+ Washington State Mathematics Fellows Heather DorseyDecember 4 th

+ Agenda Connecting with Partners Putting the Shifts into practice—How do we ensure coherence? Formative Assessment Cycle and Connecting Tasks to the Domains of Focus Planning next steps LUNCH 12:30ish-1:30ish

+ Purpose of the Fellows To be a part of and support a system that focuses on math making sense for all students. --Leadership in the Extended Community This requires all of us to be intentional about putting the shifts into practice to reflect the CCSS vision both around the student making sense of the mathematics and demonstrating that understanding. –Leadership of Others and Self The Fellows will use a formative assessment cycle that will support change in practice and experiences students have with the mathematics. –Leadership of Self

+ Plan for the year Four regional meetings One state-wide meeting (for a subset of the Fellows) Meetings centered around: Leadership of Self Learning together and learning of new resources Engaging in a formative assessment cycle Leadership of Others Reflecting on leading adult learners—Professional Development Clips Planning next steps Leadership in the Extended Community Providing feedback to the state-wide system Planning next steps

+ Reflect on the PD you accomplished since our last meeting or that you are planning Discuss with your group: What did you do? Who was your audience? How did it go? What were your challenges? OR What are you planning on doing? Who will your audience be? What challenges do you see arising?

+ Connecting with Partners Leadership in the Extended Community Consider all of the partnerships that will be important to ensure the implementation and success of your Fellows work. Write each one on a sticky note and place all of them around the circle on your poster paper.

+ Current Reality Consider the current reality of your network of partnerships as a Math Fellow. Use a solid, dashed or no line to show the strength of your network partnerships within your circle. Then post on wall.

Curriculum Leads Parents Higher Education Community Superintendent Principals You Teachers Strong Partnership Marginal Partnership No Partnership

+ Network of Partnerships Gallery Walk Find someone who has different connections than you and discuss successes

+ Connecting with Partners What is your strongest partnership within your network? (share why?) Where do you need to strengthen your partnerships in your work as a Math Fellow? How? Discuss with your administrator how they can support you as a Math Fellow.

+ Greater Focus, More Coherence Elmore urges us to do less with greater focus. Most low-performing schools don’t need more programs, or even more resources. They need a more powerful, coherent culture of instructional practice. Instructional Core StudentContentTeacher

+ The Three Shifts in Mathematics— Leadership of Self and Others Focus: Strongly where the standards focus Coherence: Think across grades and link to major topics within grades Rigor: In major topics, pursue with equal intensity: Conceptual understanding Procedural skill and fluency Application

+ Shift Two: Coherence Think across grades, and link to major topics within grades Carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. 13

+ Implications of the Task Leadership of Self Review your task if everyone did not give the same task and share how it relates to your domain: K-2 NBT 3-5 NF 6-8 RP HS F or G What patterns did you observe about your students’ work as a whole? What common misconceptions did you notice? What experiences do you need to provide your students with this year?

+ Coherence “The Standards are not so much built from topics as they are woven out of progressions.” Structure is the Standards, Publishers’ Criteria for Mathematics, Appendix

+ A Progression of Learning Leadership of Self and Others Read the progression for the grade levels that you are assigned to, as you read use the symbols: + things that are familiar to you ! things that are new to you ? things that you have a question about Discuss one item that was new to you and one item that you have a question about

+ A Progression of Learning Leadership of Self and Others K-2 Numbers and Operations in Base Ten 3-5 Numbers and Operations with Fractions 6-7, 8 Ratio and Proportion, (Expressions and Equations 8 th ) 8, HS Functions (HS can choose two options for reading: Everyone read pages 2-10: Overview, Grade 8, Interpreting Functions Everyone read the overview (pages 2-4) and each take a section depending on course: 8 th Grade- Grade 8 (pages 5-6) Alg.1- Interpreting Functions (pages 7-10) Alg.2-Building Functions (pages 11-15) Geometry-Trigonometric Functions (pages 18-21)

+ Finding Coherence Leadership of Self and Others Use the Instructional Alignment Chart to focus your conversation on the Coherence the progression provides within your identified cluster: K-2: K.NBT.A, 1.NBT.B, 2.NBT.A 3-5: 3.NF.A, 4.NF.A, 5.NF.A 6-8: 6.RP.A, 7.RP.A, 8.EE.B HS: 8.F.A, F.IF

+ Reflection of Learning Leadership of Self What are the implications for your classroom practice you discovered from looking at the Learning Progressions through the lens of coherence? What are some changes you will make with your students to raise their understanding of mathematics content using the progressions?

