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Hammill Institute on Disabilities
Mathematics Instruction in Resource Rooms: Instruction Time and Teacher CompetenceAuthor(s): Robert L. CarpenterSource: Learning Disability Quarterly, Vol. 8, No. 2 (Spring, 1985), pp. 95-100Published by: Sage Publications, Inc.Stable URL: http://www.jstor.org/stable/1510411 .
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MATHEMATICS INSTRUCTION IN RESOURCE ROOMS: INSTRUCTION TIME
AND TEACHER COMPETENCE
Robert L. Carpenter
Abstract. A survey of resource room teachers (N = 101) was used to determine: (a) the amount of time resource room teachers spend in mathematics instruction, (b) the amount of those teachers' formal training in mathematics and mathematics instruction, (c) their self-reported degrees of competence in assessing and teaching mathematics skills and concepts, and (d) the importance these teachers assign to general knowledge of mathematics, mathematics assessment, and mathematics instruction. Mathematics instruction was found to occupy about one- third of the average resource room teacher's teaching time. Although subjects reported considerable college coursework in mathematics and mathematics in- structional methods, they felt inadequate at several competencies considered necessary for teachers of learning disabled students. Differences between elemen- tary and secondary teachers are reported.
Little descriptive research is available on the daily operation of resource room programs. Ac- cording to a recent observational study of resource teachers' time utilization, services are generally provided through direct instruction; that is, programs are developed and im- plemented by the resource room teacher rather than by the regular class teacher (Sargent, 1981). Further, results of the Sargent study showed that resource room teachers spent 51% of their time on any given day in direct instruc- tion of students, 15% on preparation for instruc- tion, and 9% on assessment and evaluation. The remaining 24% of the time was spent on general school duties and consultation with parents and other teachers.
The present study was designed to further ex- plicate the nature of the direct instruction when the instructional emphasis is on mathematics. In particular, the study extends Fitzmaurice's find- ings (1980) that resource room teachers con- sider themselves deficient in several areas.
Students need mathematics skills throughout their academic and life experiences. For learning disabled students, math performance is typically
characterized by the high failure rates associated with other academic subjects (Cawley, Fitz- maurice, Shaw, Kahn, & Bates, 1978, 1979). Informal observations suggest that resource room teachers tend to address their students' learning difficulties in mathematics through direct instruction. The present research ad- dresses the nature of mathematics instruction and resource room teachers' competencies to provide this instruction. Specifically, four areas are considered: (a) time spent by special educa- tion resource room teachers in mathematics in- struction, (b) nature of these teachers' training in mathematics and methods of mathematics in- struction, (c) these teachers' self-reported degree of competence in assessing and teaching mathematics skills and concepts, and (d) the im- portance these teachers assign to mathematics competence, given the nature of their jobs and the students with whom they work.
ROBERT L. CARPENTER, Ph.D., is Assistant Professor of Special Education, Division of Pro- fessional Education, State University of New York at Binghamton.
Volume 8, Spring 1985 95
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METHOD The four-page questionnaire used in the pre-
sent investigation was developed in an earlier study (Bromley & Carpenter, 1984) of reading instruction in resource rooms. The instrument in- cludes the list of competencies published by the former Division for Children with Learning Disabilities (DCLD), Council for Exceptional Children, in the Code of Ethics and Competen- cies for Teachers of Learning Disabled Children and Youth (1978). After having been field- tested with 10 local resource room teachers, the questionnaire was revised and mailed to a ran- dom sample of 200 resource room teachers across the state of New York. The sample was drawn from a population of 2,951 elementary and secondary resource room teachers whose names were supplied by the State Education Department. All teachers had identified themselves as resource room teachers for learn- ing disabled or educable mentally retarded students. A total of 101 usable survey forms were returned.
For purposes of randomization, teachers were asked to identify the first three students from their alphabetical room roster or class list. Subse- quent estimates of mathematics instructional time were made on the basis of the three ran- domly chosen students from each class, for a total of 303 students.
