RTI: Response to Inequities - Providing an equitable mathematics program for All!

1. RTI: Response to Inequities - Providing an equitable mathematics program for All! Cindy Bryant LearnBop Director of Learning cindy@learnbop.com

2. AGENDA • A look at learners • Defining equity in learning • Responding to inequities • CCSSM connections • Resources

3. Inequities: Who struggles in mathematics and why? • Learning Disabilities (NSF, 2004) • Difficulties in reading (RD & MD) (Jordan, Hanich, & Kaplan, 2003) • Memory • Social Disapproval and Low Motivation • Parent Confusion • Gaps within Learning (Cawley, Parmer, Yan, & Miller, 1996) • Attention • Abstractness and Concept to Task confusion (Demby, 1997)

4. “Don’t Get It” Indicators • Lack of initiative – don’t self-start • Lack of retention – hands go up immediately after an explanation asking for the explanation to be repeated • Lack of perseverance – learned helplessness • Despise of word problems – 99% of all students • Requesting a formula – 1% actually look for a formula Adapted from http://www.edresourcesohio.org/files/selc2011/handouts/Peter-MMM/peter.pdf

5. Research has shown that Students Struggle: At the elementary level with: • Solving problems (Montague, 1997; Xin Yan & Jitendra, 1999) • Visually representing problems (Montague, 2005) • Processing problem information (Montague, 2005) • Memory (Krosenbergen & Van Luit, 2003) • Self-Monitoring (Montague, 2005) At the middle school level with: • Meeting content standards (Thurlow, Albus, Spicuzza, & Thompson, 1998; Thurlow, Moen, & Wiley, 2005) • Mastering basic skills (Algozzine, O’Shea, Crews, & Stoddard, 1987; Cawley, Baker- Kroczynski, & Urban, 1992) • Reasoning algebraically (Maccini, McNaughton, & Ruhl, 1999) • Solving problems (Hutchinson, 1993; Montague, Bos, & Doucette, 1991)

6. Response to Intervention (RtI) is the practice of providing research-based, high-quality instruction and progress monitoring to struggling students. 

7. NCTM’s Equity Principle Equity maximizes the learning potential for all students. • Equity requires high expectations and worthwhile opportunities for all students. • Equity requires accommodating differences to help everyone learn mathematics. • Equity requires resources and support for all classrooms and all students. Principles and Standards for School Mathematics, 2000.

8. Look at the student, not the label!!!

9. Response to Inequities: What has been found to help students with math difficulties? Procedural Instruction (Bryant, Hartman, & Kim, 2003) • EXPLICIT INSTRUCTION • “The [NMAP, 2008] recommends that struggling students receive some explicit mathematics instruction regularly” dedicated to foundational skills and conceptual knowledge. Foundations for Success: The Final Report of the National Mathematics Advisory Panel. U.S. Department of Education: Washington, DC, 2008. http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

10. Six Critical Features of Explicit Instruction • Daily Reviews • Presentation of New Content • Guided Practice • Explicit Feedback and Correctives • Independent Practice • Weekly and Monthly Reviews “Much of teaching is about helping students master new knowledge and skills and then helping them NOT to forget what they have learned.” Paul Riccomini

11. Context Students need to see how math and numbers are used in their lives so the earlier they connect with math in their environment, the more they see the need to know, do, and use mathematics…utilize everyday items/scenarios in math as often as possible!

12. Make Implied Language Experiences Explicit 8 divided by 3 or “how many sets of 3 go into 8?” CCSSM Progressions http://ime.math.arizona.edu/progressions/

13. Response to Inequities: What has been found to help students with math difficulties? Procedural Instruction (Bryant, Hartman, & Kim, 2003) • Strategy Instruction (Maccini & Hughes, 2000) • Representations, such as CRA (Maccini & Hughes, 2000; Maccini, Mulcahy, & Miller, 2007; Witzel, 2005; Witzel, Mercer & Miller, 2003)

14. Student Think-Alouds • The process of encouraging students to verbalize their thinking with a peer or the class—by talking, writing, or drawing the steps they used in solving a problem http://www.nctm.org/news/content.aspx?id=8452

15. Interweave Worked Examples:Class/Pairs/IndividualExamples Classdiscussion around an already solved problem pointing to critical features of the problem solution Pairs of students work together to solve a similar problem followed by discussion/sharing of solutions Individualstudents work independently to solve a similar problem

16. What’s Your Sign? Integer Addition https://www.teachingchannel.org/videos/adding-integers-lesson-idea CCSS: Math.7.NS.A.1b Math.7.NS.A.1d

17. CRAConcrete-Representational-Abstract Instructional Approach • A three-step instructional strategy • Each step builds off of the other • Used to explain the concept of the problem before executing the problem Based on Bruner’s theory of enactive, iconic, and symbolic reasoning.