+ The Role of Tasks in Formative Assessment Leadership of Self and Others

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+ Definition of Formative Assessment Process Formative Assessment is a deliberate process used by teachers and students during instruction that provides actionable feedback that is used to adjust ongoing teaching and learning strategies to improve students’ attainment of curricular learning targets/goals.

+ After the Task is Selected… The Formative Assessment cycle …a process not a product …the gathering of information about students to inform and guide instruction …the longer it takes to use the information the less effective it becomes Clarify Intended Learning Elicit Evidence Act on Evidence Interpret Evidence

+ Four Attributes of the Formative Assessment Process Page 24 Clarify Intended Learning Elicit Evidence Act on Evidence Interpret Evidence

+ Clarify Intended Learning Helps students and teachers understand expectations and goals (what students will learn, not activities) Learning friendly targets and success criteria which indicate the measureable behavior Clarify Intended Learning

+ Elicit Evidence No single way to elicit evidence: Interaction Appropriate questions Focused observation Analyzing student work Can be planned or spontaneous Informal assessment activities by: Teacher, Self-assessment, or Peers Elicit Evidence

+ Margaret Heritage “…whatever method teachers use to elicit evidence of learning, it should yield information that is actionable by them and their students.” (2011) Elicit Evidence

+ Interpret Evidence Used to determine where the students are in relationship to the learning target Informs adjustments to instructional plans Can be interpreted by: Teacher, Student, or Peers Interpret Evidence

+ Act on Evidence Provide Timely, Descriptive and Actionable Feedback Give active steps students can take to move toward the learning target Have students self-assess and use peer assessment Help students be aware of strategies they can use to move learning forward (draw a picture, work backward, reread a text) Adjust Instruction Mini tutoring groups Flexible student group work Act on Evidence

+ Popham “…carefully crafted descriptive feedback will improve what goes on in almost every classroom.” (2011) Act on Evidence

+ Lunch

+ Assessment for and of Learning Read pages with the 3 Levels of Text Protocol in Mind Classroom Assessment for Student Learning: Doing It Right - Using It Well (2nd Edition)-Rick Stiggins

+ Improving the Instructional Core Principle Four – Task predicts performance Principle Five – Real Accountability is in the task How is the formative assessment cycle supportive of these principles? Instructional Core StudentContentTeacher

+ A Tale of Two Tasks Think privately about the different strategies students would use to go about solving each version of the task – Martha’s Carpeting – The Fencing Task Talk with your neighbor about how the different versions might engage your students

+ Comparing Two Mathematical Tasks How are Martha’s Carpeting Task and the Fencing Task the same and how are they different?

+ Similarities and Differences Similarities Both are “area” problems Both require prior knowledge of area Differences The amount of thinking and reasoning required The number of ways the problem can be solved Way in which the area formula is used The need to generalize The range of ways to enter the problem

+ Solution Strategies: Martha’s Carpeting Task

+ Martha’s Carpeting Task Using the Area Formula A = l x w A = 15 x 10 A = 150 square feet

+ Martha’s Carpeting Task Drawing a Picture 10 15

+ Solution Strategies: The Fencing Task

+ The Fencing Task Diagrams on Grid Paper

The Fencing Task Using a Table LengthWidthPerimeterArea

+ The Fencing Task Graph of Length and Area

+ Mathematical Tasks: A Critical Starting Point for Instruction Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking. Stein, Smith, Henningsen, & Silver, 2000

