:10:48.160 --> 00:10:50.480 lesson and then going to the work, they might have stopped at the math play 00:10:50.480 --> 00:10:54.079 table. And sort of it was always very hands-on. There was 00:10:54.079 --> 00:10:58.640 pattern blocks. I had magnetic nets for them to explore 00:10:58.640 --> 00:11:03.760 with. Christopher Danielson who is a fantastic 00:11:03.760 --> 00:11:06.959 math play advocate has these fantastic tiling turtles that I had in my 00:11:06.959 --> 00:11:10.399 classroom. They all kind of had students start and 00:11:10.399 --> 00:11:14.000 then build on one another. So a great way if you don't have a math table to check 00:11:14.000 --> 00:11:17.760 in on their thinking. I think it kind of creates a cycle 00:11:17.760 --> 00:11:22.079 almost. When you're giving them a task, playful math, something really 00:11:22.079 --> 00:11:26.880 interesting, it leads to the talk and the talk leads in my mind to that 00:11:26.880 --> 00:11:29.680 reflection piece, thinking about what they're saying going back and 00:11:29.680 --> 00:11:33.519 re-examining in a natural way. 00:11:35.519 --> 00:11:38.800 So here are some ways that might promote students 00:11:38.800 --> 00:11:42.079 actively engaging and reflecting on their math thinking while they're doing 00:11:42.079 --> 00:11:45.839 it. Ways that are going to help you to as a teacher to listen 00:11:45.839 --> 00:11:50.399 in on their math thinking and change trajectory of your teaching if you think 00:11:50.399 --> 00:11:54.320 that's necessary or just really see from the beginning 00:11:54.320 --> 00:11:56.880 when they were starting the math and then at the end 00:11:56.880 --> 00:12:01.519 when you're doing that consolidation what happened from point A if you will 00:12:01.519 --> 00:12:04.240 to point B. 00:12:06.160 --> 00:12:10.160 I am going to talk about digital tools as well as just 00:12:10.160 --> 00:12:13.360 other ways to get that math talk and that math think to reflect. 00:12:13.360 --> 00:12:17.440 And the reason why I like digital tools is it's really a selfish reason for me 00:12:17.440 --> 00:12:21.120 as an educator. I get sort of that documentation 00:12:21.120 --> 00:12:24.320 piece. I get a sort of something I can look back on. I can have 00:12:24.320 --> 00:12:28.959 the students reflect on as well. And I really can then take the time 00:12:28.959 --> 00:12:32.160 to go through that documentation and say oh hey here are 00:12:32.160 --> 00:12:36.000 some of the process expectations that the student or group of students touched 00:12:36.000 --> 00:12:39.519 on and really I like the editing aspect of 00:12:39.519 --> 00:12:42.079 it. In this picture I have two students who 00:12:42.079 --> 00:12:45.120 are reflecting on a math journal and just really listening to each other 00:12:45.120 --> 00:12:48.240 thinking through what we had what we're doing in the middle of math 00:12:48.240 --> 00:12:52.240 right now um and I just like that sort of movement for 00:12:52.240 --> 00:12:54.880 them to edit to rethink about their thinking. 00:12:54.880 --> 00:12:59.440 It really helps them to become metacognitive. 00:12:59.680 --> 00:13:02.880 So we want to prompt listening and encouraging dialogue. This isn't 00:13:02.880 --> 00:13:06.240 necessarily technology. This is more things for us to 00:13:06.240 --> 00:13:10.079 be thinking about in our classroom. Who does most of the talking in a 00:13:10.079 --> 00:13:13.839 classroom during math? It can very easily be the teacher. I am 00:13:13.839 --> 00:13:17.519 extremely guilty of that. I am, this is exactly it right now. Here I am 00:13:17.519 --> 00:13:20.480 doing all the talking and you're doing all the receiving. 00:13:20.480 --> 00:13:24.320 And even if your students are doing a lot of talking, I know personally I was 00:13:24.320 --> 00:13:27.040 guilty of jumping in on that conversation. 00:13:27.040 --> 00:13:30.639 Saying things like so what you're saying is, is what you're thinking is, 00:13:30.639 --> 00:13:35.040 and it left the students with either saying yes or no not at all and 00:13:35.040 --> 00:13:38.720 and it maybe had would have derailed the conversation. 