# Mathematics achievement of hearing impaired adolescents in different placements.

ABSTRACT: This study, involving 215 students and 63 teachers,
addressed three concerns related to mainstreaming for hearing impaired
students: the selection process, the difference between a mainstream
placement with an interpreter and a self-contained placement, and the
quality of the educational experience. Almost half of the variance in
achievement between the two settings is described. Three conclusions can
be drawn. First, student background factors are a primary determinant of
achievement. Second, mainstreaming with an interpreter has no specific
effect on achievement for hearing impaired students. Third, the quality
of instruction is the prime determinant of achievement, regardless of
placement.

Two main effects and one interaction must be considered even in the simplest model of the efficacy of mainstreaming for hearing impaired children. The educationally relevant characteristics of the student, the quality of the placement experience, and the interaction of the abilities of the student with the placement experience must be taken into account. Previous research has indicated that ability (Jensema, 1975; Wolk, Karchmer, & Schildroth, (1982), race or family income (Jensema, 1975; Karchmer, Milone, & Wolk, 1979; Wolk et al., 1982) and degree of hearing loss (Karchmer et al., 1979) are predictors of the type of educational placement that hearing impaired children will experience. Higher achievement, classification as White, higher family income; and lower degree of hearing loss result in more integrated class placements. Put simply, the hearing impaired children in self-contained and mainstreamed classrooms are quite different. From this, we could expect the typical child in the special class placement to have lower academic skills, fewer resources within the home, and consequently less support for academic endeavors.

Two studies partially addressed this problem in considering the efficacy of mainstreaming for hearing impaired students. Allen and Osborn 1984), using demographic and achievement data on 1,465 hearing impaired children sampled from a national data base, computed an analysis of covariance on three subtests of the Stanford Achievement Test Hearing Impaired (SATHI) Version: reading comprehension, mathematics computation, and mathematics concepts. They reported statistically significant effects for the type of educational placement and for many of the demographic covariates, thus concluding that a positive effect for integration had been established but, more important, that demographic factors were the major contributing factor in the differences found. They made the point also that other, unstudied factors may have contributed to the differences since Allen and Osborn (I 984) accounted for only about one-third of the variance in their analysis.

Kluwin and Moores (1985), using a matched-groups design in a study of three metropolitan high school programs to assess the effect of educational placement on achievement, emulated the selection process used in the schools by using two measures of academic ability, a measure of social maturity, and a measure of disability to identify a group of students in self-contained classrooms---students who were similar to the integrated students but who had not been integrated. This selection process produced a comparison group who were different from the integrated students on the basis of their race and parental employment status. An analysis of covariance was computed using placement as the independent variable and mathematics computation achievement as the dependent variable. Prior mathematics achievement, sex, race, and degree of hearing loss were used as covariates. Placement did have a statistically significant effect on achievement. Expanding on Allen and Osborn's (1984) observation about unstudied factors, Kluwin and Moores (1985) also suggested several categories of differences in mainstreamed versus special placements that might account for the unexplained variance.

Both studies accounted for about 40% of the variance using placement, demographic information, and the interaction between the demographic characteristics of the students and their placement. Placement alone accounted for only I % of the variance. Demographics accounted for about 12% of the variance, leaving about 25% of the variance to the be accounted for by the interaction of placement and student characteristics. In summary, although previous research on the mainstreaming of hearing impaired students has found slight but statistically significant effects for placement situations and much larger effects for initial group membership, this research has not addressed the effect of the experience within a particular placement on the child's achievement.

The work of Allen and Osborn (1984) and the work of Kluwin and Moores (1985) suggest that mainstreaming may be an efficacious educational option for hearing impaired children; however, the amount of unaccounted-for variance in achievement was quite large in both studies. Further, it is apparent that serious, educationally relevant variables differentiate the two populations before placement. Because of this, the next section contains a brief consideration of the factors which define the quality of the educational experience of the child regardless of the type of placement.

Walberg (1984), in his synthesis of the general school-effectiveness literature, listed several demographic and background characterisitcs of teachers that are related to instructional effectiveness, including the level of training of the teacher, years of experience, course work in the academic major, and verbal ability. Along similar lines, Berliner (1982) also identified sets of effective instructional practices. Both lists include time on task either as a measure of student attention to the task or of the quantity of time devoted to instruction, the use of instructional strategies such as grouping in reading or direct laboratory experience in the sciences, pacing and sequencing

of the lesson content, the effective use of evaluation, and the students' perceptions of the nature of the task and their responsibilities within the classroom. Differences exist between the lists primarily on the micro-level and, in particular, when variations such as grade level and subject matter are included, but on the macro-level there is general agreement as to what constitutes effective classroom instruction.

Effective mathematics instruction as a subset of effective teaching has several components, two of which include higher level teaching and communication with the students about mathematics (Everston, Emmer, & Brophy, 1980). Higher level teaching means that both the rationale for the computational procedure as well as the various applications must be taught. What is needed by the mathematics student is a broad knowledge base in order to construct the larger conceptual networks which are needed for the retention of specific detail such as computational routines (Gregory & Osborne, 1975). Classroom communication is important in mathematics instruction because a student who is intellectually involved with a mathematics teacher becomes involved with mathematics. Everston and her associates (Everston et al., 1980) and Berliner and his associates (Fisher et al., 198 1), in studies of mathematics achievement, reported that the best predictor of achievement is the students' actual engaged time. Teachers moving about the room, explaining, and monitoring progress increase engaged time, which supports learning. When more classroom talk is devoted to instruction, more learning takes place. In other words, direct instruction by the teacher is an excellent predictor of student achievement. Communication with the students through the use of direct instruction and attention to the structure of the information is crucial.

