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Using Peer Tutoring for Math

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What is Peer Tutoring?

Peer tutoring is an instructional strategy that consists of
pairing students together to learn or practice an academic task. The pairs of
students can be of the same or differing ability and/or age range. Peer tutoring
encompasses a variety of instructional approaches including Cross-Age Tutoring,
Peer-Assisted Learning Strategies (PALS), and Reciprocal Peer Tutoring (RPT).
Variations exist among instructional approaches. However, the underlying theory
is consistent: peer interaction can have a powerful influence on academic
motivation and achievement (Light & Littleton, 1999; Steinburg, Dornbusch,
& Brown, 1992; Wentzel, 1999). The research base also suggests that
socialization experiences that occur during peer tutoring can benefit both the
tutor and tutee by motivating students to learn and increasing their social
standing among peers (Fuchs, D., Fuchs, L.S., Mathes & Martiniez, 2002;
Rohrbeck et. al, 2003; Miller & Miller, 1995).When students
understand the benefits of peer tutoring and have the tools to become effective
tutors and tutees, they make greater progress than those who are not given any
instruction on how to work together (Fuchs, L.S., Fuchs, D., Hamlett, C.L.,
Phillips, N.B., Karns, K.,& Dutka, S., 1997).

Additionally, peer tutoring allows teachers to accommodate a classroom of
diverse learners including students with learning disabilities. This
instructional strategy increases response opportunities for students, provides
additional time for positive feedback, and increases the amount of time a
student is on-task (Maheady, 2001). Regardless of achievement level, content
area, or classroom arrangement, peer tutoring demonstrates effectiveness in
facilitating progress in the general education curriculum (Cohen, Kulik &
Kulik, 1982; Cook, Scruggs, Mastropieri, & Casto,
1985;Johnson, Maruyama, Nelson & Skon, 1981).

What Does it Look Like for Math?

Teachers can simultaneously engage all students in learning and practicing
basic math or problem-solving skills using peer tutoring. This instructional
strategy reinforces math facts, computational skills, and math concepts.
Examples of math content suited for peer tutoring include addition, subtraction,
multiplication, number concepts, vocabulary, measurement, and fractions. This
list is not exhaustive: most math content can be practiced using peer tutoring.

How is it Implemented?

The process for implementing peer tutoring depends on the specific
instructional approach you choose. Regardless of the strategy you choose, it is
important to follow the process strictly to ensure positive outcomes for all
students. The general process for implementing a peer tutoring lesson is
outlined below, but to learn more specific information about the strategies,
here are some sites you can visit:

PALS: www.vanderbilt.edu/kennedy/pals/

Cross-Age Tutoring: http://www.crossagelearning.net/

The general process of implementing a peer tutoring
lesson
is the following:

1. The teacher trains students on the process of peer tutoring and strategies
for fulfilling their role of tutor or tutee.

2. The teacher assigns partners.

3. Students retrieve their tutoring materials prepared by the teacher.

4. Students follow a highly structured tutoring procedure, in which tutors
present material previously covered by the teacher, and provide feedback to the
tutee.

5. Students switch roles after the teacher’s signal. The tutee becomes the
tutor.

6. The teacher circulates around the room, monitoring and providing feedback.

Peer tutoring is a strategy that can be used with students with a wide range
of disabilities and at all grade levels. However, successful implementation
necessitates training all students in the process and roles of peer tutoring.
This training should describe how both tutors and tutees benefit from peer
tutoring. Notably, the tutor advances his or her skills through the process of
constructing an explanation of the problem for the tutee.

The following basketball analogy is one way to illustrate the benefits. When
a struggling player has trouble with his or her free throw,
he or she asks a better player to help them. The better player analyzes the
other’s throw, determines what it is that makes a good free throw, and
formulates an explanation for how to throw the basketball. Through this
activity, both students’ free throws are improved.

In addition, students must be taught methods for seeking help, such as
directly asking for help, and continuing to ask for help until they understand.
If students do not feel comfortable directly asking for help, the tutor and
tutee could develop a signal system. The tutee could signal the tutor when he or
she needs help. Examples of signals are pointing to the self, pointing to the
tutor, or taps on the hand, book, or table.

