Math
Standards
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NCTM
Common Core State
Standards for Math
(CCSSM)
Needs of Diverse Learners
NCTM Principles & Standards
for School Improvement
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Produced by the National Council of Teachers of
Mathematics (NCTM) in 2000 to set forth a national
vision for precollege mathematics education in the
US and Canada.
Includes The Equity Principle: "Excellence in
mathematics education requires equity--high
expectations and strong support for all students"
(NCTM, 2000,).
As a result of legislation, the standards movement,
and the NCTM principles; changes to the classroom
mandate the inclusion of all students in the general
education classroom.
Teachers need to possess the skills and dispositions to
teach a diverse group of students in inclusive settings.
NCTM Content Standards
 Numbers
and Operations
 Algebra
 Geometry
 Measurement
 Data
Analysis and Probability
NCTM Process Standards
 Problem
Solving
 Reasoning and Proof
 Communication
 Connections
 Representation
NCTM Goals for ALL Students
 Learn
to value mathematics
 Become confident in their ability to
do mathematics
 Become mathematical problem
solvers
 Learn to communicate
mathematically
 Learn to reason mathematically
6 NCTM principles
Equity
Curriculum
Effective
Teaching
Problem Solving
Continual Assessment
Importance of Technology
Curriculum Focal Points
(NCTM, 2006)
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Most critical mathematical topics for each
grade in elementary and middle schools
Intended to assist teachers in identifying the
most critical content for targeted attention.
A step in the implementation of the Standards
Strongly emphasized the importance of basic
arithmetic skills in lower and middle grades
Identifies 3 critical areas at each grade level
for pre-kindergarten through Grade 8
NAEP Content Strands
Number
Properties and
Operations
Geometry
Algebra
Measurement
Data Analysis and Probability
CCSSM Mathematical
Practices
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Make sense of problems and persevere in solving
them
Reason abstractly and quantitatively
Construct viable arguments and critique the
reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated
reasoning
CCSSM Mathematical
Practices
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Describe the skills that should be mastered by
students in all grade levels.
Combine the NCTM process standards and the
National Research Council strands of
mathematical proficiency.
The standards are organized by conceptual
categories rather than grade level for high school.
Provide opportunities for high school students to
apply mathematical concepts and reasoning to
real-life problems.
(National Governors Association Center for Best Practices
and Council of Chief State School Officers, 2010)
K
1st
2nd
3rd
4th
5th
6th
Counting & Cardinality
Operations & Algebraic
Thinking
Number & Operations in
Base Ten
Measurement & Data
Geometry
Number & Operations –
Fractions
Ratios & Proportional
Relationships
The Number System
Expressions & Equations
Statistics & Probability
Functions
Adapted from Common Core State Standards Initiative (http://www.corestandards.org/thestandards/mathematics/introduction/standards-for-mathematical-practice/).
7th
8th
Addressing the Needs of
Diverse Learners
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It’s important for teachers to be aware of the learning
needs of individual students and groups of learners and
meet their varying needs.
Teachers may find it necessary to modify their instruction
to make it more accessible to students with
mathematics disabilities.
When assessing curricular materials, teachers should
make certain that they contain effective instructional
features.
Evidence-based features have proven to be effective
among students with learning disabilities (LD).
Evidence-Based
Feature
Presence of Feature in Materials
Clear objectives
Are the lesson objectives specific enough that student mastery can
be easily determined?
Teaching of single skill or
concept
Does the lesson focus on a single skill or concept?
Use of manipulatives
Does the lesson promote the use of concrete objects to demonstrate
concepts and aid mathematical problem solving?
Instructional approach
Does the lesson incorporate the use of evidence-based instructional
strategies such as explicit instruction?
Teacher examples
Does the lesson provide sufficient examples that the teachers can
use to demonstrate the skill or concept being taught?
Opportunities to practice
Does the lesson include ample practice problems for students to
understand the concept or master the skill?
Review of prerequisite
skills
Does the lesson review prerequisite skills needed to learn the new
skill?
Error correction and
corrective feedback
Does the lesson integrate corrective feedback that includes
systematic procedures to help students correctly solve problems?
Vocabulary
Does the lesson identify key vocabulary terms and describe how
teachers should introduce and define the terms?
Strategies
Does the lesson include step-by-step cognitive strategies (explicitly
taught by the teacher) that students can use to solve problems?
Assessment
Does the lesson provide opportunities for the teacher to
individually assess a student's learning and mastery of the skill or
concept?
Adapted from Bryant, Bryant, Kethley, Kim, Pool, & Seo (2008).