00:13:38.720 --> 00:13:41.600 What I think is really powerful is having letting the students have that 00:13:41.600 --> 00:13:46.720 conversation between them and me almost being um the person 00:13:46.720 --> 00:13:50.160 listening in on what they're thinking and what they're saying 00:13:50.160 --> 00:13:53.839 and maybe not jumping in with a thought or a prompt immediately. 00:13:53.839 --> 00:13:58.959 Maybe letting those two students continue to have that conversation. 00:13:59.440 --> 00:14:04.160 If I am encouraging student discourse I really want to use sort of um 00:14:04.160 --> 00:14:07.839 I really enjoy the learning the knowledge building aspect 00:14:07.839 --> 00:14:10.959 which is on the Learning Exchange that's where I stumbled on my words there. 00:14:10.959 --> 00:14:14.839 They have a lot of knowledge building which is Marlene Scardamalia's work 00:14:14.839 --> 00:14:19.040 um which I have linked to some of the Learning Exchange things 00:14:19.040 --> 00:14:23.760 in this slide deck here. Even if you start with a simple prompt 00:14:23.760 --> 00:14:26.800 that you teach the students to have, "Do you agree or disagree with what's going on? 00:14:26.800 --> 00:14:30.639 Why or why not?" It continues to build that 00:14:30.639 --> 00:14:33.839 collaboration as well and also I'm putting the onus back on the 00:14:33.839 --> 00:14:38.399 students to start that dialogue and maybe from from that point I am 00:14:38.399 --> 00:14:41.199 going to encourage the students to come up with their own prompts for each other, 00:14:41.199 --> 00:14:44.320 let them collaborate and co-create any sort 00:14:44.320 --> 00:14:50.800 of those talk moves that we might need. I'm also a big, becoming better at, having 00:14:50.800 --> 00:14:54.160 students actually think on their own first. 00:14:54.160 --> 00:14:56.880 I feel like when I was in teachers college or just starting teaching there 00:14:56.880 --> 00:14:59.839 was a big movement to sort of have students get right into the group right 00:14:59.839 --> 00:15:02.959 away. But I've since sort of changed gears a 00:15:02.959 --> 00:15:07.920 little bit and let students think first. Whether that's just a few 00:15:07.920 --> 00:15:12.000 moments to think. Whether that's giving them a long think 00:15:12.000 --> 00:15:14.880 time. It depends on what we're doing and what we're moving towards. 00:15:14.880 --> 00:15:18.959 And I think having them have a physical something with them while they're thinking is 00:15:18.959 --> 00:15:22.800 helpful as well. So a tool for example um if we're creating, we're about to 00:15:22.800 --> 00:15:25.519 create some different patterns or I'm asking them to extend patterns, I might 00:15:25.519 --> 00:15:28.000 want to give them some time to play around with some pattern blocks if 00:15:28.000 --> 00:15:31.279 that's applicable and just sort of muddle 00:15:31.279 --> 00:15:35.120 around with with the tool and then especially before 00:15:35.120 --> 00:15:43.680 I send them off to go talk to somebody. So here's an example of collaboration 00:15:43.680 --> 00:15:46.880 with my class that I did. Which one doesn't belong I think is a 00:15:46.880 --> 00:15:51.519 fantastic way to open up math. You are having students justify, to 00:15:51.519 --> 00:15:56.399 use those process expectations, to communicate their thinking, to have 00:15:56.399 --> 00:15:59.600 some discourse there because they're going to have different opinions. 00:15:59.600 --> 00:16:03.040 And it got to the point where my students created their own. We had done 00:16:03.040 --> 00:16:06.240 so much work around analyzing which ones doesn't belong to 00:16:06.240 --> 00:16:09.680 the point where we would talk about why each quadrant might not belong not 00:16:09.680 --> 00:16:13.279 just one, that my students went ahead and did 00:16:13.279 --> 00:16:15.759 their own. What I'm modeling for you know is sort 00:16:15.759 --> 00:16:19.279 of two things, I'm modeling the students doing their own thinking and showing me 00:16:19.279 --> 00:16:22.800 their metacognitive thinking here but I'm also, I have a shared Google slide 00:16:22.800 --> 00:16:26.560 deck here and I have it in grid view. Actually I don't have it in grid view. 00:16:26.560 --> 00:16:29.519 But I have the slides all along numbered and what's great about this is the 00:16:29.519 --> 00:16:32.800 students in Google classroom, I created a whole 00:16:32.800 --> 00:16:36.800 bunch of blank slides and I assigned it as