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Smarter Balanced Mathematics Assessments

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Agenda Understanding the Content of the Grade 11 Summative Mathematics Assessment Exploring Innovative Ways to Use Technology to Measure, Capture, & Score Mathematical Reasoning Updates on Mathematics Performance Tasks DRAFT Calculator Policy

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Understanding the Smarter Balanced Grade 11 Summative Mathematics Assessment

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“Students can demonstrate progress toward college and career readiness in mathematics.” “Students can demonstrate college and career readiness in mathematics.” “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.” “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” “Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.” Overall Claim for Grades 3-8 Overall Claim for Grade 11 Claim #1 - Concepts & Procedures Claim #2 - Problem Solving Claim #3 - Communicating Reasoning Claim #4 - Modeling and Data Analysis Mathematics Claims

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Why should the grade 11 assessment draw on content from earlier than grade 9? Source: Common Core State Standards for Mathematics CSSM, p. 84: “…some of the highest priority content for college and career readiness comes from Grades 6-8. This body of material includes powerfully useful proficiencies such as applying ratio reasoning inreal-world and mathematical problems, computing fluently with positive and negative fractions and decimals, and solving real-world and mathematical problems involving angle measure, area, surface area, and volume.”

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Alignment of the Smarter Balanced the Common Core State Standards for Mathematics Summative Content Specifications “Tasks generating evidence for Claim #2 in a given grade will draw upon knowledge and skills articulated in the progression of standards up through that grade, though more complex problem-solving tasks may draw upon knowledge and skills from lower grade levels.” Source: Content Specifications for the summative assessment of

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How has Smarter Balanced used the research and the information in the Publisher’s Criteria? Claim 1 (Concepts and Procedures) has 16 targets in high school, which correspond to 16 CCSS-M clusters with relatively high importance for College & Career. High school standards that do not appear as a separate target in Claim 1 or on the lists for Claims 2, 3, & 4 (in the following slides) will NOT be measured on the grade 11 summative assessment.

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Claim #2: Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.

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Claim #3: Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

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Claim #4 - Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.

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Rationale for not measuring every standard on the grade 11 summative Content identified for the assessment is based on research related to prerequisite skills for college- and- career readiness Allow states to make good decisions about how to structure the content across high school, including options that spread the standards across four years instead of three Example of content not measured on Grade 11 summative –G.C.A Understand and apply theorems about circles G.C.A.1 Prove that all circles are similar.

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Pushing the Limits on Measuring Mathematical Reasoning in Assessment

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Why is capturing students’ reasoning so important? “On the CMT [Connecticut Mastery Test], I work and work and work on a problem. Then I go to fill in my answer and it’s not there. But this test [Smarter Balanced pilot] let me tell how I solved it.” -- Grade 3 student from Wethersfield, CT, when asked by the district math coordinator to give feedback on the Smarter Balanced math pilot

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But capturing and scoring students’ mathematical reasoning via technology is easiersaid than done.

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Chloe is responsm le for making 32 centerpieces for the tables at this year 's :&ehoo·l prom She v.riU place 8-inch tall cylindiica] cand es into pr -m v cs of the same height. Then she wi11 fill the space between the candles and the vases halfwary with biuc sand. candle 4.5 in. vase.. ··-· - ·· --.... -... ·- ' 5.0 in. Sand ·is so!ld in 240 cubic ·inch baat $4.79 per bag.How· much Will Chloe spend on the sand to create 32 centerpieces? Show ·your work or explain 'how yon found )'Our answer. 8.0 in.8.0 in.

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Smarter Balanced Assessment Consortium

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Attempts to “Capture” Student Work often Eliminate the Autonomous Reasoning Called for in the Content Specifications Imagine the same problem was posed as a series of questions in an attempt to “capture” reasoning: What is the volume of ½ the candle? What is the volume of ½ the vase? How much sand in each vase? How many sand for all vases? How many bags of sand? How much would that cost?

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Other System Limitations F.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a.Graph linear and quadratic functions and show intercepts, maxima, and minima. b.Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. c.Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d.(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. e.Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

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0 u and Te ller had at nt that is 8 t -by- I 0 fee. 3- fe t by 6- feet. c h adult h s slp1ng baghat 1s a. 0 ru s id h t fa u dults woutfit et of f loor spac anhent. ach a ult.8 ris n eds 1 8 squ re I 8 8 18 - 72.h t nis 80 squ r f t, so th oom to sp re. Tller said that it in ent C. htried and coul noget four adults to b. Gavin, M. K., Cas Measuring with the opley, J. II., & Sheffield, L. J. {2008}. Project M2: Using Everyday Measures: e-IIMIIfiJI'!o!:m Project M2: Mentoring Young Mathematicians series....1.Smarter s !l!£ Slide 34

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Known Gaps Some types of graphs and other mathematical models are difficult to construct in a way that mirrors the kind of student understanding gained through hand-drawn Claim 2 Problem Solving Known gap of capturing students responses via technology (graphic images as well as a seamless integration of typewritten explanations with equations/math symbols) Claim 3 Communicating Reasoning In particular, target B that asks for students to present chains of autonomous reasoning Presentation of content related to reasoning (written text on the assessment vs. audio/visual in classroom instruction)

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Purposes of the Math Reasoning Project Enhance the knowledge base regarding authentic evidence of mathematical reasoning. Increase the validity of test scores by increasing the breadth of the Common Core standards that are measurable via computers. Strengthen educator engagement and ownership of the assessments. Enable students to incorporate graphical representations using natural user interfaces in their response to mathematics items. Improve the efficiency of the scoring of mathematical reasoning by use of automated processes.

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Immediate Next Steps Expert combined mathematics content and technology panel will meet in early October to define the evidence gap between what we want to be able to measure and what we are currently able to measure Two phase development plan –Phase 1 development focused on items that we can already capture, but want to be able to score using technology –Phase 2 will focus on newer technologies as defined and prioritized after the panel meeting

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Performance Tasks in Mathematics

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Performance Tasks: What did we learn during pilot? More hand scoring is needed to measure complex reasoning, application, and research skills, and rubrics must take into account the entire task not just individual parts Early grades performance tasks take too long Classroom Interaction will be available for all performance tasks in field test

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Sample SBAC Math Performance Tasks SBAC Practice Test Portal: http://sbac.portal.airast.org/practice-test/ Scoring Guides: http://sbac.portal.airast.org/practice- test/resources/

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DRAFT Calculator Policy

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Calculators on the Smarter Balanced Math Assessments Grades 3– 5 Calculator Policy Smarter Balanced summative mathematics assessments for grades 3–5 do not allow for calculator usage. Grades 6– 8 Calculator Policy In grades 6–8, the Smarter Balanced summative mathematics assessments are divided into two sections: Calculator Available and Calculator Not Available. The Smarter Balanced summative mathematics assessment for grade 6 allows an online four-function calculator during the Calculator Available section. The Smarter Balanced summative mathematics assessments for grades 7 and 8 allow an online scientific calculator during the Calculator Available section. High School Calculator Policy In high school, the Smarter Balanced summative mathematics assessments are divided into two sections: Calculator Available and Calculator Not Available. The Smarter Balanced summative mathematics assessments for high school allow online calculators with scientific, regression, and graphing capabilities during the Calculator Available section.

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Find Out More Smarter Balanced can be found online at: SmarterBalanced.org

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