Three hypotheses can be derived from this research. First, mainstreaming is apparently an efficacious educational situation for hearing impaired students. Second, individual student characteristics will probably account for a greater proportion of the variance than would placement type per se. Third, the large amount of unexplained variance in the earlier research and the significant predictive power of research on teaching effectiveness suggests that the quality of the student's experience would be very important in explaining differences in achievement. METHOD Sample There were 215 students with an average a e of 16.7

9 years and a standard deviation of 1.6 years. Of these students, 60.8% were White; 17.5% were Hispanic; 16.6% were Black; and 4.8% were other minorities. Of the overall sample, 44. 1 % were male, and 55.9% were female. The average hearing loss was 88.3 dB in the better ear with a standard deviation of 20.2 dB. Therefore, most of the sample had severe to profound hearing losses.

A match was made between the mainstreamed and the self-contained students by taking only those self-contained students with a score on the SATHI mathematics computation subtest above 600. Some leniency was allowed in interpreting this rule to permit entire classes to be used when the majority of the students were at or above this cut-off point. This produced a sample that does not include the most able hearing impaired students because their hearing loss is not as severe, nor does it include the least able students who were excluded because of the inability to find "matches" between less able self-contained students and the more able mainstreamed students. A further limitation of the comparison groups is that almost all (97%) of the mainstreamed students had interpreters; that is, we cannot generalize to situations where hearing impaired students are without interpreting support. Even this process left considerable differences between the two groups in favor of the mainstreamed sample. Statistical controls, primarily through covariance, were applied to compensate for these remaining differences (see Table 1). Instrumentation Parent Questionnaire. The Parent Questionnaire was a 53-item instrument distributed to the parent or guardian of each student involved in the study. Three attempts were made through the mail to contact the parents. The third attempt was preceded by a telephone request to the parents to complete the questionnaire. Forms were sent out to the parents in English or Spanish, as required. Parents requiring other language interpretations were surveyed during regularly scheduled meetings with the school staff (e.g., prior to an individual education plan, IEP, meeting with an appropriate language interpreter present); however, this represented only a tiny proportion of the questionnaires.

There was good response: 83.3% of the parents returned the questionnaire. To determine the reliability of the parent questionnaire, an internal consistency statistic, Cronbach's alpha, was computed for the 31 items that were to be used in the development of factor scores for the families. The alpha coefficient for the 31 items was .843. Student Questionnaire. This was a 48-item Likert-scaled instrument given to the students individually or in small groups. Students with near-grade-level reading ability read the questionnaire and responded to it on their own. For students who were not good readers, the small group administration involved a total communication interpretation administered by the classroom teacher. The return rate was 98%. Internal consistency for the 19 items that were used in the final scale was .743 using a Cronbach's alpha. The original items were adapted from instrumentation developed by the Program on Teaching Effectiveness (at Stanford University) and pilot-tested the previous year with hearing impaired students in public school settings. Teacher Survey.

A teacher opinion instrument developed by Good (1981) was modified to eliminate questions that specifically solicited information about elementary school practices. The purpose of the survey was to solicit information about activities (e.g., planning and reward systems) that were not readily available from live observations. The return rate for the survey was 87%. Four factors were generated from the 21 items that were most consistent, having an internal reliability of .642 using Cronbach's alpha. Teacher Logs. To provide a sense of the quantity and level of the work that the teachers demanded of their classes, they were asked to keep logs of their assignments and classwork. The logs were coded according to the difficulty level and number of problems that were worked for that day. There were 14 levels of coding, ranging from simple arithmetic operations to trigonometry. The 13th category included special topics such as statistics, probability theory, or computer programming. All geometry topics were coded in the 14th category, and these few students were eliminated from further analysis because of the relative insensitivity of the dependent measure in assessing changes in this area.

The coding scheme was developed on the basis of the tables of contents of the textbooks used; that is, the categories were operationally defined in advance based on the topical sequence of six widely used algebra and general mathematics texts. The textbook pages were then assigned a category number based on the topic covered. Problems assigned from a specific set of pages were then considered to be at a certain level of difficulty. The coding convention counted all of the problems that the student did by himself and herself in class that day, including seatwork and tests or quizzes, as well as homework. Live Observation System. The classroom observation system was a data collection procedure that provided a record of activities that occurred in the classroom, the interactions between teachers and students, and the function of the interpreter in the classroom. This time-series sampling observation system was designed to be sensitive to different instructional methods, interpersonal interactions, and classroom environments.

The instrument was an adaptation of the SRI Secondary Observation Instrument (Stallings, Needles, & Stayrook, 1979). Sections of that instrument were freely adopted. The system had two parts: the snapshot" and the 5-minute interaction (FMI).

The first section was the classroom snapshot. The snapshot yielded data about the nature of the activities of each adult and student in the classroom, the size of the groups, and the materials being used. From this section, information can be obtained on how the teacher spends his or her time and with whom, how the aides or interpreters spend their time and with whom, how often the students operate independently, and the instructional activities that occur. The types of instructional materials that were used in the classroom were also recorded. By crossing the three general categories of activity, materials, and group structure, it was possible to describe in considerable detail what occurred in the classroom. For example, it would be possible to record a teacher disciplining a single hearing student while the interpreter tutored a deaf student and the rest of the class worked individually on computers or in small groups.

The second section was the FMI, which was used to observe teachers and students in group interactions or working alone. It consisted of a series of frames in which each behavior or interaction was recorded. Data from the FMI are not reported here.

