Digging Deeper into Instructional Responses to Data Analysis

1. Digging Deeper into Instructional Responses to Data Analysis 2012-2013 Webinar series January 17, 2013 3 p.m.– 4 p.m. This training is supported by a Statewide Longitudinal Data Systems grant from the U.S. Department of Education.

2. Webinar Focus • Review “Leader Look-fors” and recommendations for enhancing teachers’ and teams’ instructional responses to student learning data. • Use sample SBAC items to demonstrate how enhanced instructional responses may be supported using formative assessment and learning progressions aligned to the CCSS. • Use “professional noticing” and “purposeful pedagogy” as an example of how to integrate formative assessment and enhanced instructional responses.

3. In the last webinar, we discussed “Leader Look-fors” • Leaders look for teachers to reflect on and critically analyze effectiveness of their previous practices based ontheevidence (student learning data). • Leaders look for teachers to progress from considering whatto teach to considering the how of instruction. • Not just what do students need to learn next, but how students need to learn based on what the student learning data reveal about their conceptual understanding.

4. Recommended leaders support a culture of inquiry and reflection. They: • Promote an inquiry mindset • Use discussion protocols to promote dialogue using: • Relevant student learning data or artifacts • Guiding questions for considering artifacts • Structured roles and process • Encourage paraphrasing, clarifying, probing, focusing andreframing questions • Seek external support for teams in terms of content and pedagogy.

5. Move instructional discussions From the ‘What’ to the ‘How’ Using student learning data to support instruction and transition to teaching under Common Core State Standards

6. Which of the following describes teachers discussing the ‘what’ versus the ‘how’? • These results indicate our students are struggling to identify triangles. We need to follow up with more lessons on the properties of triangles. • This group of students appears to be tripped up if the figure looked like a triangle yet violated one property. Let’s present students with different figures that are more similar to triangles, have them work in small groups to classify the triangles, then share the properties they used to make decisions. • Let’s do shape centers based on the number of sides of the figure. We can do triangles, rectangles, other polygons and circles.

7. Goal of Collaborative Data Use for Instructional Response

8. Using CCSS Math as an example Standards for Mathematical Practice: Standards for Mathematical Content: Domains with learning progressions through the grades that define what students should know and be able to do in mathematics. K-8 grade specific H.S. conceptual categories • How students engage with content, processes, proficiencies in mathematics for K-12.

9. Standards for Mathematical Practice Standards for Mathematical Content K-8 Domains Counting and cardinality Operations and algebraic thinking Number and operations in base ten Fractions Ratios and proportional reasoning The number system Expressions and equations Functions Measurement and data Geometry Statistics and probability 9-12 Conceptual Categories Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability • Make sense of problems and persevere in problem solving. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

10. CCSS Math: Focus and Coherence Smarter Balanced Assessment Consortium (2012, March). Content Specifications for the Summative assessment of the Common Core State Standards for Mathematics. Retrieved from http://www.smarterbalanced.org/wordpress/wp-content/uploads/2011/12/Math-Content-Specifications.pdf

11. Which aspect of teaching the CCSS do you feel your teachers and teams are struggling/will struggle with most in mathematics? • Incorporating instructional tasks and activities that are aligned with and help students exercise and grow in the mathematical practices. • Teachers’ knowledge and facility with the content of mathematics sufficient to support the ‘what’ and the ‘how’ of planning instructional responses. • Teachers’ knowledge and understanding of how students develop mathematical understanding and reasoning skills. • Teachers’ skills in designing instructional activities to support student learning and development in math content.

12. Domain: Fractions Current Reality Common Core Promotes more representations of fractions as parts of one or more wholes or unit as a point on a number line. 1National Mathematics Panel (2008) as cited in Gersten, R. & Fennell, F. (2012). Improving Instruction through the Use of Data: Phase 2, webinar presented October 13, 2012 2 Siegler, R., Duncan, G., Davis-Kean, P., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., &Chen, M. (2012). Early predictors ofhigh school mathematics achievement. Psychological Science, 23(7), 691-697. doi: DOI: 10.1177/0956797612440101 • Fractions, including decimals and percents, critical for students’ success and in higher mathematics (algebra, etc.).1 • Fractions require increased levels of abstraction. • Inability to translate between fractions and decimals and locate fractions on number line. • Facility with fractions predicts knowledge of algebra and math achievement.2

13. How do you know whether students have sufficient conceptual understanding of fractions & procedures with fractions to support their readiness for Algebra and higher math? Start with learning progressions!

