WEBVTT Kind: captions Language: en 00:00:00.860 --> 00:00:08.040 Hello everyone and welcome to OAME's In Focus Virtual Conference. Today we will be 00:00:08.040 --> 00:00:12.450 talking about equity in the early years and this session was recorded in May 2020. 00:00:12.450 --> 00:00:20.789 My name is Marcia Bumbury and my partner is Lisa Rossiter-Thornton. 00:00:20.789 --> 00:00:29.910 So we started working together three years ago and I'll let 00:00:29.910 --> 00:00:35.399 Marcia explain how we met. Yes so as Lisa said three years ago I 00:00:35.399 --> 00:00:41.340 actually went to an ETFO conference in Niagara Falls and one of the guest 00:00:41.340 --> 00:00:47.250 speakers spoke about math kits and she was from British Columbia. And in these 00:00:47.250 --> 00:00:54.239 math kits were rich picture books along with math tools, manipulatives, and 00:00:54.239 --> 00:00:58.140 different materials. And together you would set up a provocation or an 00:00:58.140 --> 00:01:02.460 invitation for children to engage in. And I thought that was such a great idea. So 00:01:02.460 --> 00:01:10.799 I brought it back with me and I proposed it to my superintendent at the time and did 00:01:10.799 --> 00:01:16.229 a proposal and she connected Lisa and I together and from there we created this project. 00:01:16.229 --> 00:01:23.369 And it has flourished and many schools are using the math kits and we're very excited to be 00:01:23.369 --> 00:01:30.930 talking about math today with you. So we're just gonna go over the guiding 00:01:30.930 --> 00:01:34.950 questions of our presentation today. Marcia. 00:01:34.950 --> 00:01:41.390 Yes so the guiding questions. The first one is: What is pedagogical documentation? 00:01:41.390 --> 00:01:48.149 How does pedagogical documentation interrupt bias and professional practice? What is 00:01:48.149 --> 00:01:53.970 the impact of bias when left unexamined particularly in early years math? 00:01:53.970 --> 00:01:58.020 What does high expectations for our students in math look, sound, and feel 00:01:58.020 --> 00:02:04.800 like? Emphasizing multiple entry points for students; documenting evidence of 00:02:04.800 --> 00:02:09.930 students learning; considering next steps for students mathematical learning. So 00:02:09.930 --> 00:02:15.420 essentially there are creative ways, Ontario educators are finding creative 00:02:15.420 --> 00:02:20.490 and lasting ways to first of all share, create shared understanding. Celebrate 00:02:20.490 --> 00:02:24.330 the rights of the individual learner. Recognize student ownership of knowledge. 00:02:24.330 --> 00:02:29.670 And actualize shared responsibility. And really thinking about providing voice 00:02:29.670 --> 00:02:35.340 for everyone learning. And that includes the students of course but the teachers 00:02:35.340 --> 00:02:41.190 as well as early childhood educators and other educators that are involved with 00:02:41.190 --> 00:02:45.990 the learning in the classroom and of course families. Some guiding questions 00:02:45.990 --> 00:02:51.150 that we pulled out of the capacity-building series. So in what ways 00:02:51.150 --> 00:02:57.270 is pedagogy broader than teaching? What makes documenting pedagogical? And how 00:02:57.270 --> 00:03:01.380 does pedagogical documentation result in creative responsiveness to student 00:03:01.380 --> 00:03:06.570 learning? So these guiding questions are great and we hope that you will be 00:03:06.570 --> 00:03:09.750 able to kind of see them disperesed throughout our presentation as we move on. 00:03:09.750 --> 00:03:18.150 So guiding questions that demonstrate rigor of pedagogical documentation. 