The I I observers, all of whom were trained teachers of the deaf with several years of signing experience, were brought to Gallaudet University in two separate groups, but the training was identical for each training group. During the morning of the first day, the overall purpose of the system was explained and each category was explained and discussed. During the afternoon of the first day, short practice coding sessions with discussion and feedback were carried out using videotapes of high school math lessons with self-contained classes of hearing impaired students. During the second day, the observers practiced on classes of self-contained hearing impaired students. With each practice observation, the length of the observation cycle was lengthened until the observers were doing the full 5-minute observation. After each practice observation, the observers discussed their observations, and effant observers were brought into the agreed-upon standard. During the third day, observers were placed in regular math classes, which included hearing impaired students and their interpreters. Following each observation session, the observers discussed their observations so as to establish greater reliability.

Five sets of snapshots and FMIs were to be completed during each class period. There was up to a 5-minute rest period between each coding period of 5 minutes.

The average number of teacher observations was 3.2 with a range of 1-8 observations; the modals were 3 and 5 observations. To deal with the variation in the number of minutes of observed class time, all times were weighted on the basis of 100 minutes of observed time per teacher. All subsequent calculations are based on this adjusted time.

Interrater reliability for the categories of the observation system that were used in this analysis was .942, using an alpha coefficient for the category totals aggregated across all observations for each rater. RESULTS Parent Questionnaire Responses to the parent questionnaire were factor analyzed. From the 31 Likert-scaled items, four factors consisting of 25 items were generated. The factors were academic press, family involvement, academic support, and assisting with math homework.

Factor scores were generated for each student. Nonresponses to the questionnaire itself were considered indicative of the lack of parental involvement and were scored on the extreme point of the scale rather than as missing data. Student Questionnaire The responses to the student questionnaire were factor analyzed to yield four factors, which included

TABLE 1

Characteristics of Students by Types of

Placement

Self-Contained Mainstreamed Characteristic (N = 102) (N = 113) Age

Mean 16.87 16.22

SD 1.94 1.29 Sex

% Male 38.0 50.0 Race

Black 22.8 13.4

White 47.8 70.7

Hispanic 26.1 9.8

Other 3.3 6.1 Better ear average (dB)

Mean 90.37 87.42

SD 20.51 20.55 SATHI Math Computation Subtest (Pretest) scaled score

Mean 671.39 704.71

SD 48.75 41.97 SATHI Math Concepts Subtest (Pretest) scaled score

Mean 649.51 697.45

SD 44.96 43.48 Note: SATHI = Stanford Achievement Test Hearing Impaired Version. -------------------------- teacher's use of verbal structuring; teacher is helpful/supportive; classroom is a work place; teacher is a strict disciplinarian. Factor scores were then generated for each student. Teacher Survey The attitudinal items from the teacher survey were factor analyzed to yield four factors: degree of individualization, instructional flexibility, theoretical orientation to mathematics, and "math workshop" orientation.

By using school records and the scale scores from the various instruments, a list of variables was generated which covered the general schooling

TABLE 2

Analysis of Covariance

Computation Concepts

Covariates Achievement Achievement

t value

Previous achievement

Concepts 6.227** 8.455

Computation 4.219** 3.737

Time between testing -.690 1.243

Sex 1.044 -.608

Race -.166 1.911

Hearing loss -.566 -.230

Additional handicaps - 2.8 99 -1.264

F value

Main Effect

df = 1,145

Placement 0.007 0.310

p < 01. *p < .001.----------------------------factors of student background characteristics, both individual and family, staff quality, the quality of the educational process, and measures of achievement. These variables were then used in two separate analyses to address the hypotheses proposed previously.

This study entertained three hypotheses. First, mainstreaming is more efficacious than a more restricted placement. Second, demographics account for a greater proportion of the variance than placement per se. Third, the nature of the experience determines the bulk of the variance in achievement.

To address the first hypothesis, a repeated measures analysis of covariance was computed. The dependent measures were scores on the mathematics computation and mathematics achievement subscales of the SATHI. The covariates were previous scores on the same subtests as a control for prior ability, the length of time between the two test administrations, and the student demographic factors of sex, race, hearing loss, and presence of additional handicaps (see Table 2). To minimize remaining between-group differences, the analysis of covariance was selected.

There are three special assumptions for the use of analysis of covariance: the covariates must have existed before the treatment, the covariates must not be trivial, and there must be no design solution in an analysis of variance that will deal with the differences in a parsimonious fashion (Glass & Stanley, 1970). Analysis of covariance was selected in this case because of the covariates' preexisting differences. Further, as can be seen in Table 2 and Figure 1, the covariates are significant factors in accounting for the variance. This was also apparent from Allen and Osborn's study (1984). Finally, the use of the various covariates as factors in a full factorial design would have produced too many cells for the sample size and potentially yielded a number of uninterpretable higher order interactions. Since the point of the hypothesis is to assess the efficacy of the educational placement, the analysis of covariance becomes the most parsimonious solution.

Figure 2 shows that there are considerable between-group differences for the observed or unadjusted group means for the posttest achievement measures. After adjusting for the demographic differences between the two groups, however, these apparent achievement differences disappear. Table 2 corroborates this observation in that for both the computation and concepts posttest scores, there are no statistically significant main effects. On the other hand, the covariates are statistically significant, with previous ability being the largest single factor.

We can conclude from this that mainstreaming per se is not necessarily an efficacious educational placement and further that much of the differences between placements is attributable to between-group differences. Thus the first hypothesis cannot be supported. In this study, the relatively small effect for placement only was not found. Given the expected size of the variance accounted for by this factor, it is conceivable that in a study with a small- to moderate-sized sample the difference would not be detected.

The second and third hypotheses were addressed in the same statistic (a multiple regression), since placement, demographic, and instructional process variables could be included in the same list of predictor variables.

Predicted achievement scores adjusted for previous achievement, and the length of time between test administrations were used as the dependent variables in all subsequent computations.

