Identifying and Assisting Elementary and Middle School Students Struggling with Mathematics

1. Identifying and Assisting Elementary and Middle School Students Struggling with Mathematics The presentation will begin shortly.

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7. Welcome and Overview Lydotta M. Taylor, Ed.D. Research Alliance Lead, REL Appalachia The EdVenture Group

8. What is a REL? A REL is a Regional Educational Laboratory. There are 10 RELs across the country. The REL program is administered by the U.S. Department of Education, Institute of Education Sciences (IES). A REL serves the education needs of a designated region. The REL works in partnership with the region’s school districts, state departments of education, and others to use data and research to improve academic outcomes for students.

9. What is a REL?

10. REL Appalachia’s Mission • Meet the applied research and technical assistance needs of Kentucky, Tennessee, Virginia, and West Virginia. • Conduct empirical research and analysis. • Bring evidence-based information to policy makers and practitioners: • Inform policy and practice – for states, districts, schools, and other stakeholders. • Focus on high-priority, discrete issues and build a body of knowledge over time. http://www.RELAppalachia.org Follow us! @REL_Appalachia

11. Introductions and Webinar Goals Lydotta M. Taylor, Ed.D.

12. Speakers Russell Gersten, Ph.D.Instructional Research GroupJohn Woodward, Ph.D.University of Puget Sound

13. Webinar Goals • Equip elementary and middle school teachers and curriculum coaches with: • IES-approved, research-based recommendations for identifying students struggling with mathematics. • Guidance on strengthening mathematics instruction and support of these students.

14. Agenda • What is Response to Intervention (RtI)? • Why use RtI in mathematics instruction? • Case for RtI and Early Intervention in Mathematics • Case for RtI in the Intermediate Grades • Recommendations for identifying and assisting students struggling with mathematics • Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools • Applying the Practice Guide in the Classroom • Wrap Up and Closing Remarks

15. What is Response to Intervention (RtI)? Russell Gersten, Ph.D. Director, Instructional Research Group

16. Tier I: Core Class Instruction Tier I is defined differently by experts. Only common feature: • Universal screening of all students. Other possible components: • Ongoing professional development for classroom teachers on how to use research. • Differentiated instruction. • High quality mathematics instruction. • Scientifically based mathematics instruction.

17. Tier II: Small Group Intervention • Tier II is individual or small-group intervention in addition to the time allotted for core mathematics instruction. • Tier II includes curriculum, strategies, and procedures designed to supplement, enhance, and support Tier I. • Can backtrack and/or elaborate/reinforce classroom curriculum. • Progress monitoring of students “at-risk” on a monthly or weekly basis.

18. Updates on Current Research Since the Practice Guide Some of the most effective Tier II interventions involve grade level materials (e.g., work of Lynn Fuchs and colleagues). Some evidence that measures of working memory can be used to help with placement. Typically, takes many data points (perhaps 10-12) to determine if a child is making sufficient progress.

19. Q & AWhat is Response to Intervention (RtI)?

20. Why Use RtI in Mathematics Instruction? Russell Gersten, Ph.D.

21. Case for RtI and Early Intervention in Mathematics

22. Predictive Power of Early Mathematics Achievement Longitudinal research studies: From Kindergarten to Fifth Grade. Students who enter Kindergarten low in mathematics and fail to learn much mathematics have a high likelihood of remaining weak mathematics students . Mathematics in Kindergarten is a better predictor than reading of later academic outcomes. Attention during Kindergarten is a solid predictor of future mathematics success or failure. Source: Morgan, P., Farkas, G., & Wu, Q. (2009) Duncan, G. J. et al. (2007)

23. Beginning of Math Proficiency: Theory • Attention (+) • Persistence (+) • Impulsivity (-) • Mental Number Line • Ability to quickly and accurately compare magnitudes • Estimation • This is a core component of number sense • Working memory critical as early as the end of first grade. Source: Geary et al. (2012)

24. Case for RtI in the Intermediate Grades

25. Why Intervention in Grades 3-5 is Important • Fractions represents a new level of abstraction for students. • Mathematically, this level of abstraction is critical for success in algebra. • Recent longitudinal research supports this view: • By 5th grade, understanding of fractions is the best predictor of algebra success. Source: National Mathematics Advisory Panel (2008) Siegler et al. (2012)

26. Why Intervention is Important (continued) Fractions critical to success in algebra. Algebra a gateway to career success. So in many ways, FRACTIONS are the gateway in grades 3-7!

