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Lesson Study Team: Virginia Netwig, Abigael Quincena, and Mariangela Vergara.
Equity goal:
We want all students to have access to content and skills that will allow them to become independent learners able to decode and understand academic math language. Also, we want learners to become risk takers who actively participate in class and share their thinking with others as a way to build understanding together.
Content Understanding goal:
To teach students different multiplication strategies to help them decode multiplication word problems. Students understand that (multiplication is equal groups) and apply this understanding to solve a multiplication word problem.
Research Theme and Rationale:
Research Theme and Rationale:
We are teachers trying to make knowledge accessible so we can equip and empower students to become interdependent and independent problem solvers across classroom subjects.
Independent problem solving
We can use visual tools around the classroom
We can use math tools to solve a problem: number lines, 100 chart, multiplication chart, drawing lines between the hundreds / tens / ones, or using a scratch paper
Interdependent problem solving
We can create more opportunities for partner talks and think-pair-shares, gallery walks, and group collaboration.
We can help students create connections to help them build off of each other’s knowledge
We can help students know how to use one another as problem solver tools
Research Lesson Topic:
Research Lesson Topic:
Math language - academic vocabulary comprehension and student dialogue
Decoding english words into math terms
FOCAL STUDENT # 1
As an individual:
As an individual, I know he wants attention, and that he enjoys drawing.
He likes to be loud
He values his friends
He values having fun
He describes himself as funny, cool, and energetic. He enjoys fieldwork. He enjoys Writing about my hopes and dreams. Play on my phone roblox and I have a computer. Windows computer. It’s pretty like laggy.
As a learner in the classroom:
He doesn’t participate
He doesn’t listen to directions or redirections
He draws or wanders in the classroom instead of staying on task
He doesn’t show his math thinking
He enjoys answering whole group discussion questions
He likes being a part of the group
He enjoys project work more specifically fieldwork. He is most engaged when he is doing meaningful or “cool” work. He doesn’t enjoy tasks that are just drills or practicing.
As a member of a family/community:
As a family member, his family is going through a tough time right now.
His parents divorced last year
His dad just got a heart transplant
His mom is very caring!
Usually my mom goes to school and she got her first job like two months. She’s been working. We were trying to work at Home depot. She works at the school but she wants to work weekends. Home depot only works monday through. They think it’s really good and I’m in a good class.
As a member of a larger society:
He is “one of the boys”
He is eight years old
He is part of groups that I haven’t learned about yet!
I don’t celebrate holidays. I celebrate hanukkah. I also celebrate passover. I also celebrate about the trumpets. When you blow the thingy and menorah. I would call it a trumpet. You blow it east and pray.
I want to help, I want to go to work and fix people’s computers and build a place and be the boss.
I would want to work at like a smoothie place. I want to open a jamba juice. It’s only open on weekdays.
FOCAL STUDENT #2
As an individual:
As an individual, she likes to be sassy
She is a leader and kind
She cares deeply for her friends
She is independent in a way
She fights for what she believes in
She describes herself as Caring and Funny. When she is older she wants to be a doctor. Bella loves and lives for basketball. She also enjoys gymnastics and karate. She also did a karate demonstration for me during the interview.
As a learner in the classroom:
She talks with her friends
She gets physical with others
She distracts others when they are focused
She is work avoidant and will look for ways out mostly in writing
She is willing to participate and try things out that is new
As a learner, her learning and engagement is dependant on the relationships she makes with her teachers or the adults in the classroom. In engineering because I love engineering. She’s so nice and we built something that was so much fun! We built a big big big tower. She also says she can’t read or write.
As a member of a family/community:
She has an older sister in middle school
Her grandma died last year and she used to live with her
Mom is around but not always on top of it
Her mom and her enjoy dying their hair!
There is this thing that we do each birthday and each valentine’s day. They put balloons in my sister’s room and presents even on mother’s day. We hide it and then get presents on our bed. We gave my mom a cute yellow bear that was all wrapped up and put it in three boxes to make it hard. Her family thinks she needs more help and support in class because she “can’t read or write”.
As a member of a larger society:
She is Mexican
Her hair is dyed
She wears a mask
I don’t know what other groups she is a part of yet!
We celebrate 3 kings day, Christmas, halloween, thanksgiving. I’m going to get a doctor’s degree, and I already know how to take care of old people. Her grandma died of a heart attack because she had diabetes. Her grandma would have to draw blood and take measurements of her blood sugar. Bella has a very firm grasp on all of this and has impacted her and what she wants to do when she is older.
Emphasis on student thinking:
As teachers every time we collect students' work, we are collecting students' thinking as well. This helps us guide our lesson plans and further teaching lessons. Students work helps us identify where students are at during their learning journey, their understandings and misunderstandings.
The data during our final lesson consisted on a math word problem where students had to decode the math academic language and understand what the problem was asking them to do. Before solving a math word problem and writing down a strategy and a number sentence, students should be able to identify what we call 'part-part-whole'. This means, identify what the numbers in the word problem are representing (according to the reading 'reasoning with quantities and relationships between them). If students do not know if the numbers represent a 'part' or a 'whole' they might probably get the answer wrong. During this lesson study, our focus isn't on getting the 'right' answers but rather understanding students thinking and allowing different strategies to be used. As we know, math isn't about 'one way' of doing/solving word problems.
