天美传媒

Lesson 天美传媒: A Structure to Enhance Pedagogic Development

Donna Gee, Department of Education, Angelo State 天美传媒, U.S. 

Connie Yarema, Department of Mathematics, Abilene Christian 天美传媒, U.S. 

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Abstract

Lesson 天美传媒 is a structure for professional development, originating in Japan, which focuses on student thinking and learning (Stigler and Stevenson, 2001).  This professional development proposes that teachers work collaboratively to research the effects of student learning of a content topic identified as difficult to learn or teach.  The goal is to gain knowledge of content useful for teaching, curriculum, and student learning with a focus on implementing changes in instructional practice.  This process involves setting goals, investigating curriculum, planning a unit of study, developing a research lesson, teaching the lesson with others observing, discussing data collected from the observation, and disseminating the results. This article describes the professional development of elementary and middle school mathematics teachers involved in Lesson 天美传媒 in West Texas, United States.  Information about Lesson 天美传媒 is presented along with vignettes of teachers involved in a study that sought to answer the question: How do teachers involved in Lesson 天美传媒 describe their professional development in the teaching of mathematics?  Data, to answer the question, were collected through interviews and reflective journal responses.  An analysis of the data indicates teachers utilized the focus on student thinking and learning to improve instruction, reporting a change in the manner in which they designed and implemented lessons. A change in teaching practice occurred in areas of the structure of lessons, implementation of academic language, adjustment of time devoted to student understanding, and classroom dialogue.  The conclusion provides suggestions for incorporating Lesson 天美传媒 to support the pedagogic development of educators. 

Keywords:  lesson study, professional development, student learningPage Break 

Pedagogic Development in Action

As Elizabeth, Lisa, Kerry, and Staci, middle school mathematics teachers, are involved in a deep discussion about student responses during a mathematics lesson Lisa just finished teaching with the remainder of the group observing, we, as Lesson 天美传媒 facilitators, examine their interactions and take notes on their recommendations, what they noticed, and ideas to help enhance student thinking and understanding. As they discuss, they refer back to student work collected through photographs, notes they had written as they observed and listened to the students, and large chart papers on which students recorded their steps for solving a mathematics problem presented in the lesson.  Their discussion is intently targeted on how students displayed their understanding and the depth of that understanding.  We, who observed the lesson and students, present our recordings of the observations we made during the teaching of the lesson along with our notes of the conversations of the teachers who contributed to the conversation regarding students and how they learned mathematics.  We are participating in Lesson 天美传媒, a professional development model originating in Japan (Takahashi and Yoshida, 2004).  As university educators, we continually explore how to develop pedagogical knowledge of teachers.  This overarching quest to gain more knowledge in this exploration motivates our research question: How do teachers involved in Lesson 天美传媒 describe their professional development in the teaching of mathematics?  This article provides insight into the views of elementary and middle school mathematics teachers involved in a professional development following the framework of Lesson 天美传媒.  

Researching Teaching through Lesson 天美传媒 

Like most educators, these teachers, along with other elementary and middle school teachers, dedicate themselves to enhancing student understanding of content.  Thus, they participate in year-long professional development mathematics projects offered through two universities located in nearby cities in West Texas.  In doing so, these teachers join other teachers and higher education faculty, who serve as facilitators, to collaborate and examine student learning of mathematics through the structure of Lesson 天美传媒.  This collaborative and deep examination of student thinking and learning is a main feature of Lesson 天美传媒 (Stigler and Stevenson, 2001).  It also correlates to several of the teaching practices recommended in the Principles to Action document created by theNational Council of Teachers of Mathematics (National Council of Teachers of Mathematics, 2014), with a particularly strong correlation to the practice to “elicit and use evidence of student thinking” (National Council of Teachers of Mathematics, 2014, p. 10).   This emphasis on deeply examining, facilitating, and using student understanding and thinking, which are main components in the structure of Lesson 天美传媒, supports high quality teaching and learning of mathematics.   