14. The goal of instruction is student learning • Common Core State Standards are different from previous standards and curricula: • Scope and sequence approach to content standards • Unit approach to content standards • How may instruction and formative assessment support students’ access to and acquisition of CCSS? • “Standards are insufficiently clear about how learning develops for teachers to be able to map formative assessment opportunities to them.”3 3 Heritage, M. (2008). Learning Progressions: Supporting Instruction and Formative Assessment . Paper prepared for the Formative Assessment for Teachers and Students State Collaborative on Assessment and Student Standards of the CCSSO.

15. Hence, the “learning progression” Learning progressions: • Describe a trajectory of learning in a domain spanning a longer period, providing a multi-year developmental continuum of “successively more sophisticated performance levels.”1 (p. 3) • Allows teachers to see how grade-level standards are connected to prior learning and how grade-level standards address critical prerequisites for future learning. • How do you differentiate instruction for students at different levels of learning if you don’t understand what comes before or what comes next within a domain?

16. Learning progressions: • Provide one or more sequences of learning to undergird instruction. • Progressions guide teachers’ responses to data • What do students understand and are able to do? • Based on student learning data, what should students learn next? • Based on student learning data, how should students learn it? What instructional activities will facilitate the learning these students need?

17. Sample Learning progressions http://ime.math.arizona.edu/progressions/

18. Teachers I work with are: A. Not familiar with the concept of learning progressions. B. Somewhat familiar with the concept of a learning progression. C. Very familiar with the concept of learning progressions but not actually using them for responding to student learning data. D. Very or somewhat familiar with the concept of learning progressions and attempting to use them for responding to student learning data. E. Fluent with and using learning progressions to respond to student learning data.

19. What prior learning would help students solve this problem? • CCSS 5.NF.7 Fractions, Grade 5 • Claim 1: Concepts & Procedures, Target 1F • Apply and extend previous understandings of multiplication and division to multiply and divide fractions. (DOK 1, 2) • Builds on progression from Grades 3 & 4. Number line is offered as tool to support problem-solving. Extends use of number line for fractions in earlier grades.

20. Earlier claims for fractions • CCSS 3.NF.3a Fractions, Grade 3 • Claim 1: Concepts & Procedures, Target 1F • Develop understanding of fractions as numbers. (DOK 1, 2) • Demonstrates a shift in standards that expands concept of fractions to representation of a point on a number line.

21. What will early fraction work prepare students to do later in math? • CCSS: 7.NS.1 Integer Expressions, Grade 7 • Claim 1, Concepts and Procedures, Target 1B • Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide with rational numbers. • Students use the number line to add and subtract integers.

22. More sophisticated ideas of ‘equivalence’ • CCSS 7.EE.2, Expressions and Equations 2, Grade 7 • Claim 1: Concepts & Procedures, Target 1C • Use properties of operations to generate equivalent expressions. (DOK 1). • A high difficulty item used to discriminate top performing students. Equivalent expressions work at Grades 6 and 7 support students’ ability to solve increasingly complex equations in Grade 8 and high school.

23. Remember recommendations: • To realize the CCSS for student learning will require from teachers deeper mathematical content knowledge. • This is why team composition matters!!!! • Team members support each others’ learning. • Student learning data can help teachers plan responsive instruction that supports students attainment of CCSS. • Combining instruction with formative assessment helps teachers elicit student behavior or student work that uncovers their thinking. • Team discussions help teachers interpret student learning needs. • Instructional decisions are based on our interpretation of students thinking and understanding.

24. Caution: SBAC sample items and tasks • Sample items and tasks provide clues to how students will be expected to demonstrate their understanding and skills and the depth of knowledge they will be expected to attain. • Sample items and skills provide a relatively small sample of the complete picture of what I can expect my students to know and be able to do under CCSS.

