RTI: RESPONSE TO INEQUITIES - PROVIDING AN EQUITABLE MATHEMATICS PROGRAM FOR ALL!Cindy Bryant
LearnBop Director of Learning
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.
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)
x + 9 = 16
CONCRETE-REPRESENTATIONAL-
ABSTRACT INSTRUCTIONAL APPROACH
Making implied language explicit:X + 9 equals 16 or “what number plus 9 equals 16?”
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
ABSTRACT (SYMBOLIC/SYMBOLIZING)
The teacher uses numbers, notations, and mathematical symbols to explain the concept
Operation symbols usedX,-,+,/
• 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
Algebrahttp://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
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
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