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DISCUSSION SESSION 1 Sa tat rday, 11:00 a.m. - 12:30 pm Content arc! Learning Issues 1. Read Marcy's Dots and find a solution. How do you think students might solve the problem? What errors do you think they would make? 2. Examine the student solutions. What observations can you make? 3. Does the problem address an important mathematical concept? What mathematical areas are involved? Should these areas be in the middle grades curriculum and where? What mathematical knowledge would stu- dents need to solve the problem? How might that knowledge be built in grades K-6? What follow-up activities might be used to help students be successful on such a problem? How does this problem connect to math- ematics after grade 8? 4. Read the draft section on algebra for the middle grades from "Principles and Standards for School Mathemat- ics: Discussion Draft." What does Marcy's Dots have to do with algebra as content? DISCUSSION SECTION WORKSHEETS ,`~.~.~.r ''in DISCUSSION SESSION WORKSHEETS DISCUSSION SESSION 2 Sa tat rday, 4:00 p.m. - 5:30 p.m. Participant Sheet Renect on the videos you saw in the plenary session and the pane} discus- sions that followed. Think about your reactions, particularly in light of the focus points for the session. What are the important characteristics of effective teaching in the mi(l(lle gra(les? Of effective teaching of mathematics in the middle grades? How can instruction in middle grades classrooms be organize(1 to maximize learning? How can we tell when learn- ing is happening? What tools and strategies wait make a ifference in how mi(l(lle gra(les stu- ents learn mathematics? Observations: DISCUSSION SESSION 3 Sat n day, 10:30 a.m. - 11:30 a.m. Participant Sheet Certain issues are associate(1 with teaching and learning mathematics in

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the middle grades. These issues range from how teachers are prepared to what students do in the classroom to what the system and community expects math- ematics to look like in those grades. As a group, what statements can you make about each of the following issues? You might think in terms of: 3 areas of agreement 3 challenges/issues needing more work. Content arc! learning mathematics in the micIcIle gracIes In particular, as you think about the issues surrounding content and learn- ing, some of the points that might frame ~ your discussion are: APPE N DIX 5 1. the role of number, specifically rational numbers 2. algebra anti linearity as a major element in the middle grades 3. integration of mathematics con- tent with other (liscipline areas 4. focusing the mathematics content without eliminating important math- ematics for middle grades students Teaching in micIcIle gracIes In particular, what can you say about successful teaching in the mi(l(lle grades and about successful teaching of mathematics. Some of the points you might think about are teaching 5. for thoughtful engagement and learning with un(lerstan(ling 6. competence without acceleration an(1 specialization 7. mathematics to young adolescents 8. preparation and certification for mi(l(lle gra(les mathematics teachers