Many times, teachers who participate in Lesson 天美传媒 begin by examining student data to ascertain an area on which student performance is low.  They also write goals for the Lesson 天美传媒 based on an identified mathematical concept with which students struggle and on their schools’ mission statements. Teachers collaboratively plan a unit and develop a research lesson, which is based on those goals and requires students to problem solve.  During the development of the problem solving research lesson, teachers: 1) develop and analyze a problem to elicit student thinking, 2) anticipate student thinking about the paths that lead to a solution of the problem, 3) pose possible questions that could be used to elicit students’ thinking about the problem, and 4) form questions that are used as guidelines by observers for data collection about students and their thinking during the teaching of the problem solving lesson.  During the process of developing a research lesson, teachers specifically tie the goals for their Lesson 天美传媒 to the creation of a research lesson that addresses the needs of their students.   

As one teacher teaches the research lesson, others observe and gather data on student thinking and responses.  Later observers discuss student responses and thinking, and teachers revise the lesson to improve student understanding and achievement (Fischman and Wasserman, 2017; Groves et al., 2013; Lewis et al., 2006; Takahashi and McDougal, 2016).  From this discussion, teachers participating in Lesson 天美传媒 come to realize and acknowledge their need to research how to better teach the concept so they can strengthen students’ understanding. 

Collaborations of teachers should focus on instructional practice and student achievement (Pasatta et al., 2017).  Participating in a Lesson 天美传媒 provides educators with opportunities to collaborate on these items.  Teachers design instruction to elicit student thinking about the mathematics that is the focus of the lesson.  Involved in this practice is the opportunity for those teaching the lesson, such as Lisa, to pose questions to students with the purpose of clarifying students’ thinking about the problem.  As the lesson progresses, Outside Observers, usually other teachers, university faculty, and possibly a school administrator who are not part of the planning team, gather data on student thinking.  They hear: 1) students’ small group discussions about the problem’s solution, 2) communications between Lisa and groups of students, 3) students’ explanations as they present their solutions at the board or to their class mates, 4) a whole class discussion of students’ methods used to solve the problem, and 5) Lisa’s summing up of the lesson which incorporates student responses to help teach the mathematics content.  The order in which the presentation of student solutions occurs is pre-planned by the Lesson 天美传媒 team with the goal of building a scaffold to the teaching of the content in the lesson.  Lisa, in her teaching, uses information and ideas from the students’ thinking displayed in their work to help teach the mathematics that are the learning goals of the lesson.  As a result, Lisa begins the teaching with the students’ thinking about the problem, builds on their knowledge, and scaffolds their ideas to guide them to a deeper level of understanding, and, in so doing, tries to further extend students’ current knowledge base. 

In the next phase of the Lesson 天美传媒 process, the Lesson 天美传媒 team and Outside Observers discuss the data collected through observations, photographs of student work, students’ desk work, and student presentations.  Throughout the discussion, participants tie data collected back to the lesson goals and objectives in an effort to determine if those were met.  The discussion begins with the teacher of the lesson, Lisa, providing comments about the lesson and its outcomes.  Then, the other teachers in the Lesson 天美传媒 team provide their comments about the lesson.  Next, Outside Observers ask questions to the Lesson 天美传媒 team about the design of the lesson in regards to student learning of mathematics.  Outside Observers provide suggestions on how to further support student learning based on the evidence of collected data.  This post lesson discussion results in revisions to improve the structure of the lesson and, ultimately, instruction.  Following the revision of this particular research lesson, the process continues with another teacher on the team, Elizabeth, teaching the revised research lesson several days later while others observe and document student thinking.  This format of teaching, observing, discussing, and revising, which may be followed by another cycle of teaching, observing, discussing, and revising, offers a structure to practice how to elicit, examine, and understand student thinking at a deeper level.  Several of the teachers comment that although it is not necessary, a second teaching of the research lesson benefits the team by  providing additional data which offers further insight into student thinking and understanding.  

