RTI: RESPONSE TO INEQUITIES - PROVIDING AN EQUITABLE MATHEMATICS PROGRAM FOR ALL!Cindy BryantLearnBop Director of Learningcindy@learnbop.com

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

INEQUITIES: WHO STRUGGLES IN MATHEMATICS AND WHY?

Learning Disabilities (NSF, 2004)

Difficulties in reading (RD & MD) (Jordan, Hanich, & Kaplan, 2003)

MemorySocial Disapproval and Low MotivationParent ConfusionGaps within Learning (Cawley, Parmer, Yan, & Miller, 1996)

AttentionAbstractness and Concept to Task confusion

(Demby, 1997)

“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

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)

RESPONSE TO INTERVENTION (RTI) IS THE PRACTICE OF PROVIDING RESEARCH-BASED, HIGH-QUALITY INSTRUCTION AND PROGRESS MONITORING TO STRUGGLING STUDENTS. 

General Education Activities (80%)Small Group Instruction (15%)Indvidual Instruc-tion (5%)

NCTM’s Equity PrincipleEquity 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.

Look at the student, not the label!!!

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

RESPONSE TO INEQUITIES: WHAT HAS BEEN FOUND TO HELP

STUDENTS WITH MATH DIFFICULTIES?

SIX CRITICAL FEATURES OF EXPLICIT INSTRUCTION

1. Daily Reviews2. Presentation of New Content3. Guided Practice4. Explicit Feedback and Correctives5. Independent Practice6. 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

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!

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/

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)

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

INTERWEAVE WORKED EXAMPLES:CLASS/PAIRS/INDIVIDUAL EXAMPLES

Class discussion around analready solved problem pointing to critical features

of the problem solutionPairs of students worktogether to solve a similar problem followed by discussion/sharing of

solutionsIndividual students workindependently to solve a similar problem

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

CRACONCRETE-REPRESENTATIONAL-ABSTRACT INSTRUCTIONAL APPROACH

A three-step instructional strategy

Each step builds off of the otherUsed to explain the concept of

the problem before executing the problem

Based on Bruner’s theory of enactive, iconic, and symbolic reasoning.

Concrete (enactive/doing)

Representational (iconic/seeing)

Abstract (symbolic/symbolizing)

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.

Concrete (enactive/doing)

Representational (iconic/seeing)

Abstract (symbolic/symbolizing)

CONCRETE (ENACTIVE/DOING)683 ÷ 5 =

1 2 3 4 5 Remainder

Adapted from Riccomini & Witzel

CONCRETE (ENACTIVE/DOING)683 ÷ 5 =

1 2 3 4 5 Remainder

Adapted from Riccomini & Witzel

x + 9 = 16

CONCRETE-REPRESENTATIONAL-ABSTRACT INSTRUCTIONAL APPROACH

Making implied language explicit:X + 9 equals 16 or “what number plus 9 equals 16?”

x + 9 = 16CONCRETE (ENACTIVE/DOING)

CONCRETE MODELING TIPS

Adapted from Witzel & Allsopp (2009)

Use transparent manipulative objects on an overhead projector

Apply magnetic adhesive to a teacher set of manipulative objects to use on magnetic white boards

Develop large posterboard renditions of the manipulative objects to use on table tops or walls

Use an elevated table with an angled stand (such as a chart paper stand) that can support manipulative objects securely

Move students with visual and attention problems closer to you as you model

Provide students with their own sets of manipulative objects to use at their desks.

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

REPRESENTATIONAL (ICONIC/SEEING)

REPRESENTATIONAL (ICONIC/SEEING)

The teacher uses representations to model the problemDrawing

pictures; using circles, dots, and tallies

REPRESENTATIONAL (ICONIC/SEEING)

607: 6.RP.A.3c Percent: Ratio Per 100

REPRESENTATIONAL (ICONIC/SEEING)

Visuals Blog www.learnbop.net

ABSTRACT (SYMBOLIC/SYMBOLIZING)

The teacher uses numbers, notations, and mathematical symbols to explain the concept

Operation symbols usedX,-,+,/

Concrete (enactive/doing)

Representational (iconic/seeing)

Abstract (symbolic/symbolizin

g)

• 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 

from CRA instruction (Gersten et al., in press; Witzel, Mercer, & Miller, 2003; Witzel, 2005)

CONCRETE-REPRESENTATIONAL-ABSTRACT INSTRUCTIONAL APPROACH RESEARCH FINDINGS

COMMON CORE CONNECTIONSStandards 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)

Riccomini, P. Effective Strategies to Promote Retention of Essential Mathematics Concepts and Skills http://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

RELEVANT RESOURCES

NEXT STEPS…What do you plan to do to make mathematics more equitable for

ALL students?

WEBINAR OFFERINGSQUALITY QUESTIONING TO ELICIT MATHEMATICAL THINKINGWednesday, 11:00 a.m. ET 12/4/13

PRACTICAL DIFFERENTIATION STRATEGIES IN GRADES 5 – 8 MATHEMATICSWednesday, 11:00 a.m. ET 12/11/13

DETAILS IN THE DATA: USING DATA TO IMPROVE INSTRUCTIONWednesday, 11:00 a.m. ET 12/18/13

http://go.learnbop.net/learnbop-webinars

QUESTIONS???

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