WEBVTT Kind: captions Language: en 00:00:01.310 --> 00:00:07.830 Hello everyone and thank you very much for joining our session today regarding 00:00:07.830 --> 00:00:15.630 designing a flexible classroom. My name is Patricia Clark and I am a math 00:00:15.630 --> 00:00:20.369 teacher and department head at Earl of March Secondary School in Kanata and 00:00:20.369 --> 00:00:29.550 I'll be presenting today with my colleague Suzanne Thomas. Hello everyone 00:00:29.550 --> 00:00:34.770 my name is Suzanne Thomas and I also teach at Earl of March Secondary School 00:00:34.770 --> 00:00:38.820 with the Ottawa Carleton District School Board. I also teach in the math 00:00:38.820 --> 00:00:44.789 department and teach grades 9 to 12 with Trish. So thank you for joining us. Today 00:00:44.789 --> 00:00:49.410 we will be looking at designing a flexible classroom as Trish said. And so 00:00:49.410 --> 00:00:56.670 in this presentation we will share our department model and share with you how 00:00:56.670 --> 00:01:01.590 we collaborate and problem-solve in our planning and in our classroom. These two 00:01:01.590 --> 00:01:06.270 skills act as critical components for our program and over the course of this 00:01:06.270 --> 00:01:12.330 presentation we would like to share with you how teachers view collaboration, 00:01:12.330 --> 00:01:18.180 problem-solving based on a questionnaire that we had sent out. What our department 00:01:18.180 --> 00:01:23.270 model looks like. How collaboration and problem-solving occur in our math 00:01:23.270 --> 00:01:29.479 program and provide you with some examples on how we develop lessons and 00:01:29.479 --> 00:01:35.299 go through some specific lessons we have worked through with our students and 00:01:35.299 --> 00:01:45.869 share some insight from our department based on our experience. So moving on to 00:01:45.869 --> 00:01:56.520 our teacher thoughts, this here are the four questions that we had given to our 00:01:56.520 --> 00:02:02.420 colleagues in our questionnaire to ask them what their thoughts were on 00:02:02.420 --> 00:02:06.450 problem-solving and collaboration. So the first question was what does 00:02:06.450 --> 00:02:10.920 problem-solving mean/for in the classroom to you? What does it look like 00:02:10.920 --> 00:02:13.950 sound like? The second question was what are 00:02:13.950 --> 00:02:18.930 barriers to problem-solving? The third question was what does collaboration 00:02:18.930 --> 00:02:24.420 mean/for in the classroom to you? What does it look like and sound like? And the 00:02:24.420 --> 00:02:30.030 fourth question was what are barriers to collaboration? Now our original intent 00:02:30.030 --> 00:02:36.090 was to do this live and ask our participants these questions. So we would 00:02:36.090 --> 00:02:39.870 like you to pause the video at this moment and take a minute to reflect on 00:02:39.870 --> 00:02:46.410 what these questions mean to you and then you can continue on with it 00:02:46.410 --> 00:02:56.989 afterwards. Thank you. Okay so hopefully you had a minute to think about that. 00:02:56.989 --> 00:03:01.019 So here are some of the responses that we received. 00:03:01.019 --> 00:03:11.130 So what does problem-solving mean/for in the classroom to you? So I'm just going 00:03:11.130 --> 00:03:16.340 to read through some of our responses. So the first one here we have is research, 00:03:16.340 --> 00:03:21.329 collaborating with other professionals in the same profession, teaching the same 00:03:21.329 --> 00:03:26.900 subject, teaching different subjects, or different profession, trial-and-error, 00:03:26.900 --> 00:03:33.750 living and learning. Response number two: it sounds like a lot of work that I do 00:03:33.750 --> 00:03:39.680 not have time for. Response number three: seeking input from other teachers, 00:03:39.680 --> 00:03:45.980 brainstorming with students, working through a problem or solution chart, 00:03:45.980 --> 00:03:50.870 everyone gets to list solutions and we go through each solution and evaluate it. 00:03:50.870 --> 00:03:57.239 Number four: creative process, preparation of tools, incubation, illumination, 00:03:57.239 --> 00:04:02.220 performance. And our last response here there are two kinds of problem-solving 00:04:02.220 --> 00:04:07.109 one is learning the learning kind with teachers of students. The other is always 00:04:07.109 --> 00:04:11.540 related to making technology work like problem solving network issues, 00:04:11.540 --> 00:04:16.560 technology issues, budget issues. I don't mean the second half in a negative way 00:04:16.560 --> 00:04:20.549 everyone is trying their best but the most challenging thing I came across is 00:04:20.549 --> 00:04:27.290 managing the problem of solving this. So as you can see a lot of the responses 00:04:27.290 --> 00:04:34.250 have some sort of process involved right. Now we also asked the question around 00:04:34.250 --> 00:04:43.250 barriers to problem-solving. And what we came out with there was at the 00:04:43.250 --> 00:04:50.210 department level we see the concern around equal voice. So people's ego or 00:04:50.210 --> 00:04:57.050 pride or self-confidence hindering the process. Along the same lines we see the 00:04:57.050 --> 00:05:04.850 concern around team members not respecting technology or like sorry 00:05:04.850 --> 00:05:10.060 not not being at the same level of their 00:05:10.270 --> 00:05:14.870 knowledge with the technology or curriculum content or curriculum 00:05:14.870 --> 00:05:22.430 connections. Also the time it takes to collaborate. So finding time for teachers 00:05:22.430 --> 00:05:27.760 to meet and the idea that if you have more teachers the harder it becomes to 00:05:27.760 --> 00:05:34.930 coordinate times. At the classroom level we see concerns around varying skills 00:05:34.930 --> 00:05:41.450 levels. So for example junior grades that are quite full in numbers, we have 00:05:41.450 --> 00:05:46.820 students working below their level and then students working way above grade 00:05:46.820 --> 00:05:51.560 level. We have ELL, special education considerations that we have to take in 00:05:51.560 --> 00:05:59.050 and so the question around also like how do we differentiate a problem enough to 00:05:59.050 --> 00:06:03.170 meet all of their needs and to have entry points for all those different 00:06:03.170 --> 00:06:11.710 types of students. So we have found some of these barriers and concerns do 00:06:11.710 --> 00:06:18.100 transpire and some do not. So we will shed more light on what our department 00:06:18.100 --> 00:06:24.800 feels about these concerns later on in our presentation. So next we'll move on 00:06:24.800 --> 00:06:32.390 to the question around collaboration. So what does collaboration mean/for in the 00:06:32.390 --> 00:06:37.320 classroom to you? So once again I'll read the responses. 00:06:37.320 --> 00:06:44.020 So our first response is with other teachers sometimes casual conversation 00:06:44.020 --> 00:06:48.850 and free brainstorming works best. With students usually structure, guiding 00:06:48.850 --> 00:06:54.520 questions, setting goals for small chunks of time works best. Right now it's one 00:06:54.520 --> 00:06:58.150 person alone at home contributing to projects that could be bigger than 00:06:58.150 --> 00:07:02.980 themselves is our second response. The third response positive vibes, great 00:07:02.980 --> 00:07:09.820 teaching days, good energy, excitement about learning. Number four: I love 00:07:09.820 --> 00:07:13.120 collaborating with other teachers teaching the same class. 00:07:13.120 --> 00:07:16.630 This means meeting once per week to discuss what's what we are going to 00:07:16.630 --> 00:07:21.370 teach, who wants to organize what, what problems we've run into and how we can 00:07:21.370 --> 00:07:26.380 solve those problems. This meeting means creating tests and coming up with 00:07:26.380 --> 00:07:31.780 marking schemes together. This provides flexibility and peace of mind in terms 00:07:31.780 --> 00:07:36.490 of teacher absences. Teaching students how to collaborate. Student work in small 00:07:36.490 --> 00:07:41.680 groups. Students given group assignments and the group needs to figure out the 00:07:41.680 --> 00:07:47.380 solution together and put it on the board. And our final comment here is well 00:07:47.380 --> 00:07:56.100 we do group work and I will have one or two group presentations per a course. 00:07:56.100 --> 00:08:02.980 So here one of the responses we actually really liked was one I think that 00:08:02.980 --> 00:08:09.910 relates to the Covid 19 teaching model of us all teaching at home and that was 00:08:09.910 --> 00:08:15.900 the second response where it talks to an individual's contribute 00:08:15.900 --> 00:08:20.890 contribution sorry to something bigger than themselves and something larger. 