Lesson Study Cycle 2

As a lesson study group, we dove into the intersection of culturally relevant pedagogy and Elementary Mathematics. We noticed a problem of practice in our 4th grade classrooms where our students were craving engagement, interest, and joy in math. We are interested in providing a real world connection through mathematics and incorporate inquiry based learning into our classrooms in a way that provides access to all students through discourse and strategy sharing.

We conducted this lesson study in my own 4th Grade Class at Explorer Elementary. The lesson we designed was rooted in our project where students explored a real mathematics problem and were encouraged to be the facilitators of their own learning.

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Part I: Planning

Research Theme

We will build students’ confidence as math learners who feel confident in their mathematical abilities by engaging them in culturally relevant, open-ended mathematical tasks that attend to mathematical creativity, fun (joy), interest, and make real world connections.

Our experience as Elementary math educators has influenced our ideas of mathematics. After analyzing the research, our team found multiple instructional strategies that we decided to implement into our research lesson and our practice as Elementary Mathematics educators. As we grappled with the dilemma of implementing culturally relevant pedagogy and inquiry based instruction vs. a traditional mathematics approach, the research above proved that academic challenge can foster a growth mindset and prepare students to be problem solvers who are improvement focused rather than solution focused.

Lesson Goals

Students will understand the relationship between using open ended arrays and area to solve multi-digit multiplication problems.

(4.NBT.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.)

If we, as teachers, engage students in culturally relevant open-ended mathematical tasks while students are making sense of the relationship between open ended arrays and area to solve multi-digit multiplication problems, then students will improve their development of their mathematical creativity and agency resulting in students increased confidence to engage in the lesson and share their thinking.

Research Base

Throughout our lesson study planning phase, we did research on: student agency in Elementary mathematics, culturally relevant mathematics instruction, and academic challenge in Elementary mathematics tasks. As a lesson study group, we unpacked numerous studies, articles, and methods to implement their main ideas into our research lesson. Check out an annotated bibliography and literature synthesis below for an in depth view of our research base.

The research noted in the column to the right led us to our lesson hypothesis which reads as follows:

'If we, as teachers, engage students in culturally relevant open-ended mathematical tasks while students are making sense of the relationship between open ended arrays and area to solve multi-digit multiplication problems, then students will improve their development of their mathematical creativity and agency resulting in students increased confidence to engage in the lesson and share their thinking.'

Research Informed Lesson Plan

Based on our empathy interviews, student work samples, and PDSA lesson cycles, we implemented the following practices into our research lesson:

Utilizing a Ignite, chunk, chew, review instructional method.
Following a 3 act task structure.
Center student discourse throughout the lesson through pair shares, and strategy sharing.
Math task rooted in project based learning.
Inquiry based learning.
Culturally relevant math tasks.
Teacher modeling available as a scaffold only.
Students encouraged to create their own strategies.

Part II: Lesson Artifacts

Annotated Bibliography

Memorialization Document

Literature Synthesis

Lesson Slide Deck

Lesson Overview

Launch

Explore

Discuss

Students began the lesson by being introduced to a real world dilemma. They will be going on a field work experience to The Getty Museum in Los Angeles. Students are asked to notice and wonder, and create estimates through inquiry based learning.

Students were tasked with creating a problem given information regarding fundraising costs and numbers of fundraising groups. Students could either create a multiplication equation or division equation to solve. Students were then tasked with exploring their inquiry either in partners or independently.

Students were invited back to the group to share their strategies and participate in whole group discourse where they compared strategies and celebrated each other's hard work. This was documented on an anchor chart for future use in our project.

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Below are student work samples from three focal students. All three students were able to access the lesson content. Each student was given a blank worksheet that corresponded with the 3 Act task that was taught. Each box provided space for all students to catch their ideas, wonderings, and strategies. In box 3, you can see that students were encouraged to create their own main question with the information provided from the lesson. This maintained the inquiry based nature of the lesson. Students were also encouraged to utilize estimates to scaffold their thinking. Students who shared their strategies during the discourse portion of the lesson used box 6 to recall the details of their strategy.

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Part III: Data Analysis & Reflection

Focal Student 1 Observation

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Analysis of Data Collection

Through student work samples, formal observations, and student survey data, our team concluded that the pedagogical practices that were implemented through research were successful in that all students were able to access the lesson and complete the independent work task. From observations, students were seen engaged in the lesson and willing to participate. All focal students were seen participating, raising hands, and remaining engaged for the majority of the lesson. This is not the norm for all three focal students so the research team was pleased to see their interest in the math task. None of the students were able to use area model or open arrays as a strategy to solve the inquiry, however students were still able to use other multiplication and division strategies to solve the task. All three focal students showed more confidence in this lesson than prior lessons through their completion of the worksheet and their participation in whole group and partner discourse. The survey data for the focal students showed mixed results. Focal student 1 claimed to be uninterested in the lesson, claimed to learn nothing, and did not see the real world connection. Focal students 2 & 3 yielded more positive results as they enjoyed the lesson, saw the real world connection, and learned multiplication in the process. As a whole class, students generally reported to enjoy the lesson, were able to see the real world implications as money was involved, and could understand that the lesson taught them multiplication strategies or division strategies.

Reflection & Next Steps

My vision for mathematicians in a fourth grade classroom is for all students to be able to access all lessons with confidence, engage in inquiry based learning, yet still feel prepared to enter the dominant paradigm in higher education. As an educator, this looks like using culturally responsive and relevant pedagogy to engage all learners and particularly benefit students of color. Students should feel supported but not carried by scaffolds and should carry the majority of the cognitive load during math tasks. My biggest takeaway from this lesson study process is the power of implementing project based learning into a mathematical task. This has been a challenge for the entire research team as we have found math difficult to incorporate into PBL. However, after this research lesson, we realized the power in interest, engagement, and joy of learners through a lesson that has a real world connection for students. In addition, students experience academic challenge through inquiry based learning and have the opportunity for authentic discourse through an open ended mathematical task. It is clear that research based instructional strategies for engagement and academic challenge benefit students' confidence and ability to access higher level thinking skills in Elementary Mathematics tasks. I will continue to hold myself accountable to being a reflective practitioner and strive for