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Characteristics Of OutstandingSecondarySchool Mathematics Teachers

Don S. Balka

The Presidential Awards Program forExcellence in Mathematics Teaching hasbeen in existence for two years. Spon-sored by the National Science Founda-tion and coordinated by the NationalCouncil of Teachers of Mathematics,this program recognizes outstandingteachers of mathematics in each state,Washington, D.C., and Puerto Rico.From the two finalists selected in eachstate, a national committee selects oneas the state winner to receive a trip toWashington and a $5000 grant for im-proving instructional programs in his orher school district.

In 1984, 118 Indiana mathematics teachers were nominated, w^ith 41 (26 menand 15 women) submitting completed applications, including background infor-mation, professional experiences, and answers to three essay questions. Foursupporting letters from colleagues, students or former students, administra-tors/supervisors, or parents of students, providing evidence of the nominee’seffectiveness as a mathematics teacher, were also required. It is the content ofthese letters, indicating characteristics of the outstanding teachers, that is the fo-cus of this article.Much of the current research on teacher effectiveness reviewed by McNeil and

Popham (1973) uses process-product designs with student achievement as an out-come; consequently, in this article no attempt to generalize the relationship be-tween characteristics of effective teachers and student achievement is intended.In fact, as Fey (1969) pointed out in his review on teaching mathematics focusingon these characteristics, no clearcut statement can be made.Teacher behaviors have been classified into three categories: Affective, Cog-

nitive, and Managerial. In the Affective area are the emotive aspects of teaching(conviviality, anxiety, enthusiasm); in the Cognitive area are content-relatedtraits (use of examples and nonexamples, correctness of a lesson, variability indemonstration); and in the Managerial area are behaviors related to maintaining

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Characteristics Outstanding Teachers 323

TABLE lCharacteristics of Outstanding

Mathematics Teachers

Characteristic Number

Concern for studentsAvailabilityKnowledge of mathematicsDemands excellence in mathematicsLeadershipDedicationEffectiveness and clarity of lessonsPersonableContinuing professional involvementFairnessVariability of teaching techniquesOrganizationRigorous standardsEnthusiasmIndividualization of coursesSense of humorClassroom atmosphere conducive to learningRapportDemands respectRole modelMotivator of youthInnovativePatientIntegrityStudent involvement in classPrepared

767473624342383633312827262423212020181414126554

effective classroom control. Affective and Managerial cover across-content be-haviors, that is, traits that not only outstanding mathematics teachers possess,but also that outstanding teachers in other content areas may possess.

Research on affective variables (Tikunoff, Berliner, and Rist, 1975; Rosen-shine and Furst, 1971) has shown significant positive relationships betweenachievement and behaviors such as enthusiasm, personalizing, politeness, ac-cepting, and pacing. As indicated by Cooney (1980), the cognitive variables ofclarity and variability have received considerable attention by researchers in cor-relational studies with achievement. In the managerial category, "withitness"showed strong relationship to achievement (Kounin, 1970; Dunkin and Biddle,

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324 Characteristics Outstanding Teachers

1974; Brophy and Evertson, 1976). This behavior encompasses a teacher*s com-munication with students in regard to behavior problems, while simultaneouslyaddressing a different issue.From the 164 supporting letters for the nominees, a total of 775 characteristics

were identified. Table 1 presents a condensed, ordered listing of key terms orphrases used in the letters and the corresponding number of times the responsesappeared.

"Clarity, a cognitive behavior, was high on the list . . /’

The task of accurately classifying these characteristics into affective, cogni-tive, and managerial behaviors is somewhat difficult due to an overlapping ofthe characteristics; moreover, it is probably not germane to the major task of de-scribing outstanding mathematics teachers. One can readily attach labels tomany of the traits listed and observe that they are across-content areas and notspecific to mathematics. More characteristics appear to fall into the affectivearea than in the cognitive or managerial areas. It is interesting to note, however,the strength given by the recommenders to a sound knowledge of mathematics, ademand for excellence in mathematics, a continuing professional involvement inmathematics, and an individualization of mathematics courses for students.

Seven of the 11 strongest variables in process-product studies identified byRosenshine and Furst (1971) appear in the listing: clarity, variability, enthusi-asm, task-oriented, student involvement, classroom atmosphere, and rigor.Many of the characteristics are also described by Suydam (1984) in her article onideas for better teaching, based on research in mathematics instruction (instruc-tional time, questioning skills, discipline, differentiation of instruction, andproblem solving strategies).

Clarity, a cognitive behavior, was high on the list of characteristics given bythe recommenders. Most responses identifying this trait were from students orformer students, with common phrases being: able to explain problems and con-cepts to students so they can understand them; able to show the concepts he is ex-plaining through the use of analogies and clear examples; able to translate com-plex algebraic terminology into simple, day-to-day language; able to relate thelessons to students with lesser abilities; and able to anticipate the problems andcover them with extra care. In condensed forms, the phrases do distinguish be-haviors identified by Cruickshank, Kennedy, Myers, and Bush (1976). Bush,Kennedy, and Cruickshank (1977), and Thornton (1977) in attempting to defineclarity.