00:08:20.890 --> 00:08:27.460 And I think that applies I mean I although this person was saying talking about 00:08:27.460 --> 00:08:31.180 sitting at home and you know in this in this experience, I think that also 00:08:31.180 --> 00:08:39.419 applies to what we see in the classroom where anytime that we collaborate. 00:08:39.419 --> 00:08:46.960 So moving on to some of those challenges around collaboration. Some of them, some 00:08:46.960 --> 00:08:50.819 of the responses were similar to what we saw in problem 00:08:50.819 --> 00:08:56.230 problem-solving. So we had responses around technology, time and personalities 00:08:56.230 --> 00:09:03.100 as well. But a few things that were different here were was the concept 00:09:03.100 --> 00:09:08.230 around members not taking responsibility for their share of the work. So that 00:09:08.230 --> 00:09:14.829 workload piece, A supervisor's philosophy that may not be conducive to 00:09:14.829 --> 00:09:23.019 implementing collaboration. And also the idea of groupthink which you have many 00:09:23.019 --> 00:09:26.470 people are just always working together that sometimes you may not get as many 00:09:26.470 --> 00:09:32.980 fresh ideas so there could be a lack of innovation. Now in the classroom, some of 00:09:32.980 --> 00:09:38.679 the concerns we saw were communication barriers, students fear of the impact on 00:09:38.679 --> 00:09:43.240 their mark when working with others, and members not taking responsibility for 00:09:43.240 --> 00:09:51.129 their share of the work once again. That workload piece. So as I mentioned before 00:09:51.129 --> 00:09:57.249 we have in some of these that's challenges but not all of them. And so 00:09:57.249 --> 00:10:06.790 later on we will discuss our thoughts on what the challenges that we faced are or 00:10:06.790 --> 00:10:16.389 still facing are. And we'll kind of touch on these things here and with that I 00:10:16.389 --> 00:10:22.720 will pass it on to Trish to talk about our department model. Thanks Suzanne. 00:10:22.720 --> 00:10:27.730 So our department model, there's essentially two kind of main areas one of them is 00:10:27.730 --> 00:10:33.459 that we work on course teams and the other is that we cycle or spiral through 00:10:33.459 --> 00:10:40.480 the curriculum expectations. In terms of working on course teams, it's structured 00:10:40.480 --> 00:10:48.759 in such a way that that all teachers who are teaching the same course work 00:10:48.759 --> 00:10:55.749 together. So all teachers teaching grade ten academic math, MCR 3U, MCV, 00:10:55.749 --> 00:11:02.620 those course those those courses, they will work together. And teachers 00:11:02.620 --> 00:11:08.260 work together to develop an overall course plan. And then the teachers work 00:11:08.260 --> 00:11:15.940 together to implement that course plan by developing and preparing lessons. 00:11:15.940 --> 00:11:22.300 So what that means is is that all classes will learn the same material and follow 00:11:22.300 --> 00:11:29.290 the same pace. So what happens in my grade 10 academic math class today, it 00:11:29.290 --> 00:11:32.680 would also be the same thing that happens in Suzanne's 00:11:32.680 --> 00:11:39.880 grade 10 academic math class that day. There are definitely some like some some 00:11:39.880 --> 00:11:46.060 changes that can happen within that. So in terms of being able to suit my my 00:11:46.060 --> 00:11:54.610 teaching style but overall the same material is covered. What also happens is 00:11:54.610 --> 00:12:01.780 that teachers will work together to create evaluations and we also work 00:12:01.780 --> 00:12:08.860 together to create the criteria or the look fors that will inform what levels 00:12:08.860 --> 00:12:16.030 will be assigned on an evaluation. And then we also will conference or have 00:12:16.030 --> 00:12:22.720 moderated marking regarding not only the test levels but also your midterm and 00:12:22.720 --> 00:12:30.340 final marks. In terms of cycling, each each strand in the curriculum is covered 00:12:30.340 --> 00:12:37.330 at least once in every cycle. Curriculum expectations are taught and evaluated 00:12:37.330 --> 00:12:43.240 more than once in the course. And each subsequent visit on the strand will 00:12:43.240 --> 00:12:48.820 deepen the students prior knowledge of the concept. One of the words we like to 00:12:48.820 --> 00:13:00.060 use often is nudging. We are nudging students through. In terms of our how our 00:13:00.060 --> 00:13:08.140 departmental model supports collaboration and problem solving, it's 00:13:08.140 --> 00:13:13.420 actually twofold. It's not only what happens in our department but it's also 00:13:13.420 --> 00:13:20.119 what happens in the classroom. We feel it is really important to model 00:13:20.119 --> 00:13:25.779 to our students what we expect from them in our classrooms. Modeling collaboration 00:13:25.779 --> 00:13:31.309 it's or sorry collaboration is a characteristic that our school board 00:13:31.309 --> 00:13:37.009 wants our students to leave with as a transferable skill for future employment. 00:13:37.009 --> 00:13:42.170 And so by modeling this behavior we are teaching students how to work better 00:13:42.170 --> 00:13:50.989 with others. We push in our classrooms that their ability to collaborate is 00:13:50.989 --> 00:13:58.160 just as important as their mathematical knowledge. And so it is often that again 00:13:58.160 --> 00:14:05.689 students will see, I'll go into into Suzanne's class and I will you know say, hey you 00:14:05.689 --> 00:14:13.369 know this is what I found and they see us working together as as as the course 00:14:13.369 --> 00:14:20.199 develops. In terms of our students, our students sit in groups or pods of three, 00:14:20.199 --> 00:14:26.899 maximum four. And they also solve the problems collaboratively using vertical 00:14:26.899 --> 00:14:34.299 non-permanent surfaces. So as we break down the the list 00:14:34.459 --> 00:14:40.879 for collaboration, I'm going to kind of focus a focus on it in the two aspects 00:14:40.879 --> 00:14:47.660 of not only from our department model but also from what what it looks like in 00:14:47.660 --> 00:14:55.220 the classroom. So in the department, in terms of rich discussion, we collaborate 00:14:55.220 --> 00:15:00.799 regularly and this collaboration allows us to understand our students. As we 00:15:00.799 --> 00:15:06.499 daily discuss common struggles, misconceptions, we identify how they 00:15:06.499 --> 00:15:14.299 progress. We share supports for, our suggestions to support students that are 00:15:14.299 --> 00:15:19.879 struggling and also for those that we've taught before. We can better anticipate 00:15:19.879 --> 00:15:27.350 what the students responses are to a particular lesson. And it also this rich 00:15:27.350 --> 00:15:30.259 discussion helps prevent curriculum creep. 00:15:30.259 --> 00:15:35.629 That's where sometimes we find that curriculum expectations kind of or 00:15:35.629 --> 00:15:39.589 expectations outside the curriculum sometimes creep into what our lessons 00:15:39.589 --> 00:15:45.290 are and so having multiple teachers looking at this, it kind of helps prevent 00:15:45.290 --> 00:15:50.629 it. It keeps things in check. In the classroom, different approaches to 00:15:50.629 --> 00:15:56.029 problem solving are discussed which leads to discussions around efficiency and 00:15:56.029 --> 00:16:03.470 communication. It also provides opportunities for for extension to 00:16:03.470 --> 00:16:08.809 questions or connections that are made. In terms of well-designed lessons in 00:16:08.809 --> 00:16:14.269 the department, brainstorming as a team brings more ideas forward and allows us 00:16:14.269 --> 00:16:20.269 to select the most effective ways to get students engaged and well-prepared not 00:16:20.269 --> 00:16:26.479 only for our course but also for future courses. In terms of in the classroom, 00:16:26.479 --> 00:16:31.639 these thoughtful lessons allow students to access their prior knowledge to solve 00:16:31.639 --> 00:16:37.279 problems. As I mentioned before we are nudging students along, extending their 00:16:37.279 --> 00:16:45.169 understanding in small steps instead of large leaps. And it allows I feel for 00:16:45.169 --> 00:16:52.069 concepts to marinate before going more in depth. Students they're able to 00:16:52.069 --> 00:16:58.910 identify connections across strands. For example in grade ten academic math last 00:16:58.910 --> 00:17:05.149 semester, we were covering the equation of a circle and a student was able to 00:17:05.149 --> 00:17:09.649 recognize that they could determine the principal angle or the angle formed 00:17:09.649 --> 00:17:14.750 between the x axis