RTI & Math SASED Spring Institute February 25, 2011 Marcy Stein, PhD University of Washington, Tacoma [email protected]

RTI & MathSASED Spring Institute

February 25, 2011

Marcy Stein, PhDUniversity of Washington, Tacoma

[email protected]

Relevant Research in Math Instruction

National Math Advisory Panel (NMP): Findings and Recommendations from Executive Summary

Curricular Content Learning Processes Teachers and Teacher Education Instructional Practices Instructional Materials Assessment Research Policies and Mechanisms

NMP Recommendations

Curricular Content (7) 1. “A focused, coherent progression of mathematics learning, with an

emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula.”

5. “To encourage the development of students in Grades PreK–8 at an effective pace, the Panel recommends a set of Benchmarks for the Critical Foundations (Table 2, page 20). They should be used to guide classroom curricula, mathematics instruction, textbook development, and state assessments.”

6. “All school districts should ensure that all prepared students have access to an authentic algebra course—and should prepare more students than at present to enroll in such a course by Grade 8.”

NMP Recommendations

Learning Processes (8)10. “To prepare students for Algebra, the curriculum must

simultaneously develop conceptual understanding, computational fluency, and problem-solving skills.”

11. “Computational proficiency with whole number operations is dependent on sufficient and appropriate practice to develop automatic recall of addition and related subtraction facts, and of multiplication and related division facts. It also requires fluency with the standard algorithms for addition, subtraction, multiplication, and division. Additionally it requires a solid understanding of core concepts, such as the commutative, distributive, and associative properties.”

NMP Recommendations

Instructional Practices (8)23. “All-encompassing recommendations that instruction should be entirely “student centered” or “teacher directed” are not supported by research. If such recommendations exist, they should be rescinded.”

25. “Teachers’ regular use of formative assessment improves their students’ learning, especially if teachers have additional guidance on using the assessment to design and to individualize instruction.”

NMP Recommendations

27. “Explicit instruction with students who have mathematical difficulties has shown consistently positive effects on performance with word problems and computation. Results are consistent for students with learning disabilities, as well as other students who perform in the lowest third of a typical class.”

“Finding Common Ground”Areas of Agreement

Automatic recall of facts – need computational fluency

Calculators - with care - not to impede fluency Learning Algorithms

“A systematic procedure involving mathematical operations that uses a finite number of steps to produce a definite answer.”

Fractions “The arithmetic of fractions is important as a

foundation for algebra.

http://www.maa.org/common-ground/cg-report2005.html

NMP Recommendations

Instructional Materials (3)32. “States and districts should strive for greater agreement regarding which topics will be emphasized and covered at particular grades. Textbook publishers should publish editions that include a clear emphasis on the material that these states and districts agree to teach in specific grades.”

NMP Recommendations26. “The use of “real-world” contexts to introduce mathematical

ideas has been advocated, with the term “real world” being used in varied ways.

A synthesis of findings from a small number of high-quality studies indicates that if mathematical ideas are taught using “real-world” contexts, then students’ performance on assessments involving similar “real-world” problems is improved. However, performance on assessments more focused on other aspects of mathematics learning, such as computation, simple word problems, and equation solving, is not improved.”

Research into Practice

RtI and Math Instruction

Amanda VanDerHeyden, Ph.D.

(www.rtinetwork.org)

“To enhance the sustainability of the RTI effort in mathematics, implementers should make every attempt to integrate the RTI math effort with ongoing system reform efforts.”

http://www.rtinetwork.org/About/AdvisoryCouncil/VanDerHeyden

*The Devil is in the DETAIL

When people say that the devil is in the detail, they mean that small things in plans and schemes that are often overlooked can cause serious problems later on.

http://www.usingenglish.com/

The Three C’s

Collaboration(who)

C____ C___

Guiding Assumptions

What we do at every level has significant impact on students.

Developing the leadership and learning capacity of teachers, school-based administrators, and district leadership is the best strategy for sustained instructional improvement.

Establishing Collaborative Teams

Embed collaboration in routine practices Build time for collaboration into the school

day Focus teams on key questions Make products of collaboration explicit Generate team norms to guide collaboration Pursue specific and measurable

performance goals Ensure that teams have access to relevant

information

The Three C’s

Collaboration(who)

Curriculum(what)

C___

Some Definitions

Scientifically based reading [math] programs have been evaluated in valid scientific experiments.

