We will develop group work routines so all students can equitably access group work and create their own language and/or meaning of the content that we teach.
Lesson Study: Cycle 2
We established group roles for an open ended task in a Math 2 classroom.
Previous Goals
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Verify experimentally the properties of dilations given by a center and a scale factor (HS.G-SRT.A.1)
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Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides (HS.G-SRT.A.2)
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Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar (HS.G-SRT.A.3)
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Prove theorems about triangles (HS.G-SRT.B.4)
Currrent Goals
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Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles (HS.G-SRT.C.6)
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Explain and use the relationship between the sine and cosine of complementary angles (HS.G-SRT.C.7)
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Define the trigonometric ratios (G-SRT.6)
Our Focal Students
Focal Student 1 is a 15 year-old hispanic student that really enjoys soccer and Bad Bunny. He is an Emerging Multilingual Language Learner (EMLL) with an IEP for a specific learning impairment. FS1 enjoys learning and asks for 1-on-1 help often. He has a lot of friends in class, but he does not like to work with his friends. FS1 is self conscious of his mathematical abilities compared to his peers, but he has a lot of support at home to encourage him to continue to try.
Focal Student 2 is a 15 year old black student that enjoys making clothes, art, and spending time with his family. He is a very popular student across his grade and works well with every group. FS2 is a new tutor in the tutoring center after discovering a new found confidence in his math abilities. He is silly and makes math fun for the people he works with.
Focal Student 3 is a 16 year old Filipino student that lives by his own rules. He is very well known amongst his peers for being a unique individual. FS3 is an incredible mathematician, as he is able to visualize images in his head to solve problems. FS3 has autism and has an IEP that allows for movement, which he uses frequently. He often feels overwhelmed when working with others because he is not always able to convey his thinking in a way that others understand initially. He likes to work with people, but when it is unstructured he feels like he looks weird.
Focal Student 4 is a 17 year old Korean student that transferred to the American school system in 9th grade. FS4 is highly advanced in his mathematical abilities, as he learned most of our curriculum in earlier grades. He does not like working with others because he does not like waiting for people to figure things out. He would rather work by himself and check his own answers. However, FS4 is a new tutor and wants to improve his relationship with his peers so he can help them get "caught up" on material.
PDSA Cycles
Our group's disciplines and grade levels varied greatly: a bilingual TK teacher, a 5th grade reading teacher, special education teacher, a 6th grade math and science teacher, and a 10th grade math teacher. Our PDSA cycles, in return, gave a variety of results. Our first cycle was centered around the equity theme of developing group work routines so all students can equitably access group work. We started by playing contrasting videos where one showed what effective group work looked like and the other showed group work that needed help. Then, we as teachers would chart their ideas to gather ideas to see what working together looks and sounds like from their point of view. We wanted to find out how students interpret what collaboration looks like and feels like. Our results were promising: students were able to create group work agreements moving forward, which actually focused less on behavior but more on trying to achieve the goal for the day.
For our next cycle, we chose to adapt and add table points. We were able to keep out equity theme the same throughout the whole cycle. We decided to add table points to encourage group participation amongst teams. Students were able to come up with agreements to abide by during work time and they were keeping each other accountable for their learning. We predicted that some students or groups would get more points than others because of differing levels of motivation. We all had different results for this cycle ranging from students not wanting to participate at all to students creating competition amongst other groups.
We chose to adapt our change idea to assign group roles instead of encouraging students to fill in where they feel they can work best.
Our Lesson
Our lesson was a launch into our new unit where students will learn about right triangle trigonometry. Students had spent the first part of the semester learning about similarity and congruence, especially in triangles. They had a lot of background knowledge when it came to triangles and have expressed an interest in geometry.
Our launch started off with a notice and wonder where students looked at poorly constructed wheel chair ramps. Students talked about how ramps were not accessible because of steepness and other safety concerns. Next, students thought about what makes ramps really safe, leading into a discussion about incline, again. For the task, students were then given group roles and were to use the roles as guidelines to lead discussion and solve the problem. Students had to work together to solve the problem- which ramp is safer? Students were randomly assigned roles such as the coach, the team captain, the accountability manager, and the skeptic, to maintain equity in conversation and learning. Students were able to read sound bites to encourage staying in their assigned role, but also to act as sentence starters. After students worked together on the task, a role was randomly picked to share their group's thoughts to the class.
Reflection
Initially, this lesson seemed like a rich, open ended task that students could use their prior knowledge and experiences to figure out. The research suggested that research roles would greatly improve group work and provide the structure needed to create a positive work environment, however it needs more consistent use and did not land well with only one day of practice. While we have practiced group work before, these roles were newer to my practice so the students were not used to it in this particular setting. Some students responded really well and used the sound bites to guide conversation, and some students did not like the roles or group work at all and did not participate. Overall, students did a good job in participating with a new structure, but it was not as fruitful as I expected. Many students reported that the structures felt silly, but they were necessary so one person did not dominate the conversation, others reported they collaborated as usual and did not find a need for the roles.
Reflecting on the task, though, it was not as open ended as we planned. Some students finished really quickly and there was a lot of empty time. I think the task could have been more open ended if we added a part where students had to construct their own ramp that was a better option that both the ones presented. This could have allowed students to open up their thinking even more and share different thoughts than the two parameters that were given.
Below are some examples of student work. Students used multiple entry points and strategies to solve the ramp dilemma. Some students drew and measured angles and side lengths, while others made other visual representations to try to make sense of the problem. After the lesson, I asked the students their thoughts on what made their roles work well, what challenges they might have faced, and what would have helped them to solve the problem quicker. 3 of the 4 students turned in an exit ticket and they gave their thoughts on the lesson.