00:03:18.150 --> 00:03:23.040 So oftentimes when you are observing children playing if you are not thinking 00:03:23.040 --> 00:03:27.930 for example about the mathematical behaviors that they're representing. you 00:03:27.930 --> 00:03:31.950 may not think that there's a lot to see in their play when in fact there is 00:03:31.950 --> 00:03:38.190 quite a bit. So this again is from the revised capacity-building series on 00:03:38.190 --> 00:03:45.500 pedagogical documentation and it really outlines the different things we need to 00:03:45.500 --> 00:03:53.120 do to add rigor to our pedagogical documentation. And these reflective 00:03:53.120 --> 00:03:57.290 questions help you do that. 00:03:58.519 --> 00:04:02.550 So implications, what are the implications for deepening the learning? 00:04:02.550 --> 00:04:06.990 What additional information is needed? what actions will be taken as a result 00:04:06.990 --> 00:04:09.459 for the learner, educator, the school and/or the 00:04:09.459 --> 00:04:13.629 community? How will we differentiate teaching and learning based on this new 00:04:13.629 --> 00:04:17.739 learning? If we are adjusting our teaching for a small group of students 00:04:17.739 --> 00:04:23.139 we know well, how will this impact our teaching for the whole class? So we want 00:04:23.139 --> 00:04:26.860 to just point this one out in particular because it does really relate to equity. 00:04:26.860 --> 00:04:33.240 Students bring their lived experience from all walks of life to our community 00:04:33.240 --> 00:04:38.050 essentially our classrooms. And when it comes to numeracy, when it comes to 00:04:38.050 --> 00:04:42.580 literacy, we really want to make sure we have our high expectations around what 00:04:42.580 --> 00:04:46.930 we know they're bringing, knowing that they're competent and capable, and then 00:04:46.930 --> 00:04:52.479 bringing the the learner, the families, ourselves to next steps in learning so 00:04:52.479 --> 00:04:59.590 that we can move our students learning ahead and forward. Take this one "Multiplication 00:04:59.590 --> 00:05:04.720 is for White People". In the video you'll see Dr. Lisa Delpit talking 00:05:04.720 --> 00:05:09.460 about why she named her book "Multiplication is for White People - 00:05:09.460 --> 00:05:13.419 Raising Expectation for Other People's Children". And the reason why she did this 00:05:13.419 --> 00:05:18.550 was because she was working with a young black student and when they 00:05:18.550 --> 00:05:24.010 started doing math and they started working together the student said to her 00:05:24.010 --> 00:05:28.240 well this exact phrase: "Multiplication is for white people. Why are you teaching me this?" 00:05:28.240 --> 00:05:36.220 And so I think what's important to note here is that as educators how 00:05:36.220 --> 00:05:41.770 students are internalizing our biases, how they are seeing themselves in the 00:05:41.770 --> 00:05:48.660 classroom, is it's very crucial for us to understand and to reflect deeply upon 00:05:48.660 --> 00:05:54.550 because if we don't, we might have a child in our class that thinks of 00:05:54.550 --> 00:05:58.270 themselves as a poor mathematician when in fact they are quite competent, quite 00:05:58.270 --> 00:06:04.180 capable and for whatever reason they have internalized oppressive thoughts 00:06:04.180 --> 00:06:09.430 about how they are as a mathematician. So this book is fantastic. It doesn't only 00:06:09.430 --> 00:06:12.550 just talk about mathematical, there's some mathematical ideas but it really 00:06:12.550 --> 00:06:18.039 talks about how we as educators can view ourselves and take certain steps to 00:06:18.039 --> 00:06:23.380 being reflective practitioners and making sure that we're really having 00:06:23.380 --> 00:06:27.370 high expectations for all students especially students that are underserved 00:06:27.370 --> 00:06:36.910 in our classrooms. So the article or the capacity building series again has 00:06:36.910 --> 00:06:42.639 this as one of its final tips to getting started. So think about how you're going 00:06:42.639 --> 00:06:46.030 to communicate the learning that is captured in pedagogical documentation. 