These experiments must include: Meaningful measures of achievement and Compare several schools using a given program with

several carefully matched schools that did not.

Slavin (2003)

Some Definitions

Reading [math] programs based on scientifically based research:

-incorporate the findings of rigorous experimental research.

Slavin (2003)

Mathematics Programs (TIMSS)

U.S. textbooks compared to those of other countries: focus more on “eye catching,” irrelevant

illustrations, dedicate equal time to simple and difficult tasks, provide little information for teachers on content

and methodology.

Schmidt, Houang, & Cogan, 2002

Mathematics Programs (TIMSS)

U.S. textbooks compared to those of other countries: much larger and heavier cover more topics with less depth fail to develop linkages between topics are repetitive and spiral

Schmidt, Houang, & Cogan, 2002Schmidt, Houang, & Cogan, 2002

Spiral Curriculum

Strand Curriculum

Strands Use Track Sequencing

General track characteristics:One preskill or skill taught per trackTrack extends over days or weeksExercises within track change

systematicallyTracks are systematically integrated

Track Sequencing

Beginning of a track: Highly prompted Limited amount of information No immediate transfer

Middle of a track: Prompting gradually faded Generalization gradually expanded Transference of skill to other applications begins

End of a track: Independent Generalization complete Wide application

12

Selecting Appropriate Curriculum

A. Evidence of Effectiveness 1. Is there published evidence of the

effectiveness of the program?

2. Is there evidence that the program has been field tested with large groups of students?

(What Works Clearinghouse)

B. Explicit Strategy (algorithm) Instruction1. Are objectives clearly stated?

2. Are the steps in the strategy explicitly identified in the program?

3. Are component skills taught and/or reviewed?

4. Is math vocabulary taught?

5. Is the math Instruction scaffolded?

6. Are the math skills integrated?

Selecting Appropriate Curriculum

Teacher Objectives ?

Explicit StrategyInstruction

Explicit Strategy Instruction: Volume



Component Skills

Subtraction with Regrouping•Is the student proficient with subtraction facts?

•Does the student understand the right to left sequencing? (Is the subtraction being carried out in the proper direction?)

•Does the student know when to borrow?•Does the student know from where to borrow?•Conversion: Does the student make the appropriate conversions in the adjacent columns?

Math Vocabulary

Scaffolded Instruction: Progressing from Easy to More Difficult Contexts

34 52 85

16 38 47

•Prompt each problem•Work each problem•Check each problem

•Work Each Problem•Check Each Problem

•Work a block of problems•Delayed check

Teacher assistance gradually fades

Strategic Skill Integration

Math Facts – Fact Families

2 + 4 = 6 6 – 2 = 4

4 + 2 = 6 6 – 4 = 2

Integration: Number Family Rules

2+4=6

4+2=6

6-2=4

6-4=2

2 4

Integration: Word Problems

First: graphically represent the word problem.

Then: determine how to write the number problem.

Problem Solving - Comparisons

Fran was 14 years older than Ann.

14 AF

Ann was 13 years old.

How many years old was Fran?

14+13 27

13

Problem Solving - Sequence of Events

Mark gathered some nuts before lunch. After lunch he gathered 66 more pounds of nuts. At the end of the day, he had 121 pounds of nuts. How many pounds of nuts did he gather before lunch?

66121

121-66 55

Problem Solving - Classification

A hotel is going to buy 112 pieces of furniture. It needs to buy 57 couches. The hotel will buy chairs for the rest of the furniture. How many chairs will the hotel buy?

57112 112

-57 55

Can You Solve This Problem?

Workers planted fir trees and maples in two parks—Rock Park and Wilson Park. They planted 128 fir trees in Rock Park. The total number of maples planted in both parks was 543. In Rock Park, they planted 17 more maples than firs. A total of 400 trees were planted in Wilson Park.

What’s the total number of trees that were planted?

Were more maple trees planted in Rock Park or Wilson Park?

In which park were more trees planted?

