Problems in Teaching Mathematics in the Elementary Classroom

65

Problems in Teaching Mathematics inthe Elementary ClassroomEvelyn M. VanDevenderElementary/Early Childhood EducationUniversity of South AlabamaMobile, Alabama 36688

^. . . mathematical skills are becoming more vital . . .9

Throughout history society has consistently influenced the kind of mathemat-ics taught in the elementary schools. Originally, students needed to knowonly the rudiments of arithmetic (Baur & George, 1976). However, the trendtoday is toward more emphases on "back-to-basics" and more technologicalinformation. To function effectively, all students must be able to performmany mathematically oriented tasks. Therefore, mathematical skills arebecoming more vital to successful living.A number of concerns is troubling many elementary mathematics teachers

today. They are undergoing role changes for various reasons and thesechanges in expectations of what mathematics teachers should be able toaccomplish are related to a variety of issues (Reisman, 1982); such as, thepush for higher achievement in mathematics, "back-to-basics" pressures,state and federal legislation concerning education, and the increasingpressures on students and teachers.The push for higher mathematics achievement is partly due to low SAT

scores and other national assessments showing mathematics as an areaneeding much improvement. The Galiup Poll of Public Attitudes (Galiup,1986) cited poor curriculum and poor standards as an important problemfacing the schools in 1986. As a result, special emphases are being placed onthe improvement of mathematics instruction.

State and federal legislation is also pushing for higher achievement andteacher accountability. Policymakers are looking for ways to improve theschool curriculum (Brandt, 1986). Recent committees on excellence ineducation are also demanding higher standards and more favorable resultsfrom teachers. A major response has been to place greater emphasis onschool mathematics (Stanic, 1986).These circumstances are causing the public to demand higher standards and

greater achievement from teachers and students. As a result, teachers are

School Science and MathematicsVolume 88 (1) January 1988

66 Problems in Teaching Mathematics

required to teach more mathematical concepts to younger children. Thisplaces increasing pressures on students and teachers which is contrary toaccepted theories concerning children’s cognitive development (Piaget, 1965).Day and Drake (1986) emphasize the value of using intellectually appropriateprograms to improve young students* achievement. Elkind (1986) alsobelieves that young students’ instruction must be in keeping with their uniquemodes of learning.A review of the related literature and experiences of the author led to this

investigation. The general aim of the study was to discover ways to helpelementary teachers become more successful in teaching mathematics. There-fore, the purpose of the study was to identify specific problems teachersexperience in teaching mathematics in the elementary classroom, and todetermine if there were any differences between the opinions of earlychildhood teachers (K-3) and elementary teachers (4-6) concerning theseproblems. This comparison was to further substantiate the data for all K-6teachers.

Method

Participants

Problems in teaching mathematics were solicited by university facultymembers in their graduate classes of elementary/early childhood students,who were also practicing teachers, during the Spring and Summer quarters of1986. There were 47 teachers who responded. Their suggested problems wereidentified, summarized, formed into a questionnaire (see Table 1), and listedin priority order according to the frequency of listing as a problem.The questionnaire was then distributed and rated by an additional 108

practicing teachers during summer workshops which were held in fourdifferent counties in a southern coastal state. A scale of +2 to -2 was chosento identify the degree of opinion on each problem so that a positive valuewould reflect agreement and a negative value a disagreement.

Scale: + 2 Strongly agree+1 Agree0 No opinion

� 1 Disagree- 2 Strongly disagree

The questionnaire requested additional comments which the teachers mightconsider important to include. Demographics included grade level and thecounty of employment.

Instrument

A pilot study was conducted to support the validity of the questionnaire. Apanel of three judges consisting of university faculty members from the


Problems in Teaching Mathematics 67

TABLE 1QUESTIONNAIRE

Name of School Grade Level

Instructions: The following items represent possible problems in teaching mathemat-ics in the elementary/early childhood classroom. Circle one of thealternatives according to your opinion of its severity as a problem. (A)strongly agree, (B) agree, (C) no opinion, (D) disagree, (E) stronglydisagree. Please feel free to add any comments which you believe tobe pertinent.

