Lesson Study in Preservice Elementary Mathematics Methods Courses: Connecting Emerging Practice and Understanding

Abstract

Teacher education programs have long struggled to find the best way to prepare quality teachers, and research has shown that teacher educators face several challenges. Lortie (1975) uses the term “apprenticeship of observation” in explaining how teachers’ own schooling experiences shape their beliefs about teaching, and ultimately how they interact with students in their classrooms. Brouwer and Korthagen (2005) stipulate that teachers become socialized into the profession, adopting more traditional models of teaching that are consistent with the culture at most schools, despite the kind of experiences they have had in teacher education programs. We must question how much influence the teacher education programs can have on teachers given that such socialization is a strong factor impacting practice.

Appendices

Appendix 1: Student Assessment Assignment Guidelines

• 1. In your lesson study group, discuss key ideas for teaching and learning (Weeks 3/4)

  • a. Why is this topic challenging to teach and learn?

  • b. What are the typical mistakes students make?

• 2. Create a set of assessment items (Week 4)

  • a. Start with what you discussed in the previous lesson study meeting. What are the key ideas and what is challenging?

  • b. Design assessment items that highlight the difficulty and challenges of the topic (pay attention to materials used, order of questions, etc.). What does this assessment help you learn about your students’ thinking? Anticipate your students’ responses.

  • c. Decide whether the questions will be interview questions or paper-and-pencil questions.

  • d. Individual assessments should not last longer than 15 min (not too many questions!).

• 3. Assess student thinking (Week 4/5)

  • a. The assessment guidelines and expectations have been communicated with your CTs.

  • b. Ask your CTs to help you identify a student sample in the classroom (ideally 2 students who achieve beyond grade level, 2 right at the grade level, and 2 struggling at the level; include ELL student).

  • c. If you choose to use paper-and-pencil format, find a time to talk with each individual student afterwards and ask him/her to explain thinking process.

• 4. Bring back assessment data to class (Week 5)

  • a. You will discuss what you found in your lesson study group.

  • b. What are common mistakes? Any pattern?

  • c. Why such mistakes? [Connecting back to research]

  • d. What do the results suggest for your teaching (regarding topic, question types, methods you might use, particular student needs)?

• 5. Write up assessment summary

  • a. Attach all the assessment data with the summary.

Appendix 2: Lesson Study Lesson Plan

In writing a lesson plan, please include the following:

• 1. Title of the Lesson

• 2. Names of the teachers

• 3. Grade level of the lesson

• 4. Goals/objectives of the lesson [content objectives as well as social/affective and ELL objectives if appropriate]

• 5. Relationship of the lesson to standards [mathematics content standards for California public schools K-12, and the National Council of Teachers of Mathematics Standards]

• 6. About the Lesson [discuss how this lesson came about]

• 7. Placement of the lesson in the unit [where does this lesson fit in the unit you planned? Discuss the connections among lessons]

• 8. About the students [briefly discuss your student assessment results]

• 9. Lesson steps [use the three-column format—please see back of the page]

Teacher support [This column explains lesson flow]

Student activity [This column shows anticipated student responses to the lesson activities]

Points of evaluation [This column focus on particular aspect of the lesson]

• 10. Evaluation [this needs to correspond to the objectives you stated at the beginning of the lesson plan]

Appendix 3: What to Expect on the Research Lesson Day¼

You have worked very hard with lesson study, and the research lesson is the opportunity to celebrate your accomplishment. You chose a challenging math topic to teach, read research literature to learn why it is challenging, interviewed elementary students to find out their strategies, examined different curricular materials to see the textbook approaches to the topic, and planned your own lesson. The lesson will make your ideas and learning come to life in classroom with real “live” kids. You are the expert now, and share your pride with others who come to observe!!

Before the lesson:

• Let office people know you are expecting visitors that day.

• Make multiple copies of lesson plans.

• Get all the lesson materials ready.

• Set a video camera in the back of the room and one group member can monitor the filming (if there are students whose parents do not wish them to be videotaped, move the students to the side of the room, or set the camera so that these children won’t be in the picture).

• Decide who is giving the intro of the lesson (2-minute overview, see below) to the observers.

• Decide who is taking notes during the debriefing.

• 1. Introduction of the lesson (start approximately 15 minutes before the lesson)

  Observers gather in front of the classroom. Bring copies of lesson plans and give them to the observers. One member from the planning team (usually not the instructor) gives a brief overview of what will happen during the lesson and talk about the data they would like observers to collect during the lesson (it should be noted in the lesson plan). The team can also speak to their reasoning behind decisions they made about the lesson structure. The facilitator gives brief guidelines on observation protocol (handout provided). Allow a few minutes for observers to look over the lesson plan.

• 2. Research lesson (up to 60 minutes)

  Enjoy the lesson. Support the instructor as appropriate. Resist the urge to help students or otherwise interfere with the lesson.

• 3. Debriefing (approximately 45 minutes)

  Find a space for the lesson debriefing (staff room, empty classroom, bench at playground, nearby coffee shop, etc.). Decide one group member to be the scribe and keep notes of the discussion. The debriefing will follow the steps:

  • a. Instructor’s reflections: The instructor describes his/her experiences in the lesson and comments on what went well and was unexpected.

  • b. Planning group members’ comment on the data gathered: This may include data on student learning and engagement. Comments may be guided by two or three specific questions related to the goals of the lesson.

  • c. General discussion on the data gathered: A brief discussion period, facilitated by a moderator, focused on student learning and development, and how specific elements of the lesson promoted these.

  • d. Outside commentator: An outside expert will comment on mathematics and student learning of mathematics.

  • e. Thanks: The facilitator makes final comments and thanks everyone for the participation.

Appendix 4: Final Project Guidelines

Your finals consist with two parts: Lesson study group portfolio and group presentation.

• 1. Lesson study group portfolio:

  You will put together a portfolio as a lesson study group. Portfolio is not a mere collection of items but should be organized with coherent themes to guide your reflection. Your portfolio will have following categories:

  • a. The work we learned the most from

  • b. The work we had the most fun with

  • c. The most challenging work

  • d. The least favorite work

  • e. (Your own category)

  For each of the categories, your group will choose one item from lesson-study-related work you have done this quarter. Your group may also create your own item for a category. For example, you may say “students’ math talk during the lesson” as the most favorite part of your lesson study experience, and in that case, you can put some representation of the experience (photo, etc.) in the binder for the category and write a short description.

  In the big binder provided, label a divider with each category, include item(s) that you chose for the category, and write a short paragraph stating WHY you chose the particular item for the category. For the assignment you did not select, add them at the end of the binder. Include all the lesson-study-related materials in the binder (e.g., copies of meeting notes, debriefing notes, student work from the lesson). Please also turn in your lesson CD with the portfolio.

Individual Reflection Papers (to be included in the portfolio):

While the portfolio is assembled, reflect on the lesson study process and your learning in the quarter. Write a short individual reflection paper and include at the very end of the portfolio. The reflection paper should answer the following questions (but not limited to them):

• What do you think you learned through the lesson study process?

• What ideas from the lesson study experience do you think you can take to your future teaching?

• 2. Final lesson study group presentation:

  Prepare a group presentation to highlight your learning with the lesson study in the quarter. Each group’s presentation should be approximately 20 minutes, and I encourage you to use some visuals—powerpoint, video, overhead, handouts, etc. Please include presentation materials in your final portfolio (e.g., copy of handout, copy of powerpoint slides). I can naturally see how you may use the portfolio categories to organize your presentations, but it is not required. Be creative and have fun with itJ!!