Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Linking Assessment Targets to Instructional Tasks and DOK This material was developed for the Leadership for the Common Core in Mathematics project through the University of Wisconsin- Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. You may not use this work for commercial purposes. This project was supported through a grant from the Wisconsin ESEA Title II Improving Teacher Quality Program

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Homework Discussion What is your understanding of prioritizing the clusters as major, supporting or additional? What did you learn by reading and studying the PARCC Content Framework for your grade and the grades above and below that grade?

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Explanations of Major, Additional and Supporting Cluster-Level Emphases Major[m] (▲) clusters – areas of intensive focus where students need fluent understanding and application of the core concepts. These clusters require greater emphasis than the others based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. Supporting [s] clusters – rethinking and linking; areas where some material is being covered, but in a way that applies core understanding; designed to support and strengthen areas of major emphasis. Additional [a] clusters – expose students to other subjects; may not connect tightly or explicitly to the major work of the grade. *A Note of Caution: Neglecting material will leave gaps in students’ skills and understanding and will leave students unprepared for the challenges of a later grade.

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee D0… Recommendations for Using the Cluster Level Emphases Do...  Use the guidance to inform instructional decisions regarding time and other resources spent on clusters of varying degrees of emphasis.  Allow the focus on the major work of the grade to open up the time and space to bring the Standards for Mathematical Practice to life in mathematics instruction through sense‐making, reasoning, arguing and critiquing, modeling, etc.  Evaluate instructional materials taking the cluster‐level emphases into account. The major work of the grade must be presented with the highest possible quality; the supporting work of the grade should indeed support the major focus, not detract from it.  Set priorities for other implementation efforts taking the emphases into account, such as staff development; new curriculum development; or revision of existing formative or summative testing at the state, district or school level.

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee D0N’T… Recommendations for Using the Cluster Level Emphases Don’t...  Neglect any material in the standards. (Instead, use the information provided to connect Supporting Clusters to the other work of the grade.)  Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.  Use the cluster headings as a replacement for the standards. All features of the standards matter — from the practices to surrounding text to the particular wording of individual content standards. Guidance is given at the cluster level as a way to talk about the content with the necessary specificity yet without going so far into detail as to compromise the coherence of the standards.

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Time to Test Our DOK Knowledge 1.Take one assessment question from the envelope. 2.Read the problem to the group. 3.Decide on the grade level, assessment target and DOK for the sample item. Pass the envelope and repeat the process.

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Sorting Task – Answer Key 6-8 Tasks Task #1 Targets A & C 7.RP.2 MP 1 & 2 DOK 2 Task #2 Target A 6.RP.1 MP 1 & 2 DOK 2 Task #3 Targets B 8.EE.2 MP 6 DOK 1 Task #4 Targets B & F 6.NS.1 & 6.EE.6 MP 1 & 2 DOK Tasks Task #1 Targets D 3.OA.8, 3.OA.5, 3.NBT.3 MP 1 & 2 & 6 DOK 2 Task #2 Targets E 5.NF.1 & 5.NF.2 MP2 & 4 & 6 DOK 1 Task #3 Targets H 4.NF.5 MP1 & 2 & 6 DOK 1 Task #4 Target F 5.NF.5 MP2 DOK 2

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee The Importance of the Math Practices in Claim 1

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Mathematical Practices in Claim 1 This claim addresses procedural skills and the conceptual understanding on which developing skills depends. It is important to assess how aware students are of how concepts link together and why math procedures work the way they do. Central to understanding this claim is making the connection to the mathematical practices as stated in the CCSSM: MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for and make use of structure. MP8: Look for and express regularity in repeated reasoning. Smarter Balanced Mathematics Item Specifications Grades 3-5 p. 14

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee The Importance of the Math Practices How can I teach my kids to get the answer to this problem? as opposed to… How can I use this problem to teach the mathematics of this unit for student understanding? Explain the difference between these two ways of approaching mathematics teaching. SMP emphasizes Doing and Demonstrating and not ‘answer getting.’ The Standards of Mathematical Practice are critically important.

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Standards for Mathematical Practice The eight Standards for Mathematical Practice place an emphasis on students doing mathematics and demonstrating learning. Equitable achievement will begin with an understanding of how the selection of tasks, the assessment of tasks, and the student learning environment can support or undermine equity in our schools. If the first 2 days of this class have been about Smarter Balanced and DOK, why are we talking about SMP?

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Linking Instruction to Assessment: Recognizing Tasks with Increased Cognitive Rigor

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee DOK in Task Not all tasks are created equal: Different tasks will provoke different levels and kinds of student thinking. The level and kind of thinking students engage in determines what they learn. Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, and Human 1997

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Sample Released Item What is the grade level? Assessment Target? DOK level? Grade level 4 Assessment Target B DOK 1

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee A Cognitively Demanding Instructional Task about Factors and Multiples Make a list of the first ten multiples of 3. Which of the numbers in your list are multiples of 6? What pattern do you see in where the multiples of 6 appear in the list? Which numbers in the list are multiples of 7? Can you predict when multiples of 7 will appear in the list of multiples of 3? Explain your reasoning. Source: Illustrative Mathematics Grade 4: Operations and Algebraic Thinking What is the DOK? What Math Practices does this emphasize?

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Sample Released Item What is the grade level? Assessment Target? DOK level? Grade 7 Assessment Target B DOK 2

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee A Cognitively Demanding Instructional Task about Operations with Integers Source: Illustrative Mathematics Grade 7: The Number System What is the DOK? What Math Practices does this emphasize?

Leadership for the Common Core in Mathematics, University of Wisconsin-Milwaukee Reflection: What? So What? Now What? Understand how the assessment targets in Claim 1 are related to CCSS and understand the relative importance of each target. Clarify and enhance understanding of the Depth of Knowledge (DOK) Levels within CCSS and SBAC assessment items. What have you learned about linking assessment instruction? What actions will you take based on what we have talked about so far in regards to aligning tasks, DOK, and higher level thinking?