and the radius of the circle using the tangent ratio. And that 00:17:14.750 --> 00:17:20.899 was just something that came up in the discussion. Better assessments. So what we 00:17:20.899 --> 00:17:25.669 find is that because we are collaborating together to create a test, 00:17:25.669 --> 00:17:32.240 it takes less time and the quality of the assessment is much better. The 00:17:32.240 --> 00:17:41.510 quality of our questions and we have fewer errors. Solutions are done. Sorry 00:17:41.510 --> 00:17:44.600 I'm apologizing now the cats meowing just below me. 00:17:44.600 --> 00:17:53.210 Sorry, solutions are done before the test to check for timing and for 00:17:53.210 --> 00:18:01.520 accuracy. And we create our success criteria for evaluations as a team and 00:18:01.520 --> 00:18:07.010 it clears up any consistencies across the grade level as we collectively agree 00:18:07.010 --> 00:18:14.179 upon what skills are needed to show or sorry what skills are needed to show a 00:18:14.179 --> 00:18:19.850 particular level. In the classroom, the structure of assessments are also 00:18:19.850 --> 00:18:23.750 consistent across grades and so students know what to expect as they move through 00:18:23.750 --> 00:18:31.520 our program. And so there isn't this timing needed to adapt from you know one 00:18:31.520 --> 00:18:36.799 teacher style to another teacher style. Also consistency between sections 00:18:36.799 --> 00:18:41.360 results in students knowing that they are fairly assessed in comparison with 00:18:41.360 --> 00:18:46.250 their peers. So what a student gets in my class will be what a student gets in 00:18:46.250 --> 00:18:53.179 in Suzanne's class. The professional learning community. This is also so very 00:18:53.179 --> 00:18:58.490 important as allows for growth as we share our ideas, listen, and try different 00:18:58.490 --> 00:19:04.640 approaches, learn from our colleagues, and also train new members. So this has been 00:19:04.640 --> 00:19:08.690 really really important at times. Our department has had as many as five 00:19:08.690 --> 00:19:15.500 LTOs in the department in one semester. And so in order to help provide 00:19:15.500 --> 00:19:22.610 consistency for students, this has actually been huge. We've even had LTOs 00:19:22.610 --> 00:19:30.650 behind LTOs. So it helps students and knowing that we are preparing them for 00:19:30.650 --> 00:19:37.580 the for the subsequent grades. In the classroom, immediate feedback for period 00:19:37.580 --> 00:19:43.370 one so the lesson can be adjusted in period two and three and four to support 00:19:43.370 --> 00:19:47.780 student learning. Students benefit from teachers participating in school board 00:19:47.780 --> 00:19:52.909 initiatives as students are less wary of taking risks as it's being again modeled 00:19:52.909 --> 00:19:57.980 by the classroom teacher. Shared workload. Planning and 00:19:57.980 --> 00:20:01.460 preparation of a lesson is more efficient as teachers are open to 00:20:01.460 --> 00:20:08.030 participating in a common extra help room. So our extra help room, it's one 00:20:08.030 --> 00:20:14.120 room where students know they can go at lunch on Mondays through Thursdays. All 00:20:14.120 --> 00:20:21.020 students can attend and the teachers take turns manning the extra help room. 00:20:21.020 --> 00:20:27.320 And so what's helpful is that I only have to provide help to help to 00:20:27.320 --> 00:20:33.650 students and students in general, once a week. We have enough teachers that this 00:20:33.650 --> 00:20:37.820 model works really really well. We usually have a junior, a teacher who 00:20:37.820 --> 00:20:43.190 teaches the nines and tens, and someone who teaches the 11 and 12s in there. And 00:20:43.190 --> 00:20:48.799 then if it's you know busy because it's just before a test other teachers will 00:20:48.799 --> 00:20:53.690 come down but it's really helped share the workload in that. And then in terms 00:20:53.690 --> 00:20:57.620 of in the classroom, students feel comfortable asking their peers for help 00:20:57.620 --> 00:21:04.790 and asking teachers other than their own for support. And what's interesting is 00:21:04.790 --> 00:21:08.270 that this culture has actually let our students to organize their own peer 00:21:08.270 --> 00:21:13.940 tutors that help in the extra help room. So we have like grade 11 and 12 00:21:13.940 --> 00:21:19.429 students who come in and support our junior junior students. in terms of 00:21:19.429 --> 00:21:26.270 supportive, it is such an supportive entire environment. Overall what we found 00:21:26.270 --> 00:21:30.799 in the department is that it develops trust between colleagues and allows for 00:21:30.799 --> 00:21:37.880 a support system to be in place for each member of the department. Also teachers 00:21:37.880 --> 00:21:43.070 help each other during absences. So where possible if I can get it assigned an on 00:21:43.070 --> 00:21:51.290 call for one of my colleagues when that's being put forth. It also ensures 00:21:51.290 --> 00:21:55.820 that the lesson is going to be delivered to students and and they're not behind. 00:21:55.820 --> 00:22:01.970 And then also as Suzanne alluded to earlier, this supportive environment 00:22:01.970 --> 00:22:08.169 right now during COVID 19, it's it's been monumental in helping each other 00:22:08.169 --> 00:22:12.620 trying to figure out how to deliver lessons and 00:22:12.620 --> 00:22:18.419 supporting each other with our needs at home. In terms of the classroom, students 00:22:18.419 --> 00:22:23.039 see supporting again being modeled by the teachers and they begin to take on 00:22:23.039 --> 00:22:28.950 that role which again goes back to the extra help room. And also for example in 00:22:28.950 --> 00:22:33.269 Google classroom students post questions to homework and other students provide 00:22:33.269 --> 00:22:38.010 guidance. And it's really interesting to see how students don't just answer the 00:22:38.010 --> 00:22:43.289 question, they will prompt a student in another way giving guidance as opposed 00:22:43.289 --> 00:22:49.340 to just saying here's the solution. Problem solving, so through collaboration 00:22:49.340 --> 00:23:00.299 we have improved the outcomes for the following, so students are prepared in 00:23:00.299 --> 00:23:04.950 the next level. So this is this idea of a development of a 9 through 12 program. 00:23:04.950 --> 00:23:09.659 Within a course there are teachers with a wide variety of experiences. And many 00:23:09.659 --> 00:23:14.399 of the course teams we have teachers that teach both academic and applied and 00:23:14.399 --> 00:23:23.130 junior and senior courses. So as a result the course is prepared such that that 00:23:23.130 --> 00:23:31.830 any questions that are developed the we know the knowledge that they know from 00:23:31.830 --> 00:23:37.139 their previous courses as well as what they should know to go on to their next 00:23:37.139 --> 00:23:43.500 courses and we can address all those needs as we move through. Transition 00:23:43.500 --> 00:23:49.049 again between grades is seamless. Teachers, teaching methods, assessments and 00:23:49.049 --> 00:23:55.289 evaluations are kept consistent throughout grades 9 through 12. And this 00:23:55.289 --> 00:24:00.269 consistency is found through our collaborative planning as well as in our 00:24:00.269 --> 00:24:06.840 moderated marking or our conference marking. Also because of the professional 00:24:06.840 --> 00:24:11.549 dialogue that occurs teachers are constantly questioning the ideas and 00:24:11.549 --> 00:24:17.039 only incorporating activities that are purposeful which result in lessons that 00:24:17.039 --> 00:24:25.460 focus more on thinking than on skills. Skills are taught as they are needed 00:24:25.630 --> 00:24:34.210 to solve a problem and they are not taught in isolation. So moving on to the 00:24:34.210 --> 00:24:41.380 next slide we have, this is an example of cycling in our grade 10 academic math. 00:24:41.380 --> 00:24:46.840 This is one version. We've had multiple versions you know throughout the years. 00:24:46.840 --> 00:24:57.309 So we have three cycles and as you can see we hit each strand in each cycle. So 00:24:57.309 --> 00:25:03.280 in cycle one we start with quadratics where we're patterning linear and 00:25:03.280 --> 00:25:10.120 nonlinear which is our link from grade 9. Then we move into into properties of 00:25:10.120 --> 00:25:14.440 quadratics, looking at three forms of equations, expanding and simplifying, some 00:25:14.440 --> 00:25:20.580 some algebra. Then we go into linear relations. Then we go into trigonometry. 