A MODEL FOR HELPING STUDENT TEACHERS

A MODEL FOR HELPING STUDENT TEACHERSAuthor(s): PATRICIA F. CAMPBELL and GRAYSON H. WHEATLEYSource: The Mathematics Teacher, Vol. 76, No. 1 (January 1983), pp. 60-63Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27963310 .

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A MODEL FOR HELPING STUDENT TEACHERS

By PATRICIA F. CAMPBELL University of Maryland

College Park, MD 20742

and GRAYSON H. WHEATLEY Purdue University

West Lafayette, IN 47907

In the sequence of courses that com

prise a secondary school teacher's prepa ration program, the student teaching experience probably makes the most pro found impression on the student. Within

weeks, the student changes from a college student to a beginning teacher. The devel

opment of professional attitudes, skills, and responsibilities during that period oc curs under the guidance of an experienced supervising teacher. Although the college or university has given the student coursework and a college or university supervisor works closely with the student

teacher, a principal responsibility for the

development of the student teacher lies with the supervising teacher in the sec

ondary school. The importance of super vising teachers in the development of effective teachers cannot be minimized.

Clearly, the responsibilities delegated to the student teacher by the supervising teacher should be increased gradually, but

what should be the sequence of experi ences? And what performance can rea

sonably be expected as the student teach er progresses?

The purpose of this article is to explore the implications of identified "stages of concern" in the progression from begin ning to effective student teacher. The arti cle will consider some implications of these stages for supervisors and for teach er education programs. In particular, what

experiential preparation should the col

lege or university provide prior to student

teaching, and what are realistic expecta

tions during student teaching? The par ticular stages were observed during the

supervision of secondary mathematics student teachers at Purdue University during three consecutive years. The ob servations occurred during regular visits to the schools where the students were

teaching and during student teacher group discussion sessions held at the university.

Stages of Concern Our observations suggest that student

teachers may pass through three ordered

stages as they become responsible begin ning teachers. The sequence seems valid for each student teacher, but the rate of

progression varies greatly. Unfortunately, many students do not seem to reach the third stage during student teaching. We have labeled the three stages

1. concern with self, 2. concern with teaching actions and stu

dents' behavior, and

3. concern with learning.

Stage 1?concern with self. Initially most student teachers questioned their

ability to cope with a complex and de

manding class of unfamiliar students. Each seemed to ask, "Can I handle this? What do they think of me? What does my supervisor think? Will I have enough ma

terial to last through the period?" Their

general posture seemed one of self-analy sis. Their thoughts seemed centered on

self rather than on teaching or learning. Also, they were trying to assess what avenues would be open to them within the classroom. Unfortunately, many seemed to assume without asking that material outside the textbook or strategies not used

by their supervising teacher would be

unacceptable. Although they recognized the need to know their students, most

60 Mathematics Teacher



seemed uncertain how to do so. Through experience all seemed to learn the class room routine, but some could not charac terize the dynamics within their classes. It seemed that only after the issues of self doubt were resolved could the student teachers turn their attention to instruc tion. Prior to this point they often seemed to perform mechanically. They did not

respond naturally to students' questions or classroom events. Inappropriate be havior often led to questioning of their

maturity by the supervising teachers and sometimes even ridicule by the students.

It is important to recognize stage 1 behaviors in student teachers. Supervis ing teachers are in a much better position to assist student teachers if they under stand the concerns with which student teachers may be preoccupied. It may be

inappropriate as well as futile to raise the issue of students' learning while they are

still struggling with identity-related issues.

Stage 2?concern with teaching actions and students' behavior. At this stage the student teachers seemed to see and deal

with classroom challenges, but the focus was on their own actions rather than on

students' learning. Two distinct charac terizations appeared common. On the one

hand, an emphasis on their own actions sometimes resulted in excessive lesson

planning. These student teachers often had extremely detailed lesson plans that

they followed like scripts. The result tend ed to be a rigid, monologue presentation with little sense of timing, enthusiasm, or

class interaction. On the other hand, some student teachers seemed to be asking for someone to tell them what to do. Eager for an approach, they were ready to try to imitate any technique without much con cern as to whether it was appropriate for them or their students. These student teachers usually had ideas but seemed reluctant to discuss them, perhaps be cause of their lack of confidence as to how to adapt or to implement their ideas in the classroom. When encouraged and aided

by discussions of how to carry out their

ideas, each of these groups of student teachers gradually came to develop their own styles of teaching.