00:06:46.030 --> 00:06:50.020 How will you collaborate with students, families, and colleagues in the 00:06:50.020 --> 00:06:53.919 communication of learning in the documentation? So together you're 00:06:53.919 --> 00:06:59.530 creating an understanding and building knowledge together about their children 00:06:59.530 --> 00:07:06.880 and your students and how they are competent capable mathematicians. So the 00:07:06.880 --> 00:07:10.330 next slides we show you, we're going to show you pedagogical documentation of 00:07:10.330 --> 00:07:15.280 work that we have done in partnership with families and colleagues and 00:07:15.280 --> 00:07:25.169 students and we are going to be bringing it back to really capturing the 00:07:25.169 --> 00:07:31.300 wonderful mathematical ideas of students from all walks of life in particular 00:07:31.300 --> 00:07:40.620 in kindergarten. Thank you. So here we can see a slide and we're talking about 00:07:40.620 --> 00:07:45.130 creating an environment that is inclusive, fair, and equitable. 00:07:45.130 --> 00:07:51.010 And one that has high expectations will then lead to student success. So as you can 00:07:51.010 --> 00:07:57.310 see displayed in this classroom here, I have materials that reflect the students 00:07:57.310 --> 00:08:02.260 who are in my classroom but what I'm putting these out I'm not only thinking 00:08:02.260 --> 00:08:05.470 about the students who are in my class because you may be in a classroom that 00:08:05.470 --> 00:08:12.130 is not very diverse but we have to think of the wider society and how we can 00:08:12.130 --> 00:08:17.860 represent the society that we live in. It's a classroom where we see students 00:08:17.860 --> 00:08:23.889 are working together whether it's two students together or a whole group. And a 00:08:23.889 --> 00:08:28.930 lot of opportunities for students to show their imagination 00:08:28.930 --> 00:08:33.430 and also for many students to have different entry points into the play. 00:08:33.430 --> 00:08:38.410 We don't want to limit access to everyone in the classroom. 00:08:38.410 --> 00:08:45.430 So providing many different materials that are open to all in the room. And so when 00:08:45.430 --> 00:08:50.140 we look at this and think about high expectations we now need to also think 00:08:50.140 --> 00:08:56.740 about the curriculum documents and the importance of knowing 00:08:56.740 --> 00:09:03.400 the content and also referring back to the curriculum documentation when we're 00:09:03.400 --> 00:09:08.020 thinking about pedagogical documentation and setting up our students for success. 00:09:08.020 --> 00:09:17.380 So here you can see that there are some provocations and invitations set up and 00:09:17.380 --> 00:09:23.590 the two tables are connected to number sense and numeration and the front table is 00:09:23.590 --> 00:09:29.530 connected to patterning and algebra. And here I have set up some rich picture 00:09:29.530 --> 00:09:34.420 books that sometimes I've read or may not have been read before but it's 00:09:34.420 --> 00:09:38.950 available for students to look through as you're engaging in the materials on 00:09:38.950 --> 00:09:44.320 the table. And of course although it says you know patterning and algebra for that 00:09:44.320 --> 00:09:49.660 first table, it is not limited to that. And it's quite amazing when you sit back 00:09:49.660 --> 00:09:58.810 and watch and see what students do with the materials that are laid out. 00:09:58.810 --> 00:10:05.830 In here at this next provocation it's related to geometry and spatial sense there are 00:10:05.830 --> 00:10:10.810 some pattern blocks that are available and also geoboards with elastics and 00:10:10.810 --> 00:10:15.670 it's open-ended. It's not necessarily that the students are going to be 00:10:15.670 --> 00:10:21.930 creating just shapes. They could be measuring as the measurement 00:10:21.930 --> 00:10:28.840 documentation sorry curriculum document is also posted. But we're looking and 00:10:28.840 --> 00:10:33.970 seeing and as an educator I have the knowledge of the math. I'm watching to 