As a debrief, I observed a student who actively participated through out the lesson by raising his hand and completing his work. He identified the important/key words from the word problem which enable him to successful understand and solve the math word problem correctly. He could re-phrase and tell in his own words what he understood clearly identifying given information and missing information. He stoped and asked himself 'Is this an addition/multiplication word problem?', 'Do I start with 12?'. He understood multiplication had to do with 'equal groups' so that's what his strategy to find the missing number. It was hard for him to connect the strategy he did with a number sentence. He didn't know how to represent a visual strategy (drawings) into a more abstract (math equation) one.
Finally, I could see how this boy likes math, is engaged in a math lesson, knows how to solve a math word problem independently and actively participates. He didn't use any partner or math tool to solve it. During the math discussion (discourse) I would have loved to see him share his math strategy with the rest of the class. He has a lot to share with the class but apparently he gets distracted chatting/playing with friends.
Reflective practice:
The lesson study process itself
What they learned about teaching & learning from this particular lesson cycle.
There's a lot of learning in this lesson study. It has been my first experience going through a complete lesson cycle. Can't wait for the other two to come. Definitely lesson study cycles should be part of our school routines as teachers who are constantly questioning what/how/who we teach. There's always room for growth. As teachers we must be researchers who are always studying and staying updated. Also, as teachers we want to get to the most of our students in the classroom (focal students, marginalized students). We don't want only the 'high status' students to benefit from school. We must teach for equity and justice in our classrooms. Analyzing students' work is a great resource to understand how our students are understanding and grappling with the content and skills taught in class. I love the idea of connecting students' work with research. I love the idea of the PDSA cycles 1 and 2 we had to do before the ultimate lesson because it helps us prepare ahead of time. It was a bit tricky the whole process itself because when navigating through it there's a lot of confusion. But, we can't get overwhelmed by it and instead push forward and keep up with the hard work and persistence. One thing I found meaningful was the 'zoom calls' with the experts. Experts give us a lot of guidance and support as well, helps us clarify things through out the process.
Last but not least, a lot of learning happened out of the lesson cycle itself. We had the pleasure to work together (all three as 3rd grade teachers) and collaborate through out the process. We felt in love with a Math lesson study cycle and agreed upon working towards the same goals and agreements. As third grade teachers we could easily identify what our students struggle the most as well as their strengths. We knew we wanted to support our learners to become independent and interdependent. We wanted our learners to be autonomous and could solve math word problems on their own. Also, we wanted our learners to be risk takers and see mistakes as learning opportunities where the brain changes and grow. This lesson study helped me understand the importance of first and foremost, teaching students how to 'reason' and how to 'decode math academic language' before actually solving a math problem. I would say, I used to give a lot of focus and importance to teaching students math strategies. Students could learn a bunch of strategies to solve math word problems but if they didn't understand what the problem, identify given and missing information, how would they be able to solve a math word problem correctly? We read a lot about the importance of preparing kids for success in life and workplace. It's not about memorizing isolated facts and calculations but instead, about reasoning and engaging in open word problems where students take risks and explore a variety of possibilities.
End of Cycle Reflection & Celebrations:
Celebrations; Mathematical task giving room for students to have divergent thinking and grapple with it. What parts of the story are important. Wonderful job of asking questions regarding the different parts of the word problem. Teacher helped them hone in on the numbers and why those numbers start to relate to each other. Great questions asked by students regarding the problem and the math. Great divergent thinking! Students used manipulatives, repeated addition, and used their multiplication facts! Students asked questions about their own thinking.
Change Ideas: Structures in place to help kids stay together with their thinking and helps them hone in to shift their thinking. Start on the carpet to get them to unpack. Move to the tables to think on their own. Then, turn to your partner, and share what your strategies are. Give them 8-10 minutes and bring them back to the carpet. Ask them for their strategies. Then, ask the next question. That will help them. If we put in structures, it will help students grow. We need to have movement in math alongside structures in place to help unpack their thinking.
Having multiple numbers in the word problem was the grapple for students. They understood the first part but grappled with what to do with the numbers. How do we get them to the two step portion of the problem? How do we get students there?
Visual Aids would be a great stretch for students. We need to change the structure of the word problem to help them be flexible. Kids from third grade need to open their creativity to solve a variety of problems, not just the same problem over and over. What other tools can we offer? How can we get students to learn from their peers? At the end, not all of them were engaged with what was happening on the board. How can we come together as a whole group to build on each other’s thinking? How do we engage the class into a conversation? Maybe, we could arrange the room better. How do we make the students part of the conversation?
The division sentence on the board was incorrect. No one caught it! There was a misunderstanding with what was given in the word problem. How do we show the division and multiplication parts of the problem?
Celebrations:
Passionate and excitement over math from the teachers so when they get to higher grades, they are going to have these tools and habits set up
Using language such as friendlier to help students understand and see math in different ways. There were different ways for students to access this which was cool!
Celebrate the team for their energy for their third graders! Commonalities with getting better routines and structures to help students through math!
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