© 2013 Boise State University1 What the Shifts in the Standards Mean for Learning and Instruction Michele Carney, PhD Spring 2014

© 2013 Boise State University2 Agenda What does it mean to engage students in the practice of mathematics? Examine assessment items and categorize the type of cognitive demand that are required from students What does this mean for instruction?

What does it mean to say students need to engage in the ‘Practice of ELA/Mathematics’ Language ArtsMathematics We teach phonics, grammar, punctuation, spelling, etc. for the purpose of students’ engaging in the practice of language arts: – Reading – Writing Focused on teaching skills, facts, algorithms, procedures, etc. Now we are asking that students be able to put these into the practice of mathematics: – Problem solve – Model situations – Reason quantitatively – Critique the reasoning of others

© 2013 Boise State University4 Claim 1: Concepts & Procedures Claim 2: Problem Solving Claim 3: Communicate Reasoning Claim 4: Modeling & Data Analysis DOK 1 DOK 2 DOK 3 DOK 4 SBAC Assessment & Reporting Areas Areas assessed by the ISAT Areas assessed by SBAC

© 2013 Boise State University5 If we are going to ask students to meaningfully engage in the practice of mathematics: Then we must vary the type and depth of cognitive demand we are asking from students in classroom tasks, activities and assessments. Level of Cognitive Demand Rote, Skill or Recall Concepts Problem Solving Reasoning & Justification Modeling and Data Analysis Mathematics Practices Problem Solve Model Situations Reason Quantitatively Critique the reasoning of others

© 2013 Boise State University6 TYPES OF COGNITIVE DEMAND

© 2013 Boise State University7 Porter (2002) Memorize Perform Procedures Communicate Understanding Solve Nonroutine Problems Conjecture, Generalize, or Prove Webb (2007) RecallSkill/Concept Strategic Thinking Extended Thinking SBAC Claims Concepts and Procedures Problem Solving Communicate Reasoning Model with Mathematics

TypeDMT DescriptionExample Claim 1 Rote, Skill or Recall Rote, Skill, Recall items require students to produce a response by following a set of rote procedures, demonstrating procedural skills or recalling information (Webb, 2002). Typically procedural or algorithm focused problems Concepts Concept items require students to respond by producing models and diagrams or demonstrate an understanding of mathematical properties and their applications (Webb, 2002) Often involves asking for visual or iconic representation of a topic Claim 2 Problem Solving Problem Solving items require students to produce a response to a given problem for which there can be a variety of answers or problem-solving strategies. Solution methods are not readily apparent and require students to make decisions about how to solve the problem (Hiebert et al, 1992; Porter, 2002). Typically multi-part, contextual questions but must go beyond skill level applications Claim 3 Reasoning & Justification Reasoning and Justification items require students to justify their own reasoning or critique the reasoning of others through careful analysis and by explaining and modeling how a response is either correct or incorrect (de Lange, 1999) Identifying the incorrect solution strategy from two examples and how to correct it Claim 4 Modeling and Data Analysis Modeling and Data Analysis performance tasks require students to analyze complex, real-world scenarios and/or use mathematics models to interpret and solve problems (SBAC, 2011).

© 2013 Boise State University9 Type of Cognitive Demand As a group: – Solve each problem – Identify the type of cognitive demand required by each item

Type of Cognitive Demand: __________________________________

Type of Cognitive Demand: __________________________________

Type of Cognitive Demand: __________________________________

Type of Cognitive Demand: __________________________________

content/uploads/2012/09/performance-tasks/tulips.pdf Type of Cognitive Demand: ___________________________ p.5 p.6

© 2013 Boise State University16 Reflect upon the different types of cognitive demand: – How should these be integrated into classroom practice? – How do they promote different aspects of the mathematical practice standards? – Is there a particular order in which tasks with different cognitive demands should be sequenced? Discuss in your small groups and select one to two items to share with the whole group.

© 2013 Boise State University17 FOCUSING ON COGNITIVE DEMAND IN YOUR SCHOOL OR DISTRICT

6 th Grade Focus Areas Rate and ratio Dividing fractions and understanding rational (e.g., negative) numbers Writing, interpreting, and using expressions and equations Statistical thinking

6 th Grade Math Topics# of Days Expectations for Students Rote, Skill or Recall Concepts Problem Solving Reasoning & Justification Modeling and Data Analysis Rate and ratio A B C D Dividing fractions and understanding rational (e.g., negative) numbers A B C D Writing, interpreting, and using expressions and equations A B C D Statistical thinking A B C D Other A B C D (A) no emphasis; (B) slight emphasis (less than 25% of time spent on this topic); (C) moderate emphasis (accounts for 25–33% of time spent on this topic); and (D) sustained emphasis Adapted from Porter, A. C. (2002). Measuring the content of instruction: Uses in research and practice. Educational Researcher, 31(7), 3-14.

© 2013 Boise State University20 Sample ISAT/NWEA MAP itemSample SBAC item Is the level of cognitive demand in the CCSS and assessed on the Smarter Balanced test what Idaho students need?

© 2013 Boise State University21 Describe the relationship you see between the mathematical practice standards and the levels of cognitive demand. Level of Cognitive Demand Rote, Skill or Recall Concepts Problem Solving Reasoning & Justification Modeling and Data Analysis Mathematics Practices Problem Solve Model Situations Reason Quantitatively Critique the reasoning of others