00:25:20.580 --> 00:25:27.610 And then we cycle two, we start with trigonometry. So an extension of the 00:25:27.610 --> 00:25:33.340 tangent ratio. We go to sohcahtoa. Then we move to linear relations and then back 00:25:33.340 --> 00:25:40.320 to quadratics. Cycle three we go into quadratics then linear relations and we 00:25:40.320 --> 00:25:48.250 end up with with trigonometry. And so this is just a snapshot. It is always 00:25:48.250 --> 00:25:54.370 ever evolving and ever changing as we realize that we may want to retool 00:25:54.370 --> 00:26:00.070 what what order things are going on as we find different connections between 00:26:00.070 --> 00:26:04.750 the different strands. So I'm going to pass it off 00:26:04.750 --> 00:26:12.059 back to Suzanne to discuss the collaborating and problem-solving model. 00:26:12.059 --> 00:26:19.630 Thank You Trish. So in our next section what we like to do is walk you through a 00:26:19.630 --> 00:26:27.309 few specific lessons and take you through the questions that we ask 00:26:27.309 --> 00:26:33.190 ourselves as we plan. So there are four questions that we will take you through. 00:26:33.190 --> 00:26:39.260 The first being, what skills do students need? So when we're thinking about 00:26:39.260 --> 00:26:47.630 this question, we are trying to determine what our students need to be able to do 00:26:47.630 --> 00:26:55.100 by the end of the lesson or by the time we determine that they they've completed 00:26:55.100 --> 00:27:01.370 the concepts. So what do they need to know for this skill. The second question 00:27:01.370 --> 00:27:05.420 is what do students already know? So what kind of prior knowledge do they have 00:27:05.420 --> 00:27:13.460 that can simplify the learning process and reduce the amount of new material 00:27:13.460 --> 00:27:18.680 that they're taking in and processing. Question number three is what kind of 00:27:18.680 --> 00:27:25.490 new connections can we make to what they know? So how do we connect this new 00:27:25.490 --> 00:27:34.220 material to their prior knowledge and how do we make it something that's like 00:27:34.220 --> 00:27:40.010 an enduring understanding for them. And question number four, what are some 00:27:40.010 --> 00:27:47.030 things that we can review? So these things may not be the focus, the main 00:27:47.030 --> 00:27:51.620 focus of the lesson but additional concepts that we end up hitting just 00:27:51.620 --> 00:27:58.210 because of the way the design of the lesson is. So we may be reviewing 00:27:58.210 --> 00:28:05.830 another concept in another strand as a means to get to what we're actually 00:28:05.830 --> 00:28:13.040 trying to focus in or teach. So we're going to go through three different 00:28:13.040 --> 00:28:20.120 lessons with you which are the start of each strand in the cycle and then we 00:28:20.120 --> 00:28:27.140 will show you a cumulative task that we use at the end. So Trish is 00:28:27.140 --> 00:28:34.160 going to present our first lesson. Oops sorry. 00:28:34.160 --> 00:28:39.410 All right thank you. So when we're when we're actually starting the course, we do, 00:28:39.410 --> 00:28:46.210 grade ten academic math, we do do a little bit of review but one of our 00:28:46.210 --> 00:28:52.820 first activities that we do is in cycle one is 00:28:52.820 --> 00:28:57.290 patterning. And we look at linear and nonlinear patterns which directly 00:28:57.290 --> 00:29:03.230 relates back to what they've done in grade 9. And so in terms of what skills 00:29:03.230 --> 00:29:08.480 do students need. We're looking at representing not only linear but are all 00:29:08.480 --> 00:29:15.320 relations linear or nonlinear graphically, by an equation, also by a table of value. 00:29:15.320 --> 00:29:20.600 And also talking about characteristics. So students what do they already know? 00:29:20.600 --> 00:29:25.190 They know how to graph. They know how to create a table of values and how to form 00:29:25.190 --> 00:29:30.140 an equation using a pattern rule for both linear and nonlinear. Connections 00:29:30.140 --> 00:29:37.130 that we make, one type of nonlinear relation is the quadratic relation and 00:29:37.130 --> 00:29:42.680 it has distinct features like a linear relation. So in grade 9 it's just linear 00:29:42.680 --> 00:29:47.150 nonlinear and in grade 10 of course we're introducing a specific type of 00:29:47.150 --> 00:29:52.550 nonlinear which is quadratic. And then things that they can review are graphing 00:29:52.550 --> 00:29:57.700 skills, creating tables of values, independent variables and dependent 00:29:57.700 --> 00:30:06.530 variables. So the next part of this so this, when we talk about this lesson, it 00:30:06.530 --> 00:30:15.320 actually takes a couple of days and the next part of it is this, the first one 00:30:15.320 --> 00:30:19.190 was the linear pattern and now this is the nonlinear pattern, well actually has 00:30:19.190 --> 00:30:28.250 both, it's this activity called leapfrog. And so the the way the activity works is 00:30:28.250 --> 00:30:34.370 that we explain it where we have a pair of frogs below or on lily pads. And there 00:30:34.370 --> 00:30:39.350 is one lily pad in between them and these frogs can exchange places given 00:30:39.350 --> 00:30:44.030 the following rules: so a frog a frog can slide onto a free lily pad that is 00:30:44.030 --> 00:30:50.750 directly adjacent to the frog and a frog can jump onto a free lily pad overtop of 00:30:50.750 --> 00:30:59.090 one other frog and a frog can only move in the forward direction. And so what we 00:30:59.090 --> 00:31:05.860 go through how in the example of how to move the frogs. 00:31:05.860 --> 00:31:11.049 And then what the activity is, what is the number of moves needed to exchange 00:31:11.049 --> 00:31:18.850 places for two, three, four, and up to ten pairs of frogs. So a move is either a 00:31:18.850 --> 00:31:22.960 jump or a slide. They have to explain their thinking. They need to record their 00:31:22.960 --> 00:31:29.620 data on chart paper. How many moves are needed to exchange any number of pairs 00:31:29.620 --> 00:31:37.030 of frogs? They need to make a rule and explain their thinking. So what we what 00:31:37.030 --> 00:31:41.110 we get them to do is, and I should have mentioned this before in terms of how 00:31:41.110 --> 00:31:46.660 our pods work, is that we usually assign a role for each person in the pod when 00:31:46.660 --> 00:31:52.870 they're solving problems. And for example in this situation they have to work 00:31:52.870 --> 00:31:58.210 together because one person has to learn how to actually go through the process 00:31:58.210 --> 00:32:05.049 of moving the frogs from one side to the other. And then you need a person who is 00:32:05.049 --> 00:32:09.700 going to specifically record the number of slides and another person who's going 00:32:09.700 --> 00:32:16.510 to record the number of jumps for each set or each pairs of frogs. So it 00:32:16.510 --> 00:32:22.169 really does take a group effort in order to make sure that their data is accurate 00:32:22.169 --> 00:32:31.600 as they as they collect it. So where we end up with this is that this is an 00:32:31.600 --> 00:32:38.860 example of the data that they collect. So in terms of the table of values. So we 00:32:38.860 --> 00:32:41.860 asked them what pattern rules were developed. They should explain their 00:32:41.860 --> 00:32:46.929 thinking and then graphing each of the relations and making connections between 00:32:46.929 --> 00:32:51.910 the table of values graphs and equations. And one of the interesting things is 00:32:51.910 --> 00:32:59.160 that when they realize that the slides is a linear pattern, our jumps is 00:32:59.160 --> 00:33:03.220 nonlinear, and this is where we specifically start to talk about 00:33:03.220 --> 00:33:09.730 quadratic relations, and then when you look at the moves, the moves is actually 00:33:09.730 --> 00:33:14.940 the addition of your linear relation or equation and your 00:33:14.940 --> 00:33:23.190 or non-linear and then how does that look in the graph. So we have our linear 00:33:23.190 --> 00:33:28.650 relation which is the red line, our number of jumps which is our blue line, 00:33:28.650 --> 00:33:35.970 and then our moves which is the black line. And this is where we start to move 00:33:35.970 --> 00:33:42.650 into quadratic relations, comparing properties between linear and non, talking about 00:33:42.710 --> 00:33:49.170 how how we could extend or mirror the graphs that are represented, the 00:33:49.170 --> 00:33:56.970 quadratic ones on to the other side, and this leads into our our discussion on 00:33:56.970 --> 00:34:05.010 properties of quadratic relations. We also have, you'll see here there's a link 00:34:05.010 --> 00:34:14.250 to what our lessons are for each of the the three the three areas. So I will pass 00:34:14.250 --> 00:34:21.960 it off now to Suzanne to talk about trigonometry. Thank You Trish. 