October, 2011 Ingham ISD Michigan Mathematics Coordinators and Consultants MSP Update

Under the DELTA Umbrella Who’s on First: Building Curriculum Coherence High School Algebra For All HS Algebra For All Yr. II Supporting HS Algebra: Beyond Homework Help and Worksheets Secondary Lenses on Learning Annual Mathematics Summit Events Developing Excellence in Teaching and Learning Algebra

Under the DELTA Umbrella Who’s on First: Building Curriculum Coherence High School Algebra For All HS Algebra For All Yr. II Supporting HS Algebra: Beyond Homework Help and Worksheets Secondary Lenses on Learning Annual Mathematics Summit Events Developing Excellence in Teaching and Learning Algebra

Gerri Devine Dana Gosen Valerie Mills Edward Silver Adele Sobania Jenny Badee Tami Niemi 4 Who’s On First Building Coherence, Connections, and Retention Across Grades Developing Excellence in Teaching and Learning Algebra

Driving Questions How do we teach so much content at each grade level with deep understanding? What does it mean to teach algebra in 7th grade, 8th grade, Algebra I and Algebra II? What portion should I be teaching? Are their algebraic connections to lessons in earlier grades that I could be drawing on to help teach my content? Developing Excellence in Teaching and Learning Algebra

Connections & Coherence “When students can connect mathematical ideas, their understanding is deeper and more lasting.” (NCTM, 2000 p.64) “When students understand the interrelatedness of mathematics, they often have many more strategies available to them when solving problems and insights into mathematical relationships.” (Hiebert, 1997) “Through instruction that emphasizes the interrelatedness of mathematical ideas, students not only learn mathematics they also learn about the utility of mathematics.” (NCTM, 2000, p.64) “Toward greater focus and coherence” (CCSS, 2010, p.3) Developing Excellence in Teaching and Learning Algebra

DELTA : Building Connections and Coherence School Year –District Leadership teams meet 5 times to develop 2 to 3 Teaching and Learning Trajectories (TLT) June 2010 Summer Institute –District Leadership Teams work with their district colleagues to explore each of the TLT and prepare for the school year activities School Year –District Leadership teams meet 5 times and create 2 to 3 additional TLT –Grade level groups of teachers meet 6 times for District Dialogues bringing samples of their student’s work on Anchor Tasks to discuss: a) student progress along TLT and b) implications at both the system and classroom levels

Working to build coherence & connections at two levels Work at the systems level: –Course curriculum design within and across grades/courses –Course offerings (tracking, acceleration, integrated content) –District Assessment Systems –Collegial conversations within and across grades/courses (District Dialogues) Work at the classroom level: –Task selection –Assessment for learning –Identifying misconceptions –Connecting to prior knowledge and future lessons (mathematical language, tasks, strategies) –Considering next instructional steps for specific students or the whole class Developing Excellence in Teaching and Learning Algebra DELTA

Working to build coherence & connections with these tools Anchor Tasks with Corresponding Analysis Protocols Teaching & Learning Trajectories (TLT) Developing Excellence in Teaching and Learning Algebra DELTA

Anchor Tasks with Corresponding Analysis Protocols “So in the past we‘ve kind of talked about tasks as being a different seventh grade task than an eighth grade task, so this is another way to think about what our anchor tasks could look like. That is, it could be the same task that we use at several grade levels, but the ways in which the students solve the problems might vary, from more graphic and tabular solution strategies, or strategies that are anchored in those representations, to strategies that are more anchored in symbolic representations.” Developing Excellence in Teaching and Learning Algebra DELTA Session January 27, 2010 DELTA

Unpacking an Anchor Task Elyse: Going back to the place where we were graphing the data points, especially if you did them in different colors, the red dots for the apple trees, the dot for the apple trees is going to be below the dot for the pine trees. And then pretty soon the red dots are going to be the ones that are up above the ones for the -- so you could even do that in the seventh grade when you're using the data points on a graph rather than the function plots. Valerie: So would that be a seventh grade thing, you'd expect them to be looking at the data points? And what about by eighth grade? Developing Excellence in Teaching and Learning Algebra DELTA Session January 27, 2010 DELTA