Means and standard deviations were calculated on the data regarding mathematics in- structional time and amount of teachers' formal college coursework in mathematics and mathematics instruction. Furthermore, chi- square tests were performed to compare dif- ferences between elementary and secondary teachers' responses to the competency statements.
The sample of resource room teachers who participated in the study were asked to rate themselves on the DCLD competencies dealing with assessment and instruction of mathematics. A 4-point Likert scale ranging from "very confi- dent in this skill", "somewhat confident", "uncertain", to "not at all confident in this skill" was used. Respondents were also asked to rate the importance of each of the competencies for their particular teaching situation. The latter ratings were reported on a 4-point Likert scale: "essential skill for my class", "necessary skill", "rarely employed skill", or "skill never needed".
RESULTS Demographic Data
Of the 101 questionnaires returned, 48 came from elementary (K-6) resource teachers, whereas 44 were completed by senior-high resource teachers. The remaining responses did not indicate the level taught. Twenty-two par- ticipants held Bachelor's degrees, 66 Master's degrees, 11 reported they were educational specialists, and 2 held doctorates. All but three subjects held state certificates as special educa- tion teachers. College Preparation for Teaching Mathematics
Respondents were asked to report how many of their college credit hours specifically dealt with (a) the teaching of mathematics, (b) mathematics as a content area, and (c) more general educa- tion methods of which mathematics only con- stituted a part. Means and standard deviations are presented in Table 1 for both graduate and undergraduate education. Mathematics Instructional Time
Respondents were asked randomly to choose three students from their class rolls (N = 298 usable reports) and to report the total time per week each of these students spent in their resource room (X = 5.2 hrs) and the amount of time spent in mathematics instruction (X = 1.8 hrs). Based on these data, the average student was found to spend over one-third of the allocated time in mathematics instruction. In response to the question as to the percent of their total instructional time spent teaching mathematics, 70% of the teachers' responses fell in the 10% to 40% range. Competence in Teaching Mathematics: Self-Ratings
Ratings were collapsed for analysis purposes so that teachers who rated themselves as "very confident" or "somewhat confident" were judged as being suitably competent in the skill, whereas teachers rating themselves as "uncer- tain" or "not at all confident" were judged as not being competent in a given skill. The competen- cies in which at least one fourth of the respondents were judged not competent are listed below.
1. Familiarity with nontraditional ways of teaching algorithms, for example, Tractenberg methods of addition and equal addition method of teaching subtraction (67% not competent).
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Table 1
College Preparation for Teaching Mathematics
X SD
Credit hours specifically in teaching mathematics (N = 99) 4.68 4.00
Credit hours in mathematics as a content area (N = 99) 7.27 9.92
Credit hours in educational methods, part of which involved
teaching mathematics (N = 90) 5.78 4.75
2. Familiarity with different conceptual and theoretical approaches to math instruction (47% not competent).
3. Familiarity with several procedures that can be used to assess attitudes toward mathematics (52% not competent).
4. Familiarity with methods for conducting error analysis (42% not competent).
5. Familiarity with procedures for determining a student's problem-solving ability (29% not competent).
6. Ability to use a scope and sequence from each math area to develop and administer an evaluation instrument (27% not competent).
Using a similar methodology, Fitzmaurice (1980) identified the same competency statements as areas of greatest weakness. In addition, Fitzmaurice found the following five competencies related to general knowledge of mathematics to be areas in which teachers reported themselves as having little or no com- petence:
1. Concepts and operations involved in con- verting from one base to another (77.4% not competent).
2. Concepts of prime and composite numbers (54.8% not competent).
3. Common solid geometric figures, for exam- ple, cube, sphere, and the processes used in determining the area and volume of each (61.3% not competent).