27. National Assessment of Education Progress Results • Many American students are unable to solve fractions problems in middle or even high school • Example: NAEP Grade 8 in 2007 (Pass rate = 49%) In which of the following are the three fractions arranged from least to greatest? • Most think that the reason for poor performance on these items is that students never understood the mathematical ideas relating to fractions.

28. Poll the NAEP What is the correct set of numbers? A B C D E

29. Q & AWhy Use RtI in Mathematics Instruction?

30. Recommendations for Identifying and Assisting Students Struggling with Mathematics Russell Gersten, Ph.D.

31. Response to Intervention Practice Guide

32. Panelists Russell Gersten (Chair) Sybilla Bechmann Ben Clarke Anne Foegen Laurel Marsh Jon R. Star Bradley Witzel

33. Practice Guides Mandate Create a framework for establishing/refining instruction that is clear and practical. Include action-based recommendations that can be implemented in practice. Take risks: don’t equivocate! Create a coherent document: common themes should underlie the various specific suggestions.

34. Practice Guide Structure Recommendations How to carry out the recommendations Levels of evidence Potential roadblocks and suggestions

35. Evidence Rating Each recommendation receives a rating based on the strength of the research evidence. Strong Moderate Low simply means no rigorous evidence, not contradictory evidence or negative (i.e., minimal evidence)…

36. Evidence Rating

37. Poll Item Which level of evidence is the biggest surprise for you? Why?

38. Setup for this Segment Target areas where evidence is most provocative Give a flavor of some of the Recommendations Set the stage for next set of presentations/panelists

39. Universal Screening and Progress Monitoring • No evidence that progress monitoring (conventional) is linked to effective intervention. • Some promising ideas for universal screening measures • Increased use of number line estimation and magnitude comparison. • Consideration of screeners that provide diagnostic and placement information. Source: Gersten et al. (2009) Siegler & Pyke (2013)

40. Predictive Power of Mathematics Measures Measures using a number line seem to be strongest predictors. They are better than general mathematics achievement measures. Source: Siegler & Pyke (2013)

41. Sample Grade 2 Estimation Item

42. Magnitude Comparison Requires students to name the larger of two visually presented numbers from 0 to 20 in Kindergarten and 0 to 99 in 1st grade. Administered in Kindergarten and 1st Grade Example Items - Grade 1 Prompt: “Each box has two numbers in it. Look at the numbers. I want you to tell me which number is bigger.”

43. What to Teach in Intervention (for Recommendation 2) • Instruction includes: • Procedures • AND concepts • AND word problems • There is a reciprocal relationship between understanding principles and mathematical ideas and competence with procedures. • The better you are with one aspect, the better you become with the other. • Panelurges the integration of both understanding principles and ideas with competence. Source: Riddle-Johnson & Siegler. (1998) Singapore Mathematics, Inc. (2003)

44. What to Teach Intervention content closely aligned to the Common Core BUT May need to include related material from earlier grades

45. Recommendation 3 Instruction during the intervention should be systematic and include models of proficient problem-solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review. Level of Evidence: Strong

46. What Seems Most Essential in the Supportive Research Extensive practice with feedback. Let students provide a rationale for their decisions. Instructors and fellow students model approaches to problem solving. Source: Schunk & Cox (1986) Tournaki (2003)

47. Unresolved Issues with Explicit Instruction How to support students’ talking about mathematics. How to capitalize on helping students learn from hearing peers explain their mathematical reasoning.

48. Recommendation 5 Intervention materials should include opportunities for the student to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas. Level of Evidence: Moderate

49. Life on the Number Line

50. Use a Visual Fraction Model • Representation of as a length • Using the number line to see that