00:34:21.960 --> 00:34:28.380 So our lesson on trigonometry. This is the first lesson that we do with our 00:34:28.380 --> 00:34:39.630 students when we hit this strand. So I'll lead you through the our questions here. 00:34:39.630 --> 00:34:45.930 So what skills do students need? Well we want them to be able to use the tangent 00:34:45.930 --> 00:34:52.320 ratio and in order to do that they must identify the sides correctly so that 00:34:52.320 --> 00:34:57.510 they can input it input the correct sides into the ratio and solve for the 00:34:57.510 --> 00:35:03.750 unknown angle or side. So when we think about what students already know, they 00:35:03.750 --> 00:35:08.550 know slope, and the idea of slope from grade 9, and that it is the ratio of the 00:35:08.550 --> 00:35:14.850 rise divided by the run between two points, and they also know how to isolate 00:35:14.850 --> 00:35:25.790 for a variable. So these two skills can be used directly in order to find 00:35:25.870 --> 00:35:33.370 an angle or a side using the tangent ratio. So what kind of new connections do we 00:35:33.370 --> 00:35:37.890 want to make? Well we want them to realize that the ratio of the two sides 00:35:37.890 --> 00:35:45.940 relates to a reference angle. The other thing that we like them to learn at the 00:35:45.940 --> 00:35:52.270 end of this lesson is that when you're solving for an angle and you want to 00:35:52.270 --> 00:36:00.990 isolate the angle on its own, you'll be you need to use tan inverse, and that's 00:36:00.990 --> 00:36:08.620 the opposite of tan. We can say that, sort of. So what are some things we can review 00:36:08.620 --> 00:36:14.200 that like I said are not the main focus of this lesson? Well one thing that we 00:36:14.200 --> 00:36:22.510 end up reviewing in this as similar triangles because we show them how the 00:36:22.510 --> 00:36:27.430 angles are the same in two similar triangles, 00:36:27.430 --> 00:36:36.430 and we also do a slight review on slopes of lines. So this activity, as you can, I'll 00:36:36.430 --> 00:36:41.290 just quickly go through this activity with you. So on chart chart paper 00:36:41.290 --> 00:36:47.710 students are asked to draw one line with a positive slope, and one with a negative 00:36:47.710 --> 00:36:54.700 slope, and then they have to prove the slope is constant by drawing in a second 00:36:54.700 --> 00:37:01.150 slope triangle. So when they do that or after they do that, they're asked to use 00:37:01.150 --> 00:37:05.590 a protractor and measure the angle formed between the line and the base of the 00:37:05.590 --> 00:37:13.060 triangle which is the slope angle. Once they've done that, so that's all things 00:37:13.060 --> 00:37:20.700 that they can quite easily do and they've done for in grade 9 and grade 8. 00:37:20.700 --> 00:37:26.440 So once they've done that, we give them the table for slope angle and slope, 00:37:26.440 --> 00:37:34.320 and ask them to find or see if they see any similarities with their findings, and 00:37:34.320 --> 00:37:43.010 what we see is that they find the numbers that they found for the angle, and then 00:37:43.010 --> 00:37:48.560 they also realize that that ratio matches the angle. So the slope ratio 00:37:48.560 --> 00:37:55.220 matches the angle that they found using a protractor. And so that's our intro 00:37:55.220 --> 00:38:03.220 into tangent ratio, and then from there we use the terminology of rise and run 00:38:03.220 --> 00:38:09.800 to solve for an angle or a side in this lesson rather than having to teach them 00:38:09.800 --> 00:38:15.170 about opposite and adjacent right from the beginning. And so this brings us back 00:38:15.170 --> 00:38:19.940 to that idea that Trish was talking about, nudging them along, instead of 00:38:19.940 --> 00:38:25.660 having them to process new terminology in addition to these other things. 00:38:25.660 --> 00:38:32.840 We reduce the amount of new information by not bringing in that new terminology of 00:38:32.840 --> 00:38:40.880 opposite and adjacent and getting those two sides mixed up, and keeping the sides 00:38:40.880 --> 00:38:46.430 constant with rise and run because it's something that they're able to really 00:38:46.430 --> 00:38:52.100 easily and quickly see. As and then from there in the second and third cycle, we 00:38:52.100 --> 00:38:57.320 do move to the other terminology but we find we find that there's a lot of 00:38:57.320 --> 00:39:05.270 success using this or accessing their prior knowledge. Okay and so now let's 00:39:05.270 --> 00:39:14.630 move on to analytic geometry. So in analytic geometry we we have put in 00:39:14.630 --> 00:39:21.530 the warm-up that we normally use, and it's to show kind of what the 00:39:21.530 --> 00:39:28.850 connections we were making between strands. So in this lesson for analytic 00:39:28.850 --> 00:39:34.550 geometry, when we ask ourselves what skills do we want students to end up 00:39:34.550 --> 00:39:38.750 with, essentially we want skilled students to be able to classify shapes 00:39:38.750 --> 00:39:45.080 using slope, lengths of line segments, and diagonals. Right? So that's their endpoint. 00:39:45.080 --> 00:39:51.680 That's where we want them to end up. So what do students already know that allow 00:39:51.680 --> 00:39:55.550 them to be able to identify that information? 00:39:55.550 --> 00:39:59.990 Well from grade 9 they already know about parallel and perpendicular slopes, 00:39:59.990 --> 00:40:06.500 and they also know the Pythagorean theorem. So the new connections that we 00:40:06.500 --> 00:40:14.450 like them to make is that the idea that they can examine multiple sets of lines 00:40:14.450 --> 00:40:19.820 and compare their slopes. That's one thing because often in when we're 00:40:19.820 --> 00:40:24.320 classifying shapes, we'll need at least four sets of we'll need four sets of 00:40:24.320 --> 00:40:30.230 lines, or three sets of lines, or etc., when they're because they're doing triangles 00:40:30.230 --> 00:40:35.090 and quadrilaterals. And and the other thing that we want them to do is to 00:40:35.090 --> 00:40:41.090 determine the length of the hypotenuse is also the way that we determine the 00:40:41.090 --> 00:40:46.400 length of any line. So make that connection between those two equations 00:40:46.400 --> 00:40:52.660 instead of thinking that the length of a line equation is something that's 00:40:52.660 --> 00:41:00.410 brand-new, so length of a line segment sorry. So in this lesson, that's kind of 00:41:00.410 --> 00:41:08.300 our end game but we start this out by actually having them review the 00:41:08.300 --> 00:41:17.150 properties of linear relations and also quadratic relations, and we consolidate 00:41:17.150 --> 00:41:23.930 in their minds that these two things are relations that have specific properties 00:41:23.930 --> 00:41:29.030 and we can compare a linear equation to a quadratic equation, or table of values to a 00:41:29.030 --> 00:41:34.550 linear table of values to a quadratic one. So that's where we begin and we have 00:41:34.550 --> 00:41:42.320 a a good discussion on what those different elements are in linear 00:41:42.320 --> 00:41:49.580 relations so that they start to recall their information from grade 9. Refresh 00:41:49.580 --> 00:41:53.390 that so that they're ready to apply it to this new knowledge that they are 00:41:53.390 --> 00:41:59.420 going to be learning. The other thing, yes so exactly parallel, perpendicular, 00:41:59.420 --> 00:42:02.980 vertical, and horizontal slopes, like I said, 00:42:02.980 --> 00:42:08.920 and Pythagorean theorem which we've already talked about. So that's kind of 00:42:08.920 --> 00:42:15.010 the beginning of our analytic geometry unit, and as Trish said all of our 00:42:15.010 --> 00:42:22.960 lessons, the link to a PDF of them is at the bottom of these slides, so if you'd 00:42:22.960 --> 00:42:28.740 like to access any of them or look through them you're welcome to do so. 00:42:28.980 --> 00:42:36.730 Okay Trish is there anything else you'd like to add to any of those lessons? 00:42:36.730 --> 00:42:44.109 No I think I think that sums it up in terms of yeah the overall goals I think and 00:42:44.109 --> 00:42:48.310 the connections that we're trying to make. Okay great. 