A Smarter Balanced System for Supporting Mathematics Teaching and Learning

1. A Smarter Balanced System for Supporting Mathematics Teaching and Learning Shelbi K. Cole, Ph.D. Saint Michael’s College March 7, 2014

2. The Big Picture “The future belongs to a very different kind of person with a very different kind of mind – creators and empathizers, pattern recognizers and meaning makers. These people…will now reap society’s richest rewards and share its greatest joys.” Daniel H. Pink, A Whole New Mind

3. What does his future look like?

4. What skill set do his future employers value?

5. But are we modeling the collaboration that we need to be teaching kids?

6. Student populations are transient.

7. "The world is small now, and we're not just competing with students in our county or across the state. We are competing with the world," said Robert Kosicki, who graduated from a Georgia high school this year after transferring from Connecticut and having to repeat classes because the curriculum was so different. "This is a move away from the time when a student can be punished for the location of his home or the depth of his father's pockets." Excerpt from Fox News, Associated Press. (June 2, 2010) States join to establish 'Common Core' standards for high school graduation.

8. Common Core State Standards Source: www.corestandards.org Define the knowledge and skills students need for college and career Developed voluntarily and cooperatively by states; more than 40 states have adopted Provide clear, consistent standards in English language arts/literacy and mathematics

9. Smarter Balanced Assessment Consortium An Assessment System to Support Teaching and Learning

10. A National Consortium of States

11. The Assessment Challenge ...to here? Common Core State Standards specify K-12 expectations for college and career readiness All studentsleave high school college and career ready ...and what can an assessment system do to help? How do we get from here...

12. Each state pays for its own assessments • Each state bears the burden of test development; no economies of scale Concerns with Today's Statewide Assessments Based on state standards • Students in many states leave high school unprepared for college or career Heavy use of multiple choice • Inadequate measures of complex skills and deep understanding Results delivered long after tests are given • Tests cannot be used to inform instruction or affect program decisions Accommodations for special education and ELL students vary • Difficult to interpret meaning of scores; concerns about access and fairness Most administered on paper • Costly, time consuming, and challenging to maintain security

13. Theory of Action Built on Seven Key Principles An integrated system Evidence-based approach Teacher involvement State-led with transparent governance Focus: improving teaching and learning Actionable information – multiple measures Established professional standards

14. A Balanced Assessment System Summative assessments Benchmarked to college and career readiness Teachers and schools have information and tools they need to improve teaching and learning Common Core State Standards specify K-12 expectations for college and career readiness All students leave high school college and career ready Teacher resources for formative assessment practices to improve instruction Interim assessments Flexible, open, used for actionable feedback

15. Increased precision • Provides accurate measurements of student growth over time Using Computer Adaptive Technology for Summative and Interim Assessments Tailored for Each Student • Item difficulty based on student responses Increased Security • Larger item banks mean that not all students receive the same questions Shorter Test Length • Fewer questions compared to fixed form tests Faster Results • Turnaround time is significantly reduced Mature Technology • GMAT, GRE, COMPASS (ACT), Measures of Academic Progress (MAP)

16. How CAT Works (Binet’s Test)

18. Responding to Common Misconceptions about Adaptive Testing • Can students return to previous questions if the test is adaptive? • Will the test give students questions from higher and lower grades if they are performing very high or very low? • Do all adaptive tests work this way?

19. K-12 Teacher Involvement • Support for implementation of the Common Core State Standards • (2011-12) • Write and review items/tasks for the pilot test (2012-13) and field test (2013-14) • Development of teacher leader teams in each state (2012-14) • Evaluate formative assessment practices and curriculum tools for inclusion in digital library (2013-14) • Score portions of the interim and summative assessments (2014-15 and beyond)

20. Higher Education Collaboration • Involved 175 public and 13 private systems/institutions of higher education in application • Two higher education representatives on the Executive Committee • Higher education lead in each state and higher education faculty participating in work groups • Goal: The high school assessment qualifies students for entry-level, credit-bearing coursework in college or university

21. Performance Tasks The use of performance measures has been found to increase the intellectual challenge in classrooms and to support higher-quality teaching. - Linda Darling-Hammond and Frank Adamson, Stanford University

22. Example Grade 11

23. Usability, Accessibility, Accommodations

24. Universal Tools, Designated Supports, and Accommodations Universal tools are access features of the assessment that are either provided as digitally-delivered components of the test administration system or separate from it. Universal tools are available to all students based on student preference and selection. Designated supports for the Smarter Balanced assessments are those features that are available for use by any student for whom the need has been indicated by an educator (or team of educators with parent/guardian and student). Accommodations are changes in procedures or materials that increase equitable access during the Smarter Balanced assessments. They are available for students for whom there is documentation of the need for the accommodations on an Individualized Education Program (IEP) or 504 accommodation plan.

