using lesson study and four column lesson planning with preservice teachers(1)

8/13/2019 Using Lesson Study and Four Column Lesson Planning With Preservice Teachers(1)

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Mche E. Mtthes, Chstphe S. Hs, n Tees M. Fnken

Using Lesson Study

and Four-ColumnLesson Planning with

Preservice Teachers

Lesson study, a form of professional develop-ment that originated in Japan, is gainingpopularity in the United States. In lessonstudy, a small group of teachers (referred to

in this article as a lesson study pod) collaborativelydesigns a model lesson to address specific goals. The

lesson is taught by one of the pods teachers, while

the others observe the students and the lesson with-out intervening. The purpose of the observations isnot to assess the teacher but rather to assess whetherthe lesson design addresses the identified goals. Apostlesson debriefing may provide insights that leadto lesson revisions. The revised lesson may be taught

by a different teacher, while the other teachers in thepod observe. The cycle continues for as long as thepod determines that revisions are necessary. Once a

lesson study cycle is completed, reflections and otherinsights are disseminated to pod members and othersvia reports, Web sites, training, and other means.

Incorporating four-column lesson planning

into lesson study encourages preservice

secondary school teachers to be more

student centered and value collaboration.

504 MaTHEMaTiCS TEaCHEr |V. 102, N. 7 Mch 2009

Copyright 2009 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.This material may not be copied or distributed electronically or in any other format without written permission from NCTM.


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The lesson study cycle described here is typicalin the United States and closely mimics the Japanesecycle. One aspect of lesson study that is commonlyoverlooked, however, is the instrument used for cre-ating the lessonsthe four-column lesson plan.

WHAT IS A FOUR-COLUMN LESSON PLAN?Traditional lesson-plan formats in the UnitedStates consist of one column; they are sequentialand focus on the teachers actions for the lesson.Four-column formats use both vertical and hori-zontal dimensions. Items are arranged verticallyin sequential order and are synchronized horizon-tally (Lewis 2002). Developing a four-column planrequires predicting student responses, preparing

appropriate teacher responses (such as further

questioning, differentiation, and scaffolding), andassessing students understanding. Four-column

lesson plans are organized horizontally by thesetopics: procedures, student responses, teacherresponses, and evaluation and assessment.

Table 1shows a portion of a sample four-

column lesson plan. In the first column, the teacherlists the traditional sequence of activities, alongwith preplanned questions. The potential responsesto these questions are noted in the second column,near the corresponding activities. In the third col-umn, the teacher suggests ways in which he or shecould respond to the students reactions and inter-actions with the mathematics. The fourth columnis reserved for the teachers informal and on-going

assessment of students understanding.

Table 1 A Preservice Teachers Four-Column Lesson Plan

Overall goal: To formulate a conjecture for the volume formula for pyramids and cones from the formula of prismsand cylinders

Materials needed: Beans, hollow shapes

Steps of the Lesson:

Learning Activities and

Key Questions

Expected Student

Reactions or Responses

Teachers Response to

Student Reactions/

Things to Remember

Goals and Method(s) of

Evaluation

Review volume of prisms/cyl-inders (recently learned).

Show a right prism and right

pyramid w/ same height andcongruent bases. How many

times bigger is the volume ofthe prism?

Students explore (using beansand hollow shapes, includingoblique shapes) and recordanswers on the board.

If the volume of a prism isrepresented V1 =Bh, how canwe represent the volume (V2)of a pyramid?

Some students sayLWH instead of BaseArea H.

Likely guesses include 2 times

bigger. Some students maycorrectly guess 3.

Beans are not precise (e.g., 43beans compared to 15 beansmay not seem to be 3 timesas big).

Some may think that V2=3Bh.

Others will see the correctsolution.

2 thinkers may be confusedwhy it isnt 2 times as big.

Some students want a morethorough proof.

Present cylinder as acounterexample.

Encourage guesses/

explanations.

Discuss possible refining ofthe answer if a better unit(say # of grains of sand) had

been used.

Pyramids have more volumethan a prism?

How might a cone be relatedto a cylinder?

Showing the triangular prismthat actually is twice as big

can help.

You may choose to do arigorous (based on a limitapproach) proof or just pro-vide a reference.(mathforum.org/library/drmath/view/55041.html)

All students show that V=Base Area H.

Visually check that each stu-

dent is making a conjectureand trying to think why.

Students should recognizethat the volume of the prismis about 3 times the volume ofthe pyramid.

All students should believethe V2 = (1/3)Bhformula.Ideally all students will applythe formula to cone/pyramidvolume problems.


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USING FOUR-COLUMN PLANS TOENHANCE LESSON STUDYOne advantage ofthe lesson study model for pro-fessional development is that it can help teachers

become more adept at predicting and hence sup-porting student reasoning. The four-column plan

for lesson study provides a prescribed format inwhich participants can anticipate student reac-tions before implementing the lesson. Moreover,this format allows participants to consider theteachers responses to these student reactions. To

be successful, lesson planners must anticipate howstudents are interpreting and using the lesson con-tent through their reasoning. Columns two, three,and four enable observers to focus on how students

react with the lesson, and column four also allowsfor a variety of assessments to inform the paceand orchestration of the lesson. Once the lesson isplanned and the observations begin, teachers gaininsight from seeing student reactions and evaluating

their own anticipated responses and assessments.

PRESERVICE TEACHERS INSIGHTSFor the last few years, we have been using lesson

study and four-column lesson plans with preser-vice teachers as part of their initial professionaldevelopment. Using the Fernandez (2005) adapta-tion, which streamlined the lesson study formatfor methods courses, preservice teachers developgoals-driven lessons, use peer observation for the

lesson evaluation, and conduct postlesson debrief-ings, which lead to informed revisions. In a similar

lesson study adaptation, we incorporated coopera-tively written four-column lesson plans as part ofthe practicum and methods course content for thesepreservice teachers.

