MultiTiered System of Supports in Mathematics Part 1 Introduction Collaboration for Effective Educator Development Accountability and Reform H325A120003 CEM Overview Part 1 Introduction ID: 931991
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Slide1
Course Enhancement Module on Multi-Tiered System of Supports in Mathematics Part 1: Introduction
Collaboration for Effective Educator Development, Accountability, and Reform
H325A120003
Slide2CEM OverviewPart 1: Introduction.Part 2: Universal Intervention.
Part 3: Supplemental Intervention.
Part 4: Intensive Intervention.2
Slide3Participant GoalsBy the end of this section, participants will be able to:Discuss the importance of science, technology, engineering, and mathematics (STEM) education.Identify essential concepts in mathematics.identify areas in which students commonly struggle.Identify the essential components of a multi-tiered system of supports (MTSS).
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Slide4Part 1: IntroductionImportance of STEM education.Guiding principles in math.Common Core State Standards (CCSS) and essential math concepts.
How students learn math.
Students with math disabilities.MTSS.4
Slide5NotePart 1 comprises content and resources from:The National Center on Intensive Intervention (NCII): www.intensiveintervention.org Center on Response to Intervention: www.rti4success.org/National Council of Teachers of Mathematics (NCTM): www.nctm.org
Innovation Configuration for Mathematics (CEEDAR) The National Math Advisory Panel Report (2008)
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Slide6Why Is Mathematics Education So Important?
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Slide7The Importance of STEM Education It prepares all students for college and career.It is vital to meeting the needs of the future job market.It eliminates disparities in math achievement.
National Council of Teachers of Mathematics (NCTM), 2014
7
Slide8Nation’s Report Card (2013)National Assessment of Educational Progress, 2013 8
http://nationsreportcard.gov/reading_math_2013/#/student-groups
Slide9Nation’s Report Card (2013)Students Scoring Basic or Below Basic in Math
Student subgroup
Grade 4Grade 8
All students
58%
64%
Students with disabilities
83%
92%
English
language learners
86%
95%
9
http
://nationsreportcard.gov/reading_math_2013/#/
student-groups
National Assessment of Educational
Progress,
2013
Slide10Sample NAEP Grade 4 Math QuestionFourth-grade students scoring at the basic level should be able to solve a problem like
this:
10National Center for Education Statistics , n.d. http://nces.ed.gov/nationsreportcard/itmrlsx/default.aspx
Slide11STEM Education: The President’s ChargeThe United States’ international math status is significantly lower than other well-developed countries.Implications for the nation’s future.Implications for our quality of life.
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National Mathematics Advisory Panel, 2008
Slide12STEM EducationVideo retrieved from http://www.youtube.com/watch?v=f9NxFeCFApM&feature=player
, as posted by Mavericks Space Foundation, 2010
12Interactive Activity
Slide13STEM Education: Job Outlook3:1 increase in STEM jobs (National Science Board, 2008)“Close to half of all seventeen year olds cannot read or do math at the level needed to get a job at a modern automobile plant. Barring some other special knowledge or talent that would allow them to earn a living as, say, a plumber or artist, they lack the skills to earn
amiddle-class paycheck in today’s economy.” - Labor
economists Richard Murnane and Frank Levy13National Mathematics Advisory Panel, 2008, p. 3
Slide14Income by Graduation StatusNational Center for Education Statistics, 201514
Slide15STEM Education: Life SkillsMany Americans lack life skills that involve math.Many have difficulty with fractions, which are essential for algebra.Algebra is “gateway.”
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National Mathematics Advisory Panel, 2008
Slide16Importance of STEM Education: College SuccessSuccess in math is essential for college.High school math beyond Algebra II is highly correlated with college attendance (Horn & Nuñez, 2000; Horowitz, 2005).College graduates produce multiple benefits for society.
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National Mathematics Advisory Panel, 2008
Slide17STEM Education: Addressing DisparitiesCollege is a social escalator(Pascarella & Terenzini, 1991).College graduation rates differ between those who have and
have not taken Algebra II.High school science and math course completion can relieve or eliminate the achievement gap.Math is for ALL
.17National Mathematics Advisory Panel, 2008
Slide18Standards-Based MovementSix Principles of the Standards-Based MovementEquityCurriculumTeachingLearning
AssessmentTechnology
Van de Walle et al., 201318
Slide19Principles and Standards(NCTM, 2000)Five Content StandardsNumber and OperationsAlgebraGeometry
MeasurementData Analysis and Probability
Five Process StandardsProblem SolvingReasoning and ProofCommunicationConnectionsRepresentation
19
Van
de
Walle et al., 2013
Slide20Quest for Coherence(NCTM, 2006)Curriculum Focal Points for PreKindergarten Through Grade 8 Mathematics: A Quest for Coherence (NCTM, 2006).