Two multiple regressions were computed, one to predict achievement in mathematics computation and the other to predict achievement in mathematics concepts. The same list of predictor variables was entered for both variables. The list included type of placement, individual characteristics, family background and process characteristics, and measures of the quality of the instructional process. Individual characteristics included the age, sex, and degree of hearing loss of the students. Family process factors included the factors previously described as being derived from the parent questionnaire. Family background factors included family size, employment status, and parental education. The teacher process variables that were included in the two regressions are described as follows.

For computation achievement, 47.7% of the variance in the posttest results, and for mathematics concepts achievement, 48.4% were accounted for using the two multiple regressions. For the computation measure, demographic factors, specifically the absence of additional handicaps and the mother's education, accounted for 14.7% of the variance. For mathematics concepts achievement, 15% of the vairance was accounted for by using demographic measures. This is consistent with what had been predicted. Placement accounted for less than 1% of the variance in computation achievement, but it was not even entered in the equation for mathematics concepts achievement. The even lower-than-expected contribution of placement to the equation may be due to the fact that by using process variables we have accounted for the interaction between placement and teaching process, thus leaving the true measure of placement effects. In other words, because the teachers in the two different placement situations behave differently, when we have accounted for that behavior, the effect of placement and the interaction of placement and teaching behavior disappears.

Almost 30% of the total variance and 60% of the explained variance is attributable to a basically similar set of teaching behaviors. For effective mathematics instruction, a supportive teacher, regular and extensive reviews of the material, devoting time to direct instruction, expressions of positive affect, and a demand that the students work at the task is the key. DISCUSSION Before discussing the results and implications of this study, some cautions need to mentioned. First, the participants in this study were drawn from larger public school programs and as such do not represent the experiences of children in smaller programs. Second, no elementary school students were involved; therefore, the generalizability of the results beyond secondary-school-age students is problematic. Third, mainstreaming" needs to be interpreted as "mainstreaming with an interpreter." Consequently, generalizations to other types of mainstreaming should be made carefully.

Three conclusions can be drawn from this study. First, because of the differential selection process for mainstreaming, student background factors are a primary determinant of achievement. Second, mainstreaming with an interpreter has no specific effect on achievement for hearing impaired students. Third, the quality of instruction a hearing impaired child receives is the prime determinant of achievement. Individual student characteristics account for a greater proportion of the variance than placement type; however, they are not the major component in explaining the variance. On the other hand, the quality of the placement experience is a prime determinant of achievement. Mainstreaming is not necessarily an efficacious educational situation because the previously identified positive effect for mainstream placement was not found. In fact, placement contributes very little to accounting for the overall variance.

The quality of the experience is the factor that accounted for the bulk of the variance in achievement, regardless of the relative order in which individual variables were entered into the equation: supportive teacher, regular and extensive reviews of the material, devoting time to direct instruction, expressions of positive affect, and a demand that the students work at the task.

The teacher must be involved with the students about the subject matter. "Individual" instruction as a surrogate for "individualized" instruction is not effective. Effective instruction is a public event. Previous research on mathematics achievement has shown that a 50% time commitment to direct instruction is about the most effective use of time (Evertson et al., 1980). This time allocation permits a lesson structure where the previously taught material is reviewed on a daily basis, usually through a discussion of the homework. A similar finding can be reported from this study.

Because the effective classroom is a public place, public expressions of praise for appropriate responses are important. Two effects could be working here. The first is the obvious effect, that is, that the individual student is rewarded for doing well and is gratified and thus learns more. At the same time other students recognize that there is an emotional reward to appropriate behavior. The second effect is cognitive in that appropriate and positive affect defines what is acceptable intellectually while not denigrating misunderstandings.

Two effects are also at work in the high level of work demand found in the effective classroom. First, there is no substitute for practice. Like the frequency and length of review variables, quantity of material covered offers more opportunities to establish the concept. Second, high levels of work convey very explicitly the sense that the classroom is a place of business.

The findings of this study indicate that it is the quality of the placement experience that determines academic achievement, not the type of placement. The implication is that content knowledge, teacher experience, and actual classroom practice are the important features of the educational experience. Teaching process characteristics such as being a supportive teacher or taking a more businesslike approach to teaching math are a function of the teacher's training and experience. In actual classroom practice, activities such as maintaining a high level of contact with the content, creating an atmosphere that mathematics is a public activity, and making all students feel that they could be called on at any moment produce higher levels of achievement.

For the school to ensure that hearing impaired children are exposed to these kinds of experiences, there are two options. One is to more carefully select the regular classroom teachers that hearing impaired children will have contact with. The other is to upgrade the quality of the mathematics preparation of the teachers of the hearing impaired.

Closer scrutiny of potential teachers for mainstreaming should include attention to their previous level of mathematics training and their experience in teaching mathematics. Informal yet structured interviews with these individuals could elicit basic information about their classroom practices----particularly their use of time during the lesson. Informal observations over a few separate class periods would reinforce the interview conclusions if attention is paid to the distribution of time. At least half of the class period should be devoted to direct instruction; the teacher should emphasize public presentations of work, such as students doing problems in front of the class; and the teacher should select a variety of students for questions about the work.

Three steps can be taken quickly and relatively inexpensively to upgrade the quality of instruction in self-contained classes. First, subject matter should be departmentalized above the junior high level, at least. In other words, some teacher should be designated as the "math person." if the program is large enough to require several persons to teach math, the formation of a "mini-math" department is an excellent option. Second, the individual or individuals designated as math teachers should pursue additional training in mathematics, with the emphasis on content rather than methods of teaching mathematics. Third, additional methodological information should be provided to the mathematics teachers of the hearing impaired. The teachers of the hearing impaired should be "integrated" with the regular mathematics instructors, including attending departmental meetings, attending professional conferences with them, and allowing for mutual planning time. If the mathematics department staff is competent, then the teachers of the hearing impaired will be current in the field; and they will acquire access to a large body of practical experience.

