Magazine article Teaching Children Mathematics

Peer Tutoring with Mathematics Manipulatives: A Practical Guide

Magazine article Teaching Children Mathematics

Peer Tutoring with Mathematics Manipulatives: A Practical Guide

Article excerpt

Are you looking for a teaching method that enhances mathematical communication, develops self-awareness, builds mathematical confidence, and improves interrelationships among students, as recommended by the NCTM's Professional Standards for Teaching Mathematics (1991)? For many teachers, adopting these objectives means going through a metamorphosis in their instructional practices. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989, 20) encourages teachers to pay increased attention to the following areas:

* Use of manipulative materials

* Cooperative work

* Discussion of mathematics

* Questioning

* Justification of thinking

* Writing about mathematics

* Problem-solving approach to instruction

Peer tutoring offers an alternative teaching strategy that creates a favorable environment for these objectives to be met. It empowers both the tutor and the tutee to become more self-directed in their learning. As they participate actively in the planning, learning, and evaluation of each activity, both tutor and tutee further develop their abilities to evaluate and analyze their own skill levels and performance (Barone 1991, 1992).

This article presents two primary-level, peer-tutoring field studies and suggests ways to implement peer tutoring in a classroom. More specifically, lesson planning, students' journal writing, manipulative activities, and students' responses are discussed.

Putting Peer Tutoring into Practice

Classroom management and proper organization of any peer-tutoring project are necessary for its success. Current research recognizes that teachers who are implementing peer tutoring are required to plan and prepare lessons, deal with elevated noise levels, work out scheduling problems (Berliner and Casanova 1990), and teach the behaviors and skills that enhance peer learning (Fantuzzo, Polite, and Grayson 1990). As with cooperative learning, the planning and structuring of students' experiences are closely related to the successes experienced by students and teachers. An analysis of what worked and what did not in field studies and current research yields workable suggestions for setting up peer tutoring in a classroom.

Activity selection

Teachers need to select several concrete, engaging activities that can be taught by students to students. Starting with three to twelve activities that are "ready to go" before tutor training begins is recommended.

Tutor preparation

Each activity needs to be taught to the tutors before they teach it to their tutees. Modeling the activity with a student is advisable to ensure understanding as well as to suggest possible strategies for them to use. Next, the tutors practice explaining and carrying out the activity with another tutor as their partner. Finally, they switch roles so that each practices teaching, learning, and critically evaluating the process (Barone 1991, 1992). This strategy helps the tutors to be more confident and competent with their tutees.


To help organize these planning sessions, the teacher and students can create posters displaying the topics of giving directions (fig. 1), behaving appropriately (fig. 2), and responding to incorrect answers (fig. 3). It is helpful to display the posters at the front of the classroom during the planning sessions. Before each tutoring session, the tutors review the posters so that the information will be fresh in their minds. This strategy helps them reinforce the behavior set and maintain their own social skills.


An effective part of the peer-tutoring programs is the use of journals by both the tutors and the tutees. This practice enhances mathematical communication as advocated in the Standards documents (NCTM 1989, 1991). Journals are an excellent tool to help the tutors organize their thoughts and prepare the lessons that they will teach. …

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