BIG ideas are identified.Three focal points, along with process skills and connections, are fundamental at each grade level.
20Van de Walle et al., 2013
Slide21Birth of the Common Core State StandardsFive content standards
Five process standards
Common Core State Standards (CCSSO, 2010)11 content domains8 practice
standards
Watch the CCSS
VIDEO
21
Council
on Great City Schools, 2013; Van de Walle et al.,
2013
Slide22Characteristics of Successful Math Programs, Teachers,
and
Students22
Slide23Activity: Successful Schools, Teachers, and StudentsDirections:Move into your assigned group. Choose one person to be the recorder and one person to be the reporter.Travel to each chart as directed, read the topic on the chart, and record your ideas on the chart paper.After you visit all three charts, return back to your original chart.Read all of the additional ideas that have been added by the other teams and be ready to share out to the large group.
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Slide24Math Guiding PrinciplesTeachers must understand and demonstrate mastery of the mathematics content they teach.Teachers must understand how students learn math
content.Teachers must understand how assessment
guides and informs instruction.24VanDerHeyden & Allsopp, 2014
Slide25Knowledge of Math ContentTeachers must demonstrate:Competency in understanding the underlying concepts for the content they teach.Understanding of math concepts and skills across domains.Understanding of and engagement in the eight critical practices (i.e., CCSS).Understanding of effective teaching practices specific to the mastery of math.
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VanDerHeyden & Allsopp, 2014
Slide26Teacher’s Knowledge26
Hill et al., 2008
Slide27Understanding Underlying ConceptsTeachers must:Understand key ideas and skills.Articulate prerequisite skills.Explicitly connect the known to the new.Explain why a problem worked.Establish mastery objectives.Select tools that align with key ideas to facilitate understanding.
VanDerHyden & Allsopp,
201427
Slide28Understand the Developmental Nature of MathematicsTeachers must also demonstrate understanding of math concepts and skills across domains and how they build on each other.11 domains (CCSSO, 2010):
1. Counting
and Cardinality2. Operations and Algebraic Thinking3. Number and Operations in Base Ten4. Number and Operations–Fractions5. Measurement and Data6. Geometry7. Ratios and Proportional Relationships8. The Number System9. Expressions and Equations10. Functions11. Statistics
and Probability
Van de Walle et al., 2013
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Slide29Eight Math PracticesK–8 students should be able to:Make sense of problems and persevere in solving them.Use appropriate tools strategically.Reason abstractly and quantitatively.
Attend to precision.
Construct viable arguments and critique the reasoning of others.Look for and make use of structure.Model with mathematics.Look for and express regularity in repeated reasoning.http://www.corestandards.org/Math/Practice/
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Van de Walle et al., 2013
Handout
1
Slide30How Mathematical Thinking Develops
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Slide31Math ProficiencyWhat is math proficiency? Math proficiency means understanding key concepts with automaticity, developing
“flexible, accurate, and automatic execution of standard algorithms,
and [using] these competencies to solve problems” (National Math Advisory Panel, 2008, p. 22).For example, to prepare students for algebra, teachers must “simultaneously develop conceptual understanding, computational fluency, and problem-solving skills” (National Math Advisory Panel, 2008, p. 19).
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National Mathematics Advisory Panel, 2008
Slide32Five Domains of Math ProficiencyVan de Walle et al., 2013
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Slide33Understand the Developmental Nature of MathematicsInteractive K–8 chartInteractive K-8 chart linked above is from LearnZillion (n.d.). Retrieved from https://learnzillion.com/common_core/math/k-8
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Slide graphic from NCTM (2012), as referenced by Common Core Math Library (n.d.). Retrieved from
http://ccssmlibrary.blogspot.com/p/grade-level-math-
resources.html
Slide34Students With Math Disabilities and Struggling LearnersNumber sense.Working memory.Phonological processing.Processing speed.Executive functioning.Pattern of strengths and weaknesses.
Compton et al., 2012
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Slide35Math DisabilitiesDyscalculia: a neurologically based disorder affecting math abilities; dyscalculia is evidenced by a discrepancy between a student’s general cognitive functioning (i.e., IQ) and math abilities (i.e., academic achievement). The three types of math disabilities are:Semantic memory.Procedural memory.Visuospatial memory.Prevalence: at least 6%Language difficulties
Wadlington & Wadlington, 2008
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Slide36Math DisabilitiesMath anxiety.Additional factors: motivation, poor instruction, lack of prerequisite skills.