Using Findings to Improve Instruction

Discussions with and reflections from elementary and middle school mathematics teachers who participated in Lesson 天美传媒 indicate that they use the findings collected from the teaching of a research lesson in a variety of ways to improve instruction in their classrooms.  These teachers report a change in the way they design and implement daily lessons after participating in Lesson 天美传媒.  For example, the Lesson 天美传媒 team of Elizabeth, Lisa, Kerry, and Staci later reflect on the value of actively engaging students in a lesson and the increase in the number of lessons that they teach in which students explore, problem solve, and explain their reasoning.  Rather than showing students how “to do” a problem and giving them similar problems to solve, the teachers spend more time implementing lessons that allow for the emergence of student thinking.  They seek problems that allow for multiple paths to a solution, anticipate how students might solve a problem, and analyze a problem for possible issues that might develop misconceptions, such as considering how a problem statement should be stated to help students more clearly understand the problem.  

The focus on both teachers’ and students’ use of academic language is frequently cited in the data.  For example, during the teaching of a research lesson, Outside Observers note that some eighth grade students use the term 3-D rectangle instead of rectangular prism. Teachers, during the post-lesson discussion, share how often they use colloquial language instead of mathematical vocabulary.  Staci describes how her eighth grade students call a reciprocal a flipped number and how easy it is to continue using the term since the students are using it.  Kerry notes how Lisa uses a word wall to assist students in forming a habit of using appropriate mathematical language that also provides a visual for students.  During the next Lesson 天美传媒 meeting some of the participants share a change in their practices that include a mutual understanding that students can correct their informal use of academic language and the teachers can correct students’ colloquial language.  Thus, student thinking about mathematical vocabulary  during the teaching of a problem solving lesson in one classroom prompts changes in instruction in several teachers’ classrooms.  

An increased awareness to be more patient with students, allowing them time to develop conceptual understanding and to practice new skills, is another frequent outcome from teachers’ Lesson 天美传媒 experiences.  Sometimes this awareness manifests itself in the classroom through the resequencing of lessons, such as dividing a lesson into simpler tasks to be completed over additional days.  Other times their awareness of the need of students to have more time to develop conceptual understanding prompts teachers to create basic or foundational lessons to address misunderstandings or lack of basic skills before moving on to more sophisticated concepts.  During those supplementary lessons, the use of manipulatives or various types of visuals provide a support for student learning and understanding.    

In addition, teachers’ Lesson 天美传媒 experiences influence a change in the dialogue modeled in the classroom.  Teachers often move their position from the front of the room to the side, back, or center of the room as they become a facilitator of student discourse, mingling among students and listening to their conversations.  Teachers encourage students to ask each other questions, discuss ideas, and share their thinking about mathematical concepts.  For example, in a middle school classroom, Elizabeth arranges desks so that students work in pairs or in small groups.  As the students work on solving the problem, Elizabeth circulates throughout the room, taking note of student discussions, problem solving strategies, and any misconceptions for either immediate intervention or for use in whole group discussions.  However, teachers also report struggling with this practice, attempting not to intervene too soon in an effort to allow students time to grapple with and to try different strategies to solve a problem.   

Another change in the form of classroom dialogue occurs in the way teachers structure a whole group discussion in which students share how they solve a problem.  During a whole group discussion, the teacher might ask students to compare and contrast the various ways of solving the problems or ask students to look for patterns, find connections, and determine if there are other means of solving the problem.  In such discussions, teachers facilitate the discourse to further student understanding and address misconceptions or incorrect solutions and thinking rather than lecturing and telling students how to solve the problem. 

A Structure for Professional Development

Lesson 天美传媒 provides a structure that schools or educators might use to focus on student thinking in an effort to improve instruction.  Lesson 天美传媒 involves several elements that, collectively, make it a unique and powerful form of professional development.  First, educators spend time collaboratively developing a problem solving lesson that will be the observed research lesson.  In developing this lesson, teachers consider possible questions to ask students, discuss student approaches to solving the problem, consider how they can use student reponses to teach the mathematics in the lesson, and anticipate possible student mistakes or misconceptions.  Second, teachers observe lessons being taught in other classrooms, focusing on student thinking and learning during the lesson.  This component in the framework of Lesson 天美传媒 provides those observing opportunities to witness how the lesson is structured to promote student understanding through such aspects as the scaffolding of student learning, use of academic language, promotion of student discourse, and use of student thinking to help teach the concept.   

