Mathematics in a Responsiveness to Instruction Framework

Susan Davis, Personnel Development Consultant

North Carolina Department of Public Instruction

Exceptional Children Division

November 2008

What isthis?

We’ve got to stop asking children to

solve problems they don’t know how to solve and, instead, teach them math.

Responsiveness to Instruction

The practice of providing high quality instruction matched to student need, monitoring progress frequently to make decisions about changes in instruction or goals and applying child response data to important educational decisions.

Response to Intervention Policy Considerations and Implementation,

NASDSE

Responsiveness to Instruction (RtI) … a school-wide system of support

Core Components of RtI

Screening (Formative Assessment)A continuum of services available to all

students (from universal to intensive)Research-Based InterventionsProgress Monitoring (Formative

Assessment)Data-based Decision Making

SO WHAT ABOUT MATH in an RtI framework?

National Assessment of Educational Progress (“NAEP”)

40% of students at or above proficient (Grade 4)

7% of students at or above advanced (Grade 4)

32% of students at or above proficient (Grade 8)

7% of students at or above advanced (Grade 8)

"Arithmetic is being able to count up to twenty without taking off your shoes."

–Anonymous

5 Strands of Mathematical Proficiency

Understanding Computing Applying Reasoning Engagement

Source: National Research Council. (2002). Helping children learn mathematics. Mathematics Learning Study Committee, J. Kilpatrick & J. Swafford, Editors, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

NC Standard Course of Standard Strands (or goals):

Number and Operations

Measurement

Geometry

Data Analysis and Probability

Algebra

Problem Solving

Three General Levels of Math Skill Development (Kroesbergen & Van Luit, 2003)

** Number Sense

** Basic math operations

** Problem-solving skills

Source: Kroesbergen, E., & Van Luit, J. E. H. (2003). Mathematics interventions for children with special educational needs. Remedial and Special Education, 24, 97-114..

Common Threads in Research and Practice

Understanding

Computing

Applying

Reasoning

Engagement

Number Sense

Basic math operations

Problem-solving skills

Number and Operations MeasurementGeometryData Analysis and ProbabilityAlgebraProblem Solving

Two more …

FLUENCY (Automaticity)

LANGUAGE

Fluency (Automaticity)

There is a strong correlation between poor retrieval of arithmetic combinations (‘math facts’) and global math delays

Automatic recall of arithmetic combinations frees up student ‘cognitive capacity’ to allow for understanding of higher-level problem-solving

Source: Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293-304

Language

What does equal mean?

1=1³

Is this a correct statement?

How can CSI help?

C = Core

S = Strategic

I = Intensive

What investigative tools should be used?

Formative Assessment

Universal Screening

Benchmark assessment

Targeted progress monitoring

Tier I

Direct/Explicit

Components of Number Sense

Appropriate LANGUAGE

Components of Number Sense

Quantity and Magnitude

Numeration

Equality

Base Ten

Form of a Number

Proportional Reasoning

Algebraic and Geometric Thinking

Activity …

If Mark has 6 brown socks and 3 white socks in a drawer, how many socks will he need to blindly pull from the drawer before he is guaranteed to pull out two socks of the same color?

Tier IIDirect/Explicit

Components of Number Sense

Appropriate LANGUAGE

Targeted instruction

Tier III

Direct/Explicit

Components of Number Sense

Appropriate LANGUAGE

Targeted instruction

Smaller group/individualized, more intense and frequent

Cover, copy, compare

allows students practice at visualizing and computing through a sequence of easy to remember steps.

Math Vocabulary

Preteach Math Vocabulary

Model the relevant vocabulary

Ensure that students learn standard, widely used/accepted labels for math terms and operations

Other Instructional StrategiesTeaching …

use of known number combination (2 + 2 = 4, so 2 + 3 =5)

relations among operations (6 + 4 =10, so 10 −4 = 6)

commutative and associative properties

problem interspersal technique or incremental rehearsal

Resources:

http://www.ed.gov/about/bdscomm/list/mathpanel/index.html

www.interventioncentral.com

http://www.k8accesscenter.org/training_resources/math.asp

http://mathforum.org/math.topics.html

CASE SOLVED

… death by

inadequate instruction