Two main effects and one interaction must be considered even in the simplest model of the efficacy of mainstreaming for hearing impaired children. The educationally relevant characteristics of the student, the quality of the placement experience, and the interaction of the abilities of the student with the placement experience must be taken into account. Previous research has indicated that ability (Jensema, 1975; Wolk, Karchmer, & Schildroth, (1982), race or family income (Jensema, 1975; Karchmer, Milone, & Wolk, 1979; Wolk et al., 1982) and degree of hearing loss (Karchmer et al., 1979) are predictors of the type of educational placement that hearing impaired children will experience. Higher achievement, classification as White, higher family income; and lower degree of hearing loss result in more integrated class placements. Put simply, the hearing impaired children in self-contained and mainstreamed classrooms are quite different. From this, we could expect the typical child in the special class placement to have lower academic skills, fewer resources within the home, and consequently less support for academic endeavors.

Two studies partially addressed this problem in considering the efficacy of mainstreaming for hearing impaired students. Allen and Osborn 1984), using demographic and achievement data on 1,465 hearing impaired children sampled from a national data base, computed an analysis of covariance on three subtests of the Stanford Achievement Test Hearing Impaired (SATHI) Version: reading comprehension, mathematics computation, and mathematics concepts. They reported statistically significant effects for the type of educational placement and for many of the demographic covariates, thus concluding that a positive effect for integration had been established but, more important, that demographic factors were the major contributing factor in the differences found. They made the point also that other, unstudied factors may have contributed to the differences since Allen and Osborn (I 984) accounted for only about one-third of the variance in their analysis.

Kluwin and Moores (1985), using a matched-groups design in a study of three metropolitan high school programs to assess the effect of educational placement on achievement, emulated the selection process used in the schools by using two measures of academic ability, a measure of social maturity, and a measure of disability to identify a group of students in self-contained classrooms---students who were similar to the integrated students but who had not been integrated. This selection process produced a comparison group who were different from the integrated students on the basis of their race and parental employment status. An analysis of covariance was computed using placement as the independent variable and mathematics computation achievement as the dependent variable. Prior mathematics achievement, sex, race, and degree of hearing loss were used as covariates. Placement did have a statistically significant effect on achievement. Expanding on Allen and Osborn's (1984) observation about unstudied factors, Kluwin and Moores (1985) also suggested several categories of differences in mainstreamed versus special placements that might account for the unexplained variance.

Both studies accounted for about 40% of the variance using placement, demographic information, and the interaction between the demographic characteristics of the students and their placement. Placement alone accounted for only I % of the variance. Demographics accounted for about 12% of the variance, leaving about 25% of the variance to the be accounted for by the interaction of placement and student characteristics. In summary, although previous research on the mainstreaming of hearing impaired students has found slight but statistically significant effects for placement situations and much larger effects for initial group membership, this research has not addressed the effect of the experience within a particular placement on the child's achievement.

The work of Allen and Osborn (1984) and the work of Kluwin and Moores (1985) suggest that mainstreaming may be an efficacious educational option for hearing impaired children; however, the amount of unaccounted-for variance in achievement was quite large in both studies. Further, it is apparent that serious, educationally relevant variables differentiate the two populations before placement. Because of this, the next section contains a brief consideration of the factors which define the quality of the educational experience of the child regardless of the type of placement.

Walberg (1984), in his synthesis of the general school-effectiveness literature, listed several demographic and background characterisitcs of teachers that are related to instructional effectiveness, including the level of training of the teacher, years of experience, course work in the academic major, and verbal ability. Along similar lines, Berliner (1982) also identified sets of effective instructional practices. Both lists include time on task either as a measure of student attention to the task or of the quantity of time devoted to instruction, the use of instructional strategies such as grouping in reading or direct laboratory experience in the sciences, pacing and sequencing

of the lesson content, the effective use of evaluation, and the students' perceptions of the nature of the task and their responsibilities within the classroom. Differences exist between the lists primarily on the micro-level and, in particular, when variations such as grade level and subject matter are included, but on the macro-level there is general agreement as to what constitutes effective classroom instruction.

Effective mathematics instruction as a subset of effective teaching has several components, two of which include higher level teaching and communication with the students about mathematics (Everston, Emmer, & Brophy, 1980). Higher level teaching means that both the rationale for the computational procedure as well as the various applications must be taught. What is needed by the mathematics student is a broad knowledge base in order to construct the larger conceptual networks which are needed for the retention of specific detail such as computational routines (Gregory & Osborne, 1975). Classroom communication is important in mathematics instruction because a student who is intellectually involved with a mathematics teacher becomes involved with mathematics. Everston and her associates (Everston et al., 1980) and Berliner and his associates (Fisher et al., 198 1), in studies of mathematics achievement, reported that the best predictor of achievement is the students' actual engaged time. Teachers moving about the room, explaining, and monitoring progress increase engaged time, which supports learning. When more classroom talk is devoted to instruction, more learning takes place. In other words, direct instruction by the teacher is an excellent predictor of student achievement. Communication with the students through the use of direct instruction and attention to the structure of the information is crucial.

Three hypotheses can be derived from this research. First, mainstreaming is apparently an efficacious educational situation for hearing impaired students. Second, individual student characteristics will probably account for a greater proportion of the variance than would placement type per se. Third, the large amount of unexplained variance in the earlier research and the significant predictive power of research on teaching effectiveness suggests that the quality of the student's experience would be very important in explaining differences in achievement. METHOD Sample There were 215 students with an average a e of 16.7

9 years and a standard deviation of 1.6 years. Of these students, 60.8% were White; 17.5% were Hispanic; 16.6% were Black; and 4.8% were other minorities. Of the overall sample, 44. 1 % were male, and 55.9% were female. The average hearing loss was 88.3 dB in the better ear with a standard deviation of 20.2 dB. Therefore, most of the sample had severe to profound hearing losses.

