This document discusses strategies and techniques for improving mathematics instruction for students with mild disabilities. It covers foundational math concepts like number sense, calculation, and problem solving. Some key instructional approaches mentioned include explicit instruction, peer tutoring, drill and practice, and ongoing progress monitoring. The document emphasizes teaching math concepts in a logical sequence and ensuring students have mastered foundational skills before moving on.

1. Sheena E. Bernal SpEd 8 MW 4:00-5:30PM
3rd Year / BEEd-SpEd Dr. Fely Colansi
Chapter 8 - Math: Strategies and Techniques
Developing a Foundation in Mathematics
 We learn the foundational concepts and skills of mathematics in much the same
way we learn language for communication.
 Daily experiences all help developing children to recognize mathematical
concepts such as proportion, time, linearity, and additive properties.
 However, ineffective mathematics instruction is part of the explanation for
mathematics difficulties.
 In addition, mathematics involves complex language; a single term can
represent an entire mathematical concept, which can be uniquely challenging
for English language learners (ELLs) with mild disabilities.
 Each of the mild disabilities may be a cause of mathematics difficulties. To be
"literate" in mathematics requires learning a variety of mathematical process
and how to apply them.
 An estimated 4.6 percent to 6.5 percent of school age students actually have a
"mathematics disability" (Seethaler and Fuchs 2006)
Mathematics Difficulties for Students with Mild Disabilities
 Rodney's performance inand out of school is representative of the mathematics
difficulties that manystudents with mild disabilities encounter in their lives. They
are literate in some, but not all of the concepts we would expect. Based upon
their age and grade, they can perform certain operations with moderate
profiency at least, but routinely make errors and have little understanding of
what they are doing.
 Teachers sometimes characterize students as "careless," when, in truth, they
have only partially mastered certain concepts and skills before the teacher
moved on in instruction without supporting the development of those basics.
Foundational Concept and Skills
 Children learn concepts such as sets, one-to-one correspondence, and
number names and values through instruction, games, and daily experiences.
 Foundation concepts of number sense are essential pre-skills of
mathematics.
 The National Council of Teachers of Mathematics (NCTM) has identified

2. standards in ten areas of mathematics that should be addressed across
mathematics curricula. The skills identified in the ten areas are: understanding
and applying one-to-one correspondence, number, grade-level appropriate
vocabulary, relationships, and counting.
Content Standards Process Standard
Numbers and operations
Algebra
Geometry
Measurement
Data analysis and probability
Problem Solving
Reasoning and proof
Communication
Connections
Representations
 One-to-one correspondence is one of the very first math concepts students
should learn because it is essential for much of mathematical understanding.
It simply means recognizing that units have numerical values.
 Vocabulary for numbers means memorizing the names of various digits can
be helpful for developing number sense, but is insufficient by itself.
 Vocabulary for relational concepts should also be developed.
 Place value identifies the value of each digit in a number.
 Counting is a vital skill for computation.
 Counting by twos, fives, and tens is particularly useful for calculation
operations.
 Students with mild disabilities should learn how to count backwards and
count down from 100.
Memorizing Calculation Facts
 Memorizing calculation facts can be a challenging task for students.
 Once students develop conceptual understanding of the procedures,
however, fluent performance depends on facts memorization.
 Students with mild disabilities are particularly likely to engage in inefficient
calculation practices, rather than to memorize and automatically recall math
facts.
Using Calculator
 Learning to perform mathematical operations on a calculator should be
viewed as a compensatory skill. Using a calculator can be facilitate for
students for whom memory or attention is a persistent block in practicing

3. calculations or performing more advanced mathematics. They may always
have to rely on calculator to perform some of those operations but not always.
 Students for whom using a calculator may be an appropriate accommodation
during standardized test, using the calculator to learn and practice the same
types of operations that will be on the test is essential.
Basic Computation Concepts and Skills
 Computation includes addition, subtraction, multiplication, and division.
 Algorithmic computation involves operations from the preceding calculation
type for borrowing, reducing, and estimating.
 One-to-one correspondence is one of the very first math concepts students
should learn because it is essential for much of mathematical understanding.
It simply means recognizing that units have numerical values.
 Vocabulary for numbers means memorizing the names of various digits can
be helpful for developing number sense, but is insufficient by itself.
 Vocabulary for relational concepts should also be developed.
 Place value identifies the value of each digit in a number.
 Counting is a vital skill for computation.
 Effective mathematics instruction also progresses from concrete concepts
and skills to sem-concrete and, eventually, abstract representations.
 Vocabulary of computation includes the term add, subtract, multiply, and
divide. It also includes terminology for the outcomes of those operations: sum,
difference, product, and quotient, respectively.
Skills that Build Upon Numeracy and Calculation
 Number sense is needed to comprehend each and reinforced by learning.
 Fractions - they learn about proportions and parts of wholes.
 Decimals may make more intuitive sense to students than fractions do. The
appreciation of place value is critical to comprehending decimals.
Other Basic Skills for Mathematical Operations and Daily Living
A variety of other basic mathematical concepts and skills must be mastered for
both daily living and more complex mathematics as well. Measuring, telling time, and
recognizing shapes are example of these other types of mathematics.
Estimating is to approximate an outcome to a problem. It is commonly used in
daily life, to approximate distance, time, and costs.
 Students canround up or round down numbers to convert them to numbers
to convert them to numbers that they are good at counting by.