4. All concepts involved in measurement of time, linear planes, weight, liquids, and
temperature (50% not competent). 5. Metric system (85.5% not competent). Table 2 shows the competencies for which
teachers reported themselves as being the weakest and the importance assigned to each. Inspection of the data reveals that a substantial percentage of teachers judged the competency in which they were least confident as represent- ing skills they rarely or never used in their classrooms. (The data on general knowledge understanding are taken from Fitzmaurice [1980].) Differences Between Elementary and Secondary Teachers
Chi-square tests revealed significant dif- ferences between elementary- and secondary- level teachers' judgments of the importance of certain skills for their teaching situations. Specifically, secondary teachers considered the following general knowledge competencies to be more important than did elementary teachers: Understanding of the concepts of prime and composite numbers x2(4) = 11.275, p < .03; understanding of all operations involved in add- ing, subtracting, multiplying, and dividing frac- tions, decimal numbers, and numbers expressed as percentages x2(4) = 29.046, p < .0001; understanding of simple common plane geometric figures and processes involved in determining area and volume x2(4) = 23.639, p < .0001; and understanding of all the con- cepts involved in the measurement of time, linear planes, weight, liquids, and temperature
Volume 8, Spring 1985 97
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Table 2
LD Teachers' Self-Reported Competencies
Specific Competence General Knowledge Skills
Percent reporting Percent reporting limited or no skill rarely or never
understandinga used 1. Concepts and operations involved in converting from one base
to another 77.4 73.2 2. Concepts of prime and composite numbers 54.8 37.9 3. Common geometric figures 61.3 42.3 4. Concepts of time, linear planes, weight, liquid and temperature
measurement 50.0 16.2 5. Metric system 85.5 29.2
Assessment
Percent reporting Percent reporting uncertainty or no skill rarely or never confidence used
1. Scope and sequence for evaluation 26.5 34.7 2. Attitude assessment 52.1 42.4 3. Error analysis 42.4 36.1 4. Problem-solving ability assessment 29.3 13.4
Instruction
1. Different conceptual and theoretical approaches 46.9 29.5 2. Nontraditional ways of teaching algorithms 67.3 48.9
aData from Fitzmaurice (1980).
x2(4) = 11.659, p < .02. In assessment and instruction, elementary and
secondary teachers only differed in the impor- tance assigned to one skill, that is, elementary teachers felt that using a variety of manipulative math materials to teach a specific skill was more important than did secondary teachers x2(4) = 38.544, p < .0001.
DISCUSSION AND CONCLUSIONS First, the instructional time data clearly show
that mathematics is an important area of content instruction for resource room teachers. The amount of instructional time was not found to differ significantly between elementary and secondary classrooms. On the average resource room teachers reported that one-third of their instructional time was engaged in mathematics.
Second, the math preparation of our sample of resource room teachers was found to exceed the minimal requirements for both New York
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State Certification (currently no mathematics preparation is required) and typical teacher preparation programs in New York state. Com- pared to the average requirement of 3.3 credit hours of mathematics content (Gazzetta, 1981), participants reported an average of 4.68 credit hours in mathematics instruction and 7.27 credit hours of coursework in mathematics. (The sec- ond average appears to be inflated by the responses of several subjects for whom mathematics was apparently an undergraduate major.)
Given their preparation, the teachers' self- reported high levels of inadequacy are difficult to understand. In an attempt to explain this discrepancy, Fitzmaurice (1980) suggested that the orientation and quality of college coursework in mathematics and mathematics instruction might be responsible. Thus, it seems that the skills identified in the DCLD competencies as be- ing necessary for resource room teachers were not those emphasized in college coursework.
It is indeed disturbing to note that one resource teacher in four was found to be uncer- tain or not at all confident in his/her ability to assess students' mathematics skills through the use of a scope-and-sequence chart, or that five out of six teachers of learning disabled students reported little or no understanding of the metric system.