Students also must be taught how to offer help. Some ways to offer to help
are as follows:

Pay close attention to your partner. If it seems they need help, offer
help.

Explain to your partner how he or she can find the answer, rather than
giving the answer.

Construct another explanation if the first explanation does not help.

Ask your partner to repeat your explanation back to you to find out if he
or she really understands.

Tips for Successfully Implementing a
Peer Tutoring Lesson
1. Design lessons to reinforce skill
already taught to students.
2. Identify a specific learning objective to
be presented by tutor.
3. Teach students how to be tutors.
4. Provide
a script of prompts for the tutor.
5. Provide necessary flash cards or
lists of skills to the tutors.
6. Provide a daily log to record tutoring
session.

Examples:

The following is an example of using peer tutoring to reinforce a
math lesson for third grade regarding understanding fractions as parts of unit
wholes.

Tutor: The purpose of this lesson is to understand fractions
as part of a whole. (Tutor states the learning objective.) You will practice
writing a number as a fraction by looking at the parts and the whole in
different examples.

Tutor: Look at Picture #1. Tell me how many small squares
there are in the picture.

Tutee: Four small squares

Tutor: Good! This is the number of small parts in the whole
figure. Write that number in the square at the bottom of the fraction sheet.

Tutor: Now, how many of those small squares are shaded?

Tutee: One small square.

Tutor: Great! This is the number of shaded squares in the
whole figure. Write this number on the top in the shaded square of the fraction
sheet.

Tutor: Now we want to name this fraction by using the number
of shaded squares and the number of small squares. What are the numbers?

Tutee: 1 and 4

Tutee: That is correct! To name the fraction we say
1 out of 4. The bar divides the parts on the top with the whole on the bottom.
Another way is to say it is that 1 shaded square out of 4 squares means ¼, or
one fourth.

In this example, you are defining parts of a
whole (a fraction) and establishing a definition of division by explaining the
symbols and relationship of the numbers. You are moving the child from a
concrete to an abstract form of the concept.

Tutor: Let’s try another example with 6 circles and 5
shaded.

Go through the process several times until the tutee understands the name and
the concepts of parts of a whole.

After a few more pictures, the roles should switch.

The second example not only shows a different
shape from
the first example but also a random arrangement of
circles. Students
may have an incorrect assumption that a visual of a
fraction must be connected or arranged in a specific order. The tutor should
practice
until he or she achieves mastery. It is important to practice many

different examples with different visuals for students to master the
concept
of fractions, reading fractions, and writing fractions.

The following is an example of using peer tutoring to reinforce a
math lesson involving reading and understanding a chart. This form of peer
tutoring would work best with cross-age tutoring or pairing a highly skilled
tutor with a lower- skilled tutee.

Apples Picked at the Orchard:

How many apples did Natalie pick?

Natalie

Raj

Tamara

Josh

Each stands for four apples.

Tutor: The purpose of this lesson is to read, to identify
parts of a chart and to interpret information from a chart in order to solve a
problem or answer a question. (Tutor states the learning objective.)

Tutor: Look at the chart and tell me what you see.

Tutee: Apples and names of people.

Tutor: Good! What is the title of this chart?

Tutee: Apples Picked at the Orchard

Tutor: Do you know what orchard means? (Explain words that are unfamiliar to
students to make the exercise more meaningful.) What does the picture of the
apple below the chart show?

Tutee: The picture of the apple stands for 4 real
apples.

Tutor: What do 2 apples and 3 apples show you?

Tutee: 2 apples mean Tamara has 8 apples and 3
apples means that Raj has 12 apples.

Tutor: How do you know that? Can you show me with a picture
or tallies?

Tutee: For one apple, I have 1 1 1 1. That is 4.
For 2 apples, I have 11111111. That is 8.

Tutor: What does the mean?

Tutee: I think it means that she ate the apples.

Tutor: What does the question on the right ask you?

Tutee: It wants to know the number of apples
Natalie picked. Not the number of apples she ate.

Tutor: So what is your answer?

