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Assessing standards-based curricula for students with learning disabilities.

Abstract

The present investigation sought to assess the extent to which elementary teachers' self-efficacy beliefs translate into instructional decisions for students with learning disabilities in the context of standards-based mathematics curricula. Findings indicate that, uniformly, teachers reported relatively low personal efficacy and outcome expectancy, according to Bandura's (1977a, 1977b, 1986) theory of self-efficacy, when confronted with scenarios in which students displayed learning styles associated with learning disabilities.

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The curricula promulgated in most standards-based reform documents, as guided by NCTM recommendations (NCTM, 1989, 1991, 1995, 1998), are designed to benefit the mathematical learning of "all" students (NCTM, 1998), and it is assumed in most instances to include students with disabilities (McDonnell, McLaughlin, & Morison, 1997). However, a number of educators have expressed concern pertaining to the degree that access to standards-based mathematics curricula translates to meaningful participation for this particular group of students (e.g., Hofmeister, 1993; Jones, Wilson, & Bhojwani, 1997; Kameenui, Chard, & Carnine, 1996; Mercer, Harris, & Miller, 1993; Miller & Mercer, 1997; Rivera, 1993, 1997). Approximately, 80% of the hours spent by students with disabilities is in general education settings (U.S. Department of Education, 1997). In recent years, there has been widespread implementation of standards-based mathematics curricula into practice, with many students with disabilities receiving standards-based instruction in general education classrooms (McDonnell et al., 1997). Therefore, it is surprising that there has been limited empirical evidence validating the instructional efficacy of standards-based curricula for this group of students, who represent approximately 10% of school-age students attending schools in the United States (McDonnell et al., 1997).

Bandura's (1977a, 1977b, 1986) theory of self-efficacy underscores the importance of teachers' self-efficacy beliefs in effectively influencing instruction as a response to apathetic student behaviors. Indeed, teachers' self-efficacy beliefs have been operationalized as (a) level of confidence (i.e., teacher personal efficacy); (b) the amount of instructional effort they were likely to expend (i.e., outcome expectancy); and (c) the degree of teacher's self motivation to influence successfully student learning (i.e., outcome expectancy) (Ashton & Webb, 1982; Gibson & Dembo, 1984). The accumulated research assessing the degree that teachers' self-efficacy beliefs are impacted by students' achievement and behavioral characteristics indicates that, although teachers are positive concerning their willingness to accommodate diverse learning styles, they are less positive concerning their efficacy in realistically implementing what they perceive to be a challenging endeavor in practice (Schumm & Vaughn, 1991; Scott, Vitale, & Masten, 1998). In the context of NCTM (1989) recommended practices, Collins and Gerber (2001), utilizing a survey instrument developed specifically for their investigation, assessed the degree to which teachers' self-efficacy is influenced by student self-regulatory styles (i.e., poor strategy use and poor motivation) associated with learning disabilities (LD). Teachers' responses revealed relatively low self-efficacy when confronted with vignettes in which students exhibited self-regulatory styles associated with LD.

The present study sought to replicate the research conducted by Collins and Gerber (2001). Specifically, the purpose of the current investigation was to examine empirical data concerning the extent that teachers' self-efficacy beliefs, operationalized as levels of personal efficacy and outcome expectancy (Bandura's 1977a, 1977b, 1986), are mediated by students' self-regulatory styles (i.e., poor strategy use vs. poor motivation vs. efficient motivation/strategy use). As a measure of classroom practice, also assessed was the degree to which teachers' perception of the effectiveness and practicality of grouping strategies is influenced by students' self-regulatory styles. It was hypothesized that self-regulatory styles associated with LD in the context of mathematics might lead teachers to modify even strongly held beliefs about learning and instruction that underlie NCTM recommendations.

Method

Participants. The two elementary schools agreeing to participate in this research project were located in a county in New Jersey. Nine teachers who taught mathematics returned the survey. Seven teachers taught in one school and the remaining two teachers taught in the other school. Appendix A contains the demographics for the sample of teachers participating in this study.

Instrumentation. The revised Teachers' Assessment of Mathematics Instruction (TAMI-R-NJ) questionnaire utilized nine vignettes to measure teachers' belief systems with respect to different student self-regulatory styles. The nine vignettes represented three sets of learning behaviors (each set typified by three vignettes). In each vignette, the hypothetical students were engaged in mathematical problem-solving activities. In each set of vignettes, students demonstrated characteristics defined as poor strategy use or poor motivation or baseline characteristics that exemplified efficient motivation and strategy use. Appendix B presents these nine vignettes.