00:10:33.970 --> 00:10:39.490 see what the children are doing and knowing when to step in to name the math 00:10:39.490 --> 00:10:46.360 and asking them those questions that are not yes and no questions or questions 00:10:46.360 --> 00:10:50.590 that I'm assuming what they are doing. So I wouldn't come to this table 00:10:50.590 --> 00:10:56.110 and be like, "Oh did you make a flower with those triangles?" I would say to the 00:10:56.110 --> 00:11:01.890 students, "Tell me about what you've done here." or "I've noticed that you used a 00:11:01.890 --> 00:11:07.300 hexagon. Why did you choose to use that?" And so that is getting them to show 00:11:07.300 --> 00:11:12.750 their thinking and for me I am documenting what they are saying and 00:11:12.750 --> 00:11:18.550 part of the pedagogy when we say pedagogical documentation is taking this 00:11:18.550 --> 00:11:23.680 information and deciding where does the student need to go next. How can I take 00:11:23.680 --> 00:11:34.710 them along the continuum? And here again you can see some other provocations and 00:11:34.710 --> 00:11:41.620 invitations that are set up. And and when we use intentional materials, I'm not 00:11:41.620 --> 00:11:45.910 necessarily telling the students what to do with the materials but the materials 00:11:45.910 --> 00:11:52.540 I have chosen are intentional so that I'm leading them in a way in a 00:11:52.540 --> 00:12:00.090 mathematical way and just seeing what they do with what's provided for them. 00:12:00.150 --> 00:12:09.520 And here you can see another example related to patterning and algebra and the 00:12:09.520 --> 00:12:15.630 great picture books as well. And one thing I'd like to point out too is that 00:12:15.630 --> 00:12:21.610 some of the books have been read ahead of time or others have not been read and 00:12:21.610 --> 00:12:27.520 that you can revisit books many times throughout the year. It's not that we see 00:12:27.520 --> 00:12:33.490 it one time and then put it away. We continuously are revisiting the 00:12:33.490 --> 00:12:37.930 different strands throughout the school year and as Lisa said looking at those 00:12:37.930 --> 00:12:49.600 conceptual understandings and how they're related to the expectations. 00:12:49.600 --> 00:12:55.450 And here is another provocation related to geometry and spatial sense and 00:12:55.450 --> 00:13:00.430 along with measurement and the geoboards and elastics are there for the 00:13:00.430 --> 00:13:05.399 students to enter and it's available you know in a 00:13:05.399 --> 00:13:09.580 full-day kindergarten class. We have JKs and SKs and it's not that there's 00:13:09.580 --> 00:13:15.430 necessarily, we don't have activities just for JKs and just for SKs. It's many 00:13:15.430 --> 00:13:20.440 entry points are available for all students within the class and you know 00:13:20.440 --> 00:13:25.620 they're learning from each other and the mathematical language that takes place 00:13:25.620 --> 00:13:32.640 when they're engaged with the materials really shows their mathematical thinking. 00:13:32.640 --> 00:13:40.410 We're bringing it back now to really when we start with relationship first 00:13:40.410 --> 00:13:45.940 and this is one of the parts that is so important with pedagogical documentation 00:13:45.940 --> 00:13:49.540 because we're building knowledge together. We're valuing all knowledge 00:13:49.540 --> 00:13:55.720 that is brought to the learning space. It's something to to really understand 00:13:55.720 --> 00:14:02.740 when you are, when you are thinking about how you're creating learning 00:14:02.740 --> 00:14:09.190 environment that has a foundation of equity in it as well. So reciprocal 00:14:09.190 --> 00:14:12.310 relationships are cultivated through collaboration conversations using 00:14:12.310 --> 00:14:17.890 pedagogical documentation. Perspectives of children and youth, their 00:14:17.890 --> 00:14:21.490 parents and guardians, educators and the broader community, can be