In teaching a problem solving lesson in mathematics, teachers often find it difficult to “give up control” of the classroom by allowing students to determine how to solve the problem.  The teachers also report that it is challenging to not “spoon feed” the information to students, but to allow them to struggle and wrestle with “the how” to solve the problem so that educators support “productive struggle” as recommended in the Principles to Action document (National Council of Teachers of Mathematics 2014, p. 48).  However, to give in to our desire to “help” students hinders their ability to develop thinking and problem solving skills.  In this regard, the structure of Lesson 天美传媒 allows teachers to practice teaching a lesson that they specifically designed to elicit student understanding, to support productive struggle of student thinking and reasoning, and to receive non-threatening feedback and suggestions from other educators based on student responses to ultimately improve instruction.   

However, implementing Lesson 天美传媒 outside of Japan faces several challenges that are identified by researchers (Brown and Taylor, 2016; Ngang and Sam, 2015; Perry and Lewis, 2008).  The collaboration that is an essential component of Lesson 天美传媒 requires time and space.  Brown and Taylor (2016)  indicate teachers often find demands of collaboration a challenge as school administrators propose additional school initiatives.  Establishing a professional community and the sharing of a research lesson as a basis for collaborative reflection support the implementation of Lesson 天美传媒 but are non-existent in some schools (Perry and Lewis, 2008).  The need to disintegrate the hierarchical relationships that support classrooms as private places, make student thinking a focus, seek external knowledge as a source on which to glean information (Perry and Lewis, 2009), and involve school administrators (Ngang and Sam, 2015) are necessary for Lesson 天美传媒 to be embedded into schools.  Thus, implementing Lesson 天美传媒 may require a major change in school structure.     

Adding to the challenges is the development of understanding of Lesson 天美传媒 as proposed in Japan.  “A lack of understanding of how the Lesson 天美传媒 process is supposed to help teachers deepen their understanding of content and of new pedagogical ideas” may occur (Takahashi, 2014, p.2).  Misinterpretations from discussions may invoke defensive mechanisms that lead teachers to refrain from making changes (Bozkurt and Yetkin- 脰zdemir, 2018).  As a professional development model based on research, Lesson 天美传媒 invokes a perspective of a process of change over time rather than a recipe type model to which teachers in the U.S. may be accustom (Lewis, 2006).   Thus, cultural factors that influence teachers’ understanding of what professional development should entail can impede the implementation of Lesson 天美传媒 in countries outside of Japan.  

Currently, the culture of U.S. schools does not provide educators with a structure for professional development that is embedded in the work of the classroom.  In addition, time and space needed for collaboration to deeply reflect on teaching, student learning, and data on student learning collected from classroom observations is difficult to manage in the culture of U.S. schools.  Although information exists about Professional Learning Communities to enhance teaching and student learning (DuFour et al., 2005; Hipp et al., 2008), teachers may lack a structure that would support such a community.  On the other hand, Lesson 天美传媒 offers such a structure for this type of professional development of teachers, one that focuses on student thinking and instruction.  However, educators may need to think of ways to reform the structure of schools before it can be adapted to the U.S. educational system.  

Conceivably, teachers could meet together for one week during the summer to set learning goals, investigate curriculum and issues with student learning, and plan and develop a problem solving lesson.  Then, a few school days could be provided for them to observe, along with invited Outside Observers, the teaching of their lesson and to discuss student thinking and understanding.  Later, teachers can write a report of their findings to disseminate at district levels or professional meetings.  This dissemination of findings from teachers’ research to advance what we know about teaching and learning is an essential feature of Lesson 天美传媒.  As emphasized by Crawford (2014), research findings could be dissemated in a variety of ways, including blogs or publication in academic journals.  Perhaps it is time to rethink professional development and the collaborative model needed so that isolation will not be a hindrance to student learning (National Council of Teachers of Mathematics, 2014). A structure, such as Lesson 天美传媒, can help provide assistance to teachers in supporting the teaching practices that are recommended in the Principles to Action document so that the principles are actually put into action (National Council of Teachers of Mathematics, 2014, p. 10).    

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