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<ul><li><p>499</p><p>in</p><p>William S.Department of Curriculum and InstructionUniversity of KentuckyLexington, Kentucky 40506-0017</p><p>Over the past fifteen years, mathematics educators have become keenlyaware of the importance of affect in the learning and teaching of mathematics(Aiken, 1970, 1976; Kulm, 1980; Reyes, 1987; McLeod, 1988). An affectivefactor of particular interest to both educational psychologists and mathematicseducators is mathematics anxiety, defined as "feelings of tension and anxietythat interfere with the manipulation of numbers and the solving ofmathematical problems in a wide variety of ordinary life and academicsituations" (Richardson & Suinn, 1972, p. 551). Recent research revealsparticularly high incidences of mathematics anxiety in preservice elementaryteachers (Battista, 1986; Kelly & Tomhave, 1985; Sovchik, Meconi & Steiner,1981). These findings raise two pertinent questions for mathematics teachereducators. Do elementary teachers with mathematics anxiety transmit it totheir students? Do these teachers teach mathematics differently than teacherswithout mathematics anxiety?</p><p>Several educators (Bulmahn & Young, 1982; Kelly & Tomhave, 1985;Lazarus, 1974) argue that elementary teachers transmit their avoidance andfear of mathematics to their students. Many teachers teach as they were taughtand thereby perpetuate mathematics anxiety in their students. Previousresearch on the effects of teachers attitudes toward mathematics and subjectmatter on student attitudes provides support for this argument (Aiken, 1970,1976; McMillan, 1976). On the other hand, Widmer and Chavez (1982) foundthat elementary teachers had generally positive attitudes toward teachingmathematics, and that the teachers felt secure in their mathematics teachingeven though they had developed some negative attitudes toward mathematicsas students. Teachers with mathematics anxiety seemed eager to break thecycle and to reduce mathematics anxiety in their students.</p><p>Purpose</p><p>This study investigated teacher mathematics anxiety as it related to (a)changes in student mathematics anxiety and achievement, (b) selected teachingpractices, and (c) various teacher characteristics. It also described differencesin selected teaching practices, student outcomes and characteristics of teacherswith and without mathematics anxiety.</p><p>School Science and MathematicsVolume 89 (6) October 1989</p></li><li><p>500 Mathematics Anxiety</p><p>Method</p><p>SubjectsThe subjects of this study were 31 fourth, fifth, and sixth grade teachers</p><p>and their students in six suburban elementary schools in a metropolitan schooldistrict in Kentucky. Of the 31 teachers, two were male. Upper elementaryteachers were chosen because (1) high incidences of mathematics anxiety havebeen found in elementary education majors (Bulmahn & Young, 1982; Kelly &Tomhave, 1985; Sovchik, Meconi, & Steiner, 1981) and (2) mathematicsanxiety is more easily measured in upper elementary students than in youngerchildren. The teachers, after being informed of the purpose of the study,volunteered and were paid a small stipend. Table 1 provides the followingteacher information: number of years teaching experience, number ofgraduate level mathematics and education courses, and scores on each sectionof the Iowa Test of Basic Skills. The means and standard deviations of thesedata are found in Table 6. Table 2 provides such class data as school, grade,size, and reported ability level.Although 739 students participated in pretesting and 707 students in</p><p>posttesting, only 584 students completed both batteries of tests. Data from the584 students were used for analysis.</p><p>InstrumentsTeacher mathematics anxiety was measured using the 98-item Mathematics</p><p>Anxiety Rating Scale (MARS) (Richardson & Suinn, 1972). The instrument iscomprised of brief descriptions of ordinary life and academic situationspertaining to mathematics which may arouse mathematics anxiety. Subjectsare asked how anxious a particular situation makes them feel and to recordtheir responses on a Likert scale with range from 1 (none at all) to 5 (verymuch). The item scores are summed to give a total range of 98 to 490, withhigher scores reflecting higher mathematics anxiety.