18. CRAConcrete-Representational-Abstract Instructional Approach This strategy allows for more opportunities for teaching for conceptual understanding - a major emphases of the CCSSM - by connecting concrete understanding to abstract math processes/procedures.

19. Concrete (enactive/doing) 683 ÷ 5 = 1 2 3 4 5 Remainder Adapted from Riccomini & Witzel

20. Concrete (enactive/doing) 683 ÷ 5 = 1 2 3 4 5 Remainder Adapted from Riccomini & Witzel

21. Concrete-Representational-Abstract Instructional Approach x + 9 = 16 Making implied language explicit: X + 9 equals 16 or “what number plus 9 equals 16?”

22. Concrete (enactive/doing) x + 9 = 16

23. ConcreteModeling Tips Adapted from Witzel & Allsopp (2009)

24. Representational (iconic/seeing) • For special education students, explicit systematic instruction that involves extensive use of visual representations appears to be crucial, Gerstung and Clarke (2007, p. 2) • Crucial components of programs used in nations that perform well on international comparisons, such as Singapore, Korea, or the Netherlands Virtual Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html

25. Representational (iconic/seeing) • The teacher uses representations to model the problem • Drawing pictures; using circles, dots, and tallies

26. Representational (iconic/seeing) 607: 6.RP.A.3c Percent: Ratio Per 100

27. Representational (iconic/seeing) Visuals Blog www.learnbop.net

28. Abstract (symbolic/symbolizing) • The teacher uses numbers, notations, and mathematical symbols to explain the concept • Operation symbols used • X,-,+,/

30. Concrete-Representational-Abstract Instructional Approach Research Findings • Students with learning difficulties using this model outperformed peers on posttest and follow-up measures (Witzel, Mercer, & Miller, 2003) • Students with a history of high math achievement scores also show benefit on the posttest (and the follow-up despite pretest favoring of traditional (Witzel, 2005) • Highest effect sizes with secondary students were  • fromCRA instruction (Gerstenet al., in press; • Witzel, Mercer, & Miller, 2003; Witzel, 2005)

31. COMMON CORE CONNECTIONS • Standards for Mathematical Practice (MP) – Conceptual Understanding • …student practitioners of mathematics increasingly ought to engage with the subject matter (CCSSM, p 8) • Make sense of problems and persevere in solving them (MP1) • Reason abstractly and quantitatively (MP2) • Construct viable arguments and critique the reasoning of others (MP3) • Model with mathematics (MP4) • Use appropriate tools strategically (MP5) • Attend to precision (MP6)

32. Relevant Resources • Riccomini, P. Effective Strategies to Promote Retention of Essential Mathematics Concepts and Skillshttp://www.kansasmtss.org/2011Symposium/Math%20Retention%20Strategies.pdf • Research Supported Strategies for Instruction and Intervention: Number Sense through Algebra http://www.kansasmtss.org/2011Symposium/Numeracy%20Workshop.pdf • http://nlvm.usu.edu/en/nav/vlibrary.html • CCSSM Progressions http://ime.math.arizona.edu/progressions/ • Illustrative Mathematics http://www.illustrativemathematics.org/ • NCTM Illuminations http://illuminations.nctm.org/ • LearnBop www.learnbop.net

33. Next Steps… What do you plan to do to make mathematics more equitable for ALL students?

34. Webinar Offerings Quality questioning to Elicit Mathematical Thinking Wednesday, 11:00 a.m. ET 12/4/13 Practical Differentiation Strategies in Grades 5 – 8 Mathematics Wednesday, 11:00 a.m. ET 12/11/13 Details in the Data: Using Data to Improve Instruction Wednesday, 11:00 a.m. ET 12/18/13 http://go.learnbop.net/learnbop-webinars

35. QUESTIONS??? cindy@learnbop.com 417-720-1748 (office) 573-247-2462 (cell) @LearnBop https://www.facebook.com/LearnBop