Tutee: 4 apples since one apple stands for 4
apples.

This example includes a discussion of the key components
of a chart (title, names, and symbols). The example also allows the student to
translate symbols of apples into numbers and then multiple these numbers. The
title and the sentence below the chart help the student understand what the
symbols represent. Without this information, the simple question, “How many
apples did Natalie pick?” cannot be answered correctly. In addition, this
example requires a conversation between the tutor and tutee about new
vocabulary.

Upon attempting and answering the question
wrong, the tutor might come up with a real life example to help explain the
problem.

Teachers and tutors should keep in mind that drilling
skills helps the tutee master math concepts but peer tutoring should move beyond
drilling skills. This example illustrates peer tutoring as a discussion of
vocabulary words, symbols, numbers and their relationship. With a combination of
visual representation, communication of the process, and a description of the
math concept, a student with disabilities will benefit from the peer tutoring
process. This combination can result in mastery of a math concept.

Bibliography

Cohen, P.A., Kulik, J.A., & Kulik, C.C. (1982). Educational outcomes of
tutoring: A meta-analysis of findings. American Educational Research
Journal, 19(2), 237-248.

Cook, S.B., Scruggs, T.E., Mastropieri, M.A., & Casto, G.C. (1985).
Handicapped students as tutors. Journal of Special Education, 19,
483-492.

Fuchs, L. S., Fuchs, D., Hamlett, C. L., Phillips, N. B., Karns, K., &
Dutka, S. (1997). Enhancing students' helping behavior during peer tutoring with
conceptual mathematical explanations. Elementary School Journal,
97(3), 223-250.

Fuchs, D., Fuchs, L.S., Mathes, P.G. & Martinez, E.A. (2002). Preliminary
evidence on the social standing of students with learning disabilities in PALS
and No-PALS classrooms. Learning Disabilities Research & Practice,
17(4), 205-215.

Johnson, D.W., Maruyama, G., Johnson, R., Nelson, D., & Skon, L. (1981).
Effects of cooperative, competitive, and individualistic goal structures on
achievement: A meta-analysis. Psychological Bulletin, 89, 47-62.

Light, P.L., & Littleton, K. (1999). Social processes in children’s
learning (pp. 91-100). Cambridge, England: Cambridge University Press.

Maheady, L. (2001). Peer-mediated instruction and interventions and students
with mild disabilities. Remedial & Special Education, 22(1), 4-15.

Miller, S.R., & Miller P. F. (1995). Cross-age peer tutoring. A strategy
for promoting self-determination in students with severe emotional
disabilities/behavior disorders. Preventing School Failure, 39(4),
32-38.

Rohrbeck , C.A. et al. (2003). Peer-assisted learning interventions with
elementary school students: a meta-analytic review. Journal of Educational
Psychology, 95(2), 240-257.

Steinberg, L., Dornbusch, S.M., & Brown, B.B. (1992). Ethnic differences
in adolescent achievement: An ecological perspective. American Psychologist,
47, 723-729.

Wentzel, K.R. (1999). Social-motivational processes and interpersonal
relationships: Implications for understanding motivation at school. Journal
of Educational Psychology, 91, 76-97.

This strategy is identified as a Promising Practice. View the Access
Center Research Continuum.

For additional information on this or other topics,
please
contact The Access Center at [email-masked].
The Access Center:
Improving Outcomes for All Students K-8
The Access Center is a
cooperative agreement (H326K020003) funded by the U.S. Department of Education,
Office of Special Education Programs, awarded to the American Institutes for
Research 1000 Thomas Jefferson St. NW,
Washington, DC 20007
Ph:
202-403-5000 | TTY: 877-334-3499 | Fax: 202-403-5001 |
e-mail: [email-masked] website: www.k8accesscenter.org

This report was produced under U.S. Department of Education
Cooperative Agreement H326K020003 with the American Institutes for
Research. Jane Hauser served as the project officer. The views expressed
herein do not necessarily represent the positions or policies of the Department
of Education. No official endorsement by the U.S. Department of Education of any
product, commodity, service or enterprise mentioned in this publication is
intended or should be inferred.

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