00:42:48.310 --> 00:42:56.800 So then we will move on to our, one of our final activities that we have used 00:42:56.800 --> 00:43:06.030 at, well we used it at the end of the semester last term, and that was an 00:43:06.030 --> 00:43:14.280 activity where we were asked students to write a fact, a statement, formula, 00:43:14.280 --> 00:43:22.270 property, or a connection to one of the strands. So at the top of every board we 00:43:22.270 --> 00:43:27.820 had written down, written each strand. So analytic geometry on one board, 00:43:27.820 --> 00:43:32.710 quadratics on another, and trigonometry, and the board was completely blank, 00:43:32.710 --> 00:43:38.590 and students were asked to go up in small groups and fill in these boards 00:43:38.590 --> 00:43:49.150 around the room. And so what we saw was very interesting because as you know at 00:43:49.150 --> 00:43:54.820 the end of the semester, some of the questions as teachers that we have are 00:43:54.820 --> 00:43:58.180 you know what what are students retaining at the end of the semester? 00:43:58.180 --> 00:44:07.930 What gaps still exist? And what sort of things we have to review at the end for 00:44:07.930 --> 00:44:14.080 their final summative evaluation? And so we thought, okay we'll start from them, 00:44:14.080 --> 00:44:20.619 we'll see what knowledge they have and they have retained. And so they 00:44:20.619 --> 00:44:26.500 went up and started putting things on the board, and what we found was most of 00:44:26.500 --> 00:44:30.940 the things that we wanted them to know were on the board, and they were making 00:44:30.940 --> 00:44:37.359 these connections not only within a strand but also between strands, and 00:44:37.359 --> 00:44:42.099 that's kind of what we aim for, and that's what our goal is for them. So as 00:44:42.099 --> 00:44:47.650 through the semester, you know we try to connect concepts from one strand to 00:44:47.650 --> 00:44:54.099 another. So whether it be slope angle to the tangent ratio as we saw, you know, so 00:44:54.099 --> 00:44:58.599 connecting analytic geometry to take trigonometry. Or the fact that both 00:44:58.599 --> 00:45:02.650 linear and quadratic relations have properties, so connecting analytics and 00:45:02.650 --> 00:45:07.930 quadratic. Or the Pythagorean theorem is connected to the distance formula and 00:45:07.930 --> 00:45:12.009 the equation of the circle. Ao trigonometry to analytic 00:45:12.009 --> 00:45:18.250 geometry. So we try to make these connections for them, and it was 00:45:18.250 --> 00:45:22.029 interesting to see as they went around the room, and they started filling in 00:45:22.029 --> 00:45:25.450 these boards, you know some of them didn't know where to start, and then they 00:45:25.450 --> 00:45:32.200 started to look at their peers, and started to get ideas. And oh that's what 00:45:32.200 --> 00:45:35.769 that is, and you know, and then they they could go from there, 00:45:35.769 --> 00:45:40.000 and I think that's where you see the power of collaboration and problem 00:45:40.000 --> 00:45:44.230 solving, and all this all these things that we've been talking about in this 00:45:44.230 --> 00:45:52.150 presentation kind of culminating together. And you can see our boards, 00:45:52.150 --> 00:45:59.230 Trish has got the second set of boards up there, that have a lot of good 00:45:59.230 --> 00:46:04.299 thinking, and like I said we didn't really, they're only prompt was to 00:46:04.299 --> 00:46:10.119 write a fact or a statement or equation, and you know they reviewed their notes, 00:46:10.119 --> 00:46:24.099 they talked to each other, and they came up with all of this. So we have seen a 00:46:24.099 --> 00:46:30.250 lot of benefits from it, and I don't know Trish, is there anything 00:46:30.250 --> 00:46:36.250 else you want to add with this activity here? This activity, I I've actually done 00:46:36.250 --> 00:46:42.130 it at different times in the in the semester. I used to actually, when I first 00:46:42.130 --> 00:46:45.609 started doing it, it was actually after the end of the second cycle because by 00:46:45.609 --> 00:46:51.460 then they'd actually seen pretty much almost everything, and it was it was 00:46:51.460 --> 00:46:55.990 fascinating to see the connections that students made. So it doesn't necessarily 00:46:55.990 --> 00:47:00.940 have to be at the at the end of the course, it can be done at any point in 00:47:00.940 --> 00:47:07.359 time, and you know it could also be used at the end of each cycle where students 00:47:07.359 --> 00:47:14.220 actually create their own, and then they add to it as the as the semester goes. 00:47:14.220 --> 00:47:20.710 And so it's a it is it's a fascinating activity to see, and what I also noticed 00:47:20.710 --> 00:47:26.020 in my class is that when students started looking at other boards, they 00:47:26.020 --> 00:47:30.820 realized well, oh we'll wait a minute, it's not only that, oh that's a starting 00:47:30.820 --> 00:47:41.380 point but they were able to identify any any errors that were done in in in 00:47:41.380 --> 00:47:48.160 someone else's board. So that idea of collaboration was not only within their 00:47:48.160 --> 00:47:57.369 particular groups but it also became as a class that it opened up to to all 00:47:57.369 --> 00:48:08.579 groups not just the you know three or four that that they were working with. 00:48:08.579 --> 00:48:18.940 So what what we want to go into next is some of the I guess challenges that 00:48:18.940 --> 00:48:25.240 arise when you're working in this type of environment, and I I'm going to say 00:48:25.240 --> 00:48:33.849 that these challenges that we see are not restricted to to the to the 00:48:33.849 --> 00:48:40.270 department at the the teacher level but it's also what we see in in our classes 00:48:40.270 --> 00:48:49.770 or in our classrooms with our students. So the points outlined on this slide 00:48:49.770 --> 00:48:57.070 were were comments made by our department. We we asked for, we sent out a 00:48:57.070 --> 00:49:02.680 Google Form and asked their opinions on this, and so these are the thoughts on 00:49:02.680 --> 00:49:08.110 some of the challenges that they that they see. So in terms of personal 00:49:08.110 --> 00:49:12.160 attitude, and this is not only you know teacher and student, you really do have 00:49:12.160 --> 00:49:17.920 to be open to working with different people, and confident in other people's 00:49:17.920 --> 00:49:23.830 abilities, and also accepting of their backgrounds. We we have people in the 00:49:23.830 --> 00:49:32.050 department that have different degrees, and so some people are more proficient 00:49:32.050 --> 00:49:38.500 with certain areas of the curriculum than others, and you have to be confident 00:49:38.500 --> 00:49:45.060 in in respecting their abilities, and not being concerned about going to ask 00:49:45.060 --> 00:49:48.310 questions if you're not really sure of something, 00:49:48.310 --> 00:49:56.410 and also being accepting of other teachers when they are not confident in 00:49:56.410 --> 00:50:01.060 a certain area. So that kind of speaks to the the first two points about 00:50:01.060 --> 00:50:06.910 personal attitude and self confidence, and that also we we model that with our 00:50:06.910 --> 00:50:10.840 students which I think is important when we don't understand something. I have no 00:50:10.840 --> 00:50:15.730 problem going into Suzanne's class and saying, oh hey, you know I'm not quite 00:50:15.730 --> 00:50:19.660 sure about this what do you think? And students see that, and I think that 00:50:19.660 --> 00:50:25.210 that's an important part for them, and having to explain to them the importance 00:50:25.210 --> 00:50:30.160 of being accepting of where other students are at. In terms of 00:50:30.160 --> 00:50:34.720 accountability, you have to keep on track with your colleagues, and you're 00:50:34.720 --> 00:50:42.010 accountable to get certain things done and completed by agreed deadlines. It can 00:50:42.010 --> 00:50:46.840 be challenging when you have a weaker class or you have school events such as 00:50:46.840 --> 00:50:52.210 assemblies that that conflict or your personal situations that that come up 00:50:52.210 --> 00:50:57.460 but what we've experienced is that our teams are very understanding, 00:50:57.460 --> 00:51:03.160 and we're always there to help each other out, and so and I think that's an 00:51:03.160 --> 00:51:10.230 important piece. And again we model that for our students. Our students see it and 00:51:10.230 --> 00:51:16.000 you know we start to see, especially in grade 9, attitudes change with the 00:51:16.000 --> 00:51:20.319 students about being more supportive with their colleagues. In terms of 00:51:20.319 --> 00:51:24.700 differences in opinions, again we see that both between teachers and students, 00:51:24.700 --> 00:51:29.769 and sometimes we disagree on what topics should be emphasized. How 00:51:29.769 --> 00:51:33.849 much time we should spend on a particular activity? How difficult the 00:51:33.849 --> 00:51:38.829 assessment should be and you know how how to level it? What are what are our 00:51:38.829 --> 00:51:44.019 look fors? But what we find is that through discussion, these moments really 00:51:44.019 --> 00:51:49.779 lend