Self Perceptions of Special Educators Toward Teaching Mathematics

136

Self Perceptions of Special EducatorsToward Teaching Mathematics

Gerard P. ThibodeauSaint Joseph CollegeWest Hartford, Connecticut 06117

Lori S CebelillS While there appears to be a renewed in-

Rocky Hill Public Schools terest in the Provision of mathematics

Rocky Hill, Connecticut 06067 instruction in the public school (Nation-al Commission on Excellence in Educa-tion, 1983) numerous problem areas stillrequire attention. Suydam (1981) andCarpenter, Corbitt, Kepner, Lindquistand Reys (1981), in their reviews per-taining to the state of the art in mathe-matics education, indicate that the ma-jority of students at all age levels werenot proficient in solving problemsdeemed appropriate to their age level.This concern is accentuated when the

abilities of handicapped children in mathematics are discussed. Cawley (1981),Gearheart, DeRuiter, and Sileo (1986), and Houck (1984) affirm the paucity ofresearch on the abilities of handicapped children in mathematics and on ways ofassisting these children in this area.

Research by Cawley and Goodman (1968) and Goodstein, Kahn, and Cawley(1976) focused on the generally lower achievement levels of handicapped chil-dren, i.e., achievement in mathematics not commensurate with the handicappedchild’s ability to achieve. Interpretation of the results suggested that loweredmathematics achievement reflected inappropriate instructional interventions.Consequently, lowered mathematics achievement is not necessarily an assumedcharacteristic of a handicapped child, per se. This problem of appropriatemathematical programming for handicapped children was also studied in a morerecent investigation by Schenck and Levy (1979) in which 300 individualized edu-cation programs (IEPs) were examined. An IEP as mandated by Public Law 94-142, Education for All Handicapped Children Act, reflects the programs of eachhandicapped child primarily through delineation of goals, short term objectives,and related services. The data available to Schenck and Levy (1979) indicatedmathematical achievement levels as great as 3 to 4 years below indicated gradeplacement for a substantial number of handicapped children. In spite of theseobvious discrepancies in mathematical achievement, no instructional objectivesin mathematics were provided in the IEPs for these children.

School Science and MathematicsVolume 87 (2) February 1987

Set/Perceptions 137

The time allocated to mathematics instruction for handicapped children maybe related to the perceived importance of such instruction. Special educators mayview mathematics as a low priority area within the total scope of an appropriateeducation. Special education teachers may not receive proper training to enablethem to provide instruction in mathematics. In many states, the requirements forspecial educators in mathematics instruction are often realized through mathe-matics content courses or general teaching methodology courses. As such, theburden of modifying the scope, sequence, and methods of teaching mathematicsfor handicapped children may be assumed by the neophyte teacher without thesupport of formal coursework.The purpose of this study was to examine the perceptions of special education

teachers toward the teaching of mathematics to handicapped children. Informa-tion was gathered for three general areas: (1) teacher perception of student re-action to mathematics; (2) teacher perception of the importance of mathematicseducation in the scope of each child’s curriculum; and (3) teacher perception oftheir own preparedness to teach mathematics.

Procedure

The Mathematics Education Survey, a two-page questionnaire designed for thisstudy, was administered to all special educators employed in the public schoolspecial education programs of three New England suburban school districts. Thesample of special educators consisted of 124 females and 17 males. Due to thefewer number of males (12%) in the sample, no attempt was made to differenti-ate responses on the basis of gender. Additional demographic data may be foundin Table 1.

"The time allocated to mathematics instruction for handi-capped children may be related to the perceived impor-tance . . /’

Results

The data obtained from items in the survey has been integrated in a question-answer format addressing the three general areas of concern. When responses tothe items in the survey were incomplete or when multiple responses were al-lowed, the percents reported below were adjusted accordingly.DO YOU TEACH MATHEMATICS AND IS IT AN ENJOYABLE ACTIV-ITY FOR YOU AND YOUR STUDENTS?As suggested by the results presented in Table 2, special education teachers ap-

pear to be teaching mathematics to their students and enjoying the activity ofteaching mathematics. In addition to the favorable response toward the teaching


138SelfPerceptions

"Additional demographic data may be found in Table I."