25. Most of my teachers are expecting to be able to: • Continue to plan and teach the way they’ve been teaching, and not change what they will need to teach to meet CCSS. • Continue to plan and teach the way they’ve been teaching, but change some of the ‘what’ they will need to teach to meet CCSS. • Change a lot of the ‘what’ they’ve been teaching and some of ‘how’ they’ve been teaching. • Change the ‘what’ to some degree to meet CCSS, but mostly change the ‘how’ of their teaching to meet CCSS.

26. There will be changes to the ‘what’ and the ‘how’ What can we do to help teachers change the ‘how’ of their teaching to meet CCSS?

27. Gather student learning data through Professional Noticing4 • Teachers will need to employ professional noticing and responding • Attending to students’ strategies, • Interpreting students’ understanding, and • Deciding how to respond on basis of students’ understanding.

28. Professional responding and purposeful pedagogy5 • Teachers provide students with experiences that allow them to construct meaning through carefully designed tasks and facilitated discourse. • Use this type of instructional response to engage students in the content of the domain and in the Mathematical Practices of CCSS. • 5Jaslow, L., & Evans, A. L. (2012). Purposeful Pedagogy and Discourse Instructional Model: Student Thinking Matters Most. Retrieved from http://commoncore.aetn.org/mathematics/ccss-mathematics-4/CCSS%20Math%204-Purposeful%20Pedagogy%20and%20Discourse%20Model.pdf

29. Questions to ask yourself when observing students or interpreting student work • What strategies are students using to solve this problem, perform this task or calculation? • What do their strategies tell me about their thinking and understanding?

30. What did this student do? What big mathematical ideas are embedded in her strategy? • How would you notate her reasoning? • What is it that teachers have to know to be able to understand the mathematics of this student’s thinking?

31. How did the student solve the problem? • To solve the problem of ¼ x 36, the student transformed the problem using commutative property • Then she solved by finding half (½) of 36 = 18. • Then she found half (½) of 18 = 9 • What was the mathematical sequence of thinking? • Commutative Property 36 x ¼ = ¼ x 36 • Decomposing ¼ x 36 = (½ x ½) x 36 • Associative Property (½ x ½) x 36 = ½ x (½ x36) • To solve ¾ x 36 cupcakes she used the relationship between ¼ and ¾.

32. Most of the teachers I work with use professional noticing to uncover student thinking… • Most of the time. • More often than other techniques. • Less often than other techniques. • Not at all.

33. Purposeful pedagogy & classroom discourse7 • Assess students • Set learning goal • Design instruction- • Anticipate likely responses students will have for demanding tasks • Monitor students’ responses during the tasks • Select particular students to present their mathematical responses (discussion and summarizing) • Purposefully sequence the student responses for display and discussion • Help the class make mathematical connections • Between different students’ responses • Between students’ responses and the key concepts.

34. Monitoring strategy

35. Team & Teacher Instructional Response Stoplight activity: Part I Start with reflecting on the instructional tasks in which students engaged. Did students demonstrate their understanding of fractions to solve the problem? What did the students’ strategies tell us about their thinking and understanding?

36. Team & Teacher Instructional Response Stoplight activity: Part 2 Developing the Instructional Response Team dialogue could be structured using this approach. Hint: it helps to capture this on big paper or on projected computer. Red-Which aspects of instruction didn’t appear to be as effective as planned? Don’t repeat unless seriously modified. Yellow-Caution-what did I miss in terms of student learning progression, instructional approach, etc.? Proceed after team has helped troubleshoot and develop next steps. Green-This appeared to be effective. Continue this strategy where needed or plan next steps to move on.

37. In summary, we: • Connected the Leader Look Fors and Recommendations for our last session to the focus of this session on instructional responses. • Used sample SBAC items to demonstrate how enhanced instructional responses may be supported using learning progressions aligned to the CCSS. • Used an example of professional noticing and purposeful pedagogy to demonstrate how to integrate formative assessment and enhanced instructional responses. • Connected the instructional response to analyzing effectiveness in data teams.

38. Next webinarFebruary 21, 2013 • Connecting key concepts from DATA Project Training to key concepts in CCSS and Smarter Balanced Assessments