Smarter BalancedMathematics Assessments

Agenda

• Understanding the Content of the Grade 11 SummativeMathematics Assessment

• Exploring Innovative Ways to Use Technology toMeasure, Capture, & Score Mathematical Reasoning

• Updates on Mathematics Performance Tasks

• DRAFT Calculator Policy

Understanding the Smarter BalancedGrade 11 Summative Mathematics Assessment

“Students can demonstrate progress toward college and careerreadiness 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 -

CommunicatingReasoning

Claim #4 - Modeling and Data Analysis

Mathematics Claims

Why should the grade 11 assessmentdraw 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 in real-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.”

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

How has Smarter Balanced used the research andthe 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.

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.

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

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

and solve problems.

Rationale for not measuring everystandard 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.

Pushing the Limits on Measuring Mathematical

Reasoning in Assessment

Why is capturing students’ reasoning soimportant?

“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

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

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SmarterBalanced

Assessment Consortium

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?

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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opley, J. II., & Sheffield, L. J. {2008}. Project M2: Using Everyday Measures: e-IIMIIfiJI'!o!:m Project M2: Mentoring Young Mathematicians series.

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Slide 34

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)

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 theCommon Core standards that are measurable via computers.

• Strengthen educator engagement and ownership of theassessments.

• Enable students to incorporate graphical representations

usingnatural user interfaces in their response to mathematics items.

• Improve the efficiency of the scoring of mathematical

reasoning byuse of automated processes.

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 andprioritized after the panel meeting

Performance Tasks inMathematics

Performance Tasks: What did we learnduring 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

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/

DRAFT Calculator Policy

Calculators on the Smarter BalancedMath Assessments

Grades 3– 5 Calculator PolicySmarter Balanced summative mathematics assessments for grades 3–5 do notallow 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 anonline four-function calculator during the Calculator Available section.

• The Smarter Balanced summative mathematics assessments for grades 7 and 8allow 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 allowonline calculators with scientific, regression, and graphing capabilities during theCalculator Available section.

Find Out More

Smarter Balanced can be found online at:

SmarterBalanced.org