CALIFORNIA DEPARTMENT OF EDUCATION Tom Torlakson, State Superintendent of Public Instruction Mathematics Assessment and Performance Tasks Jane Liang, Ed.D. Mathematics Consultant California Assessment of Student Performance and Progress (CAASPP) Office California Department of Education Pre-Good Teaching Conference Seminar California Teachers Association San Jose, California January 10, 2014

TOM TORLAKSON State Superintendent of Public Instruction Topics Overview of Smarter Balanced mathematics assessment blueprints Overview of performance task features Access and administration of performance tasks Example of a mathematics performance task 2

TOM TORLAKSON State Superintendent of Public Instruction Objectives Understand Smarter Balanced assessment in mathematics Understand performance tasks Incorporate performance tasks in mathematics instruction 3

4 Smarter Balanced Mathematics Assessment Claims

TOM TORLAKSON State Superintendent of Public Instruction Proposed Reporting Categories for Summative Mathematics Assessment Total Mathematics Composite Score Claim #1: Concepts and Procedures Claim #2: Problem Solving Score Claim #3: Communicating Reasoning Score Claim #4: Modeling and Data Score Score 1Score 2*Score 3Score 2* Overall math score 5 *Claim 2 (Problem Solving) and Claim 4 (Modeling and Data Analysis) have been combined because of content similarity and a desire to reduce test length. There are still four claims, but only an overall math score and 3 claim scores will be reported.

TOM TORLAKSON State Superintendent of Public Instruction Assessment Targets 6 Each claim is accompanied by a set of assessment targets that provide more detail about the range of content and Depth of Knowledge (DOK) levels. Targets are intended to support the development of high-quality items and tasks that contribute evidence to the claims.

Webb’s Depth of Knowledge The levels of complexity of the cognitive demand: ‒Level 1: Recall and Reproduction Requires eliciting information such as a fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. – Level 2: Basic Skills and Concepts Requires the engagement of some mental processing beyond a recall of information. – Level 3: Strategic Thinking and Reasoning Requires reasoning, planning, using evidence, and explanations of thinking. – Level 4: Extended Thinking Requires complex reasoning, planning, developing, and thinking most likely over an extended period of time.

TOM TORLAKSON State Superintendent of Public Instruction Targets for Claim #1, Concepts and Procedures Assessment targets for claim #1 are grade/subject level dependent. Targets are the cluster-level headings of the content standards in the Common Core State Standards for Mathematics (CCSS-M). Smarter Balanced designations –Major [m] clusters –Additional/supporting [a/s] clusters 8

TOM TORLAKSON State Superintendent of Public Instruction Targets for Claim #1, Concepts and Procedures (cont.) Example of targets for grade 3: Target A [m]: Use the four operations with whole numbers to solve problems. (DOK 1, 2) Target B [a/s]: Gain familiarity with factors and multiples. (DOK 1) Target C [a/s]: Generate and analyze patterns. (DOK 2, 3) Target D [m]: Generalize place value understanding for multi-digit whole numbers. (DOK 1, 2) 9

TOM TORLAKSON State Superintendent of Public Instruction Targets for Claims #2, #3, and #4 Claims #2, #3, and #4 are aligned to the Mathematics Practice Standards (MPS) from the CCSS- M. Assessment targets for claims #2, #3, and #4 are consistent across grade/subject levels. 10

TOM TORLAKSON State Superintendent of Public Instruction Targets for Claim #2 Problem Solving Target A: Apply mathematics to solve well- posed problems arising in everyday life, society, and the workplace. (DOK 2, 3) Target B: Select and use appropriate tools strategically. (DOK 1, 2) Target C: Interpret results in the context of a situation. (DOK 2) Target D: Identify important quantities in a practical situation and map their relationships (e.g., using diagrams, two-way tables, graphs, flowcharts, or formulas). (DOK 1, 2, 3) 11

TOM TORLAKSON State Superintendent of Public Instruction Targets for Claim #3 Communicating and Reasoning Target A: Test propositions or conjectures with specific examples. (DOK 2) Target B:Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures. (DOK 3, 4) Target C: State logical assumptions being used. (DOK 3) Target D: Use the technique of breaking an argument into cases. (DOK 2, 3) 12

TOM TORLAKSON State Superintendent of Public Instruction Targets for Claim #3 Communicating and Reasoning (cont.) Target E: Distinguish correct logic or reasoning from that which is flawed, and–if there is a flaw in the argument–explain what it is. (DOK 2, 3, 4) Target F: Base arguments on concrete referents such as objects, drawings, diagrams, and actions. (DOK 2, 3) Target G: At later grades, determine conditions under which an argument does and does not apply. (For example, area increases with perimeter for squares, but not for all plane figures.) (DOK 3, 4) 13

TOM TORLAKSON State Superintendent of Public Instruction Targets for Claim #4 Modeling and Data Analysis Target A: Apply mathematics to solve problems arising in everyday life, society, and the workplace. (DOK 2, 3) Target B:Construct, autonomously, chains of reasoning justify mathematical models used, interpretations made, and solutions proposed for a complex problem. (DOK 2, 3, 4) Target C: State logical assumptions being used. (DOK 1, 2) Target D: Interpret results in the context of a situation. (DOK 2, 3) 14