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Characteristics Outstanding Teachers 325

Variability is also rated strong. This behavior includes factors such as using avariety of materials in teaching, providing alternate explanations when needed,and questioning on different cognitive levels. Again, most responses identifyingthis trait were from students or former students.As an affective behavior, concern for students ranked first in the list. Con-

densed in form for classification purposes, "concern" included several of the di-mensions cited in the research studies: politeness, acceptance, friendliness, en-couragement and receptiveness to students’ comments. A large number of rec-ommenders from all levels listed leadership and organization as traits of theseoutstanding mathematics teachers, lending support to earlier results on the man-agerial variable of "withitness."The results of this study do show that outstanding mathematics teachers, in

the eyes of students, administrators, parents, and fellow teachers, display multi-dimensional behaviors. Whether or not these behaviors are effective in terms ofstudent achievement cannot be answered by the analysis. Educational research inthe area of teacher effectiveness must use process-product studies in order tohelp improve instruction, but the wealth of information available on outstandingmathematics teachers in this awards program throughout the country is a sourcethat must also be tapped.

References

Brophy, J. E., and C. M. Evertson. Learning from teaching: A developmental perspec-tive. Boston: Allyn& Bacon, 1976.

Bush, A. J., J. J. Kennedy, and D. R. Cruickshank. An empirical investigation of teacherclarity. Journal ofTeacher Education, March-April 1977, 28(2), 53-58.

Cooney, T. J. Research in teaching and teacher education. In R. J. Shumway (Ed.), Re-search in Mathematics Education. Res\or\: NCTM, 1980.

Cruickshank, D., J. Kennedy, B. Myers, and A. Bush. Teacher clarity�What is it? Paperpresented at the Conference on Innovative Practices in Teacher Education, Atlanta, Jan-uary 1976.

Dunkin, M. J., and B. J. Biddle. The study of teaching. New York: Holt, Rinehart &Winston, 1974.

Fey, J. T. Classroom teaching of mathematics. In J. W. Wilson and L. R. Carry (Eds.),Review of Recent Research in Mathematics Education (Studies in Mathematics, Vol. 19).Stanford, Calif.: School Mathematics Study Group, 1969.

Kounin, J. S. Discipline and group management in classrooms. New York: Holt, Rinehart&Winston, 1970.

McNeil, J. D. and W. J. Popham. The assessment of teacher competence. In R. M. W.Travers (Ed.), Second Handbook of Research on Teaching. Chicago: Rand McNaIIy,1973.

Rosenshine, B. and N. Furst. Research in teacher performance criteria. In B. 0. Smith(Ed.), Symposium on Research in Teacher Education. Englew^od Cliffs: Prentice-Hall,1971.

Suydam, M. Ten essential ideas for better teaching. Ohio Journal of School Mathematics,9(2), 1984.

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326 Characteristics Outstanding Teachers

Thornton, C. D. An evaluation of the mathematics-methods program involving the studyof teaching characteristics and pupil achievement in mathematics. Journal for Researchin Mathematics Education, January 1977, 8(1), 17-25.

Tikunoff, W. J., D. C. Berliner and R. C. Rist. An ethnographic study of the forty class-rooms of the beginning teacher evaluation study known sample (Tech. Rep. 75-10-5).San Francisco: Far West Laboratory, 1975.

Don S. BalkaSaint Mary’s CollegeNotre Dame, Indiana 46556

TDRS-1 RESCUE MISSION

TDRS-1 was launched April 4, 1983 from the STS-6 shuttle orbiter in a 150mile orbit. Approximately two thirds of the way through the second stage burnof the Air Force Inertial Upper Stage (IUS) rocket, which was to boost theTDRS-1 into its final 22,300 mile geosynchronous orbit, the rocket malfunc-tioned.The IUS rocket, with the TDRS-1 still attached, began tumbling. Ground sta-

tion telemetry was unable to lock onto the IUS to command it to separate fromthe TDRS. Time was critical because the satellite’s solar arrays could not be de-ployed while still attached to the IUS, and the IUS batteries w^re only good for afewr hours. If the batteries died before commands to separate succeeded then thespacecraft would essentially become (*space junk.’ *

Approximately 3 hours after the first sign of trouble, ground engineers issueda set of commands the IUS accepted, and separation from TDRS occurred just20 seconds after the IUS batteries died.The TDRS spacecraft slowed its tumbling by firing its attitude control thrust-

ers, a job they were not designed to do. When the TDRS stabilized itself it wasdiscovered to be in an "egg-shaped" orbit w^ith a high point of 21,972 miles anda low point of 13,574 miles (statute miles).

Initial checkout of the status of the TDRS indicated a set of thrusters wasdamaged. One conjecture was that the IUS could have done it upon separationduring the tumbling motion.With the spacecraft in an elliptical orbit it was impossible to perform its mis-

sion. The satellite’s orbit had to be made circular at about 22,300 miles. Shuttlecould not rescue the satellite because it could not reach an altitude beyond a few^hundred miles. However, TDRS was designed with 24 attitude control thrustersfor "station keeping" and attitude control, and, luckily, extra fuel was onboard. It was thought the spacecraft could be moved into the final geosyn-chronous orbit by using these attitude control thrusters and the extra fuel.The unlikely use of tiny one pound attitude thrusters to do the job of 15,000

Ib. IUS booster rocket did not deter the TRW/NASA/SPACECOM team ofground engineers from calculating and modeling a possible burn pattern thatmight lift the TDRS into its final and proper orbit.

School Science and MathematicsVolume 86 (4) April 1986