By the fourth week of the field experi ence the prime concern of the student teachers seemed to shift to discipline and classroom atmosphere. Of course, these

problems existed prior to this point, but the student teachers did not seem able

effectively to address these issues previ ously. Overall, the student teachers seemed somewhat disheartened but open to suggestions. Generally they viewed dis

ruptions or apathy as problems rather than as symptoms of other problems. As the supervising teachers offered sugges tions (e.g., techniques for discipline) and

expressed a willingness to discuss, with out judgment, the classroom atmosphere, the student teachers seemed to gain confi dence. The key may have been the experi ence of success coupled with the develop ment of good, varied lessons that kept their students involved.

Stage 3?concern with learning. During the second stage, planning a lesson usual

ly centered on "What will I do?" or

"What will I say?" The third stage seemed marked by the question "Did they learn?" This concern for learning seemed to be accompanied by an increased aware ness of individual students rather than

only of the class. The student teachers that reached stage

3 began to address the needs of individual students. These student teachers would consider the need to provide for special problems such as math anxiety, boredom, frustration, or laziness. Additionally, they began to develop their own teaching styles and acquired the self-confidence to be lieve in themselves as teachers. The ob

servation of other teachers produced a

different response in these student teach ers because it was approached with a new

interest. It seemed as if these beginning teachers viewed the remainder of their field experience as a time not only to

practice teaching but also to study teach

ing.

January 1983 61



Implications for

Supervising Teachers

It is important that teacher educators have realistic expectations concerning the

performance of a student teacher. To ex

pect too much too soon may cause student teachers to doubt their ability and to fear

admitting their weaknesses. Similarly, overly to restrict the responsibilities of student teachers may hinder their devel

opment and smother their creativity. In either case, the result is a lack of commu nication between the student teacher and the teacher educator that may limit the

potential of the student teacher. The supervising teacher may find it

helpful to keep these stages of concern in mind. Initially, student teachers are not

very receptive to a discussion of tech

niques or ideas, since many have not yet recognized that they have problems or

they may not be able to cope at that level

yet. It is necessary for the student teacher to become comfortable in the classroom before such discussions are meaningful. During the first two weeks, student teach ers may not be at ease when exchanging ideas during conferences, whereas later on they may be able to express their

thoughts and concerns as they move to ward self-evaluation. Rather than inter

preting a reserved manner as disinterest or incompetence, the supervising teacher should consider the student teacher's

stage. While the supervising teacher is

teaching, daily preclass conferences be tween the supervisor and the student teacher are invaluable. It is through these sessions that the student teacher comes to see that planning involves more than sim

ply determining what they will do today. The student teacher can observe how the

supervising teacher plans a sequence of

lessons, assesses the pace for a particular class, recognizes the needs of certain stu

dents, determines when testing is benefi

cial, or organizes outside resources. At the same time, the student teacher learns the desired format for lesson plans as well as the amount of detail expected. When

preclass conferences are followed by a

postteaching analysis of observed teach

ing moves (teaching as performed by the

supervisor as well as the student teacher), the student teacher not only comes fully to perceive the aspects of classroom in struction but also to see the supervising teacher as an ally and the conference as an

aid.

During the second stage, student teach ers become more open to discussions of

problems and how to solve them. This

may be an ideal time to focus on lesson

planning. The student teachers may have ideas about different approaches or out side resources, but they need encourage

ment in developing lesson plans incorpo rating these ideas. Policies or procedures for establishing or maintaining discipline are of interest at this time. By maintaining an open-door policy, supervisors can help student teachers talk about their concerns and develop effective approaches.

Those student teachers who develop to the third stage are receptive to the teach er's responsibility for students' learning. At this time, supervisors should encour

age the student teachers to express their ideas and to evaluate their own teaching. It is the time to guide the student teacher in understanding the teaching-learning process.