themselves as opportunities for professional growth, and that 00:51:49.779 --> 00:51:55.029 they're approached with mutual respect, and I think that's a really important 00:51:55.029 --> 00:52:00.670 aspect, and and again students see this modeled by us, and so they understand the 00:52:00.670 --> 00:52:07.720 importance of it. In terms of time, it can be time-consuming if you have members of 00:52:07.720 --> 00:52:17.440 the team that don't buy in or or or contribute. It really you know all all 00:52:17.440 --> 00:52:22.180 members do need to participate and buy-in, and granted there's going to be times in 00:52:22.180 --> 00:52:27.369 the semester where you know, depending on what is going on in people's personal 00:52:27.369 --> 00:52:30.940 lives, that they may not be able to participate as much, but what we find is 00:52:30.940 --> 00:52:37.619 that overall throughout the semester, everybody does contribute, you know 00:52:37.619 --> 00:52:44.349 equally. And in terms of disjointed, and this refers to cycling, cycling can feel 00:52:44.349 --> 00:52:48.579 disjointed at times, and especially when you're first starting out, when there 00:52:48.579 --> 00:52:53.650 just isn't a connection that can be made, but there are many more opportunities to 00:52:53.650 --> 00:53:00.009 make connections in comparison to when teaching in units or teaching in silos. 00:53:00.009 --> 00:53:05.619 Also since concepts and skills are revisited multiple times, students 00:53:05.619 --> 00:53:10.859 abilities to identify types of problems and efficient ways to 00:53:10.859 --> 00:53:18.390 solve them become instinctive and natural. And we also do find, like from 00:53:18.390 --> 00:53:23.099 the student perspective, students do have some difficulty at the beginning, moving 00:53:23.099 --> 00:53:27.450 through the topics because we're only touching on the surface of them in in 00:53:27.450 --> 00:53:33.720 the first cycle, and they feel you know it's it's hard to move on when they're 00:53:33.720 --> 00:53:38.279 just you know starting to get it but us realizing that it's not to worry we're 00:53:38.279 --> 00:53:44.339 going to go back to it. In terms of comprehensive assessments, coming up with 00:53:44.339 --> 00:53:49.289 creative assessments can be a challenge, especially in the first cycle. And 00:53:49.289 --> 00:53:52.650 there's a bit of a learning curve because you have to understand that a 00:53:52.650 --> 00:53:59.309 level four in cycle one may be different than a level four in cycle three, or 00:53:59.309 --> 00:54:05.880 cycle two or cycle three. So the criteria will change as you move through. And that 00:54:05.880 --> 00:54:10.920 also kind of lends itself in reporting because marks can be higher at midterm 00:54:10.920 --> 00:54:19.260 than in the final because you are going more in depth as the cycles continue on. 00:54:19.260 --> 00:54:24.180 In terms of creative lesson planning, trying to figure out how to best cover 00:54:24.180 --> 00:54:29.369 it all, keeping it interesting, and develop a cohesive course, can take many 00:54:29.369 --> 00:54:35.960 iterations just to get it right. And it is definitely, constantly evolving as 00:54:35.960 --> 00:54:45.420 both Suzanne and I have said a few times throughout this presentation. So I will 00:54:45.420 --> 00:54:51.420 pass it off to Suzanne to talk about advice from our department. 00:54:51.420 --> 00:54:58.680 Thanks Trish. So as Trish said, we tried to get some feedback from our department 00:54:58.680 --> 00:55:05.700 and this is their advice to you. So when looking to start collaborating and in 00:55:05.700 --> 00:55:13.019 implementing a model such as this, it's best to start small. So find a friend or 00:55:13.019 --> 00:55:18.390 find like-minded colleagues who are willing to collaborate, and maybe start 00:55:18.390 --> 00:55:21.920 with one lesson or activity 00:55:22.039 --> 00:55:26.939 that way it's manageable, it's easy. You'll find success and then you can 00:55:26.939 --> 00:55:35.459 move on to the next thing that you'd like to try. Individuality is our next 00:55:35.459 --> 00:55:42.089 piece of advice, and that's so although we create lessons as a team, we often 00:55:42.089 --> 00:55:49.369 adapt to how we present them to complement our teaching styles. 00:55:49.369 --> 00:55:55.349 So sometimes you know we even modify the examples depending on what the class 00:55:55.349 --> 00:56:01.079 needs. If the class needs a little more time on something, you know I may go a 00:56:01.079 --> 00:56:07.829 little bit slower with a certain example and take a little more time, and Trish 00:56:07.829 --> 00:56:15.269 may be you know moving through at a different pace on in in a lesson. And 00:56:15.269 --> 00:56:19.589 that's okay. And that's just because that's what your class needs and that's 00:56:19.589 --> 00:56:25.349 how and that's what works for your teaching style as well. So allow room for 00:56:25.349 --> 00:56:34.079 individual individuality. The next thing we like to say is make use of a release 00:56:34.079 --> 00:56:39.089 time. So use opportunities wherever you can to collaborate on lessons and 00:56:39.089 --> 00:56:46.619 evaluations, and make use of any time that you can be given by your school or 00:56:46.619 --> 00:56:52.529 your school board. Those are really great opportunities to collaborate. 00:56:52.529 --> 00:56:59.880 Be organized. So for our department, we have a shared folder, and for every course we 00:56:59.880 --> 00:57:07.499 have shared folders within that as well as a course schedule. So everyone can see 00:57:07.499 --> 00:57:15.809 where we're going, what's happening next. Everyone has access to the files and we 00:57:15.809 --> 00:57:20.429 can all work on it as well together. So you know even if we have to go home or 00:57:20.429 --> 00:57:27.989 and or we're working in different rooms, we can access the file and you know 00:57:27.989 --> 00:57:32.219 collaborate on that. And for us we use Google and Google is great for that 00:57:32.219 --> 00:57:40.579 because we can all jump on a doc and collaborate on that document. Be patient. 00:57:40.579 --> 00:57:48.619 So it takes more time at the beginning and but it gets easier and saves you 00:57:48.619 --> 00:57:56.180 time later on. So you at the beginning you know some things may take a little 00:57:56.180 --> 00:58:00.789 more time as I said but just be patient with yourself and your colleagues, and 00:58:00.789 --> 00:58:10.520 realize that you know it takes it takes practice. The next thing is reflect 00:58:10.520 --> 00:58:16.400 frequently. So evaluate and revise or note things down that you want to change 00:58:16.400 --> 00:58:21.349 so it's ready for the next time. Often this is one of the most challenging 00:58:21.349 --> 00:58:26.470 things for us to do because you know we're in the moment. We're all very busy 00:58:26.470 --> 00:58:31.789 but it really makes a difference if you just take that a couple extra minutes to 00:58:31.789 --> 00:58:36.950 just write you know whatever you your thoughts are down, so that when you go 00:58:36.950 --> 00:58:40.760 back to it later you remember what you want to change, or what didn't work so 00:58:40.760 --> 00:58:50.270 well, or what worked really well. And finally have a growth mindset. So be 00:58:50.270 --> 00:58:59.420 flexible, ready to listen, and share your ideas, and be open because as Trish was 00:58:59.420 --> 00:59:03.500 saying earlier, you know you do need everyone to buy in, and so you want to 00:59:03.500 --> 00:59:12.319 work with people who are ready and willing to collaborate. And I think that 00:59:12.319 --> 00:59:15.289 completes our list. I know I went slightly in a different order than 00:59:15.289 --> 00:59:20.720 what's there but... yeah yeah yeah go ahead. Just add something. I just want to actually, 00:59:20.720 --> 00:59:25.039 this whole find a friend, how our departmental collaboration, and I should 00:59:25.039 --> 00:59:28.160 have said this earlier, how it all started was actually when the curriculum 00:59:28.160 --> 00:59:35.779 changed in 2005 and 2007. There were no textbooks. And so the teachers in the 00:59:35.779 --> 00:59:40.069 department, we had to create everything because there was no like a homework, 00:59:40.069 --> 00:59:45.650 right there was no no resources for homework because the curriculum has changed 00:59:45.650 --> 00:59:49.250 quite a bit. So what ended up happening was is our 00:59:49.250 --> 00:59:54.740 department just thought, well you know let's not have three teachers trying to 00:59:54.740 --> 01:00:00.170 reinvent the wheel, or coming up with different different lessons, or different 01:00:00.170 --> 01:00:04.910 you know homework, or different you know it just didn't make any sense, and so 01:00:04.910 --> 01:00:13.760 that's when this idea of collaboration as a as a group started. And I think you 01:00:13.760 --> 01:00:17.900 know, it was, sure there are definitely some challenges, but it it 01:00:17.900 --> 01:00:24.680 when it came and we first started to see cycling, and cycling being introduced in 01:00:24.680 --> 01:00:29.870 different in different schools across the province, this idea of finding a 01:00:29.870 --> 01:00:36.230 friend to implement it, it was a lot easier because we already had this model 01:00:36.230 --> 01:00:45.850 of collaboration. So making I would say a huge change and how you how you 01:00:45.850 --> 01:00:52.790 outline a course, it made it so much easier because you had people to bounce 01:00:52.790 --> 01:01:01.850 ideas off of you know as we went through that that process, as well as you know 01:01:01.850 --> 01:01:07.940 making changes and reflecting on it. And I have to say this, 01:01:07.940 --> 01:01:13.760 yep find a friend is is really really important and it just makes things 01:01:13.760 --> 01:01:20.090 easier to adapt. Same with moving to vertical non-permanent surfaces. We it 01:01:20.090 --> 01:01:25.220 was easier to do it when you had people to talk with about what's working, what's 01:01:25.220 --> 01:01:30.770 not working, how many should be in a group. Originally we had four, and I just 01:01:30.770 --> 01:01:35.090 kept finding that it wasn't working as well, and so this year we moved to three. 01:01:35.090 --> 01:01:44.030 And then also again, this idea as I mentioned earlier, it working as a team, 01:01:44.030 --> 01:01:51.440 working through this this pandemic that we have, I I think that it has made it 01:01:51.440 --> 01:01:54.530 much more manageable for everyone knowing that we can rely on our 01:01:54.530 --> 01:01:59.990 colleagues to help design lessons that will support their learning, 01:01:59.990 --> 01:02:07.420 and we can talk about it, and I think that that's a really you know important 01:02:07.420 --> 01:02:16.010 important aspect of this idea of not only having a flexible classroom but 01:02:16.010 --> 01:02:23.510 having a flexible department. So all right. Sorry Suzanne, kind of took over 01:02:23.510 --> 01:02:29.420 there. That's okay. So just yeah our final thoughts on this as you know we find 01:02:29.420 --> 01:02:35.150 this to be this collaborative model to be very empowering as Trish was you know 01:02:35.150 --> 01:02:41.390 speaking to there for both our teachers and students. And we've shown you you 01:02:41.390 --> 01:02:46.310 know the many benefits that can come out of it. As you saw with our students 01:02:46.310 --> 01:02:51.290 enjoying that consistency between grades and in their assessments. You know 01:02:51.290 --> 01:02:58.730 feeling greater levels of support, and engaging in learning that is getting 01:02:58.730 --> 01:03:05.359 them to critically think right. And our department members enjoy being part of a 01:03:05.359 --> 01:03:08.869 professional learning community where they're able to engage in professional 01:03:08.869 --> 01:03:13.970 dialogue with their colleagues and are challenged to think and reflect on the 01:03:13.970 --> 01:03:19.490 work they produce right. It's commonplace, as we said earlier, for us to drop 01:03:19.490 --> 01:03:25.840 into each other's classes or and to hear questions both from students and 01:03:25.840 --> 01:03:31.580 teachers such as like how far did you get? Do you think the lessons worked today 01:03:31.580 --> 01:03:36.530 you know? Was the lesson hard today? Did I make a mistake here? Does this make sense? 01:03:36.530 --> 01:03:46.270 Where to next? Do we agree? And that's great that we get to hear that every day. 01:03:46.270 --> 01:03:51.970 And so we enjoy this collaborative model and appreciate the way it 01:03:51.970 --> 01:04:01.850 naturally lends itself to solve solving problems and yeah let's just say we 01:04:01.850 --> 01:04:09.830 enjoy it very much. Trish? Yes. So one and one thing I guess 01:04:09.830 --> 01:04:13.760 I'm just going to add on to this, so there's this additional slide after 01:04:13.760 --> 01:04:20.660 after this and I wanted to just quickly talk about it. 01:04:20.660 --> 01:04:26.870 And that's the curriculum design into like it's an intro to quadratics. And 01:04:26.870 --> 01:04:33.860 this actual lesson stemmed from actually NTIP and the New Teacher Induction 01:04:33.860 --> 01:04:39.130 Program. And when I was a new teacher and I was working with my department head on 01:04:39.130 --> 01:04:48.260 how can we create an activity for students, for them to understand that a 01:04:48.260 --> 01:04:53.900 quadratic relation has three different forms of the equation because one of the 01:04:53.900 --> 01:04:57.860 things that I'd always found is that students they didn't quite understand 01:04:57.860 --> 01:05:03.170 that we have this this graph, or we have this table of values, and the equation we 01:05:03.170 --> 01:05:06.320 can actually have three different equations that that represent the same 01:05:06.320 --> 01:05:12.170 thing. And so we do this activity, once once we've identified properties, so this 01:05:12.170 --> 01:05:16.700 happens in cycle one. So the students know properties of a quadratic relation, 01:05:16.700 --> 01:05:21.140 and we give them three pieces of paper, and on each of the pieces of paper, it 01:05:21.140 --> 01:05:24.740 has this table of values, it has this graph, and it has one of the three 01:05:24.740 --> 01:05:29.840 equations at the top. And what we do is we ask them to identify all the 01:05:29.840 --> 01:05:35.930 properties in the table of values and in the graph, and then once they've done 01:05:35.930 --> 01:05:42.260 that for all three pieces of paper, what they have to do is is then look at the 01:05:42.260 --> 01:05:47.810 fact that, okay well, what's different in these in this piece of paper or 01:05:47.810 --> 01:05:50.960 these three pieces of paper, and it's the fact that the equations are different. 01:05:50.960 --> 01:05:57.140 And the fact that that it's interesting that we can have these three different 01:05:57.140 --> 01:06:02.000 equations that that they do look quite different but they actually in fact 01:06:02.000 --> 01:06:08.930 represent the same relation. And then we move into, okay well how do we get these 01:06:08.930 --> 01:06:17.600 properties, or are there any, do you notice any you know similarities between the 01:06:17.600 --> 01:06:22.720 properties and what's in the equation, and so it's a way that we move into 01:06:22.720 --> 01:06:27.050 identifying properties of a quadratic from 01:06:27.050 --> 01:06:34.430 different equations. And it's a it's a really good activity, this idea of not 01:06:34.430 --> 01:06:39.980 just looking at factored form, and not just looking at vertex form, and not just 01:06:39.980 --> 01:06:46.400 looking at standard form, but the fact that all of these represents a quadratic 01:06:46.400 --> 01:06:56.120 relation. And and I think that from my perspective, this activity really helps 01:06:56.120 --> 01:07:00.860 them as we go through quadratic relations in that they understand there 01:07:00.860 --> 01:07:09.680 can be three different forms of the equation, and which which form is the 01:07:09.680 --> 01:07:16.880 most useful under what circumstances. And so we wanted to add this in on this 01:07:16.880 --> 01:07:23.480 presentation just because we think it's a good, it's a good activity, but it's not 01:07:23.480 --> 01:07:33.200 necessarily the start of of the of the quadratics strand in cycle one. 01:07:33.200 --> 01:07:41.480 It comes after leapfrog. So anyway, but I wanted to again thank you very much for 01:07:41.480 --> 01:07:47.710 listening to our presentation today. We do have the links for the different 01:07:47.710 --> 01:07:57.260 activities in each of the slides, and if you do have any questions for Suzanne or 01:07:57.260 --> 01:08:05.540 myself, you are more than welcome to email us and we'd be happy to discuss 01:08:05.540 --> 01:08:15.470 our thoughts and ideas, and and if you are considering using this model in in 01:08:15.470 --> 01:08:20.390 your department or with another teacher. Suzanne is there anything you want to? 01:08:20.390 --> 01:08:25.130 Just maybe we'll flip through to the splash slide again so they can have our 01:08:25.130 --> 01:08:32.680 contact info. Oh yep. Sorry. Sorry I'm doing this in completely the not 01:08:32.680 --> 01:08:39.710 technical way. There you go. Yeah there we go. Just so if you'd like to contact us, 01:08:39.710 --> 01:08:44.030 if you have any questions, feel free to shoot us an email and we 01:08:44.030 --> 01:08:47.780 will get back to you. So thank you for listening today. All right. 01:08:47.780 --> 01:08:50.740 Okay. Bye.