To examine the possible impact of our lessonstudy adaptation, we analyzed surveys conducted atthe end of the course, follow-up surveys conductedsix months later, comments from the preserviceteachers student teaching supervisor, and the pre-service teachers journal entries from the methods

course. To analyze the data, we used qualitativemethods, scouring the data for consistent themesthat appeared in multiple data sources (triangular-

ization). In this article, we focus on findings abouttwo of these themes: student-centered learning andthe usefulness of peer collaboration. Because quali-tative research does not contrast findings againsta control group, these results should be consideredsuggestive, not causal.

The preservice teachers reported that the four-column planning and lesson study helped them

become more student centered in their approachto teaching, planning, and reflection. One teacherstated, Really trying to think from a studentsperspective instead of always thinking about what,

as a teacher, Im going to be teaching [was my mostintense experience]. I really thought it was benefi-

cial to think how the students would react and tothink of their activities. What will they be doing?Another teacher commented on the four-columnplan, particularly the second and third columns:

I really like this section, because it gets you tostart thinking about how students will be thinkingin the classroom. Even if you are completely offin your predictions of their thinking, it still helpsprepare you for what might happen. This teacher,

like many others in our study, went beyond simpleappreciation of the focus on students to the rec-ognition that this focus was the reason that the

four-column plan helped the pods lesson plannersand teachers be more prepared. A third teacherdiscussed the potential contrast between using tra-ditional and four-column plans in future teaching,noting, Im not sure that my practice would bethat different, because either way Ill still be think-ing ultimately about the studentsbut with a fourcolumn plan, things might be smoother because stu-dent responses are recorded and anticipated.

Many of the preservice teachers in our study recog-

nized that devising four-column plans requires addi-tional time in their daily planning for lesson study.However, most indicated that, as the third teacher

quoted earlier implied, they will continue to be stu-dent centered in their future activities as teachers.

The preservice teachers in our study also foundthat the lesson study process helped them recog-nize the value of collaboration and become morecollaborative in their planning and reflection. One

teacher, when asked how the lesson study experi-ence would influence his or her short- and long-range planning, said, Lesson study has made merealize how important it is to reflect on lessons andtalk them over with other teachers. Collaborationwas also deemed useful during the planning stages:

Rening the lesson in apostlesson conference

PHoTograPHbyMiCHaElE.MaTTHE

wS;allrigHTSrESErVEd


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Collaboration is very helpful. People see differentthings in different ways and can help give another

way a student might perceive something.Many of the preservice teachers in our study saw

the four-column format as enhancing collaboration.One teacher commented, I think the last two times

(with pairs or small groups) worked well with afour-column design. It works well for communicat-ing ideas to others. A second teacher, respondingto a question about how well collaboration workedwhile planning, said, I found when I used thefour-column plans, I always found things I wantedto add to it when I shared it with someone. Bothcomments indicate that collaborating with a four-

column format helped these teachers find concreteways to improve their lesson plans. As these resultsshow, lesson study and the four-column format may

have helped these preservice teachers by encourag-ing and focusing their collaborative efforts.

CLOSING THOUGHTSLesson study is inherently collaborative in nature,and many of the preservice teachers in our studythought the four-column format enhanced their

collaborative planning and revising. Each believedthat, because of the lesson study experience, heor she became more student focused in his or her

practice. Lesson study naturally leads participantsto focus on students thoughts, especially during theobservation and debriefing stages. Four-column for-mats may enhance this student-centered focus byrequiring participants to craft careful responses toanticipated student thinking during lesson develop-

ment and thus improve the subsequent observationand debriefing experience.

Becoming student centered and recognizing thevalue of collaboration are important traits for allteachers, not just preservice teachers, to acquire.We view collaborating and becoming student cen-

MICHAEL E. MATTHEWS,

[email protected],

CHRISTOPHER S. HLAS, hlascs@uwec.

edu, and TERESA M. FINKEN, tnken@

iwc.edu, teach preservice teachers at

the University of Nebraska at Omaha,

the University of Wisconsin at Eau-

Claire, and Iowa Wesleyan College in

Mount Pleasant, respectively. They are

interested in early and later profession-

al development with teachers as well

as problem solving. PHoTograPHS by ColiNa

MaTTHEwS, bill HoEPNEr, barbara barrowS; all rigHTS rESErVEd

tered as on-going, self-generativetraitstraits that,once learned, generate more learning and can serve

teachers throughout their careers (for more on self-generative traits, see Franke et al. [2001]). Lessonstudy may also allow teachers to develop other traitsnot explored here, such as reflective dispositions

and goal-oriented instruction. Our experiences overthe last few years and our research lead us to see

lesson study as a worthwhile initial professionaldevelopment experience for preservice teachers.

REFERENCESFernandez, Maria Lorelei. Learning through

Microteaching Lesson Study in Teacher Preparation.

Action in Teacher Education26, no. 4 (2005): 3747.Franke, Megan Loef, Thomas P. Carpenter, Linda

Levi, and Elizabeth Fennema. Capturing Teach-

ers Generative Change: A Follow-up Study of Pro-

fessional Development in Mathematics.American

Educational Research Journal38 (2001): 65389.

Lewis, Catherine.Lesson Study: A Handbook of

Teacher-Led Instructional Improvement. Philadel-

phia: Research for Better Schools, 2002.

Lesson study and the four-column

format may have helped

these preservice teachers byencouraging and focusing their

collaborative efforts


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