brought 00:14:21.490 --> 00:14:25.690 into these conversations for the purpose of furthering learning and connecting 00:14:25.690 --> 00:14:36.399 learners to their world. So here is an example of students engaging with the 00:14:36.399 --> 00:14:41.950 materials and this, what you're seeing here also relates to the counting 00:14:41.950 --> 00:14:48.640 principles. So the very first picture a student was grabbing handfuls of jams 00:14:48.640 --> 00:14:52.750 and one student said "That's not how you count. You should be taking one at a time." 00:14:52.750 --> 00:14:57.490 And so we had a discussion about the different ways that you could count. 00:14:57.490 --> 00:15:03.100 And so we realized she was doing or she said I'm taking one handful, two handfuls, 00:15:03.100 --> 00:15:10.089 three handfuls. So listening to and knowing the students, giving them a 00:15:10.089 --> 00:15:12.880 chance to explain their thinking, we realize that there are many different 00:15:12.880 --> 00:15:15.880 ways to count. And the other pictures are showing 00:15:15.880 --> 00:15:20.470 that you can count on your own or with a partner. And that there are many 00:15:20.470 --> 00:15:32.020 different ways to count the different loose parts. And here a student has the 00:15:32.020 --> 00:15:37.870 opportunity to, they were materials out and they did many different things with them. 00:15:37.870 --> 00:15:43.000 So when I went over to take a look I took a picture and asked them to explain 00:15:43.000 --> 00:15:47.230 all the different things that they did do. You'll see on the next slide that 00:15:47.230 --> 00:15:52.500 each part was labeled. What they did do. 00:15:52.950 --> 00:15:58.030 So at the top they said they made a pattern. You could see the pink orange 00:15:58.030 --> 00:16:05.920 pink orange. They just showed numbers by the numerals of 4 9 6 and also they 00:16:05.920 --> 00:16:10.600 created a number line and used dominoes. So many different things happening on 00:16:10.600 --> 00:16:18.940 this one section of the cork board but once I was able to engage with the 00:16:18.940 --> 00:16:24.010 student and listen to what they had to say I could see wow a lot of different 00:16:24.010 --> 00:16:28.300 thinking has happened. They've touched on patterning. They've touched a number 00:16:28.300 --> 00:16:32.980 sense and numeration. Many different things are happening here. 00:16:32.980 --> 00:16:44.890 And so they were showing their understanding this way. And here we have a student, 00:16:44.890 --> 00:16:53.020 she was a first year JK student and she had put some beads down on a five 00:16:53.020 --> 00:16:58.360 frame and I asked her "How many do you have?" And she had already counted one, two, 00:16:58.360 --> 00:17:04.030 three. And when I asked her how many she had she had to go back and count from 00:17:04.030 --> 00:17:09.550 the beginning one, two, three instead of just saying I had three or I 00:17:09.550 --> 00:17:15.010 counted three. And we're gonna come back to this student again later and this is 00:17:15.010 --> 00:17:22.209 and we have her here because it shows that I really have gotten to know the 00:17:22.209 --> 00:17:26.680 student and know where to where do I need to take her next. And through my 00:17:26.680 --> 00:17:32.530 pedagogical documentation witness how far she has come within her 00:17:32.530 --> 00:17:44.970 first year in kindergarten. And here we have Isaiah and he's going to explain 00:17:44.970 --> 00:17:49.380 what he knows about the number five. 00:17:49.380 --> 00:17:54.300 I am showing 5 in different ways. 00:17:54.300 --> 00:18:01.300 And here is 5. 00:18:01.300 --> 00:18:07.300 This is a tenframe. 00:18:14.300 --> 00:18:16.300 This is a dice. 00:18:16.300 --> 00:18:18.300 Can you show me 5 on the dice? 00:18:25.300 --> 00:18:28.300 And what's this? 00:18:28.300 --> 00:18:30.300 These are all 5. 00:18:30.300 --> 00:18:39.300 On a five frame, what is that telling us? I noticed something. How many green ones do you have? 00:18:39.300 --> 00:18:41.300 One, two, three. 