</p><p>Student mathematics anxiety was measured using an adaptation of theadolescent version of the Mathematics Anxiety Rating Scale (MARS-A)(Suinn, 1979). The purpose of the adaptation was to make the scale moremeaningful to upper elementary students. Because some items of the MARS-Alacked meaning for upper elementary students, the reading level of the itemswas lowered and some items were omitted. The adaptation reduced thenumber of items from 98 to 75 giving a new range from a low of 75 to highof 375. To obtain an estimate of the reliability of the adapted MARS-A, twoclasses, one fourth-grade and one sixth-grade, were selected and administeredthe scale on a test-retest basis with a one week interval. The test-retestreliability coefficient obtained was r = .72, p < .0001.Achievement in mathematics was measured by the Mathematics Concepts</p><p>and Mathematics Problem Solving sections of the Iowa Test of Basic Skills(ITBS), Form 6 (Hieronymus & Lindquist, 1971). Students at each grade were</p><p>School Science and MathematicsVolume 89 (6) October 1989</p></li><li><p>Mathematics Anxiety 501</p><p>Table 1Teacher Data</p><p>TeacherNo</p><p>12345678910111213141516171819202122232425262728293031</p><p>YrsExp</p><p>176</p><p>212519111141</p><p>111214161014221114168</p><p>15015101424615171428</p><p>NumberGradMathCourses</p><p>0000</p><p>.0</p><p>2</p><p>; 01</p><p>1 00021111211000502110112</p><p>NumberGradEducCourses</p><p>101220010871051</p><p>2010129713188</p><p>2010100510109510101010</p><p>ITBSConcepts(45 items)</p><p>43424242444341424140404342424443424143413542403639434438423443</p><p>ITBSProb Solv(31 items)</p><p>30302829282826302829263028283029293028232826262826313022282929</p><p>administered their respective grade-level version. Teachers achievement inmathematics was measured using the sixth-grade versions of the ITBS.Audio-recorded mathematics lessons were coded using an investigator-designedLesson Coding Form intended to measure time and frequency of selectedteaching behaviors and classroom discourse. Instruction was described bytiming various instructional tasks and by classifying and tallying classroomquestions and the mathematics content of the lesson. The variables measuredand their definitions can be found in Table 3. All lessons were coded by the</p><p>School Science and MathematicsVolume 89 (6) October 1989</p></li><li><p>502Mathematics Anxiety</p><p>Table 2Class DataTeacher</p><p>12345678910111213141516171819202122232425262728293031</p><p>School</p><p>1112222222334444445555666666666</p><p>Grade</p><p>6445564546555456465444554665444</p><p>Level</p><p>AverageAverageAverageAverageAboveBelowAboveBelowAverageAverageBelowAboveBelowBelowAboveAverageAboveAboveBelowBelowAboveAverageAverageBelowBelowAverageAboveAboveBelowAboveAbove</p><p>r^</p><p>1818201819161921202414221620281720201413211720i516183017131624</p><p>denotes number of students taking both ore- and posttests</p><p>investigator. Three lessons were randomly selected to be coded by a secondperson to establish a coding reliability. A Pearson product moment correlationwas calculated by comparing all time and frequency categories of the threelessons of the investigator and second person. The correlation between thethree codings was r = .94, p < .0001.</p><p>ProcedureDuring the last two weeks of September, less than one month from the start</p><p>of school, the investigator visited each of the 31 classes. During the visits, theteachers were administered the MARS and the sixth-grade ITBS, and the</p><p>School Science and MathematicsVolume 89 (6) October 1989</p></li><li><p>Mathematics Anxiety 503</p><p>Table 3</p><p>Definitions and Examples of Lesson DataVariablesDefinitions/Examples</p><p>Time Measures</p><p>checking home/seatwork</p><p>reviewing</p><p>development</p><p>seatwork</p><p>giving directions</p><p>playing game</p><p>problem solving</p><p>total lesson</p><p>whole class</p><p>small group</p><p>individualized</p><p>Frequency Measures</p><p>total questions</p><p>high-level question</p><p>low-level question</p><p>choral question</p><p>individual question</p><p>student-initiated question</p><p>concepts introduced</p><p>Teacher directs checking of home/seatwork by callingout answers, asking for answers, etc.