In-Service Mathematics Education as Viewed byElementary School Teachers

James M. SherrillDepartment of Mathematics Education, The University of

British Columbia, Vancouver, B.C., Canada

It is a well documented fact1 that a revolution has occurred inschool mathematics. Both the content of school mathematics and themethods of teaching school mathematics encountered changes in thelast two decades. By 1960, organizations such as The School Math-ematics Study Group, The University of Illinois Committee on SchoolMathematics, and the Greater Cleveland Mathematics Programwere producing materials to aid the revolution in school mathematics.The changes that were being made were in the interest of a bettermathematics education for the students. The question soon arose asto what effect the changes would have upon the teachers of math-ematics.The question, ^Can any of the programs be taught successfully by

teachers who are accustomed to traditional programs and have nothad special training?",2 was soon posed in print. The authors whoposed the preceding question in print also provided the followinganswer:No. All groups developing programs have recognized that most teachers,through no fault of their own, are not properly equipped to present these pro-grams successfully.3

Clarence Ethel Hardgrove expressed the feeling of the Committeeon the Undergraduate Program in Mathematics with respect to thepreceding question, as well as other questions, when she said thefollowing :That the curriculum has changed and is changing is a fact. The changes aremade in an attempt to provide a better mathematics education for children.The important question for us to consider in relation to the changes is: What dothey imply for elementary teachers? The answer is. . . The elementary teachersshould know the mathematics necessary to teach the content of the new cur-riculum. . . What can we do to insure that children get better teachers of math-ematics?. . . We can improve the undergraduate mathematics program in thetraining of elementary teachers. And we can provide summer institutes and ex-tensive in-service programs.4

1 Adier, Irving. The New Mathematics. 1960.Alien, Frank B.. el al. "Teacher Training�In-Service and Pre-Service," The Revolution in School Mathematics,

1964, 75-78.Corle, C. G. "The New Mathematics," The Arithmetic Teacher,XIl (April, 1964), 242-245.Murphy, Franklin D. "The Real Meaning of the Satellite," The Educational Record, XXXIX, (January 1958),

35-39.2 Op. cif.. Alien, 75.s Ibid., 75.4 Hardgrove, Clarence Ethel. "National Problems and Trends in the Mathematical Training of Elementary

School Teachers," The Committee on the Undergraduate Program in Mathematics, Number 7, 1963, 27.

615

616 School Science and Mathematics

It is the inservice programs with which this article is concerned.As one reads the literature regarding what should be done to

continue the mathematics education of the present teachers in theelementary schools, one notices that the content and implementationof most inservice programs are decided upon by the administrationof the school or school system involved and/or the personnel from aninstitution of higher learning. In most cases, the teachers for whomthe inservice programs are implemented have the least to say and doin the development of the programs.

Sixteen schools were randomly selected from the local schoolsystem. Within each of the selected school all of the teachers wereincluded in the study. The study provided approximately 350 ele-mentary school teachers the opportunity to make recommendationswith respect to content, organization, and implementation of aninservice program in mathematics education. The teachers were nottold whether or not the program would actually be implemented. Thisarticle presents a description of the inservice program developed bythe teachers surveyed.

CONTENTThe teachers were asked whether they preferred to have content

material or methods material presented in a program of continuingeducation. Table I contains the teachers^ preferences with respect tocontent and/or methods materials. Also in Table I one finds the

TABLE I. TYPE or MATHEMATICS COURSES THE TEACHERSPREFERRED TO CONTINUE THEIR EDUCATION

Type

Content

Methods

Both

Where

Summer SchoolInservice

Summer SchoolInservice

Summer SchoolInservice

Number of Teachers

1219

1946

32186

teachers’ opinion as to whether summer school courses or inserviceprograms would be the best tool for presenting the material. The chisquare test was applied to the data presented in Table I. The resultsof the chi square test showed that both differences were significant atthe .01 level. The teachers preferred to have both content and meth-ods materials in their continuing education program. The teachersalso preferred inservice programs over summer school courses for

In-Service Mathematics Education 617

presentation of the material. Knowing that the teachers preferred tohave both content and methods materials represented in the inserviceprogram, the author surveyed the teachers as to the emphasis of theinservice program. Table II contains the preferences of the teachers

TABLE II. EMPHASIS OF THE INSERVICE PROGRAM

Proportion ofContent to Methods Total

All/Nonemmm

None/All

11381546915

as to the proportion of content material to methods material to bepresented in the inservice mathematics education program. The chisquare test revealed that the differences were significant at the .01level. The teachers preferred that content and methods materials beequally represented in the inservice program.

ORGANIZATIONThe data collected for each question concerning the organization

of an inservice program yielded differences significant at the .01 level.The teachers did not want the inservice program planned and imple-mented by university personnel exclusively nor did the teachers wantthe inservice program implemented entirely by school personnel. Theteachers preferred that the inservice program be led by a team con-sisting of both university and school personnel.

In answering the question, ^Should the program involve more thanone school?5’, 240 out of the 285 teachers responding were in favor ofinvolving more than one school in each inservice program. Also, 262of the 287 teachers responding wanted some degree of grade organiza-tion for each inservice program. A majority of the teachers wantedan inservice program for each grade level. The teachers wanted theinservice program organized according to grades not schools.

IMPLEMENTATIONIn considering the implementation of an inservice program, the

teachers were concerned with questions such as how often the teachersshould meet, how long should each meeting last, and other questionsof a mechanical nature.When the time comes to implement an inservice program almost

60% of the teachers were in favor of requiring attendance of allteachers for whom the program was designed. Of the teachers sur-

618 School Science and Mathematics

veyed 67% were in favor of the teachers receiving some form of pay-ment for attending an inservice program. The teachers were not ableto decide upon a means of payment.The teachers decided that the inservice program should be imple-

mented in the fall semester of the school year.The means of the data gathered for the questions concerning the

number of weeks, days, and hours the inservice program should meetare presented in Table III.

TABLE III. MEANS OF THE DATA GATHERED FOR THE QUESTIONS CONCERNINGTHE NUMBER OF WEEKS, DAYS, AND HOURS THE

INSERVICE PROGRAM WILL MEET

Time Total

WeeksDays/WeeksHours/Meeting

3.671.691.49

The teachers surveyed preferred that the inservice program meetapproximately four weeks in two l|r hour sessions per week.

CONCLUSIONSOn the basis of the data collected from the 350 teachers surveyed

the following conclusions were made:1. Mathematics education inservice programs should stress both the content

of mathematics and the methods of teaching mathematics.2. Mathematics education inservice programs should be led by a team con-

sisting of both university and school personnel.3. Though more than one school may be involved, each of the elementary

grades should have its own separate mathematics education inservice program.4. The teachers should be required to attend the inservice program which is

designed for them and the teachers should receive some form of payment fortheir attendance.

5. The mathematics education inservice program should extend over a four-week period; the program should meet twice a week; each session should lastone and a half hours long.

REFERENCES[1] ABLER, IRVING, The New Mathematics, 1960.[2] ALLEN, Frank B., et al. "Teacher Training�In-service and Pre-Service,"

The Revolution in School Mathematics, 1964, 75-78.[3] CORLE, C. G., "The New Mathematics," The Arithmetic Teacher, XII (April,

1964), 242-245.[4] HARDGROVE, CLARENCE ETHEL, "National Problems and Trends in the

Mathematical Training of Elementary School Teachers," The Committee onthe Undergraduate Program in Mathematics, Number 7,1963,27.

[5] MURPHY, FRANKLIN D., "The Real Meaning of the Satellite," The Educa-tional Record, XXXIX, (January 1958), 35-39.