A match was made between the mainstreamed and the self-contained students by taking only those self-contained students with a score on the SATHI mathematics computation subtest above 600. Some leniency was allowed in interpreting this rule to permit entire classes to be used when the majority of the students were at or above this cut-off point. This produced a sample that does not include the most able hearing impaired students because their hearing loss is not as severe, nor does it include the least able students who were excluded because of the inability to find "matches" between less able self-contained students and the more able mainstreamed students. A further limitation of the comparison groups is that almost all (97%) of the mainstreamed students had interpreters; that is, we cannot generalize to situations where hearing impaired students are without interpreting support. Even this process left considerable differences between the two groups in favor of the mainstreamed sample. Statistical controls, primarily through covariance, were applied to compensate for these remaining differences (see Table 1). Instrumentation Parent Questionnaire. The Parent Questionnaire was a 53-item instrument distributed to the parent or guardian of each student involved in the study. Three attempts were made through the mail to contact the parents. The third attempt was preceded by a telephone request to the parents to complete the questionnaire. Forms were sent out to the parents in English or Spanish, as required. Parents requiring other language interpretations were surveyed during regularly scheduled meetings with the school staff (e.g., prior to an individual education plan, IEP, meeting with an appropriate language interpreter present); however, this represented only a tiny proportion of the questionnaires.

There was good response: 83.3% of the parents returned the questionnaire. To determine the reliability of the parent questionnaire, an internal consistency statistic, Cronbach's alpha, was computed for the 31 items that were to be used in the development of factor scores for the families. The alpha coefficient for the 31 items was .843. Student Questionnaire. This was a 48-item Likert-scaled instrument given to the students individually or in small groups. Students with near-grade-level reading ability read the questionnaire and responded to it on their own. For students who were not good readers, the small group administration involved a total communication interpretation administered by the classroom teacher. The return rate was 98%. Internal consistency for the 19 items that were used in the final scale was .743 using a Cronbach's alpha. The original items were adapted from instrumentation developed by the Program on Teaching Effectiveness (at Stanford University) and pilot-tested the previous year with hearing impaired students in public school settings. Teacher Survey.

A teacher opinion instrument developed by Good (1981) was modified to eliminate questions that specifically solicited information about elementary school practices. The purpose of the survey was to solicit information about activities (e.g., planning and reward systems) that were not readily available from live observations. The return rate for the survey was 87%. Four factors were generated from the 21 items that were most consistent, having an internal reliability of .642 using Cronbach's alpha. Teacher Logs. To provide a sense of the quantity and level of the work that the teachers demanded of their classes, they were asked to keep logs of their assignments and classwork. The logs were coded according to the difficulty level and number of problems that were worked for that day. There were 14 levels of coding, ranging from simple arithmetic operations to trigonometry. The 13th category included special topics such as statistics, probability theory, or computer programming. All geometry topics were coded in the 14th category, and these few students were eliminated from further analysis because of the relative insensitivity of the dependent measure in assessing changes in this area.

The coding scheme was developed on the basis of the tables of contents of the textbooks used; that is, the categories were operationally defined in advance based on the topical sequence of six widely used algebra and general mathematics texts. The textbook pages were then assigned a category number based on the topic covered. Problems assigned from a specific set of pages were then considered to be at a certain level of difficulty. The coding convention counted all of the problems that the student did by himself and herself in class that day, including seatwork and tests or quizzes, as well as homework. Live Observation System. The classroom observation system was a data collection procedure that provided a record of activities that occurred in the classroom, the interactions between teachers and students, and the function of the interpreter in the classroom. This time-series sampling observation system was designed to be sensitive to different instructional methods, interpersonal interactions, and classroom environments.

The instrument was an adaptation of the SRI Secondary Observation Instrument (Stallings, Needles, & Stayrook, 1979). Sections of that instrument were freely adopted. The system had two parts: the snapshot" and the 5-minute interaction (FMI).

The first section was the classroom snapshot. The snapshot yielded data about the nature of the activities of each adult and student in the classroom, the size of the groups, and the materials being used. From this section, information can be obtained on how the teacher spends his or her time and with whom, how the aides or interpreters spend their time and with whom, how often the students operate independently, and the instructional activities that occur. The types of instructional materials that were used in the classroom were also recorded. By crossing the three general categories of activity, materials, and group structure, it was possible to describe in considerable detail what occurred in the classroom. For example, it would be possible to record a teacher disciplining a single hearing student while the interpreter tutored a deaf student and the rest of the class worked individually on computers or in small groups.

The second section was the FMI, which was used to observe teachers and students in group interactions or working alone. It consisted of a series of frames in which each behavior or interaction was recorded. Data from the FMI are not reported here.

The I I observers, all of whom were trained teachers of the deaf with several years of signing experience, were brought to Gallaudet University in two separate groups, but the training was identical for each training group. During the morning of the first day, the overall purpose of the system was explained and each category was explained and discussed. During the afternoon of the first day, short practice coding sessions with discussion and feedback were carried out using videotapes of high school math lessons with self-contained classes of hearing impaired students. During the second day, the observers practiced on classes of self-contained hearing impaired students. With each practice observation, the length of the observation cycle was lengthened until the observers were doing the full 5-minute observation. After each practice observation, the observers discussed their observations, and effant observers were brought into the agreed-upon standard. During the third day, observers were placed in regular math classes, which included hearing impaired students and their interpreters. Following each observation session, the observers discussed their observations so as to establish greater reliability.