Working to build coherence & connections with these tools Teaching & Learning Trajectories (TLT) “So you might be talking about steepness at the seventh grade. What would the conversation need to look like by the eighth grade? What language would you want to see out on the table describing their reasoning about which one grows more quickly?” DELTA Session January 27, 2010 Developing Excellence in Teaching and Learning Algebra DELTA

Modeling Strategies for District Dialogues Participant: Also, putting it in the context of our broader task of figuring out what gets sequenced when, I know all of us get overwhelmed on how much we feel we have to cover, and can you cover multiple representations of everything when you have to cover so much. But if we get the other task done well on where things fall, then I think it allows you more flexibility to dig a little deeper and go into the multiple approaches to problems if you don't feel that you have to cover everything because some of it's been taken care of. DELTA, November 18, 2009 DELTA Developing Excellence in Teaching and Learning Algebra

I. Collect, Organize, and Display Data A. Task Prep - Solve task, identify mathematics, and anticipate student solution strategies and misconceptions B. Identify productive dimensions of student thinking for analysis (solution strategies, representations, and errors) C. Sort papers by categories and graphically represent data II. Systems Level Use data to analyze your students’ progress along the appropriate Teaching and Learning Trajectory and consider changes in learning opportunities needed to improve student performance. III. Classroom Level Select representative samples of student work and consider next steps for individual students or further explorations for a class. Apple Task: Students using explicit equations in Grs 7 – Alg. II From Anchor Tasks to Actionable Data Developing Excellence in Teaching and Learning Algebra

Sort and Represent Graphically 1. Sort your district papers using the categories the group agreed upon. 2. Create bar graphs to summarize the student approaches across grade levels in your district Developing Excellence in Teaching and Learning Algebra

Working to build coherence & connections with this tools and at two levels Work at the systems level: –Course curriculum design within and across grades/courses –Course offerings (tracking, acceleration, integrated content) –Instructional tasks –Collegial conversations within and across grades/courses (District Dialogues) Work at the classroom level: –Task selection –Assessment for learning –Identifying misconceptions –Connecting to prior knowledge and future lessons (mathematical language, tasks, strategies) –Considering next instructional steps for specific students or the whole class Anchor Tasks Teaching and Learning Trajectories (TLT) Developing Excellence in Teaching and Learning Algebra DELTA

Who: Math/Science Center Teams When: May 9, 2012 Where: Oakland Schools What: DELTA Resources –Teaching and Learning Trajectories –Anchor Tasks –Data Analysis Tools/Protocols CCSS Progressions Dr. William McCallum – The University of Arizona Developing Excellence in Teaching and Learning Algebra DELTA “Toward Greater Focus and Coherence” State-wide Dissemination Save the Date !

Under the DELTA Umbrella Who’s on First: Building Curriculum Coherence High School Algebra For All HS Algebra For All Yr. II Supporting HS Algebra: Beyond Homework Help and Worksheets Secondary Lenses on Learning Annual Mathematics Summit Events Developing Excellence in Teaching and Learning Algebra

Mathematical Tasks Framework (MTF) Teacher Analysis of Student Knowledge (TASK) Mathematical Representation Star Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000) Tasks as set up by teachers Tasks as they appear in curricular materials Tasks as enacted by teacher and students Student learning Developing Excellence in Teaching and Learning Algebra DELTA Tools to Support and Cohere Project Professional Development Series

Developing Excellence in Teaching and Learning Algebra

Oakland Schools 2012 Mathematics Summit Assessing the Common Core Balanced Assessment Consortium Framework MAPS Assessment Resources  Hugh Burkhardt – Shell Center  Oakland Schools  May 17, 2012 Developing Excellence in Teaching and Learning Algebra SAVE THE DATE!