Skill Integration

Rock ParkWilsonPark Total

Fir Trees 128

Maple Trees 543

Total Trees 400400

Skill Integration


Skill Integration


Fir Trees 128

Maple Trees 145 543

Total Trees 400400

MaplesFirs17128

145

Skill Integration


Fir Trees 128 2 130

Maple Trees 145 398 543

Total Trees 273 400400 673673

MaplesFirs17128

145

Strategic Skill Integration


What’s the total number of trees that were planted?

Were more maple trees planted in Rock Park or Wilson Park?

In which park were more trees planted?

The Three C’s

Collaboration(who)

Curriculum(what)

Coaching(how)

48

Instructional Coaching

What is an instructional coach?

“an on-site professional development educator who collaborates with educators to identify and assist with implementation of proven teaching methods.”

Knight, 2006

49

Math Coaching Framework

Instructional coaching provides a structure for problem solving.

Design & Implement Action Plans

Evaluate Progress

Gather Information

50

Problem Solving

Term used in 3 ways:

1) When general education teachers differentiate instruction;

2) When offering specially designed instruction for students with disabilities;

3) For schoolwide decision-making.

(Fuchs & Deshler, 2007)

Math Coaching Framework

Math coaching provides a structure for problem solving. The math coach helps:

I. Gather informationII. Design action plans (collaboratively)

III. Implement plans (professional development)

IV. Evaluate student progress (data based decision making)

I. Gather Information

A. Materials and Instruction

B. Instructional Time and Grouping

C. Professional Development

D. Goals and Assessment

E. Data Utilization

53


Is the instruction provided to students systematic and explicit?

54


Is sufficient time being devoted to teacher directed instruction?

Is the number of students in classes appropriate for students’ skill level?

55

Professional development may be needed in these areas: Assessment (including RTI) Content (aligning content with state

standards) Behavior (discouraged learners) Instruction (curriculum evaluation, error

analysis)


56


Are teachers receiving sufficient, high quality inservice training in using their core program materials?

Are teachers and assistants receiving sufficient, high-quality inservice training in using supplemental and intervention materials?

57


Are teachers and assistants receiving sufficient high-quality in-class coaching?

Are there sufficient provisions to support teachers needing extra help (e.g., with positive behavioral management).

58

Goals and assessment pertain to these areas:

Academic goals (individual, class, school) Behavioral goals (individual, class,

school) Multiple assessments


59


Are beginning-of-year assessments administered within the first days of the school year to identify students performing below grade level and to determine their starting points in the curriculum materials?

60


What general progress monitoring assessments are administered during the school year?

Are these assessments administered frequently enough to discover when students are not making satisfactory progress?

61


What program-specific assessments are used to determine if students are learning content taught in core, supplementary, and intervention programs?

62


Have mid-year and end-of-year performance goals been established on critical instructional indicators?

Have content coverage goals (pacing guides) been established for the core program?

63


Have content-coverage goals (e.g., lessons, units, pages to be completed) for groups in supplemental and intervention programs been established?

64


Are teachers receiving sufficient support to reliably administer assessments and use data from assessments to adjust instruction?

65

Facilitating data utilization by designing and implementing:

Systems for making data available Systems for analyzing data Systems for using the data

(making instructional changes!)

E. Data Utilization

66

E. Data Utilization

Are there sufficient useful reports available to teachers addressing:student performance on assessments content coverage in core,

supplementary and intervention programs?

67

E. Data Utilization

Are grade-level team meetings held to analyze progress monitoring assessments and data on content coverage, and to generate plans to solve problems?

68

E. Data Utilization

What procedures exist to assist teams in designing action plans to solve problems of inadequate student performance or progress?

69

E. Data Utilization

What follow-up procedures are in place to determine if the action plans are producing desired results?

70

II. Design & III. Implement Plans

Based on information gathered regarding:





E. Data Utilization

71


Supplemental Instructional Programs Purpose: to provide additional instruction in one

or more areas of instructional

Example: Rocket Math (math facts programs)

72


Intervention ProgramsPurpose: to provide additional/alternative

instruction to students performing below grade level

Examples: The Corrective Math Program

73


Strategic Use supplemental

programs – e.g. math fact programs

Provide supplemental instruction – e.g., institute works checks

Intensive Use a replacement

core program (intervention program)

Provide a “double dose”