Five sets of snapshots and FMIs were to be completed during each class period. There was up to a 5-minute rest period between each coding period of 5 minutes.

The average number of teacher observations was 3.2 with a range of 1-8 observations; the modals were 3 and 5 observations. To deal with the variation in the number of minutes of observed class time, all times were weighted on the basis of 100 minutes of observed time per teacher. All subsequent calculations are based on this adjusted time.

Interrater reliability for the categories of the observation system that were used in this analysis was .942, using an alpha coefficient for the category totals aggregated across all observations for each rater. RESULTS Parent Questionnaire Responses to the parent questionnaire were factor analyzed. From the 31 Likert-scaled items, four factors consisting of 25 items were generated. The factors were academic press, family involvement, academic support, and assisting with math homework.

Factor scores were generated for each student. Nonresponses to the questionnaire itself were considered indicative of the lack of parental involvement and were scored on the extreme point of the scale rather than as missing data. Student Questionnaire The responses to the student questionnaire were factor analyzed to yield four factors, which included

TABLE 1

Characteristics of Students by Types of

Placement

Self-Contained Mainstreamed Characteristic (N = 102) (N = 113) Age

Mean 16.87 16.22

SD 1.94 1.29 Sex

% Male 38.0 50.0 Race

Black 22.8 13.4

White 47.8 70.7

Hispanic 26.1 9.8

Other 3.3 6.1 Better ear average (dB)

Mean 90.37 87.42

SD 20.51 20.55 SATHI Math Computation Subtest (Pretest) scaled score

Mean 671.39 704.71

SD 48.75 41.97 SATHI Math Concepts Subtest (Pretest) scaled score

Mean 649.51 697.45

SD 44.96 43.48 Note: SATHI = Stanford Achievement Test Hearing Impaired Version. -------------------------- teacher's use of verbal structuring; teacher is helpful/supportive; classroom is a work place; teacher is a strict disciplinarian. Factor scores were then generated for each student. Teacher Survey The attitudinal items from the teacher survey were factor analyzed to yield four factors: degree of individualization, instructional flexibility, theoretical orientation to mathematics, and "math workshop" orientation.

By using school records and the scale scores from the various instruments, a list of variables was generated which covered the general schooling

TABLE 2

Analysis of Covariance

Computation Concepts

Covariates Achievement Achievement

t value

Previous achievement

Concepts 6.227** 8.455

Computation 4.219** 3.737

Time between testing -.690 1.243

Sex 1.044 -.608

Race -.166 1.911

Hearing loss -.566 -.230

Additional handicaps - 2.8 99 -1.264

F value

Main Effect

df = 1,145

Placement 0.007 0.310

p < 01. *p < .001.----------------------------factors of student background characteristics, both individual and family, staff quality, the quality of the educational process, and measures of achievement. These variables were then used in two separate analyses to address the hypotheses proposed previously.

This study entertained three hypotheses. First, mainstreaming is more efficacious than a more restricted placement. Second, demographics account for a greater proportion of the variance than placement per se. Third, the nature of the experience determines the bulk of the variance in achievement.

To address the first hypothesis, a repeated measures analysis of covariance was computed. The dependent measures were scores on the mathematics computation and mathematics achievement subscales of the SATHI. The covariates were previous scores on the same subtests as a control for prior ability, the length of time between the two test administrations, and the student demographic factors of sex, race, hearing loss, and presence of additional handicaps (see Table 2). To minimize remaining between-group differences, the analysis of covariance was selected.

There are three special assumptions for the use of analysis of covariance: the covariates must have existed before the treatment, the covariates must not be trivial, and there must be no design solution in an analysis of variance that will deal with the differences in a parsimonious fashion (Glass & Stanley, 1970). Analysis of covariance was selected in this case because of the covariates' preexisting differences. Further, as can be seen in Table 2 and Figure 1, the covariates are significant factors in accounting for the variance. This was also apparent from Allen and Osborn's study (1984). Finally, the use of the various covariates as factors in a full factorial design would have produced too many cells for the sample size and potentially yielded a number of uninterpretable higher order interactions. Since the point of the hypothesis is to assess the efficacy of the educational placement, the analysis of covariance becomes the most parsimonious solution.

Figure 2 shows that there are considerable between-group differences for the observed or unadjusted group means for the posttest achievement measures. After adjusting for the demographic differences between the two groups, however, these apparent achievement differences disappear. Table 2 corroborates this observation in that for both the computation and concepts posttest scores, there are no statistically significant main effects. On the other hand, the covariates are statistically significant, with previous ability being the largest single factor.

We can conclude from this that mainstreaming per se is not necessarily an efficacious educational placement and further that much of the differences between placements is attributable to between-group differences. Thus the first hypothesis cannot be supported. In this study, the relatively small effect for placement only was not found. Given the expected size of the variance accounted for by this factor, it is conceivable that in a study with a small- to moderate-sized sample the difference would not be detected.

The second and third hypotheses were addressed in the same statistic (a multiple regression), since placement, demographic, and instructional process variables could be included in the same list of predictor variables.

Predicted achievement scores adjusted for previous achievement, and the length of time between test administrations were used as the dependent variables in all subsequent computations.

Two multiple regressions were computed, one to predict achievement in mathematics computation and the other to predict achievement in mathematics concepts. The same list of predictor variables was entered for both variables. The list included type of placement, individual characteristics, family background and process characteristics, and measures of the quality of the instructional process. Individual characteristics included the age, sex, and degree of hearing loss of the students. Family process factors included the factors previously described as being derived from the parent questionnaire. Family background factors included family size, employment status, and parental education. The teacher process variables that were included in the two regressions are described as follows.