SA A NO D SD Comments1. Different ability levels of students A B C D E2. Need for more concrete materials A B C D E3. Too many students per classroom A B C D E4. Not enough classroom time for A B C D E

mathematics5. Parent apathy toward homework A B C D E

assignments6. Organization of textbook (sequenc- A B C D E

ing of topics)7. Lack of teacher input into program A B C D E8. Extensiveness of record keeping A B C D E9. Careless mistakes of students A B C D E10. Low reading levels of students A B C D EPlease list any additional comments you consider important to include:

Responses

Rl, different ability levelsR2, need concrete materialsR3, too many studentsR4, more classroom timeR5, parent apathyR6, textbook organizationR7, teacher inputR8, record keepingR9, careless student mistakes 83.2RIO, low reading levels

*Chi square test statistic significant at the .05 level.

TABLE 2

Percent of MeaTeachers Agreeing (BE

or Strongly Disagreeing + 2

90.789.986.144.472.250.950.948.1

76.9

n Scasedto -

1.251.331.280.190.900.290.340.410.930.86

oreson-2)

P Valuefor Differencein Opinion

0.039*0.4460.5020.4700.1600.6750.5660.7840.003*0.188



department of elementary/early childhood education was used to supportconstruct validity of the questionnaire. A sample of graduating students,consisting of teachers, was used to establish face validity of the question-naire. Participants in the panel and sample were asked to critique andrespond to the instrument. Their suggestions were incorporated into therevision of the questionnaire to improve its validity as a data gatheringinstrument.

Procedure

The questionnaire was rated by 69 early childhood teachers (K-3) and 39elementary teachers (4-6) making a total of 108 rated questionnaires.Percentages and means were computed to determine the degree of emphasisplaced on each problem in teaching mathematics. Chi square was thestatistical technique used in the study to determine if there were significantdifferences between the opinions of early childhood teachers (K-3) andelementary teachers (4-6). All the teachers’ additional comments weresummarized and presented to further substantiate their opinions.

Results

The study was conducted to identify problems in teaching mathematics in theelementary classroom, and to determine if there were any significantdifferences between the opinions of early childhood teachers (K-3) andelementary teachers (4-6) of the specified problems in teaching mathematics.The questionnaire shows the problems which were identified by the teachers.The percent of emphasis on each problem can be seen in Table 2.A majority (90 percent) of the teachers agreed that different ability levels

of students (Rl) and the need for more concrete materials (R2) wereproblems. Most of the teachers (86 percent) agreed that they had too manystudents per classroom (R3). Fewer than one-half (44 percent) believed therewas not enough classroom time for mathematics (R4). In other words, morethan one-half (56 percent) of the teachers felt they had sufficient time toteach mathematics. More than 72 percent of the teachers said parent apathytoward homework assignments (R5) was a problem. Fifty percent of theteachers agreed that textbook organization (R6) and lack of teacher inputinto the program (R7) were problems. Only 48 percent felt that theextensiveness of record keeping (R8) was a problem, but 83 percent thoughtcareless mistakes of students (R9) presented a problem. Low reading levels ofstudents (RIO) were ranked as a problem by 77 percent of the teachers.The mean scores provide a second way of measuring agreement of

emphasis placed on each problem. A scale ranging from +2 to -2 was usedto identify the degree of emphasis. For example, Response 1 was computedas follows:

47(2) + 51(1) 4- 1(0) + 8(-1) + 1(-2)^

135^ ^ ^108 108



The results of these computations are presented in Table 2. The meansreflect the same conclusions as shown by the percentages.

Using chi square to compare the two groups, all responses were tested forsignificant differences in problem perceptions at the .05 level. Only on Rl(different ability levels of students) and R9 (careless mistakes of students)were significant differences indicated (see Table 2). Of those who responded,one-half early childhood teachers (K-3) and only one-third elementaryteachers (4-6) strongly agreed that the different ability levels of studentspresented a problem. Fewer than one-tenth early childhood teachers (K-3),but more than one-third elementary teachers (4-6) ranked careless mistakes ofstudents as a problem. No significant differences were indicated on any ofthe other responses.

Additional data in the form of comments were collected to further explorethe teachers’ views toward problems in teaching elementary mathematics. Thecollected data are summarized and presented in Table 3. Frequencies were notlisted due to the variety of comments.

TABLE 3Additional Comments or Problems to Include Concerning Teaching Mathematics

Comments

Pacing

Ability grouping would be helpful

Need more time if stay self-contained

Ability grouping would save classroom time

Can make more time for math by doing math in other subjects

Need smaller classes

Kindergarten and the lower grades need fewer students per classroom

Student apathy is a problem in upper elementary

Too many students per classroom and student apathy are the number one problems

Fifth and Sixth grade students should know the basic facts

Students have not learned the basic facts which hinders their learning fractions,decimals, etc.