00:18:41.300 --> 00:18:43.300 How many yellow ones do you have? 00:18:43.300 --> 00:18:45.300 One, two. 00:18:45.300 --> 00:18:47.300 What does that tell us? 00:18:47.300 --> 00:18:50.600 3 green and 2 yellow. 00:18:50.600 --> 00:18:52.600 Is how many? 00:18:52.600 --> 00:18:54.600 Five. 00:18:54.600 --> 00:18:58.300 Five. Look at that. 00:18:58.710 --> 00:19:02.899 Thank you. So that Isaiah and he was able to explain all the 00:19:02.899 --> 00:19:08.809 different ways that he knows to show the number-5. And throughout the year we as a 00:19:08.809 --> 00:19:14.960 whole group, in small groups, we discuss numbers and through their play, they are 00:19:14.960 --> 00:19:20.990 able to show their learning. And so the next slide will show how Isaiah has 00:19:20.990 --> 00:19:24.980 taken what he learned about the number five, composing and decomposing numbers, 00:19:24.980 --> 00:19:32.059 and related to a story that we read in class. And the story was about Scott who 00:19:32.059 --> 00:19:39.080 worked in a fruit store and selling raspberries and blueberries. And we read 00:19:39.080 --> 00:19:42.950 through the story and it's related to the ten frame and different ways to 00:19:42.950 --> 00:19:48.770 compose ten. And what I did after was just put materials out on the table and 00:19:48.770 --> 00:19:54.740 Isaiah recreated his own store and this is what he had to say. "At my store I put 00:19:54.740 --> 00:19:59.419 out some blueberries and raspberries. And one customer said "Could I please have 00:19:59.419 --> 00:20:04.669 two raspberry and three blueberries?" The next customer said "lots of raspberries" 00:20:04.669 --> 00:20:10.279 but he changed his mind to take ten. I said "no you can take up to three or four 00:20:10.279 --> 00:20:18.140 baskets. The customer took four and four basically eight. And so quickly right 00:20:18.140 --> 00:20:23.360 away he knew four and four was eight. And on the picture you can see he set up his 00:20:23.360 --> 00:20:29.500 cups which were his baskets of blueberries and raspberries and also had 00:20:29.500 --> 00:20:36.080 a ten frame available to help him if he needed to compose and decompose 00:20:36.080 --> 00:20:43.490 the number up to number ten. So one of the things we like is being able to have 00:20:43.490 --> 00:20:47.600 the actual expectations with the conceptual understanding. So just a 00:20:47.600 --> 00:20:51.559 simple idea of measurement as using different tools to measure different 00:20:51.559 --> 00:20:58.610 things and how does that relate to actual expectations that you have to 00:20:58.610 --> 00:21:04.340 evaluate. Well here we are again with our pedagogical documentation. 00:21:04.340 --> 00:21:09.770 This particular educator was looking at this question "What tools can we use to 00:21:09.770 --> 00:21:13.930 measure length?" And this was they asked it in this way. 00:21:13.930 --> 00:21:20.860 They used different kinds of documentation to do that. And then 00:21:20.860 --> 00:21:27.970 they also co-created this anchor chart to demonstrate the ways in which you can 00:21:27.970 --> 00:21:32.170 use different tools to measure length. And so you'll see here their anchor 00:21:32.170 --> 00:21:37.870 chart and also two different materials that they used. And what's interesting is 00:21:37.870 --> 00:21:43.270 we move forward in math and we know that it builds on top, you know every year 00:21:43.270 --> 00:21:47.200 there's new concepts and they build one on top of the other. You can really see 00:21:47.200 --> 00:21:53.680 how a student could then perhaps extend their understanding of the relationship 00:21:53.680 --> 00:22:01.660 between the popsicles to measure the boa and then the little paper clips or I think they're 00:22:01.660 --> 00:22:05.260 clipits or the linkits to measure the boa. And then you could have 00:22:05.260 --> 00:22:09.340 conversations around "Okay well how many