For computation achievement, 47.7% of the variance in the posttest results, and for mathematics concepts achievement, 48.4% were accounted for using the two multiple regressions. For the computation measure, demographic factors, specifically the absence of additional handicaps and the mother's education, accounted for 14.7% of the variance. For mathematics concepts achievement, 15% of the vairance was accounted for by using demographic measures. This is consistent with what had been predicted. Placement accounted for less than 1% of the variance in computation achievement, but it was not even entered in the equation for mathematics concepts achievement. The even lower-than-expected contribution of placement to the equation may be due to the fact that by using process variables we have accounted for the interaction between placement and teaching process, thus leaving the true measure of placement effects. In other words, because the teachers in the two different placement situations behave differently, when we have accounted for that behavior, the effect of placement and the interaction of placement and teaching behavior disappears.

Almost 30% of the total variance and 60% of the explained variance is attributable to a basically similar set of teaching behaviors. For effective mathematics instruction, a supportive teacher, regular and extensive reviews of the material, devoting time to direct instruction, expressions of positive affect, and a demand that the students work at the task is the key. DISCUSSION Before discussing the results and implications of this study, some cautions need to mentioned. First, the participants in this study were drawn from larger public school programs and as such do not represent the experiences of children in smaller programs. Second, no elementary school students were involved; therefore, the generalizability of the results beyond secondary-school-age students is problematic. Third, mainstreaming" needs to be interpreted as "mainstreaming with an interpreter." Consequently, generalizations to other types of mainstreaming should be made carefully.

Three conclusions can be drawn from this study. First, because of the differential selection process for mainstreaming, student background factors are a primary determinant of achievement. Second, mainstreaming with an interpreter has no specific effect on achievement for hearing impaired students. Third, the quality of instruction a hearing impaired child receives is the prime determinant of achievement. Individual student characteristics account for a greater proportion of the variance than placement type; however, they are not the major component in explaining the variance. On the other hand, the quality of the placement experience is a prime determinant of achievement. Mainstreaming is not necessarily an efficacious educational situation because the previously identified positive effect for mainstream placement was not found. In fact, placement contributes very little to accounting for the overall variance.

The quality of the experience is the factor that accounted for the bulk of the variance in achievement, regardless of the relative order in which individual variables were entered into the equation: supportive teacher, regular and extensive reviews of the material, devoting time to direct instruction, expressions of positive affect, and a demand that the students work at the task.

The teacher must be involved with the students about the subject matter. "Individual" instruction as a surrogate for "individualized" instruction is not effective. Effective instruction is a public event. Previous research on mathematics achievement has shown that a 50% time commitment to direct instruction is about the most effective use of time (Evertson et al., 1980). This time allocation permits a lesson structure where the previously taught material is reviewed on a daily basis, usually through a discussion of the homework. A similar finding can be reported from this study.

Because the effective classroom is a public place, public expressions of praise for appropriate responses are important. Two effects could be working here. The first is the obvious effect, that is, that the individual student is rewarded for doing well and is gratified and thus learns more. At the same time other students recognize that there is an emotional reward to appropriate behavior. The second effect is cognitive in that appropriate and positive affect defines what is acceptable intellectually while not denigrating misunderstandings.

Two effects are also at work in the high level of work demand found in the effective classroom. First, there is no substitute for practice. Like the frequency and length of review variables, quantity of material covered offers more opportunities to establish the concept. Second, high levels of work convey very explicitly the sense that the classroom is a place of business.

The findings of this study indicate that it is the quality of the placement experience that determines academic achievement, not the type of placement. The implication is that content knowledge, teacher experience, and actual classroom practice are the important features of the educational experience. Teaching process characteristics such as being a supportive teacher or taking a more businesslike approach to teaching math are a function of the teacher's training and experience. In actual classroom practice, activities such as maintaining a high level of contact with the content, creating an atmosphere that mathematics is a public activity, and making all students feel that they could be called on at any moment produce higher levels of achievement.

For the school to ensure that hearing impaired children are exposed to these kinds of experiences, there are two options. One is to more carefully select the regular classroom teachers that hearing impaired children will have contact with. The other is to upgrade the quality of the mathematics preparation of the teachers of the hearing impaired.

Closer scrutiny of potential teachers for mainstreaming should include attention to their previous level of mathematics training and their experience in teaching mathematics. Informal yet structured interviews with these individuals could elicit basic information about their classroom practices----particularly their use of time during the lesson. Informal observations over a few separate class periods would reinforce the interview conclusions if attention is paid to the distribution of time. At least half of the class period should be devoted to direct instruction; the teacher should emphasize public presentations of work, such as students doing problems in front of the class; and the teacher should select a variety of students for questions about the work.

Three steps can be taken quickly and relatively inexpensively to upgrade the quality of instruction in self-contained classes. First, subject matter should be departmentalized above the junior high level, at least. In other words, some teacher should be designated as the "math person." if the program is large enough to require several persons to teach math, the formation of a "mini-math" department is an excellent option. Second, the individual or individuals designated as math teachers should pursue additional training in mathematics, with the emphasis on content rather than methods of teaching mathematics. Third, additional methodological information should be provided to the mathematics teachers of the hearing impaired. The teachers of the hearing impaired should be "integrated" with the regular mathematics instructors, including attending departmental meetings, attending professional conferences with them, and allowing for mutual planning time. If the mathematics department staff is competent, then the teachers of the hearing impaired will be current in the field; and they will acquire access to a large body of practical experience.

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Title Annotation: | study addressing mainstreaming of students including selection process, difference in placement types and quality of educational experience |
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Author: | Kluwin, Thomas N.; Moores, Donald F. |

Publication: | Exceptional Children |

Date: | Jan 1, 1989 |

Words: | 4792 |

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