students can edit 00:16:36.800 --> 00:16:39.440 and then the students could pick, I gave the student each a number 00:16:39.440 --> 00:16:41.839 and they put their "Which one doesn't belong" in. 00:16:41.839 --> 00:16:45.279 And this was great because they could look at each other's and have that 00:16:45.279 --> 00:16:47.839 conversation and I could see that conversation 00:16:47.839 --> 00:16:50.240 happening live because the comment function 00:16:50.240 --> 00:16:54.399 in slides comes up live so I can be watching those conversations happen 00:16:54.399 --> 00:16:57.680 putting in my comments as well but it was just a great place for them to go 00:16:57.680 --> 00:17:02.959 look at each other's. In the present notes of that "Which one 00:17:02.959 --> 00:17:07.039 doesn't belong" student example slides, I had my students create, 00:17:07.039 --> 00:17:10.880 do some planning while they were exploring their own "Which one doesn't 00:17:10.880 --> 00:17:13.280 belong". So that is in the slide notes. I just 00:17:13.280 --> 00:17:18.000 thought I'd show you that they each had to tell me about their 00:17:18.000 --> 00:17:22.079 quadrants. What the possible reasons were and why to sort of help justify 00:17:22.079 --> 00:17:25.120 because in the end we were going to present these to another class 00:17:25.120 --> 00:17:29.200 and I wanted them to anticipate what those other students were thinking. 00:17:29.200 --> 00:17:32.640 So in that act of the students anticipating what other students would 00:17:32.640 --> 00:17:34.799 say, they were becoming metacognitive 00:17:34.799 --> 00:17:39.600 about their own "Which one doesn't belong". I'm really thinking about what they were 00:17:39.600 --> 00:17:44.320 presenting and the reasons why. For example some of them were saying 00:17:44.320 --> 00:17:47.360 things like "Oh well this quadrant in quadrant c for example 00:17:47.360 --> 00:17:49.919 I only can think of one or two reasons it could not belong. 00:17:49.919 --> 00:17:54.400 It's not really gonna spark dialogue." So they were changing and 00:17:54.400 --> 00:17:58.320 fixing and reflecting um and making their math 00:17:58.320 --> 00:18:02.240 different based on that without me necessarily telling them "Hey 00:18:02.240 --> 00:18:05.360 have you considered?" The feedback was coming out on its own just through this 00:18:05.360 --> 00:18:09.760 metacognitive piece of having them reflect and anticipate what my other 00:18:09.760 --> 00:18:12.559 students might say. 00:18:13.440 --> 00:18:17.360 We have some math thinking websites. We're creating dialogue in our classroom. 00:18:17.360 --> 00:18:21.440 It's becoming really playful and of course we're going to want to give them 00:18:21.440 --> 00:18:25.360 interesting problems that invite thinking conversation and 00:18:25.360 --> 00:18:28.320 action, that they want to do them, they want to they want to get up and try them out. 00:18:28.320 --> 00:18:32.160 Here is something I did with a grade 00:18:32.160 --> 00:18:37.280 7 class and it's based on Marian Small. I think I changed the numbers up. 00:18:37.280 --> 00:18:41.760 A parallel task here around surface area. Again in my slide notes you're going to 00:18:41.760 --> 00:18:45.280 see this slide in more detail. You can use it if you 00:18:45.280 --> 00:18:48.240 want or make a copy for yourself to do it. 00:18:48.240 --> 00:18:56.160 And the students went right to it. So in this case they are using flipgrid. 00:18:56.160 --> 00:19:01.120 And I asked the students to record, before we started, 00:19:01.120 --> 00:19:05.520 they paused, they started to work and then I literally stopped the room 00:19:05.520 --> 00:19:08.799 and said I want everybody to record whatever you're doing, whatever's going 00:19:08.799 --> 00:19:10.640 on in your minds, whatever you're working on 00:19:10.640 --> 00:19:15.600 right now. And it was interesting to watch the students 00:19:15.600 --> 00:19:19.600 sort of not, not be too sure how they were going to do that 00:19:19.600 --> 00:19:22.480 and so really giving them the permission to go, just whatever you're doing, like 00:19:22.480 --> 00:19:26.000 literally what you are saying or thinking or the point in the math that 00:19:26.000 --> 00:19:28.320 you're at. And it was interesting to watch them 00:19:28.320 --> 00:19:34.080 