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