</p><p>Teacher reviews information presented in previouslesson.</p><p>Teacher introduces new concepts, principles or skills tostudents.</p><p>Students practice or work individually at their seats.</p><p>Teacher gives directions for seatwork, homework,activity, etc.</p><p>Students play an instructional game.</p><p>Teacher poses or discusses a challenge or non-routinemathematics problem.</p><p>Entire time teacher devotes to mathematics instructionthat day.</p><p>All students involved in same tasks.</p><p>Groups of students collectively involved in differenttasks.</p><p>Individual students involved in different tasks.</p><p>Questions asked by teacher except during seatwork.</p><p>Question asked by teacher requiring analysis, inferring,judgement, transfer.Question asked by teacher requiring rote memory.Giving examples, explaining procedures, applyingdirectly included.</p><p>Question asked by teacher to whole class or group ofstudents.</p><p>Question asked by teacher to particular student.</p><p>Question asked by student except during seatwork</p><p>New mathematics concepts (fraction, triangle)introduced during a lesson.</p><p>School Science and MathematicsVolume 89 (6) October 1989</p></li><li><p>504 Mathematics Anxiety</p><p>Table 3 (continued)Variables Definitions/Examples</p><p>concept behaviors Different behaviors (defining, giving examples/nonexamples, discussing properties, comparing andcontrasting) used by teacher to introduce new concept.</p><p>principles introduced New mathematics principles (Pythagorean Theorem,The sum of two odd numbers is an even number)introduced during a lesson.</p><p>principle behaviors</p><p>skill introduced</p><p>skill behaviors</p><p>Different behaviors (stating, paraphrasing, analyzing,applying, justifying) used by teacher to introduce newprinciple.</p><p>New^ mathematics skills (adding two-digit numbers,finding averages) introduced during a lesson.</p><p>Different behaviors (prescribing, demonstrating,justifying, making analogy) used by teacher tointroduce new skill.</p><p>students were administered the adapted MARS-A and their respective grade-level versions of the ITBS.Throughout the school year, the teachers were required to audio-record</p><p>typical mathematics lessons. On three separate occasions, once in October,January, and March, the investigator called the school before classes andasked the secretary to instruct the teachers to audio-record their mathematicslesson that day. If they were testing, reviewing or doing atypical activities thatday, they were instructed to audio-record the next typical mathematics lesson.The audiotapes were collected the following week. Two teachers had extendedabsences during one month and recorded one lesson at a later date. Oneteacher taped only two lessons. The Lesson Coding Forms were subsequentlycompleted on the audio-recorded lessons.During the last two weeks of May, the investigator again visited each</p><p>classroom to administer the battery of post-tests. The teachers were given theMARS; the students were given the adapted MARS-A and the ITBS.