start to record because as they were recording they were again 00:19:34.080 --> 00:19:37.200 right away giving themselves that feedback. They were listening to each 00:19:37.200 --> 00:19:39.039 other's record, talking about the recording, 00:19:39.039 --> 00:19:42.720 having their flip grid sort of feed back to them reflect back to them and they 00:19:42.720 --> 00:19:45.520 were saying, they were making conjectures about their 00:19:45.520 --> 00:19:48.320 own thinking, um they realized some of them that they had 00:19:48.320 --> 00:19:50.960 some misconceptions they needed to go back and clarify 00:19:50.960 --> 00:19:55.200 they wanted to use a tool because they realized what they were recording 00:19:55.200 --> 00:19:58.559 wasn't really convincing enough or communicating clearly enough, 00:19:58.559 --> 00:20:02.080 representing clearly enough the math they were trying to 00:20:02.080 --> 00:20:05.600 show. Ao you can see from the messiness of the chart paper 00:20:05.600 --> 00:20:09.600 of these students that they were going back and forth in that recording process 00:20:09.600 --> 00:20:14.720 which was extremely powerful for them and for me to hear that and then in the 00:20:14.720 --> 00:20:18.960 end when they felt they were complete or they felt they were confident to 00:20:18.960 --> 00:20:21.360 share their work they recorded again at the end 00:20:21.360 --> 00:20:25.280 and the act of them walking through and watching the beginning, the middle, and the 00:20:25.280 --> 00:20:28.159 end was really interesting because they started making comments 00:20:28.159 --> 00:20:32.080 right away on oh at the beginning I wasn't I thought this for sure but 00:20:32.080 --> 00:20:35.039 now that I've come to the end of this particular surface area problem, I 00:20:35.039 --> 00:20:37.679 realized that I wasn't calculating the surface area 00:20:37.679 --> 00:20:42.320 for missing steps for example. And it was extremely powerful to watch them go 00:20:42.320 --> 00:20:46.640 through that process. And I really hope that there was some 00:20:46.640 --> 00:20:53.280 retention there for them as well. So "Which one doesn't belong". I really 00:20:53.280 --> 00:20:56.960 also and like. "Convince me that". And I really like 00:20:56.960 --> 00:21:01.760 "Convince me that" because it it forces us to use reason and prove. 00:21:01.760 --> 00:21:07.360 The reason why I like reason and prove is and "Convince me that" and yes they're 00:21:07.360 --> 00:21:10.960 best done together at least even if individually they're 00:21:10.960 --> 00:21:13.280 thinking a little bit on their own but sharing together is because 00:21:13.280 --> 00:21:16.559 "Convince me thats" force you to use math to prove your answer. 00:21:16.559 --> 00:21:20.240 In "Which one doesn't belong" you could justify which one doesn't belong 00:21:20.240 --> 00:21:24.080 without necessarily any math strategies which is which is great because it's the 00:21:24.080 --> 00:21:26.880 act of justifying, it's the acts of thinking and communicating. 00:21:26.880 --> 00:21:30.960 So "Convince me thats" are really powerful and the students really quickly realize 00:21:30.960 --> 00:21:32.960 the more convinced they are, so they actually bring in 00:21:32.960 --> 00:21:38.400 some of the math. And they're going to come up with reasons 00:21:38.400 --> 00:21:40.159 but they're going to start digging for more. 00:21:40.159 --> 00:21:44.320 Again this natural intuitiveness to want to go back and keep going 00:21:44.320 --> 00:21:49.520 comes back with these sort of metacognitive thinking tasks that happen 00:21:49.520 --> 00:21:52.960 that have the ability to reflect while i'm doing the math 00:21:52.960 --> 00:21:55.600 and especially with some of these technology tools. When I'm looking at a 00:21:55.600 --> 00:21:58.159 shared slide of my work and my peers work 00:21:58.159 --> 00:22:01.919 or when i'm watching myself in a flipgrid or any sort of sort of video 00:22:01.919 --> 00:22:05.039 piece where I can see how I've come from one point to 00:22:05.039 --> 00:22:07.520 another. 