Sally Keyes (math coach), Kamaljit Sangha (7/8 math teacher/department leader), Deb Negrete (principal), and Cecilio Dimas (7/8 math teacher) have a conversation following the lesson to share observations and discuss next steps.
The team made some modifications to the lesson based on the continuous reflection that took place before and after this lesson, such as reiterating the purpose of the tables and connecting them to the prompt, the role of zero, and having students reflect on how they started organizing their own table(s) as a way to activate prior knowledge for this particular lesson.
Based on this lesson, the team found that Student J would provide an opportunity for students to show their thinking and understanding of using tables to depict the three different DVD rental plans and whether the three plans would ever cost the same amount of money on their own. The lesson study team assigned this as homework and processed it in a class discussion.
7th & 8th Grade Math - Comparing Linear Functions
Cecilio Dimas , Ida Price Middle School, Cambrian School District, San José, California
DEB NEGRETE: ...and so I think that's why students feel safe in your class. I mean that's just kudos to you for that. Um, but absolutely because she was lost at one point, but still continued and didn't feel intimidated sitting next to Charles.
KAMALJIT SANGHA: Let's look at the beginning because you said you wanted the girls watched, that Lisa and Jessica were very quiet at the beginning. They really, you know, one comment and that's it. And then they started talking as the lesson kept going into the mathematics. Um, that Lisa actually, I remember she said, "That one is actually missing a label. That one is labeled, the other two are not, don't have a label." So they were having a deep discussion about how important a label is so we don't know what's going on because there's no label. Are they two different movies or...
DEB NEGRETE: And I think at times, you prompted that in earlier lessons but not so much this time, but the kids brought it up. So there, and again, first time lesson, so I mean that's where I felt like, yeah that was rich.
SALLY KEYES: It was really nice, I thought that they, so when we ask for additions, or clarifications, or corrections on the student work, um, they changed the labels, so the movie wasn't really, is really the number of rentals, which was really cute and he wasn't, Kyle wasn't the only one. And I thought, okay, you know, I mean, they are really making it clear even though it says movies and money. And we could've just done movies and money, which is what a lot of other students had done; no need to make sure, it's really clear the number of rentals, so I thought that was good.
SALLY KEYES: What are, is a main goal or goals of the math department here at Price?
KAMALJIT SANGHA: Well...
DEB NEGRETE: I'm actually going to give a little bit of background. Let's just get back to how long we have been around. So Kamaljit, how many years have you been in this school?
KAMALJIT SANGHA: I think eighteen or nineteen.
DEB NEGRETE: Okay, okay. So department...and this is starting my eleventh. And so that comes into play when you're talking about developing professional learning communities, and things like that, and strong people on board, which is really critical. And I have to give her a ton of credit because she's been a lead for many years. She's an awesome teacher and that plays a part; and she's dedicated and not one student in her classroom is going to fail.
SALLY KEYES: That's right.
KAMALJIT SANGHA: We hope not. Um, well thank you.
DEB NEGRETE: People need to know who you are and...
KAMALJIT SANGHA: We came up with...we wanted all our staff, math members team department to start teaching with big ideas, so we started with that. And then we all met together and designed a scope and sequence with our big ideas, and then we wanted to have common assessments. And so we got together and decided on common assessments, three benchmarks, and then a post test. Um, from that, big ideas, we also wanted to have...so all the teachers will be doing what...the 7th graders that come to us from 6th grade, they all have a common language and then 7th going to 8th. Well, they have common tasks, for example, we do piles and tiles in 7th grade. And it's amazing this year in 8th grade, every kid has done it and we can always refer back to it. From that point of view, we also, we wanted to make sure, after we have the big ideas, we also want to make sure the students can articulate their math, and they can follow a mathematical thinking process. For example, this is what the question is asking and this is the procedure I took, this is the mistakes I had, and this is the math behind why I took these procedures. And then after that, come up with a validation. Why is my answer correct? Validate it. And then a generalization of how to answer all these type of questions. And then at the end, a validation of the whole process. So sort of mathematical thinking. So we do write up some reports for the students to do. That's how it went and now naturally our next step was to do lesson studies so we can fine tune our teaching and be done with it.
SALLY KEYES: I think...any additional comments about that from the math department teacher or the principle?
CECILIO DIMAS: I think that the structure that has been set up within our math department will be sustainable because it is very clear what the structures are in place with our scope and sequence, and the benchmarks, and the task that we have connected with our benchmarks, and the big ideas that we're working on, that whenever there's a new addition to the team, it's very clear what the goals and objectives are within a specific time frame. And so that clarity is very much appreciated in all of these support that comes along with options of curriculum that we get to use with those big ideas.
DEB NEGRETE: And Cecilio being a newer person coming in a couple of years now and seeing that, it's taken a lot of years to get to where we are and so we were...first of all, I think we've done a lot of work in regards to building norms as a staff, and as a department, and as our other collaborative teams. So it takes a lot to honor those norms, and to make sure that we're following them. So that's been one piece that's been really helpful. A strong math teacher and a math lead is really, really critical. And I think for years we've heard, there's so many standards, and so staff we're teaching a standard a day. And we've created a schedule one year, years ago and we were almost like a standard every other day. We were overwhelmed and I heard that for years, and years, and years. Kamaljit and I kind of understood the big idea piece and it really...Kamaljit would say, I forgot. And understood that how do we umbrella a big idea with those standards embedded in that. And then we had the opportunity of having Sally and Sally took about a year or so to really build trust in our team. Because we know how difficult it is to just come in and say, "Well, I've got experience in math, and I can come into your classroom and help you," or "I can do this." So she deserves a ton of credit for being an unbelievable coach because she built trust with the staff, and then after about a year, we said, "We need to do this. We now need to move to this process." I'm tired of hearing the complaining, and so let's look at what we can do to build a scope and sequence that teachers can live with, and feel that they're not, it's not about quantity, but more about the quality of the instruction. Go for it.