Provide supplemental instruction – e.g. preteach lessons; institute work checks

74


Strategic Add minutes of peer

tutoring or peer practice

Implement a homework incentive program

Intensive Group students

homogenously Add minutes of

teacher- directed instruction

Preteaching Work checks Supplemental programs

75


Instructional Coaches provide inservice training for teachers and

assistants provide in-class coaching for teachers and

assistance present model lessons guide teachers in error analysis and curriculum

modification facilitate team meetings to analyze data

76

IV. Evaluate Student Progress

Use data to analyze progress and design interventions: progress monitoring data program specific assessments error analysis procedures content coverage

The Three C’s of Tiered Math Interventions

Collaboration (who)

Curriculum(what)

Coaching(how)

Putting it all together

78

District Leadership

Math Coaches

Grade Level Teams

Teachers

Questions/Comments?

References & Resources

Daniels, D. C. (2002). Becoming a reflective practitioner. Middle School Journal, 33, 52-56.

Deno, S. L. (2002). Problem-solving as best practice. In A. Thomas & J. Grimes (Eds.), Best practices in school psychology IV (pp. 1-17). : Washington, D.C: National Association of School Psychologists.

Fuchs, D., & Deschler, D. (2007). What we need to know about responsiveness to intervention (And shouldn’t be afraid to ask). Learning Disabilities Research and Practice, 22, 129-136.

Gersten, R., Morvant, M., & Brengelman, S. (1995). Close to the classroom is close to the bone: Coaching a means to translate research into classroom practice. Exceptional Children, 62, 414-429.

References & ResourcesKinder, D., & Stein, M. (2006). Quality mathematics programs for students with

disabilities. In M. Montague & A. K. Jitendra (Eds.), Teaching mathematics to middle school students with learning disabilities (pp133-153). NY: Guilford.

Knight, J. (2005). A primer on instructional coaches. Principal Leadership, 5 (9), 16-21.

Knight, J. (2006). Instructional coaching: Eight factors for realizing better classroom teaching through support, feedback and intensive, individualized professional learning. The School Administrator, 63(4), 36-40.

Lau, M.Y., Sieler, J. D., Muyskens, P., Canter, A., VanKeuren, B., & Marston, D. (2006). Perspectives on the use of the problem-solving model from the view point of a school psychologist, administrator, and teacher from a large midwest, urban school district. Psychology in the Schools, 43(1), 117-127.

Little, M. E., & Houston, D. (2003). Research into practice through professional

development. Remedial and Special Education, 24, 75-87.

References & ResourcesSchaughency, E., & Etvin, R. (2006). Building capacity to implement and sustain

effective practice to better serve children. School Psychology Review, 35, 155-166.

Speece, D. L., Molloy, D. E., & Case, L. P. (2003). Responsiveness to general education instruction as the first gate to learning disabilities identification. Learning Disabilities Research & Practice, 18, 145-156.

Stein, M., Kinder, D., Zapp, K., & Feuerborn, L. (in press). Promoting Positive Mathematics Outcomes. In M. R. Shinn, G. Stoner & H. M. Walker (Eds.), Interventions for Achievement and Behavior in a Three-Tier Model including RTI, Bethesda, MD: National Association of School Psychologists.

Stein, M., Kinder, D., Silbert, J. & Carnine, D. (2006). Designing effective mathematics instruction: A direct instruction approach (4th ed.). Columbus, OH: Merrill/Prentice Hall.

Stein, M., Kinder, D., Zapp, K. & Feuerborn, L. (in press). Promoting Positive Math Outcomes In M. R. Shinn, H., M. Walker & G. Stoner (Eds.), Interventions for achievement and behavior problems: Preventive and remedial approaches. Bethesda, MD: National Association of School Psychologists.

References & Resources

American Federation of Teachers - http://www.aft.org/American Educator - previous issues – Schmidt et al. A Coherent Curriculum, Summer 2002

Center on Instruction - http://www.centeroninstruction.org/Special education: http://www.centeroninstruction.org/files/ImplementationOfRtI.pdf

Kansas University Center for Research on Learningwww.instructionalcoach.org

National Mathematics Advisory Panel. (2008). Foundations for Success: The Final Report of the National Mathematics Advisory Panel, U.S. Department of Education. Available: http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

www.rtinetwork.org

Documents

RTI & Math SASED Spring Institute February 25, 2011 Marcy Stein, PhD University of Washington, Tacoma [email protected]