00:22:07.919 --> 00:22:11.760 So I'm going to talk a little bit more about a class I did with some two grade 00:22:11.760 --> 00:22:15.600 six classes and we had some great space. The learning space 00:22:15.600 --> 00:22:18.000 really helps which was really beneficial for us. 00:22:18.000 --> 00:22:20.320 We had lots of white boards and different tools 00:22:20.320 --> 00:22:24.000 and talk a little bit about the "Convince me's" that we did today 00:22:24.000 --> 00:22:27.919 on this day and talk a little bit about the students response, 00:22:27.919 --> 00:22:32.000 the students thinking around this math. So here are some "Convince me that's" that 00:22:32.000 --> 00:22:35.120 we did with the students the two grade six classes. 00:22:35.120 --> 00:22:38.880 The first time I heard of "Convince me that" was on Twitter 00:22:38.880 --> 00:22:45.200 and the website that I was inspired by what is by Daniel Kaufmann and 00:22:45.200 --> 00:22:48.480 Chris McCaffrey and again in the presenter notes you're 00:22:48.480 --> 00:22:53.760 going to see the live links to the slide. I also have dabbled in making up 00:22:53.760 --> 00:22:57.280 my own. So the teachers that of the class I 00:22:57.280 --> 00:23:00.320 was working with in an educational technology role, so we 00:23:00.320 --> 00:23:03.600 were examining shared Google slides and flipgrid and we were using 00:23:03.600 --> 00:23:07.280 math to facilitate that are around measurement. 00:23:07.280 --> 00:23:12.159 So I'm just going to flash through these here and 00:23:12.480 --> 00:23:15.520 let you see sort of what the students were working on. 00:23:15.520 --> 00:23:23.200 They could choose anyone they wanted and they were using this planner which I 00:23:23.200 --> 00:23:27.120 I really sort of liked because um they could choose how they wanted to 00:23:27.120 --> 00:23:31.039 show their work. Which one they were going to do. 00:23:31.039 --> 00:23:35.600 And we talked a lot about sort of what kind of 00:23:35.600 --> 00:23:38.799 debate stems they were going to use to start their "Convince me that". 00:23:38.799 --> 00:23:42.159 And we talked about how in the middle of this of your 00:23:42.159 --> 00:23:45.679 "Convincing me that", you're going to have to really start giving some proof here 00:23:45.679 --> 00:23:52.080 and to wrap up your final thoughts. It's interesting I had the students sort 00:23:52.080 --> 00:23:55.520 of stop and pause and they came up with these on their own 00:23:55.520 --> 00:23:58.640 just based on them going through a "Convince me that" and 00:23:58.640 --> 00:24:01.039 then talking about what really worked for them. 00:24:01.039 --> 00:24:04.320 So I'll let you sort of look through this list here. Again you have 00:24:04.320 --> 00:24:08.159 access to this slide deck as well, linked in 00:24:08.159 --> 00:24:11.600 the OAME presentation slide deck I'm presenting on. 00:24:11.600 --> 00:24:15.279 And I really like their midpoint. You know another way to look at this is, this 00:24:15.279 --> 00:24:17.520 is the math we this is like the math we did. So they're 00:24:17.520 --> 00:24:21.279 making connections here and my favorite is we're changing our mind based on new 00:24:21.279 --> 00:24:24.240 information. Ultimately that is sort of my goal that 00:24:24.240 --> 00:24:27.760 students are always open to changing their minds, to changing 00:24:27.760 --> 00:24:31.200 their math trajectory, based on what's happening around them 00:24:31.200 --> 00:24:34.480 with the math. So these were some of the tasks that 00:24:34.480 --> 00:24:38.480 those students were doing. And you can see from the photos there 00:24:38.480 --> 00:24:41.679 was palpable engagement. The students were 00:24:41.679 --> 00:24:46.240 talking and talking. And it was just amazing to hear them ask 00:24:46.240 --> 00:24:48.559 each other "Are you sure?" "What do you think?" "I don't 00:24:48.559 --> 00:24:52.949 know if that was strong enough. I think we could come up with another reason." 00:24:52.949 --> 00:24:55.200 And recording and revisiting their slides. 