This blog series documents how our network of schools became interested in lesson study. We have shared how our lesson study teams got started – by creating a shared vision of their hopes and dreams for students, determining a research question and theory of action, narrowing in on a specific content area for their research lesson, and then exploring the mathematical content and selecting a mathematical understanding goal and an equity goal for their research lessons. We have also documented our first three public lesson study events, a 3rd grade lesson on comparing fractions, an 8th grade lesson on negative exponents, and a 10th grade lesson on quadratics.
Teachers observe a 3rd grade lesson study comparing fractions.
After our research teams had explored the mathematical content, selected a mathematical understanding goal, and determined an equity goal they were ready to plan the research lesson. To begin, the teams reviewed what they knew about their focus students – what they had learned from their empathy interviews and their hopes for their focus student growth as learners and mathematicians. They also reviewed current work samples related to the content they planned to explore in the research lesson. By grounding themselves in this understanding, teams could think about what new understanding each student might develop during the lesson.
To begin planning the lesson, each teacher completed their teams research lesson problem by anticipating how the focus student they would be observing might approach the problem. If we are to effectively plan instruction for our students, it is important that we have considerable knowledge about what they understand and how they engage in problem-solving. Implicit in this part of the planning process is the question: How well do you know what your students understand? With the multitude of things that teachers attend to during the average lesson, focusing deeply on the thinking of each student does not always happen naturally. It is a habit that benefits from cultivation and practice. During a lesson we are often listening for a right answer, instead of to how a student is thinking. This can shortchange our own learning about how our students learn mathematics. Interestingly, our network teachers have reported that when they have made the shift to listening to how a student is thinking about a problem, they find teaching math more enjoyable.
In addition to listening to students as they pair share during class discussions, or asking students, “How did you think about the problem?” one of the easiest ways to build these noticing muscles is to regularly look at student work. Great times to engage in looking at student work include during Professional Learning Community meetings (PLCs), discipline meetings, or in the lesson study planning process. A looking at student work protocol for establishing this routine can be found here. Lesson study teams who regularly look at student work and analyze student problem-solving strategies can often more accurately anticipate how each focus student will solve a particular problem, which helps in the lesson planning process.
By looking at recent examples of student problem-solving, and anticipating how each focus student might solve the problem, teams were ready to script their research lessons. Our research lessons use a launch, explore, discuss format and focus on deeply exploring multiple ways to solve a problem. This format is also called teaching through problem solving and has many benefits for student learning, motivation, and identity development. During this type of lesson, 2-4 different student problem-solving strategies are shared with the whole class followed by a class discussion about how the strategies are similar, different, and what they illuminate about problem-solving and the math concepts being explored. Using the anticipated focus student responses and problem-solving strategies, the teams think about which focus student strategies could be shared during the lesson and what sequence would best support student exploration of the mathematical understanding goal.
The 3rd grade cross site lesson study research team shares their anticipated student thinking.
Using the anticipated student responses, teams determine what questions to ask that would support students in thinking about and discussing the mathematical understanding goal. Most teams started with general questions such as:
What is similar and what is different in these students strategies?
Who can build on that idea?
How do we know that?
Do we agree or disagree? Why?
After asking questions to surface students' ideas, the lesson study teams created questions that would push students to discuss the core mathematical ideas. While these targeted questions were more focused on the chosen mathematical understanding goal, teachers were careful to design them to still require students to reason and justify their thinking:
Is 3/2 more than a whole? How do you know?
How can benchmark fractions help us?
How is the pattern growing? How do you know?
How do we know what the rate of change is in these different representations?
Is the rate of change constant? How do you know?
How does the idea of rate of change relate to our previous discussion about proportions?
What other explanations can we think of for these data?
When would you want to use Sarah’s problem solving strategy? How about Jose’s? When would you want to use Jamelle’s? Why?
For an example of anticipated focus student responses and a team’s planned questioning strategy, see pages 12-16 in the 3rd grade public lesson study memorialization document. (The whole 3rd grade public lesson can be found here.) All of the research team’s questions focused students on discussing the mathematical understanding goal: Students understand that fractions can be represented as less than one whole and greater than one whole and can use this as a source of comparison.
With the lessons taking shape, lesson study teams were ready to think about the next step – data to collect during the research lesson.
For educators looking to try lesson study in their own contexts, we found that:
Looking at focus student work helped teams anticipate what focus students might say or do during the research lesson and helped teams plan their lessons.
Teachers found it useful to use a Looking at Student Work Protocol during PLCs, discipline meetings, and lesson study planning times to more deeply understand how students make sense of important mathematical ideas.
The mathematical understanding goal is a useful ‘north star’ for developing questions that focus the class discussion.
Up Next: Deciding on Data to Collect
Daisy Sharrock works at the Center for Research on Equity and Innovation at the High Tech High Graduate School of Education, and is part of a Student-Centered Learning Research Collaborative-sponsored research team that is currently engaged in the following study: Leveraging the Power of Improvement Networks to Spread Lesson Study. Read more about their current study here. We are grateful to JFF, KnowledgeWorks’, and the Student-Centered Learning Research Collaborative and its funders for their support. Learn more at sclresearchcollab.org