The National Center for Learning Disabilities., 2012
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Slide37Poor Outcomes for Students With DisabilitiesStudents with disabilities have a history of poor outcomes (compared with their non-disabled peers) in:Academic achievement.Involvement with criminal justice system.Employment.
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National Mathematics Advisory Panel, 2008
Slide38Multi-Tiered System of Supports (MTSS)
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Slide39MTSS
39Slide graphic and
information from www.rti4success.org
Slide40Multi-Level Prevention System
Supplementary
l
evel
of
prevention
(~15
%
of students)
Intensive
l
evel
of
prevention
(~
5%
of students)
Universal level
of
prevention
(~80% of students)
40
Information from
www.rti4success.org
Slide41Multi-Level Prevention SystemStudents with disabilities and English language learners receive services at all levels, depending on need
Universal level of prevention
Intensive level of preventionSupplemental level of prevention
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Information from
www.rti4success.org
Slide42MTSS FrameworkMulti-Level Prevention SystemUniversalFocus:
All student.Instruction: District curriculum
and instructional practices that are evidence based, align with state or district standards, and incorporate differentiated instructionSetting: General education classroom.Assessments: Screening, continual progress monitoring, and outcome measures.
Supplementary
Focus
: Students identified (through
screening) as at risk for poor
learning outcome.
Instruction
: Targeted, supplemental
instruction delivered to small groups.
Setting
: General education classroom
or other general education location
within the school.
Assessments
:
Progress
monitoring, diagnostic.
Intensive
Focus
:
Students who have not responded to universal or supplementary instruction.
Instruction
:
Intensive, supplemental instruction delivered to small groups or individually.
Setting: General education classroom or other general education location within the school.Assessments: Progress monitoring, diagnostic.42Information from
www.rti4success.org
Slide43MTSS: ScreeningPurpose: Identify students who are at risk of poor learning outcomes.Focus: All students.Tools: Brief assessments that are valid, reliable, and demonstrate diagnostic accuracy for predicting learning or behavioral
problems.Timeframe: Administered more than once per year (e.g., fall, winter
, spring).43Information from www.rti4success.org
Slide44Progress MonitoringPurpose: Monitor students’ responses to primary, secondary, or tertiary instruction in order to estimate rates of improvement, identify students who are not demonstrating adequate progress, and compare the efficacy of different forms of instruction.Focus: Students identified
through screening as at risk for poor learning outcomes.Tools: Brief assessments that are valid, reliable, and evidence-
based.Timeframe: Students are assessed at regular intervals (e.g., weekly, biweekly, monthly).44Information from www.rti4success.org
Slide45Data-Based Decision MakingData analysis is used at all levels of RtI implementation (e.g., state, district, school, grade level) and all levels of prevention (e.g., universal, supplementary, intensive).It requires established routines and procedures for making decisions.
It also requires explicit decision rules for assessing student progress (e.g., state and district benchmarks, level and/or rate).
Data is used to compare and contrast the adequacy of the core curriculum and the effectiveness of different instructional and behavioral strategies.45Information from www.rti4success.org
Slide46Implementing the MTSS FrameworkSelect and implement evidence-based practices and procedures.Implement essential components and the identified framework with integrity.Ensure that cultural, linguistic, and socioeconomic factors are reflected in
the RtI framework and its components.
46Information from www.rti4success.org
Slide47Considerations for English Language LearnersProvide interventions that: Include high-quality vocabulary instruction.Take into account the student’s level of language proficiency.Address cultural and prior educational experiences.
47Information from www.rti4success.org
Slide48Linguistic and Cultural Factors to ConsiderNative language.Current levels of proficiency in first language and in English.Early exposure to first language and English.Country of origin.
Educational and cultural experiences.
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48
Information from
www.rti4success.org
Slide49How CCSS-M Aligns With MTSS
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Information
and graphic from
http://
www.intensiveintervention.org/sites/default/files/NCII_Computation_Fractions_Example.pdf
Slide50Benefits of MTSSMaximize academic growth.Minimize behavioral problems.Culturally responsive.
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Slide and graphic Information from www.rti4success.org
Slide51Reflect and Revise: Closure ActivityTake 3 minutes to reflect on five to eight of the big ideas you learned from this module.Revisit the chart paper. Update your definition of “successful math instruction, teachers, and students.”Add or delete ideas in your definitions based on new information you learned from this module.
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Interactive Activity