+ What makes a “high quality” task different from a “rich” task? Adapted from: Common Core Mathematics in a PLC at Work 3-5 Larson,, et al The Scope of the mathematics Can address a single standard within a cluster Although not focused on connections it must be a task that enriches the students understanding of mathematics May also focus only on one or two of the Standards for Mathematical Practice May be an opportunity for students to demonstrate individual thinking or building of concepts The Time required Rich tasks typically take an extended period of time while a high quality task(s) could be done during the course of a single period

+ Differences between a rich task and high quality tasks Lots of overlap - both provide students with opportunities for develop mathematical content and use standards for mathematical practices High quality tasks have a smaller scope… Curriculums often provide opportunities for rich tasks, although they may need tweaking, but most do not provide high quality tasks.

+ Criteria for a Rich Task 1. Is the task interesting to students? 2. Does the task involve meaningful mathematics? 3. Does the task provide an opportunity for students to apply and extend mathematics? 4. Is the task challenging to all students? 5. Does the task support the use of multiple strategies and entry points? 6. Will students’ conversation and collaboration about the task reveal information about students’ mathematics understanding? Adapted from: Common Core Mathematics in a PLC at Work 3-5 Larson,, et al

+ Optional for a high quality task 1. Is the task interesting to students? 2. Does the task involve meaningful mathematics? 3. Does the task provide an opportunity for students to apply and extend mathematics? 4. Is the task challenging to all students? 5. Does the task support the use of multiple strategies and entry points? 6. Will students’ conversation and collaboration about the task reveal information about students’ mathematics understanding? Adapted from: Common Core Mathematics in a PLC at Work 3-5 Larson,, et al

+ Environment for Rich/High Quality Tasks Learners not passive recipients of mathematical knowledge Learners are active participants in creating understanding and challenge and reflect on their own and others understandings Instructors provide support and assistance through questioning and scafolding as needed

+ Impact of Teachers Read the scenarios of how the Fencing Task was implemented. Determine what has happened to the mathematics as the task was implemented. Use the SMP #3 rubric to determine what the scenarios demonstrate

+ Real Accountability is in the Tasks Leadership of Self and Others E lmore mentions that: “it is essential that educators work on the observation and analysis of teaching practice and watch students (not just see what they are assigned to do, but what they are actually doing).” Instructional Core StudentContentTeacher

+ Impact of Teachers Consider Scenario A Highlight opportunities to use formative assessment to gather information about student scores for SMP #3 How would you gather the data? And what would you do with it? How does this connect to Elmore’s principles?

+ Assessment for and of Learning Discussion of Strategies 5-7 now that we have data from our tasks how do we “close the gap” in the domain that is a major focus for our grade band and SMP#3

+ Can’t see it in the Core, it isn’t there— Leadership of Self and Others Often through curriculum mapping and common assessment schedules we think all students are getting the same instruction, but Elmore finds that while curriculum and assessments may be common what different teachers expect of their students, variance in the skill with which the teachers deliver the curriculum, and the varying levels in which students were actively involved (not just “doing” what they are given but digesting it, making connections and new applications to deepen and extend knowledge) produce significant differences in student learning Instructional Core StudentContentTeacher

+ Focusing Together— Leadership of Others and in the Extended Community Domains of Focus: K-2 NBT 3-5 NF 6-7, 8 RP, EE 8, HS F Link progression/Instructional Alignment Chart/Mathematical Practice Piece to ideas of teaching

+ From Research to Classroom Practice— Leadership of Others and in the Extended Community Take a few moments to consider your year and your role as a CCSS-M Fellow Sketch out a plan/commitments for implementing/deepening formative assessment for instruction in classroom - how do we know we are on the path to success? Talk with your group for ideas Focus on what you will do between now and January 22 Connect with your Partners Progression Professional Development Clip Instructional Alignment PD Clip Utilize an idea connected to the focus domain

+ See you at 9:00 am on January 22 nd Remember to: Implement your plan to Heather before Jan 22 nd Your Task Idea Your “Leading Professional Learning Plan” Clock Hours—register for Course ID 46611