TABLE iDemographic Data

Degree StatusBachelor’sMaster’sSixth Year +

Years Teaching ExperienceNo Response0-34-67-910 +

Educational SettingResource RoomSelf-containedOther

Primary Exceptionality of Children TaughtLearning DisabilitiesMental RetardationEmotional DisturbanceNoncategoricalOther

Chronological Age of Children Taught3-67-910-1213-1516 +

Number

626019

141

664361421

141

545433

141

8113291812

153*

3071834923

256*

%ofSample

43.9742.5513.47

4.2545.3925.539.9214.89

38.2938.2923.40

52.948.49

18.9511.767.84

11.7127.7332.4219.148.98

*Multiple responses were allowed.


Set/Perceptions 139

of mathematics, special educators also indicated that a large majority of theirstudents appear to enjoy learning mathematics.

TABLE 2Involvement in and Enjoyment of

Mathematics Education

Questions

Do you teach mathematics to your students?Do you enjoy teaching mathematics?Do you feel your students enjoy learning mathemat-ics?

Number ofTeachers

139135

127

Response (%)

Yes92.8092.33

84.25

Using three of the demographic groupings presented in Table 1 (Years of Teach-ing Experience, Primary Exceptionality of Children Taught, and ChronologicalAge of Children Taught), response percentages to the questions presented in Ta-ble 2 were computed. The results were nearly identical to those found in Table 2.It would seem that years of teaching experience, nature of the handicap and ageof children being taught did not appear to influence teacher responses.An attempt to determine whether special education teachers perceived a differ-

ence in enjoyment of learning mathematics dependent on the sex of the child in-dicated that the majority of teachers (84.67%) did not perceive any male/femaledifferences. When teachers did perceive a difference, some (13.13%) viewedboys as enjoying mathematics more than girls while a few teachers (2.18%) indi-cated that the reverse was true.

HOW IMPORTANT DO YOU THINK MATHEMATICS IS FOR HANDI-CAPPED CHILDREN?A series of questions, comparing the importance of mathematics vs reading

and the comparative instructional times for those subjects, elicited responsesfrom special education teachers on the perceived importance of mathematics.When asked whether mathematics might be more important for average chil-

dren than for handicapped children, the responses obtained from 137 specialeducation teachers indicated that only 5.83% viewed mathematics as more im-portant for the average child. A large majority of the sample (94.16%) did notattribute importance of mathematics as being contingent on a child’s handi-capped or nonhandicapped status.A comparison of the relative importance of mathematics and reading for the

exceptional child indicated that a large majority of the special education teachers(86.13%) rated the teaching of reading as more important than mathematics.


140SelfPerceptions

Only 2.19% of the teachers rated the teaching of mathematics as being more im-portant while 11.67% of the teachers viewed reading and mathematics as beingequivalent in importance.While the teaching of mathematics was viewed as less important than the

teaching of reading, this perception was not obvious in terms of recommendedinstructional time allotments. Table 3 presents the frequency of responses andconcomitant percent of special education teachers recommending instructionaltime allotments for mathematics and reading. From these responses, there ap-pears to be little difference in terms of how often reading and mathematicsshould be taught. Most special education teachers indicated that both mathemat-ics and reading should be taught on a daily basis.

TABLE 3Frequency of Instruction ForMathematics and Reading

Content Area

Mathematicsshould betaught:

Readingshould betaught:

Instruct

On a dailybasis

132(94.28%)

136(97.14%)

At least3 timesper week

8(5.71%)

3(2.14%)

ional Time AllotmentAt least2 timesper week

0

0

At leastonce

per week

0

0

Other

0

1(.71%)

In summary, special education teachers appear not to discriminate betweenhandicapped and nonhandicapped children regarding the importance of mathe-matics. The perception, widely shared, that reading is of more importance thanmathematics and the lack of differentiation in the recommended instructionaltimes for these two content areas may at first appear to suggest contradictorystatements. While not excluding this possibility, alternate explanations may bemore realistic. First, the content area of reading may be seen as permeating awider range of school subjects than the content area of mathematics. While theallocated time for reading instruction may not differ from the allocated time formathematics instruction, the understanding might be that informal reading in-struction and opportunity to rehearse reading skills is an ongoing functionthroughout a child’s day. The application of mathematical knowledge, however,may occur only within the time constraints of formal mathematics instruction.


Set/Perceptions 141

Hence, reading instruction actually is offered in proportion to its perceived im-portance. An alternate explanation is that while reading is perceived as more im-portant than mathematics, special education teachers may still view mathematicsas sufficiently important to warrant daily instruction.DO YOU THINK YOU ARE PREPARED TO TEACH MATHEMATICS?

