Teaching Strategies for Remedial Mathematics

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According to the Institute of Educational Sciences, (http://ies.ed.gov/ncee) remedial math instruction

should be explicit and systematic. This includes providing models of proficient problem solving,

verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.

The National Mathematics Advisory Panel defines explicit instruction as follows (2008, p. 23):

“Teachers provide clear models for solving a problem type using an array of examples.”

“Students receive extensive practice in use of newly learned strategies and skills.”

“Students are provided with opportunities to think aloud (i.e., talk through the decisions they

make and the steps they take).”

“Students are provided with extensive feedback.”

Regardless of the severity of the learning disability, a student should find some level of achievement in

mathematics, as mathematics is crucial to survival in further schooling as well as adult life. Proper

instruction and successful teaching strategies on the educator’s part are instrumental in assure student

success in remedial math classes. If an instructor takes heed to and uses the effective strategies for

teaching remedial math, she may help the student succeed where he may have not found success.

Encourage Student Participation: It is essential for the instructor to put emphasis on student

participation. This participation should be not only teacher-student participation but student-

student participation as well. This is a form of guided discussion, which allows the whole class to

progress as a group, lowering the probability that an individual student is left behind.

Use Role Reversal Techniques: Role reversal techniques put the students in the teacher’s shoes.

An example would be writing a problem on the board and having a student come to the board to

solve it, rather than the instructor solving it. This strategy allows the educator to know with

certainty that the students understand the material. It is often the case in remedial classes that

students are not truthful about whether they grasp the material; this method will let the teacher

bypass subjective statements and see objectively how the class is progressing.

Use Cognitive Modeling: Cognitive modeling is, in short, thinking aloud while solving a

problem. Not only should you use cognitive modeling when you are instructing students, but

students also should make attempts and employing cognitive modeling while solving problems.

The action of displaying your thoughts to the class shows students what paths successful problem

solving should take. In addition, by requesting that your remedial students think aloud while

solving math problems, you can easily correct incorrect thought processes.

Mathematics can be a difficult subject for elementary schoolchildren to grasp. The abstract nature of the

concept often makes it challenging to explain to young learners. Teaching elementary math is much

easier with the help of a variety of teaching tools that help make mathematical concepts more concrete

and demonstrate to students how they will use math in their everyday lives.

Number Lines: A number line is a simple, affordable and incredibly valuable mathematical

teaching tool. When students begin to learn math, they develop number sense. Number sense is

the understanding of what numbers are and how they relate to each other. A student who knows

that six is a larger number than four, has a basic concept of number sense. Number lines provide

students with a concrete representation of the number system. When students first begin counting

or start to learn the basic operations of addition and subtraction, number lines can help them

compare the values of numbers as well as remember the order of the digits.

Times Tables: When developing early math skills, students must learn basic multiplication facts

by heart. Times tables have been a fall-back tool for years, but they remain valuable. By

practicing times tables with students, teachers can ensure that their students can quickly recall the

basic multiplication facts needed when they move on to more advanced mathematical concepts in

higher grades.

Manipulatives: Manipulatives are hands-on tools that help students figure out simple or complex

math problems. Teachers commonly use brightly colored plastic or wooden blocks as

manipulatives, but you can use any concrete object, including small plastic fruits, little pieces of

candy or even toothpicks. When students first see an addition problem, the concept is foreign to

them. It can be difficult for them to visualize a situation in which a quantity is added to another

quantity. Through the aid of manipulatives, teachers can demonstrate how the concept works. If

a student is trying to determine what two plus two is, (s)he can easily solve the problem by taking

two manipulatives then taking two more. Then all (s)he has to do is count to determine the sum

of the numbers.

Story Problems: Story problems allow students to see how they will use mathematical concepts

in class in real life. Learning how to add, subtract, multiply and divide is only half the battle.

The skills are nearly useless if students cannot apply them to real-life situations. By integrating

story problems into daily lessons, teachers can effectively ensure that their students understand

how to use math in everyday life. Also, story problems help students understand the relevance of

math. Through story problems, students can begin to see that the concepts they are learning are

not only useful in school, but that they have inherent value due to real-world applications.

Try the Tennessee Instructional Model (TIM) to help reinforce the math skills being taught:

I’ll do one; you watch. (model)

I’ll do one; you help. (group guided practice)

You’ll do one; I’ll help. (individual guided practice)

You’ll do one; I’ll watch. (independent practice)

Learning Strategies

(www.k8accesscenter.org)

Learning strategies are an individual’s approach to a task. They are how a student organizes and uses a

set of skills to learn content or to accomplish a particular task more effectively and efficiently either in or

out of school (Schumaker & Deshler, 1984). Teachers who teach students learning strategies teach

students how to learn and how to be successful in and out of the academic setting. Learning strategies

give students a way to think through and plan the solution to a problem.

Students with mathematics disabilities often do not learn these strategies naturally (Montague, 1998).

They switch from strategy to strategy because they do not know how to use them effectively. However,

they can be taught to use the two types of learning strategies: cognitive and metacognitive. Cognitive

strategies, include how to read, visualize, estimate, and compute. They can easily be taught as the teacher

repeatedly models the strategies,

monitors the students’ use of the strategies, and

provides feedback to students.

Metacognitive strategies are more difficult to teach because they involve self-questioning and self-

checking techniques. Students with disabilities often have less developed strategy banks and do not have

access to these important problem-solving strategies unless the strategies are taught to them. However,

learning to use the metacognitive strategies will enable learners to be successful throughout the learning

opportunities in their lives.

Manipulatives are an excellent way for students to develop self-verbalizing learning strategies. As they

use the senses of sight, touch, and hearing, students should be encouraged to talk their way through each

problem, either with peers or to themselves. They gain an understanding of the “why” of basic facts. The

more time that teachers give students to use the manipulates and to talk through mathematics problems,

the easier it is for students to retrieve that knowledge. Using manipulatives makes way for more abstract

thinking.

An important way to teach students learning strategies is for teachers to model the strategy. Teachers

must show students the thinking process that they use to analyze and solve problems and then the way

they check the reasonableness of the answer. The example below demonstrates this process. The teacher

demonstrates the process of subtracting 8 from 15 by using manipulatives. As students hear the teacher

talking her way through each problem, they imitate the teacher’s dialogue as they approach similar

problems. If students spend time talking their way through problems, they develop a better understanding

of the process of problem solving. When the teacher has solved the problem, she discusses aloud her

check for the reasonableness of her answer.

As students learn these strategies through practice, the teacher models less and students gradually take

over the responsibility of determining which strategy to use. Students become more independent learners.

The goal is for students to generalize these strategies into other learning situations.

Learning strategies should be part of every lesson, but they are more than the lesson. As teachers model

these problem-solving strategies daily, monitor the students’ use of them, and encourage students to use

the strategies in a variety of ways, students learn to generalize these strategies into other areas to become

independent learners for life.