</p><p>AnalysisResidual gain scores for the adapted MARS-A and the ITBS were computed</p><p>by regressing the posttest scores on the pretest scores. Class mean residualgain scores for each instrument were computed for each teacher. Table 4reports the class means and standard deviations for the adapted pre- and post-MARS-A and class means of the residual gain scores. Means for the codedcriteria of the three audiorecorded mathematics lessons were calculated foreach teacher to provide a profile of their teaching practices. Two separatestatistical analyses were performed with these data. First, Pearson productmoment correlations between the teacher postMARS scores and the means</p><p>School Science and MathematicsVolume 89 (6) October 1989</p></li><li><p>Mathematics Anxiety 505</p><p>from the coded lessons, as well as the teacher data and the class mean residualgain scores of the adapted MARS-A and ITBS, were calculated. Second,teachers were grouped by the average of their two MARS scores. One groupwas comprised of the seven teachers with the highest average MARS scoresand labeled mathematics anxious (MA) teachers. The second group wascomprised of the seven teachers with the lowest average MARS scores andlabeled non-mathematics anxious (NMA) teachers. Table 4 reports the teacherTable 4Teacher MARS Scores and Class Mean Residual Gain Scores</p><p>Teacher</p><p>I3</p><p>3^4563789131011123131415s16"17131819202122233241325326273281329b3031</p><p>TeacherPre-MARS</p><p>143270190169216160196194239207217161162152118342280175243169177176121303140233100260282167233</p><p>Post-MARS</p><p>120215217213218144146200248212171140161172117316275155200150218170107334143209101274295179185</p><p>AdaptedMARS</p><p>-7.783.87</p><p>-5.08-11.35-6.750.96</p><p>-9.536.7716.0123.16-8.23-9.364.53</p><p>-3.745.65</p><p>-5.63-6.6715.36-4.1623.72-4.178.17</p><p>-24.762.81</p><p>-8.55-2.24-5.72-8.983.68</p><p>23.75-5.75</p><p>Class ResidualITBS</p><p>Concepts-0.52-0.79-0.020.650.22</p><p>-0.50-2.13-0.452.043.59</p><p>-1.032.420.15</p><p>-0.482.196.32</p><p>-0.382.51</p><p>-0.410.01</p><p>-0.93-0.85-6.180.41</p><p>-2.63-0.800.78</p><p>-2.900.690.82</p><p>-1.85</p><p>GainsITBS</p><p>Prob Solv0.040.731.611.37</p><p>-1.560.580.620.091.322.00</p><p>-1.64-0.43-2.99-1.302.00</p><p>-0.893.920.50</p><p>-2.02-2.28</p><p>1.203.15</p><p>-3.74-1.90</p><p>1.51-1.63-0.98-0.95-0.06-0.11</p><p>1.82</p><p>denotes teacher in NMA groupDenotes teacher in MA group</p><p>School Science and MathematicsVolume 89 (6) October 1989</p></li><li><p>506Mathematics Anxiety</p><p>pre- and postMARS and ITBS scores, as well as the teachers selected for eachgroup. Analyses of variance comparing the MA and NMA teachers withrespect to the coded lesson means, nominal data and the class means of theadapted MARS-A and ITBS gain scores were conducted.</p><p>Results</p><p>The range of mathematics anxiety in the teachers of this sample was quitelarge101 to 334 (Table 4). Table 5 compares the means and standarddeviations of the teacher MARS scores with the findings of other studies ofmathematics anxiety in elementary majors (Battista, 1986; Kelly & Tomhave,1982; Sovchik, Meconi & Steiner, 1981). The mathematics anxiety of theseteachers, even though they volunteered for the study, was not substantiallyless than the mathematics anxiety of prospective elementary teachers in otherstudies.</p><p>Table 5Number, Means and Standard Deviations of Elementary Teachers andPreservice Teachers of Various StudiesStudy</p><p>Present PreMARSPresent PostMARSKelly & TomhaveBattista PreMARSBattista PostMARSSovchik et al. PreMARSSovchik et al. PostMARS</p><p>Number</p><p>31314336365959</p><p>Mean</p><p>200.63193.71230.00211.25192.81200.76181.18</p><p>SD</p><p>57.0260.01</p><p>54.9067.4961.0656.40</p><p>Table 6 reports (I) the overall mean and standard deviation for eachvariable, (2) Pearson product moment correlations between MARS scores andvariables, (3) each variables contribution to the variance in MARS scores,and (4) results of the analyses of variance comparing MA and NMA teachers.Two significant correlations (p < .05) and one significant F value (p < .05)were found. Teacher mathematics anxiety correlated positively with timedevoted to whole-class instruction and negatively with the number of questionsasked by students during lessons. That is, MA teachers tended to spend moretime in whole-class instruction and have fewer students ask questions duringclass than did their NMA counterparts.The analysis of variance yield...</p></li></ul>