Responses to the general question of preparedness to teach mathematics tohandicapped children were obtained from 132 special education teachers. Themajority of responses (83.33%) indicated that special education teachers per-ceived themselves as being prepared to teach mathematics. The possibility thatthese perceptions of preparedness might be affected by the category of handi-capped children which the teachers taught led to the computation of percentagreements for different categories of special education teachers, i.e., teachersof learning disabled children, teachers of mentally retarded children, etc. The re-sults indicated that independent of the category of handicapped children taughtby the teachers, agreement on preparedness to teach mathematics was consist-ently in the 80% to 89% range.The effect of years of teaching experience on the perception of preparedness to

teach was also examined. The information presented in Table 4 permits the fol-lowing interpretations: First, regardless of the number of years of teachingexperience, the majority of special educators appear confident in their prepared-ness to teach mathematics. Second, this confidence appears to increase slightlywith increased teaching experience.

TABLE 4Perception of Preparedness to Teach

Mathematics

Number of SpecialEducation Teachers

633534

Years of TeachingExperience

0-34-67+

Do you think youare prepared to

teach mathematics?

Yes (%)77.7782.8591.17

Do you think you needadditional

mathematicseducation courses?

Yes(%)79.6678.7855.88

Third, while special education teachers generally perceive themselves as preparedto teach mathematics, they also see a need for additional training in mathematicseducation. The perceived need for additional mathematics education courses wasindicated by more than half (74.24%) of the special education teachers. As these


142 Set/Perceptions

teachers gained in years of teaching experience however, the perceived need foradditional coursework appears to decline.

Conclusions

While the findings of this investigation are necessarily limited by the small num-ber of special education teachers surveyed, the data presented suggests a recon-sideration of the status of mathematics instruction in special education classes. Ifthe responses obtained in the survey reflect the practices of special educators,then mathematics instruction is an activity enjoyed by both teachers and theirhandicapped students. The recommended time allotments for mathematics in-struction appear to support the perceived importance of this content area forhandicapped children. Finally, the frequent criticism that special educationteachers are inadequately prepared to deliver mathematics instruction did notappear to be shared by the special education teachers participating in the survey.While the perceptions reported in this study reflect an encouraging attitude to-

ward mathematics instruction for handicapped children, additional research isnecessary to establish the accuracy of these perceptions. Several questions re-main to be answered. For instance, is the perception of special teachers towardtheir preparedness to teach mathematics justified, i.e., are these teachers able toteach the complete scope of mathematical content appropriate for handicappedchildren? Is there a correlation between the perception of special educators to-ward mathematics education and the actual performance of teaching? Answersto these questions will provide information with important consequences in theprovision of appropriate education to handicapped children.

References

Carpenter, T. P., M. K. Corbitt, H. S. Kepner, M. M. Lindquist, and R. E. Reys (1981).II. National assessment. In E. Fennema (Ed.), Mathematics education research: Impli-cations for the 80’s. Alexandra, Virginia: Association for Supervision and CurriculumDevelopment.

Cawley, J. F. (1981). Commentary. Topics in Learning and Learning Disabilities, 1, 89-94.Cawley, J. F. and J. 0. Goodman (1968). Interrelationships among mental abilities,

reading, language arts, and arithmetic with the mentally handicapped. ArithmeticTeacher, 15,631-636.

Gearhart, B. R., J. A. DeRuiter, and T. W. Sileo (1986). Teaching mildly and moderatelyhandicapped students. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.

Goodstein, H. A., H. Kahn, and J. F. Cawley (1976). The achievement of educable men-tally retarded children on the Keymath diagnostic arithmetic test. Journal of SpecialEducation, 10,61-70.

Houck, C. K. (1984). Learning disabilities, understanding concepts, characteristics, andissues. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.

National Commission on Excellence in Education (1983). A nation at risk: The imperativefor educational reform. Washington, D.C.: U.S. Department of Education.


Self Perceptions 143

Schenck, S. J. and W. K. Levy (1979). IEPs: The state of the art in Connecticut. NewJersey State Department of Education: Northeast Regional Resource Center.

Suydam, M. N. (1981). Mathematics education. ASCD Curriculum Update, February, 1-4.

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Self Perceptions of Special Educators Toward Teaching Mathematics