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lL~ L'1`' 1~- -1 r~.01 As representatives of the co-sponsor- ing organizations and the education community, we would like the Convoca- tion to be viewed as the first step in a continuing dialogue. In particular, we hope that the essence of the Convocation wall be replicated by states and regional groups affiliate(1 with the parent organi- zations. To support such state and regional groups, the thinking anti struc- ture we used to design the program is described below. The intent was to contrast the perspectives brought by each of the sponsoring organizations and their constituencies, to raise issues about these perspectives, to promote interac- tion, and, through small discussion groups, to engage participants in renect- ing on their own role in middle grades mathematics education. To reinforce the points illustrated by the plenary speak- ers, the small group discussions involved participants in an analysis of a "site of practice," grounding the conversation in what teachers and students actually do in classrooms. Discussion group leaders were given instruction and direction for working with their groups fohow~ng the opening plenary session and were provided with complete packets of materials for use with their groups over the two days. Before the conference, participants were given materials as background reading and to help them begin to focus on the issues framing the Convocation. (See page 5.) The Convocation began with speakers who presented teaching mi(l(lle school mathematics from two points of view: teaching mathematics with a focus on the subject matter content or teaching math- ematics with a focus on the whole child and whole curriculum. The purpose of this session was to set the stage for thinking about mi(l(lle gra(les mathemat- ics classrooms from these two perspec- tives and to stimulate thinking throughout the rest of the Convocation about teaching and learning mathematics through these (lifferent lenses. Within this framework, the Convocation was organize(1 around three central themes with a set of organiz- ing questions for each theme: content and learning in mi(l(lle gra(les mathematics; mi(ldle gra(les mathematics teaching; and organization of mi(l(lle gra(les instruc- tional programs and their impact on mathematics teaching anti learning.

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Each of these themes was introduced with a plenary session, where individual speakers or a pane} described some part of the landscape. Discussion groups that addressed the issues in terms of an activity selected from the actual practice of teaching followed the first two plenary sessions. The discussion groups were composed of ten or fewer participants that by design represented a mix of three groups: classroom teachers, teacher educators and university representatives, and those in some way responsible for a system including administrators, repre- sentatives from state and local systemic initiatives, and curriculum supervisors. In addition, time was provided for district teams to meet and address their con- cerns in light of the Convocation conver- sation. The teams were configured differently depending on the needs of the system they represented, with some team members from a given school district while other teams were a blend of teachers and university mathematics educators with common goals for a district. THE CONVOCATION THEMES Middle Grades Content and Learning Issues The plenary session on content and learning mathematics in the middle grades focused on the questions: . What developmental considerations are important in thinking about middle school students as learners? as learners of mathematics? Are these compatible? What do we know about middle school students' capacity for learning? for learning mathematics? What are important ideas in math- ematics for the middle grades and how are these related to (levelopmen- tal learning considerations? There were two speakers, one presenting a middle grades perspective about learning, including comments about thematic units and integrated curricula, and the second addressing how students learn certain mathemat- ics concepts in the middle grades from the perspective of mathematics educa- tion research. The discussion group participants worked through Marcy's Dots (see page 58), an algebraic rea- soning problem from the 1992 National Assessment of Educational Progress, then reflected on student strategies (Appendix 4, page 240) in light of their own thinking. This was followed by a discussion about learning mathematics based on the middle grades algebra section from the 1998 National Council of Teachers of Mathematics Principles and Standards for School Mathematics: Discussion Draft using the lens of the child and the lens of content. MATHEMATICS EDUCATION IN THE MIDDLE GRADES

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MicIcIle GracIes Teaching Issues Two videos about the practice of teaching were the focus of the plenary session on teaching. In the first video, students discussed the nature of mathematics teaching and how they had learned mathematics through the actions and beliefs of their teacher. The second featured an eighth grade class during a lesson on algebraic thinking. The audience was asked to view the videos in light of the following questions: . What are the important characteris- tics of effective teaching in the middle grades? of effective teaching of mathematics in the middle gra(les? How can instruction in middle grades classrooms be organized to maximize learning? How can we tell when learning is happening? What tools and strategies wait make a difference in how middle grades students learn mathematics? Following each video a pane} composed of a middle grades teacher, a mathematician, and a mathematics educator reacted to the three ques- tions. The comments and reactions of the pane} within the framework of the focus questions were used to shape the participant discussion sessions. PROGRAM STE E Rl NO COMMITTE E MicIcIle GracIes School Organizational Issues How middle grades are organized and the impact of that organization on the teaching and learning of mathematics was the theme of a pane} discussion in this plenary session. Panelists were asked to consider: What are the important characteris- tics of school organization and math- ematics programs that support teaching and learning meaningful mathematics in the middle grades? How can the schedules of teachers and students be organized to implement what we know about effective teaching and learning in the middle grades? What are the issues surrounding specialists vs. generalists? What kind of teaching assignments maximize program effectiveness in mathematics? Following the pane} presentation, the panelists were asked to address specific questions raised during the Convocation with questions and reaction from the audience. The chair of the Steering Committee gave a closing summary of the issues anti challenges raise(1 (luring the Convocation. It is our hope that this overview will be useful for the rea(ler to both un(ler- stand the nature of the Convocation and to think about the (resign as one that might energize other communities to structure a similar venture.

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