The intent of this paper is to suggest that student teachers are not equally sen sitive to all aspects of teaching throughout their field experience?that there are

stages of concern that can serve as guide lines to supervisors in planning interven tion strategies. Although we may feel it essential that student teachers become aware of the needs of individual students and the learning process, such efforts may not be effective if introduced early in the field experience. As student teachers overcome concern for self they become sensitive to the classroom atmosphere and

may then develop effective means of set

ting a productive learning environment. As with all learning, individual differ

ences do exist. Some student teachers move through some or all of the stages

62 Mathematics Teacher



rapidly, whereas others may never reach

stage three. Although the stages-of-con cern model does not lead to a day-by-day prescription for all students, it does sug gest a sequence for addressing the needs of student teachers in the classroom.

M?bius molecule In the Journal of the American Chemical Society

(2 June 1982), David M. Walba and colleagues at the University of Colorado at Boulder report that they have synthesized the first molecular M?bius strip. The researchers formed the figure when they joined the ends of a double-stranded strip of carbon and

oxygen atoms called tris- (tetrahydroxymethyleth ylene) diol ditosylate.

The researchers aimed for their M?bius molecule

target in part because it was "sort of a classical

problem in organic chemistry that's been around for a long time," Walba says. "Chemists are intrigued with symmetry," he says, and the M?bius band "is a

unique structure with novel and esthetically pleasing properties."

Chemists' increased ability to synthesize such

unique and esthetically pleasing structures has con

tributed to the recent growth in the field of chemical topology. In some chemical circles, topology has come to mean studies of novel molecular rings; more

broadly defined, it is the study of patterns among the atoms connected to other atoms in molecules. "Peo

ple are interested in topology because it's so funda mental?because it's got to be controlling things [in

chemistry]," says Steven H. Bertz of Bell Labora tories in Murray Hill, New Jersey (Science News 122 [17 July 1982]:36).

(Continued from page 10)

Assume that AABC contains a right angle C and that BC is the shorter leg of the right triangle. A circle with center has its radius equal to the mea sure of AC. Let BC = a, CA =

b, and AB = c. CA is a tangent segment, since a segment per

pendicular to a radius of a circle is tangent to the circle at the point of contact. When AB is extended it will intersect the circle

at a point ?>. The point where AB intersects the cir

cle^ named point E. DA is a secant segment. It intersects the circle at

two points, D and E. We also know that DB =

BC = a._ _

Since AC is a tangent segment and AD is a se cant segment, we know that

DA - EA = (AC)2.

By substitution we have

(c + a)(c -

a) = b2

or

c2 -

a2 = b2

and

a2 + b2 = c2.

Anthony Adrignolo HI Pascack Valley High School Hillsdale, NJ 07642

One of the first appearances of this proof was in 1821. It is included as proof 73 (of 370 proofs) that

were collected by E. S. Loomis and published in 1940. This collection is available from the National

Council of Teachers of Mathematics under the title The Pythagorean Proposition ($11 for nonmem

bers; $8.80 for individual NCTM members)?-Ed.

Pythagorean serendipity IV In "Pythagorean serendipity HI" (December

1981), Alan B. Jones showed how to generate a Py thagorean triple that includes any given positive odd integer. Two alternative methods can be used without taking recourse to any formulae, as the tri

ples occur "naturally."

Method 1 Recall the identity

1 + 3 + ? ? ? + (2/1 -

3) + (2n -

1) = n2.

Now, given any odd integer In - 1, we have

1 + 3 + ? ? ? + [(2/1 + l)2 -

2] + (2/1 + l)2 = 1 + 3 ? ? ? + [2(2n2 + 2/i)

- 1]

+ [2(2n2 + 2/1 + 1) - 1]

= (2n2 + 2/i + l)2 = (2n2 + 2n)2 + [2(2n2 + 2n) - 1] = (2n2 + 2n)2 + (2n + l)2.

So, we obtain the identity

(2n2 + 2/i + l)2 = (2n2 + 2/i)2 + (2n + l)2.

Examples

(1) (1 + 3 + 5 + 7) + 9 = 52. (2) 42 + 32 = 52.

Method 2

(2/1 + l)2 = (2n2 + 2/1 + 1) + (2n2 + 2/i) = (2n2 + 2n+ l)2

- (2n2 + 2/i),

where the fact that 2n2 + 2n + 1 and 2n2 + 2n are consecutive numbers has been used.

Examples

(3) 32 = 9 = 5 + 4 = 52 -

42.

(4) II2 = 121 = 61 + 60 = 612 - 602. Uko Ugochukwu University of Ibadan

Nigeria

January 1983 63



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A MODEL FOR HELPING STUDENT TEACHERS