TOM TORLAKSON State Superintendent of Public Instruction Targets for Claim #4 Modeling and Data Analysis (cont.) Target E: Analyze the adequacy of and make improvements to an existing model or develop a mathematical model of a real phenomenon. (DOK 3, 4) Target F: Identify important quantities in a practical situation and map their relationships (e.g., using diagrams, two-way tables, graphs, flowcharts, or formulas). (DOK 1, 2, 3) Target G: Identify, analyze, and synthesize relevant external resources to pose or solve problems. (DOK 3, 4) 15

TOM TORLAKSON State Superintendent of Public Instruction Smarter Balanced Assessment: Technology Computer-based testing –Tests are administered electronically. Computer adaptive testing (CAT) –Item difficulties are adjusted to each student’s performance. 16

TOM TORLAKSON State Superintendent of Public Instruction Smarter Balanced Assessment: Item Types Using various types of items and tasks to connect mathematics content and practice standards: Selected response (SR) Short constructed response (CR) Extended constructed response (ECR) Technology enhanced (TE) Performance tasks (PT) 17

18 Smarter Balanced Preliminary Mathematics Assessment Blueprint

19 Smarter Balanced Preliminary Mathematics Assessment Blueprint (cont.) P(6)=1.0 indicates that each student will have a 100% probability of receiving at least 6 CAT items.

20 Smarter Balanced Preliminary Mathematics Assessment Blueprint (cont.)

21 Smarter Balanced Preliminary Mathematics Assessment Blueprint (cont.)

TOM TORLAKSON State Superintendent of Public Instruction 22 Source: m

TOM TORLAKSON State Superintendent of Public Instruction Components of Mathematics Performance Tasks 23 Stimulus presentation Information process

TOM TORLAKSON State Superintendent of Public Instruction Types of Smarter Balanced Performance Tasks 24 1.Performance task only Task overview Student task 2.Classroom activity plus performance task Task overview Classroom activity Student task

TOM TORLAKSON State Superintendent of Public Instruction Classroom Activity As part of its research agenda during the pilot test, Smarter Balanced is exploring the implementation of a classroom-based activity prior to the individually administered and scored portion of the performance task. The purpose of the classroom activity is to reduce the experiential bias of the task context across test takers and level the playing field for students. –For example, in a task about horseback riding, we would want to introduce any potentially unfamiliar terms about horseback riding unrelated to the construct (e.g., mathematics). Existing and ongoing research will inform the consortium’s decision about whether to include the classroom-based activities during the live summative assessment in

TOM TORLAKSON State Superintendent of Public Instruction 26 TA: task administrator

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TOM TORLAKSON State Superintendent of Public Instruction 28 Example of a Performance Task

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TOM TORLAKSON State Superintendent of Public Instruction Sample Performance Task: Taking a Field Trip 1.Classroom activity 2.Setting the context 3.Student task 4.Task specifications 5.Scoring rubric 31

TOM TORLAKSON State Superintendent of Public Instruction Classroom Activity Some suggestions for turning “Taking a Field Trip” into a rich, classroom-based learning task: Change the information to reflect locations that are within driving distance of your school. Ask students to collect the necessary information to inform the important variables. –How far is each location? –How many does a bus hold? What is the cost? –How much will we have to pay to enter? Are teachers and other adults free? Collect student data on preferences for these locations similar to the provided data in the task. 32

TOM TORLAKSON State Superintendent of Public Instruction Setting the Context Engage students –Ask things students like about field trips: volunteering responses, 2- minute pair share, summary on board Select a place –Ask students to nominate places for polling list: 2 rounds of vote Consider other issues –Proximity, safety, etc. Calculate costs 33

TOM TORLAKSON State Superintendent of Public Instruction Student Task Determine where the class should go on the field trip based on The survey results The cost per student 34

TOM TORLAKSON State Superintendent of Public Instruction Survey Results 35

TOM TORLAKSON State Superintendent of Public Instruction Question 1 Based only on the results of the class votes, where would you recommend the class go on the field trip? Show your work or explain how you found your answer. 36

TOM TORLAKSON State Superintendent of Public Instruction Distance Map 37

TOM TORLAKSON State Superintendent of Public Instruction Cost Chart 38

TOM TORLAKSON State Superintendent of Public Instruction Cost Considerations The teacher and parent helpers do not pay an entrance fee. There are 30 students in the class. Only 1 bus is needed. The bus charge is for the entire busload of students (not for each student). Each student will pay the same amount. The school will pay the first $200 of the trip. 39

TOM TORLAKSON State Superintendent of Public Instruction Question 2 How much will each student pay to go on each trip? Show your work or explain how you found your answer. 40

TOM TORLAKSON State Superintendent of Public Instruction Question 3 Daniel thinks that it will cost less to go to the zoo because the entrance fee is only $2.50 per person. Explain why you agree or disagree with Daniel’s thinking. 41

TOM TORLAKSON State Superintendent of Public Instruction Final Task Write a short note to your teacher stating where you think the class should go on its field trip, based on how you would evaluate all the different factors, including student votes, costs, distance, and what you think would be fun. 42

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TOM TORLAKSON State Superintendent of Public Instruction Sample Performance Task Scoring Criteria 44

TOM TORLAKSON State Superintendent of Public Instruction Sample Performance Task Scoring Criteria (cont.) 45

TOM TORLAKSON State Superintendent of Public Instruction Resources Smarter Balanced Web Site: California Department of Education Smarter Balanced Web Page: d.asp Subscribe to CDE Smarter Balanced listserv by sending a blank to: 46

TOM TORLAKSON State Superintendent of Public Instruction Questions and Answers Jane Liang, Ed.D. Mathematics Consultant California Assessment of Student Performance and Progress (CAASPP) Office California Department of Education