KAMALJIT SANGHA: I think the benefit of having a coach has been...I can't even mention it, it's so priceless, well especially because we're working with her. But we're so busy as teachers and it's so nice to have somebody we can... "Sally, I need this," or "I'm worried about this lesson." And she'll bring a whole bunch of lessons that we can choose from, and then research. And it helps us get connected with what's going on in the research world, in the other districts. It doesn't leave us being isolated in our little district here; it helps us keep connected with everything, and that is a huge help. There's another pair of eyes when she's there watching what students are having difficulties. And even being just helpful for emotional, we've got a tough day, she's there. And outside, she's coming out...we're living in a world of students in here and it's nice to have an objective opinion come in.
KAMALJIT SANGHA: ...just like having the lesson studies for teachers to step back. They're part of it. They might not be the front runners but they're part enough that it changes how they teach in their own classrooms. And that's where our main goal is. All of us aren't front line people, some likes to work in the background, and that helps in that situation. And I also what to mention about their assessment. One of the big deals was we changed all of our multiple choices, to have half multiple choices and half performance task. And then performance task, we get together, that's the strong piece is when we...everybody in 7th grade give this performance task and then we get together, we calibrate, and afterwards we discuss where the downfalls are; what can we own our next steps so the students can learn? And we have something to compare and then go back to our classroom. That is more powerful than any professional data.
DEB NEGRETE: That is professional element. I mean that naturally is and that's where the re-engagement lessons occur and from there. And then everybody's bought into it because they all sat there and had their two cents into it, and then there's where I feel like we get a hundred percent buy in. Whether or not they may be totally on board with some things, everyone feels like, "I've got to go back out and do this re-engagement lesson."
SALLY KEYES: Thank you all very, very much, and I know that I would like to add a few things about being a math coach and so... It's been a real pleasure to be here and to work with this department. And I've found that my role is actually in a way like liaison with the teachers themselves, with the administration, here on-sight with Deb as well as the district office. And so it is, building trust is huge, and then I think the other piece too is working with teachers who are very, very excited about what we're doing, and helping those to come along who maybe are a little bit more reticent; and peer pressure has a lot to do with that. But peer pressure in a positive way because they see the excitement, and they see the scores. I mean they see the evidence of the work that's being done in the classroom. And there are teachers who are coming, in fact it's really nice. I had one come to me and say, "I really would like to meet with you. What can you do to help me in my classroom?" And so I'm meeting with him on Monday, and he's been one of my hardest nuts to crack. So it was really nice that he came to me on his own, and we have a meeting all scheduled. So my job then has really been to be a facilitator, a mediator, a person available to help anyone where they are, to encourage those who may be more reticent, to support them. And to support and encourage, and move the others who are just jumping on board. So it's been a real pleasure to be here.
KAMALJIT SANGHA: Thank you. We enjoyed it.
SALLY KEYES: Okay, the end.
CECILIO DIMAS, TEACHER: During the lesson Charles articulated his interpretation of the three different plans and the mathematical reasoning of the student work that was presented. It wasn’t until the student interview that I realized that he wasn’t quite sure about one of the student errors, which was contrary to what he had written down. Melanie and Daniel did not speak much on film. However, Melanie did share with the class her understanding of the mathematical sense found in the error made on Online Flix. I was happy to hear the conversation that occurred between Tracy and Tricia. Their voices aren’t often heard. Jocelyn and Charles was an interesting partner pair. She was persistent in clarifying her questions and gaining full understanding, even when Charles was quick to reply. The benefits of participating in a lesson study centered on addressing student misconceptions through the creation of re-engagement lessons have enhanced my lessons and teaching. The level of excitement and interest during our meetings has been energizing. Bringing this enthusiasm into the classroom and continuously sharing it with my students is another one of my goals as a middle school math teacher actively participating in lesson study. SALLY KEYES, MATH COACH: As the math coach, it has been a truly remarkable experience working in a lesson study situation. Determining the mathematical purpose and goal of the re-engagement lesson, selecting student work to specifically address and highlight the mathematical purpose and goal, determining the prompts and questions to ask of students to flesh out and make transparent to all students this mathematical purpose and goal, teaching the lesson, reflecting upon the lesson, and using the observation notes to make changes to improve the lesson with these two teachers who are intently focused upon improving instruction for all students by using data to inform all aspects of instruction has been remarkable. The merits and demerits of each question and sequence has been thoughtfully and thoroughly discussed among the three of us always keeping in mind the purpose and goal of maximizing the mathematical understanding of the lesson for the students. After our math team taught these lessons to all eleven 7th grade math classes (accelerated and regular) we began drafting the next phase of this lesson that was based on the MARS/MAC task Gym. Our lesson study team increased in number by adding the other grades 7 and 8 math teachers in the department to the team. We created a new scenario, going to the Fair/Carnival and compared the cost of regularly priced tickets, a one time cost of a bracelet regardless of the number of tickets used, and a discounted ticket price. In the DVD Plans, our focus had been on verbal and tabular representations. However, the focus of Carnival Ticket Plans began with the verbal and tabular representations leading to graphing the three plans. Analysis of the graphs was the focal point of Carnival Ticket Plans. As a math coach, it was a thrill having the remainder of the upper grade math department join the lesson study team for the next lessons. They have added to our deep discussions, reflections, and focus as well as providing another opportunity to solidify the professional learning community fostered, encouraged, supported and expected by our site principal.