4.  Compatible numbers are numbers that easy for students to calculate, so
they depend on which numbers the students are good at counting by.
 Front-end estimation is used to estimate when the student encounters
multi-digit calculation. The student needs to observe the numerals on the
"front," or that are leftmost.
The Sequencing of Math Concepts ad Skills
 Appreciation for the relevancy of certain concepts and skills can be enhanced
by linking them to other aspects of mathematics.
 Addition, subtraction, multiplication, and division are best introduced in
sequence.
 Advocate teaching the myriad concepts and skills of numeracy and the four
basic calculations by centering instruction on "big ideas."
 Using the variety of mathematical procedures that students practice to learn
for even a single operation will be meaningful if they understand the big ideas
behind them.
Problem Solving and Advanced Mathematics
 Students with mild disabilities who have difficulties learning computation
sometimes been denied instruction in problem solving or more advanced
forms of mathematics.
 Students with mild disabilities do participate in studying math at higher levels,
and those who continually struggle need more on lower-level skills and also
need instruction in higher mathematics.
Problem Solving
 Refer to tasks calculations imbedded mostly in the form of story problems.
 Students with math-related disabilities often have difficulty with
problem-solving tasks.
 Story problems (also knownas word problems) canpresent a math problem to
solve as simple as single-digit addition.
 For students with mild disabilities, attending factors and organizing
information is overwhelming.
 They may find four factors that can cause story problems to be uniquely
difficult: motivation, mathematical and other literacy, confounded story
problems, and complex math tasks.
Research Evidence

5.  Recognize cue words for mathematical problems.
 Need strategies to help them understand the mathematical questions and
operations the problem requires.
 English language learners have demonstrated greater math proficiency when
taught in their native language.
Strategies and Techniques for Improving Problem Solving
 The difficulty may be in their ability to (a) analyze the task, (b) perform the basic
operations accurately, and (c) manage the process.
They can follow the Mnemonic DRAW to remember the process. This
strategy is for math problems written out in numeric form.
Discover the sign.
Read the problem.
Answer, or draw and check.
Write the answer.
Students who have mastered DRAW may benefit from proceeding to learn
the FAST DRAW Strategy.
Find what you're solving for.
Ask yourself, "What are the parts of the problem?"
Set up the numbers.
Tie down the sign.
SOLVE Strategy gives more guidance on the overall process to follow.
See the sign.
Observe and answer; continue if you cannot answer.
Look and draw.
Verify your answer.
Enter your answer.
Montague and Bos offer a strategy designed to guide students who have
difficulty conceptualizing the problem.
Read the problem aloud.
Paraphrase the problem aloud.
Visualize the information.
State the problem aloud.
Hypothesize and think the problem through aloud.
Estimate the answer.
Calculate and label the answer.
Self-check by using self-questioning to ask if the answer makes sense.

6. General Approaches to Math Instruction
 A PAL (Peer-assisted learning strategies) prescribes instructional procedures
and peer tutoring approach.
 CWPTS (Classwide peer tutoring) model procedures involve more generally
effective teaching practices.
 Both approaches are rooted in Curriculum-Based Measurement (CBM).
 Direct Instruction is a specific approach to teaching and calls for systematically
checking on students' prior knowledge and re-teaching as necessary.
 Reteaching begins with a variety of forms of feedback that include prompting
students to try again, telling students the correct response, and reminding
students of a strategy to determine the response.
 Explicit instruction means teaching information overtly in a teacher-directed
lesson incorporating some of the principles of direct instruction.
Advanced Mathematics
 In high schools can include geometry, pre-algebra and calculus, trigometry and
statistics, as well as related courses such as physics. Approximately 25 states
require meeting algebra standards for earning a high school diploma.
 Algebra is a "gateway to abstract thought."
 It requires students to think abstractly, not just to translate abstract concepts into
concrete representations.
 Attempts to represent abstract problems in concrete forms can be inconsistent
with the task some advanced math problems pose.
Mathematics Curricula
 Replacing "general" or lower track mathematic classes with inclusive college
preparatory math classes has resulted in marginally improved math achievement
for students with mild disabilities, but they continue to perform below with their
peers and levels.
 The math difficulties many students with mild disabilities exhibited 20 year ago
are still commonly observed.
 Current traditional mathematics curricula are at least partially responsible.
Critical Elements of Effective Math Curricula

7.  The focus of math instruction for students with math-related disabilities should
include a focus on detecting errors and re-teaching those skills and concepts
(Riccomini 2005).
 Time drills have improved automaticity for students with LD.
 Advocate teaching of "conspicuous strategies," or those that have wide
applicability.
Seven Principles of Intensive Education
1.Ongoing progress monitoring
2.Drill and practice
3.Instructional explicitness
4.Instructional design to minimize learning challenge
5.Cumulative review
6.Systematic motivation to promote self-regulation and encourage students to
work hard
7.Conceptual foundation