25. New Graphic

26. General Table, Appendix A

27. Text-to-Speech • On Items • Designated support for math items • Designated support for ELA items • On ELA Reading Passages • Grades 3-5, TTS for passages is not available • Grades 6-HS: for passages available accommodation for students whose need is documented in an IEP or 504 plan

28. Guidelines & Frameworks Smarter Balanced Usability, Accessibility and Accommodations Guidelines http://www.smarterbalanced.org/wordpress/wp-content/uploads/2013/09/SmarterBalanced_Guidelines_091113.pdf Smarter Balanced Translation Framework http://www.smarterbalanced.org/wordpress/wp-content/uploads/2012/09/Translation-Accommodations-Framework-for-Testing-ELL-Math.pdf

29. Focus, Coherence & Rigor in the Smarter Balanced Assessments

30. The CCSSM Requires Three Shifts in Mathematics • Focus strongly where the standards focus • Coherence: Think across grades and link to major topics within grades • Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity

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

32. Shift #1: Focus Strongly where the Standards Focus The shape of math in A+ countries Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states Mathematics topics intended at each grade by at least two-thirds of A+ countries 1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

33. Shift #1: FocusKey Areas of Focus in Mathematics

34. Grade 7 Example • In grades 6 and 7, proportional relationships are a crucial pivot from multiplicative reasoning to functional thinking; sets stage for 8.F. • Meanwhile, probability in grade 7 has potentially misleading grain size—uses almost twice as many words as for proportional relationships standards.

35. Shift #1: FocusContent Emphases by Cluster The Smarter Balanced Content Specifications help support focus by identifying the content emphasis by cluster. The notation [m] indicates content that is major and [a/s] indicates content that is additional or supporting.

36. At what grade should students be able to solve these problems?

37. Shift #2: Coherence Think Across Grades, and Link to Major Topics Within Grades Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years. Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

38. Shift #2: CoherenceThink Across Grades 4.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Grade 4 5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Grade 5 6.NS. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Grade 6

39. Beyond the Number Line: Other Representations that Support Student Understanding of Fractions BAD BAD BAD What fraction is represented by the shaded area?

40. Do students really understand unit fractions and the concept of one “whole”? • The fraction represented by the green shaded area is ¾. Based on this: • Draw an area that represents ¼. • Draw an area that represents 1.

41. Do students really understand the concept of the unit fraction and of one “whole”? • The fraction represented by the green shaded area is 3/2. Based on this: • Draw an area that represents ½. • Draw an area that represents 1.

42. Linking Operations with Fractions to Operations with Whole Numbers “Children must adopt new rules for fractions that often conflict with well-established ideas about whole number” (p.156) Bezuk & Cramer, 1989

43. What is ?

44. Fractions Example The shaded area represents . Which figures from below can you use to build a model that represents ? You may use the same figure more than once. B D A C

45. Student A drags three of shape B, which is equal in area to the shaded region. This student probably has good understanding of cluster 5.NF.B he knows that 3 x 3/2 is equal to 3 iterations of 3/2. Calculation of the product is not necessary because of the sophisticated understanding of multiplication. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

46. Student B reasons that 3 x 3/2 = 9/2 = 4 ½. She correctly reasons that since the shaded area is equal to 3/2, the square is equal to one whole, and drags 4 wholes plus half of one whole to represent the mixed number. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Note that unlike the previous chain of reasoning, this requires that the student determines how much of the shaded area is equal to 1.

47. Student C multiplies 3 x 3/2 = 9/2. She reasons that since the shaded area is 3/2, this is equal to 3 pieces of size ½. Since 9/2 is 9 pieces of size ½, she drags nine of the smallest figure to create her model. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. This chain of reasoning links nicely back to the initial development of 3/2 in 3.NF.1 “understand a fraction a/bas the quantity formed by a parts of size 1/b, illustrating the coherence in the standards across grades 3-5.

48. Grade 3 – Number Line 3.NF.A.3b Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

49. Grade 7 – Number Line

50. Grade 8 – Number Line