DeFoorSpringEALRProjDeFoorSpringEALRProj.2DeFoorSpringEALRProj.3DeFoorSpringEALRProj.4DeFoorSpringEALRProj.5DeFoorSpringEALRProj.6DeFoorSpringEALRProj.7DeFoorSpringEALRProj.8DeFoorSpringEALRProj.9DeFoorSpringEALRProj.10DeFoorSpringEALRProj.11DeFoorSpringEALRProj.12DeFoorSpringEALRProj.13DeFoorSpringEALRProj.14DeFoorSpringEALRProj.15DeFoorSpringEALRProj.16DeFoorSpringEALRProj.17DeFoorSpringEALRProj.18DeFoorSpringEALRProj.19DeFoorSpringEALRProj.20DeFoorSpringEALRProj.21DeFoorSpringEALRProj.22Positive Impact on Student Learning Project Teaching Linear Relationships to 6th and 7th Grade Math Students Lorri DeFoor June 1, 2009 The Evergreen State College MIT 20091 Table of Contents Section 1: Contextual Factors 2 • 1A: Introductory Letters to Parents 6 • 1B: Classroom and Student Characteristics 8 Section 2: Learning Goals 9 Section 3: Assessment Plan 11 • 3A: Unit Assessments 14 Section 4: Design for Instruction 34 • 4A: WA State IP Rationale 42 • 4B: Unit Lesson Plans 48 Section 5: Instructional Decision Making 109 Section 6: Analysis of Student Learning 113 • 6A: Classroom Data 118 • 6B: Sub Group Data 123 • 6C: Case Study Data 124 • 6D: Examples of Student Metacognition 136 • 6E: Case Study Student Work 138 Section 7: Teacher Reflection and Self Evaluation 1392 Section 1: Contextual Factors Community, District, and School Characteristics The middle school at which this study was conducted is located in Lakewood, WA, just south of Tacoma. It serves a diverse population of 630 sixth through eighth grade students from many racial backgrounds, including White (31%), Black (26%), Hispanic (24%), and Asian/Pacific Islander (15%). The school is close to Fort Lewis and McChord Air Force Base, and serves a number of students from military families. This is an important, though not the sole contributing factor to the school’s high turnover rate (about two-thirds of the students who began the year at this middle school will finish elsewhere). Seventy-three percent of the students at this school qualify for free and reduced lunch. Academically, the school has failed to meet overall AYP requirements and is in Improvement Step 3, which has included the introduction of new administrative staff to coach current faculty, Failure on state tests has also led to the introduction of a remedial math program in which all students were enrolled at the beginning of the school year. This class is taken in addition to students’ regular math classes. Classroom Characteristics The math class in which this study took place is for sixth and seventh grade students in the Advanced Study Program (ASP). On a regular day, math took place during a seventy minute period. Physical space was limited by the presence of sinks and lab stations around the perimeter of the room. Students were seated in groups of three or four, based on their academic readiness as determined by the pre-assessment for this unit. The primary form of technology in this math classroom was graphing calculators. Each student was provided access to a graphing calculator during class time. Parents were not significantly involved in the daily classroom routine, nor were any para-educators provided as aides to the3 students in this classroom. Classroom routines generally included a ten to fifteen minute entry task and debrief, which prepared the students for their investigation for the day. Most activities were inquiry-based, with mini-lesson and inquiry debriefs included strategically to help students bring together a clear understanding of the important mathematical content of the unit. Often, an individual exit task was provided at the end of a class period to assess each student’s understanding of the important content for the day. Student Characteristics and Instructional Implications In order to accommodate the age range and developmental stages of students between 11 and 14, I designed instruction in this unit to introduce linear relationships through primarily context-based investigations. Though this was a class of generally high achieving students, about half of the students in this classroom had taken this course the previous year, and therefore had more prior knowledge of the topic than those students in sixth grade who were new to the class. Therefore, from the beginning, some tasks were differentiated based on students’ readiness to accommodate for both students whose understanding was strong, and those whose understanding was still emergent. All students in this class were proficient in reading, writing, and understanding English, though some spoke another language as their primary or home language. Additionally, no students in this classroom had been identified as having a disability that interfered with their learning or required accommodations or specially designed instruction. I constructed the unit to be responsive to students' cultural backgrounds, in particular SES. In order to do this, I designed learning experiences where students could access a mathematical understanding of linear relationships through the lens of investigating the minimum and living wages in the city of Lakewood, where most of them live. In order to ensure respect for the backgrounds of the4 students and their families, extreme care was taken to present the service-sector jobs that the students were examining as honorable and important positions so that the focus of students’ skepticism would be on the wages and not the jobs themselves. Case Study Student Profiles Ty, (all student names have been changed to protect privacy) a Caucasian female, is the first student whose case study is presented in this project. She comes from a low SES background and her parents seem to take little or no interest in her schooling. She is in seventh grade and took this class before as a sixth grader. She is 13 years old, and though she struggled significantly in the program last year, she has experienced a great deal of mathematical success this school year. Ty has strong discussion skills and a willingness to engage other students in mathematical conversations without always going through the teacher. She is also generally a willing participant in classroom discussions. Ty needs very clear instructions about what is expected of her and has some trouble working with students that she is good friends with. She is aware of this and generally requests to be partnered with or seated by those students who