We have an ungraded program



Most of the comments further emphasized problems presented on thequestionnaire. For example, different ability levels, too many students perclassroom, and classroom time were all stressed. Additional problems notlisted on the questionnaire concerned pacing and student apathy. Thecomment concerning an upgraded program was a suggestion for alleviatingsome of the problems identified on the questionnaire.

Conclusions

From the results of the study, some specific conclusions may be derived:

1. The most heavily emphasized problems concerning elementary teachers were thedifferent ability levels of students, the need for more concrete materials, and toomany students per classroom.2. Strong emphases were placed on parent apathy, careless student mistakes, andthe low reading levels of students.3. Less emphases were placed on textbook organization, the lack of teacher inputinto the program, and extensive record keeping.4. The problem which received the least emphasis from the teachers was the needfor more classroom time.5. The perceptions of early childhood teachers (K-3) and elementary teachers (4-6)were significantly different on problems concerning the different ability levels ofstudents and careless student mistakes.

It is recommended that the problems concerning the different ability levelsof students, the need for more concrete materials, and too many students perclassroom be given serious consideration relative to the responses of theteachers surveyed. These heavily emphasized problems appear to be the typeof problems over which teachers have little control. However, solutions tothese problems are possible. They seem to be the kinds of problems overwhich administrators do have some control. For example, money is needed toincrease concrete materials. Administrators could give high priority tofunding for instructional materials and for controlling the number of studentsper classroom. Teaching different ability levels of students has long been aproblem for teachers. With the recent emphasis on teacher accountability andstudent testing for promotion, a solution to this problem may be forthcom-ing.

Teachers strongly emphasized the problems concerning parent apathy,"careless" student mistakes, and students^ low reading levels. These couldalso be identified as problems over which administrators have some control.Low reading levels can improve with funding and testing. Administrators cando much to involve parents and build community support. Further inquiryneeds to be made to determine the reasons behind student apathy and the"careless" mistakes of students in the upper elementary grades.Although the results of this study are not likely to be an impetus for major

changes in mathematics teaching they may serve as part of the total data



bank in the areas of major findings. As remedies are found for theseproblems, mathematics teaching will become more successful. Additionalstudy and research are needed to explore how these teachers’ problems relateto current and future educational needs.

References

Baur, G. R. and L. 0. George. (1976). Helping children learn mathematics. MenioPark, California: Cummings Publishing Company.

Brandt, R. S. (1986). A privileged class. Educational Leadership, 44(3}, 3.Day, B. and K. N. Drake. (1986). Developmental and experiential programs: The key

to quality education and care of young children. Educational Leadership, 44(3),24-27.

Elkind, D. (1986). Formal education and early childhood education: An essentialdifference. Phi Delta Kappan, 67, 631-636.

Galiup, A. M. (1986). The 18th annual Galiup Poll of the public’s. Phi Delta Kappan,68, 43-59.

Piaget, J. (1965). The child*s conception of number. New York: W. W. Norton &Company.

Reisman, F. K. (1982). A guide to the diagnostic teaching of arithmetic. (3rd ed.).Columbus, Ohio: Charles E. Merrill.

Stanic, G. M. A. (1986). The growing crisis in mathematics education in the earlytwentieth century. Journal for Research in Mathematics Education, 17, 190-205.

NEW SCIENCE LEARNING COURSE DEVELOPED

Arizona State Media Productions, supported by a grant from theNational Science Foundation, has developed courses for facilitators ofscience learning. The workshops can be adapted in any of the followingways:

� As a two- or three-credit-hour university course for potential or in-service librarians.

� As an in-service, after-school course sponsored by a school district ordiocese, etc. and conducted under the direction of the library coor-dinator.

� As the basis for staff meetings or conference workshops.

The material falls basically into three parts:� Science Education and You� Science Education and the School Library� Science Education and the World Beyond

The material also includes a video script, written and produced byAlleen Pace Nilsen and directed and filmed by John P. Barnard, titledElementary School Librarians: Partners for Excellence in ScienceEducation.

Contact: Dr. Alleen Pace NilsenGraduate College, Wilson HallArizona State UniversityTempe, AZ 85287


Documents

Problems in Teaching Mathematics in the Elementary Classroom