popsicles does it take? How many linkits 00:22:09.340 --> 00:22:14.890 does it take? What's the relationship of size or length between the two?" And then 00:22:14.890 --> 00:22:21.190 you're going to be getting more focus on proportional reasoning and then also 00:22:21.190 --> 00:22:30.280 fractional thinking. So you can see that rich deep complex ideas come out 00:22:30.280 --> 00:22:34.780 naturally even with our youngest learners. Again here one of the 00:22:34.780 --> 00:22:38.710 conceptual understandings we like to point out is quantity can be represented 00:22:38.710 --> 00:22:43.630 in many ways. The slides that Marcia already showed you have that very well 00:22:43.630 --> 00:22:51.310 that concept very well pointed out. Here what's interesting is a student is using 00:22:51.310 --> 00:22:57.310 a balance to show the quantity of six. But what is interesting here to note is 00:22:57.310 --> 00:23:05.650 that three, the notation that the student has written here. And this is where 00:23:05.650 --> 00:23:09.700 we as educators have to pay attention very closely and you can begin to see 00:23:09.700 --> 00:23:14.380 the expectations or the curriculum expectations how they connect all the 00:23:14.380 --> 00:23:19.200 way from kindergarten all the way to grade nine. So if a student is 00:23:19.200 --> 00:23:24.460 experimenting with this idea of balance and they're notating it in this way, 00:23:24.460 --> 00:23:28.730 three plus three equals six. We want to be thinking about how we can 00:23:28.730 --> 00:23:32.179 prompt they're thinking to say things like "Well what happens when we only put 00:23:32.179 --> 00:23:38.300 two on one side and we take one off? Will it still be three plus three equals six?" 00:23:38.300 --> 00:23:44.510 And in fact actually the notation for this really is three equals three. 00:23:44.510 --> 00:23:50.660 So when we ask them to take numbers off of, the counters off of the balanced scale 00:23:50.660 --> 00:23:56.179 then we can start to develop and bring their thinking along to be able to see 00:23:56.179 --> 00:24:00.559 how they're annotation might not actually match what they are showing in 00:24:00.559 --> 00:24:04.809 their I guess you could say manipulatives or their use of 00:24:04.809 --> 00:24:11.679 representing their thinking using concrete materials. Here again we have 00:24:11.679 --> 00:24:17.630 notation and we have play happening. So a student has a parking lot and is 00:24:17.630 --> 00:24:22.940 creating a abstract notation or the way that they're representing their thinking 00:24:22.940 --> 00:24:29.300 is using a subtraction sentence if you will. And what we want to be paying 00:24:29.300 --> 00:24:34.580 attention to as educators is, Are they seeing the total part? Are they seeing 00:24:34.580 --> 00:24:38.960 the total whole? And how are they demonstrating that and acting that out 00:24:38.960 --> 00:24:44.210 in their play and how is that and how are they representing that with 00:24:44.210 --> 00:24:51.290 mathematical notation. And here again patterning and algebra the ability to 00:24:51.290 --> 00:24:55.809 recognize and understand patterns is helpful in all aspects of everyday life. 00:24:55.809 --> 00:25:00.800 So this is the conceptual understanding listed in the curriculum document as you 00:25:00.800 --> 00:25:05.480 can see. And these are the ways that they're playing it out. You can see a 00:25:05.480 --> 00:25:10.250 growing pattern happening on the right picture with the stacking of the cups. 00:25:10.250 --> 00:25:16.309 And what's interesting here is there is a repeating pattern happening with this 00:25:16.309 --> 00:25:20.420 particular student. How would this play out in grades seven and eight math? 00:25:20.420 --> 00:25:25.280 So again these essential foundations are happening in kindergarten and how as we 00:25:25.280 --> 00:25:30.500 as educators are noticing and naming them and passing that information along 00:25:30.500 --> 00:25:37.970 to our