Third, the strong relationship noted between competencies reported as inadequately mastered and competencies not needed in the classroom requires some discussion. One possi- ble interpretation of these findings is that the sub- jects might have been inclined to minimize the importance of skills they did not possess. Teachers who are unfamiliar with how to teach algorithms, for instance, and therefore do not teach them, might be disposed to view instruc- tion in algorithms as unnecessary in the classroom. This type of self-serving response is a characteristic weakness of self-reported data. At the same time, however, such an interpretation cannot be applied to the responses to several competency statements in which relatively high percentages of teachers reported limited or no mastery and yet considered the competency necessary or essential for their classrooms.
When initially formulated, the DCLD com- petencies were not intended to be final statements exempt from further revision
(Newcomer, 1978). Thus, anticipating that not all competencies would be appropriate to all situations, the DCLD committee expected and welcomed further refinement. The data compar- ing the differences between elementary and secondary teachers' responses show that the two groups do not consider all competencies equally important. Thus, needs regarding general knowledge of mathematics were perceived dif- ferently, whereas the two groups of teachers ex- pressed the needs regarding assessment and in- struction similarly.
The DCLD competency statement is an almost unique document. No other professional group in the field of special education, with the exception of the severely/profoundly handi- capped (Burke & Cohen, 1977), has disseminated a similar set of teacher competen- cies. Interest in national standards of com- petence should not be allowed to wane. Rather, research testing the appropriateness of specific competencies should be ongoing, and the initial DCLD competency statements should be revised periodically. On the basis of such a document, professional groups can begin to guide state cer- tification requirements and assist local ad- ministrators in hiring and retaining competent teachers.
REFERENCES Bromley, K., & Carpenter, R. L. (1984). Reading in-
struction in resource rooms. Reading World, 23(3), 209-217.
Burke, P. J., & Cohen, M. (1977). The quest for competence in serving the severely/profoundly handicapped: A critical analysis of personnel preparation programs. In E. Sontag (Ed.), Educa- tional programming for the severely and profoundly handicapped. Reston, VA: CEC, 1977..
Cawley, J. F., Fitzmaurice, A. M., Shaw, R., Kahn, N., & Bates, N. (1979). LD youth and mathematics: A review of characteristics. Learning Disability Quarterly, 2, 29-44.
Cawley, J. F., Fitzmaurice, A. M., Shaw, R. A., Kahn, N., & Bates, N. Mathematics and learning disabled youth: The upper grade levels. Learning Disability Quarterly, 1978, 1, 37-52.
Council for Exceptional Children. (1978). Code of ethics and competencies for teachers of learning disabled children and youth, Division for Children with Learning Disabilities. (ERIC Document Repro- duction Service No. ED 161198)
Fitzmaurice, A. M. (1980). LD teachers' self-ratings on mathematics education competencies. Learning
Volume 8, Spring 1985 99
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Disability Quarterly, 3, 90-93. Freeman, M. A., & Becker, R. L. (1979). Competen-
cies for professionals in LD: An analysis of teacher perceptions. Learning Disability Quarterly, 2, 70-78.
Gazzetta, V. C. (1981, October). Memorandum to teacher education contact persons on knowledge of mathematics content by persons preparing for elementary certification. Albany, NY: State Educa- tion Department.
Newcomer, P. L. (1978). Competencies for profes-
sionals in learning disabilities. Learning Disability Quarterly, 1, 69-77.
Sargent, L. R. (1981). Resource teacher time utiliza- tion: An observational study. Exceptional Children, 47(6), 420-425.
Requests for reprints should be addressed to: Robert Carpenter, Division of Professional Education, State University of New York, Binghamton, NY 13901.
? ? CHANGE OF ADDRESS ? ? Please attach label with your old address and PRINT your new address and CLD membership number below.
PLACE LABEL HERE
Name CLD # (Soc. Sec. #)
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City / State / Zip
Mail to: D. Kim Reid P.O. Box 830688 University of Texas-Dallas Richardson, TX 75083-0688
100 Learning Disability Quarterly
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