00:24:55.200 --> 00:24:59.200 It was just really powerful to see and hear it. 00:24:59.200 --> 00:25:04.559 So again the two technology tools that I used and that I feel are really great 00:25:04.559 --> 00:25:08.400 for capturing that mid-point learning are flipgrid. Just 00:25:08.400 --> 00:25:11.360 because it records what students think and it reflects back at them their 00:25:11.360 --> 00:25:15.200 their thinking. And Google slides especially in that shared 00:25:15.200 --> 00:25:20.799 um slide feature where multiple students are working on one slide deck. Please 00:25:20.799 --> 00:25:24.559 feel free to contact me if you would like more information on 00:25:24.559 --> 00:25:28.720 how to set that up. Flipgrid is free. They have a great 00:25:28.720 --> 00:25:31.600 website with a lot of information on how to get 00:25:31.600 --> 00:25:35.360 started and I'm sure there's somebody in your school board who will be able to 00:25:35.360 --> 00:25:37.520 assist you with that. And google slides is a 00:25:37.520 --> 00:25:40.960 G suite tool that many of us have access to. So again 00:25:40.960 --> 00:25:45.120 something that is simple but really powerful. 00:25:45.120 --> 00:25:48.880 And I already walked you through the students coming up with their debate 00:25:48.880 --> 00:25:52.320 stem. So this is just another "Convince me that". It was a different class with the 00:25:52.320 --> 00:25:57.679 odd and even numbers. And their thinking around that 00:25:57.679 --> 00:26:01.279 uh which we saw earlier in the presentation. Again these will be linked 00:26:01.279 --> 00:26:05.679 in the bottom. So I actually sent a Google form 00:26:05.679 --> 00:26:09.279 to the students and asked them what they thought 00:26:09.279 --> 00:26:12.320 about thinking during the process of math. 00:26:12.320 --> 00:26:15.679 So the question I asked was "Did you change your mind about your math as you 00:26:15.679 --> 00:26:19.440 worked?" So I wondered if the "Convince me that" 00:26:19.440 --> 00:26:22.720 or the tech tool is helping that. And it's really great that many of the 00:26:22.720 --> 00:26:26.320 students said yes um they did thinking and reconsidering 00:26:26.320 --> 00:26:29.679 for their math worked. Maybe not as many as I wanted to, not 00:26:29.679 --> 00:26:32.880 really but still a a great just to hear the 00:26:32.880 --> 00:26:36.480 students notice that about themselves. And another 00:26:36.480 --> 00:26:39.840 thing was "Did the tool help you explain your math?" So the tools being flipgrid 00:26:39.840 --> 00:26:43.440 and Google slides. And I like to see that the four and fives 00:26:43.440 --> 00:26:46.559 are at the higher end in terms of helping them explain their 00:26:46.559 --> 00:26:50.240 thinking which was really a great way for them to represent 00:26:50.240 --> 00:26:53.360 what they were working on. And I really did notice that students were changing 00:26:53.360 --> 00:26:56.559 their representations because they were really considering 00:26:56.559 --> 00:26:59.440 their audience who was listening to their math and who was going to be 00:26:59.440 --> 00:27:03.520 trying to get understanding out of their math thinking. 00:27:04.320 --> 00:27:08.000 So to close up, in my experience if students are talking out loud about 00:27:08.000 --> 00:27:10.240 their math and are being encouraged to talk through 00:27:10.240 --> 00:27:12.960 their thinking they will naturally carry themselves through the process 00:27:12.960 --> 00:27:17.679 expectations and in turn explore math with richness and ideally 00:27:17.679 --> 00:27:22.240 metacognition. Really becoming aware of their thinking as they're doing the 00:27:22.240 --> 00:27:24.559 math. 00:27:27.919 --> 00:27:31.520 Thank you so much for again taking the time 00:27:31.520 --> 00:27:37.120 out of your day to be here with me. I'm really really happy that you decided to 00:27:37.120 --> 00:27:41.120 come and join me. Thank you for being part of my first OAME talk. 00:27:41.120 --> 00:27:45.520 Again, I am reachable at my email 00:27:45.520 --> 00:27:49.760 and I am reachable on Twitter and please feel free to 00:27:49.760 --> 00:27:53.520 check out my blog at any time and ask me questions. 00:27:53.520 --> 00:27:58.399 Snd don't forget to take that bitly and type it in so that you can take a copy 00:27:58.399 --> 00:28:02.000 of this slideshow with some of the links that I provided 00:28:02.000 --> 00:28:07.120 in there if you feel that would help you. Have a great time during the rest of 00:28:07.120 --> 00:28:10.399 your OAME sessions. I'm sure you're going to learn lots, 00:28:10.399 --> 00:28:14.720 think about lots and I'm hoping to hear from you 00:28:14.720 --> 00:28:18.399 and your thoughts and thinkings about midpoint math 00:28:18.399 --> 00:28:25.200 thinking. Thank you again.