junior teachers, our intermediate teachers, our primary teachers, to really 00:25:37.970 --> 00:25:43.120 show the competency and the the the capableness of students and their 00:25:43.120 --> 00:25:50.320 mathematical thinking and ideas. Here again data management. We pulled this one 00:25:50.320 --> 00:25:53.680 out. We can collect and organize data in different ways for 00:25:53.680 --> 00:25:59.440 different purposes. And of course you're going to see that the students are just 00:25:59.440 --> 00:26:04.360 sorting here but really this is collecting data. They're sorting sort of 00:26:04.360 --> 00:26:10.440 a typical kindergarten manipulative that you might see in most classrooms. 00:26:10.440 --> 00:26:16.240 And this is how they're showing their understanding of quantity. 00:26:16.240 --> 00:26:24.010 Well they can easily translate that to a graph as well and they can do by it color 00:26:24.010 --> 00:26:28.840 or they might choose a different way to do it by size. 00:26:28.840 --> 00:26:34.060 So the way this one started it was I came in one morning I received my stock 00:26:34.060 --> 00:26:39.550 order and I had all these boxes. And I had the book "Not A Box". So I 00:26:39.550 --> 00:26:45.040 put it out and wanted to see what would happen. What would the students do? And so 00:26:45.040 --> 00:26:50.320 they looked through the book and came across this page that had a building on 00:26:50.320 --> 00:26:55.540 fire and together they decided to build the building using the 00:26:55.540 --> 00:27:01.420 boxes. And it was really interesting to see how they just came together and 00:27:01.420 --> 00:27:07.320 right away got started. They made a list of all the items that they needed and 00:27:07.320 --> 00:27:17.140 got to work right away. And here as they're working, how it relates to 00:27:17.140 --> 00:27:22.900 math. There is geometry that's happening because we were using 3D solids, the 00:27:22.900 --> 00:27:29.110 boxes. They are measuring the paper to know how much paper they needed to put 00:27:29.110 --> 00:27:36.070 onto the boxes. You can see also here some paper towel rolls, so again 3D 00:27:36.070 --> 00:27:41.140 shapes. And as they're working through this, there's collaboration that's 00:27:41.140 --> 00:27:46.720 happening, problem solving, and innovation and a lot of mathematical thinking. 00:27:46.720 --> 00:27:52.660 And again as they kept going they decided to also make a hose to show the water 00:27:52.660 --> 00:27:56.460 coming out. And what's interesting is that they had 00:27:56.460 --> 00:28:00.960 to think about, you can see the student at the back is using two toilet paper 00:28:00.960 --> 00:28:06.480 rolls so that the proportion of the hose matched that of the building that they 00:28:06.480 --> 00:28:17.220 were building as well. And they included a Canadian flag and there you 00:28:17.220 --> 00:28:21.510 know they had to think about the shape of the flag and what goes 00:28:21.510 --> 00:28:28.670 on the flag and where they would put it on their 3D building that they're doing. 00:28:28.670 --> 00:28:35.520 And finally you can see their finished product and together they recreated the 00:28:35.520 --> 00:28:42.480 building on fire and for many days they engaged it with what they created and 00:28:42.480 --> 00:28:48.750 then not only did it stay within the realm of math but it also led into 00:28:48.750 --> 00:28:54.270 creative play, into their imagination, and ideas if they wanted to build something 00:28:54.270 --> 00:29:01.970 else again. Final thoughts. I think just remembering the key points. 00:29:01.970 --> 00:29:07.920 The pedagogical documentation. Really getting to know each and every one of your 00:29:07.920 --> 00:29:15.060 students and setting them up for success and taking them along the continuum in 00:29:15.060 --> 00:29:24.000 the way that is meaningful for them and will bring them to success. Thank you so 00:29:24.000 --> 00:29:27.740 much for watching. Thank you.