Teachers' beliefs were measured by asking teachers to read each vignette and to indicate (a) their level of confidence that they felt the hypothetical students would reach their instructional objectives (i.e., teacher personal efficacy); (b) the amount of instructional effort they were likely to expend (i.e., outcome expectancy); and (c) the extent to which they believed that the hypothetical students would reach grade level expectation (i.e., outcome expectancy). Additionally, as a measure of support available within the school environment, teachers were asked to report the level of instructional support that they would expect to receive when teaching the hypothetical students. Responses to these four indicators were made on a 7-point Likert-type scale, ranging from "very low" to "very high." For the current inquiry, Cronbach's coefficient alphas ranged from .48 to .91 for responses to this component of the questionnaire.

In the remaining components of the TAMI-R-NJ, teachers were asked to indicate the degree to which they believed that seven grouping strategies, involving various classroom practices, represented (a) an effective instructional response and (b) a practical response to each of the three sets of vignettes. Selection of grouping strategies was (a) small group activity involving students of varied ability levels; (b) one-on-one with classmate; (c) one-on-one with teacher or aide; (d) strategy instruction; (e) independent seatwork; (f) intact/whole class instruction; and (g) small group activity involving students of similar ability levels. Responses to the seven instructional strategies were measured using a Likert-type scale ranging from 1 (not very effective) to 7 (very effective). In response to the practical response, the Likert-type scale ranged from 1 (not very practical) to 7 (very practical). For the present investigation, Cronbach coefficient alphas ranged from .82 to .98 for responses in this component of the questionnaire components. Table 1 presents the reliability data for the second through the fourth component of the questionnaire. See <http://rapidintellect.com/AEQweb/sum02.htm>

Procedure. The nine participants were administered a packet containing a cover letter that guaranteed confidentiality regarding their responses and explained the purpose and importance of their participation in the investigation. To prompt participation, a lottery slip was included and participants were asked to return the lottery slip with their completed questionnaire to the school secretary. A researcher associated with the project collected the completed questionnaires.

Analysis. Teachers' belief systems with respect to different student self-regulatory styles were based on their responses to three sets of vignettes. These vignettes yielded three composite scores that comprised the sum of teachers' responses to each set of self-regulatory characteristics. Because data were not normally distributed, the statistical analyses utilized the Wilcoxon signed rank test, and the Friedman's two-way analysis of variance test (Marascuilo & McSweeney, 1977).

Results

Table 2 presents the means and standard deviations pertaining to teacher personal efficacy (teacher confidence) and outcome expectancy (teacher effort and expectation regarding student performance) and the level of instructional support expected with respect to the three self-regulatory styles. See issue's website <http://rapidintellect.com/AEQweb/sum02.htm>

Teachers reported statistically significantly lower levels of confidence in response to vignettes describing students exhibiting poor strategy use and poor motivation, in contrast to vignettes describing students exhibiting baseline learning styles. Utilizing a Bonferroni-adjusted alpha (p < .0167) as a criterion for statistical significance (Onwuegbuzie & Daniel, in press-a, in press-b), there was not a statistically significant difference between responses to poor strategy use and poor motivation self-regulatory styles. In contrast, teachers reported statistically significantly higher levels of extended effort in response to vignettes describing students exhibiting poor strategy use and poor motivation, compared to baseline learning styles. Interestingly, a statistically significant difference was found between poor strategy use and poor motivation self-regulatory styles. Specifically, teachers reported statistically significantly higher levels of extended effort in response to vignettes describing students exhibiting poor motivation, than they did in response to vignettes describing students exhibiting poor strategy use. The effect size associated with this difference was 1.11, which was very large (Cohen, 1988). Further, teachers reported statistically significantly lower levels of expectation in response to vignettes describing students exhibiting poor strategy use and poor motivation, in contrast to baseline learning styles. Moreover, a statistically significant difference was found between poor strategy use and poor motivation self-regulatory styles. Specifically, teachers reported statistically significantly lower levels of expectation in response to vignettes describing students exhibiting poor motivation in contrast to vignettes describing students exhibiting poor strategy use. The associated effect size of 0.46 was moderate.

Finally, teachers reported statistically significantly higher levels of instructional support in response to vignettes describing students exhibiting poor strategy use and poor motivation, in contrast to baseline learning styles. Utilizing an Bonferroni-adjusted alpha (p < .0167) as a criterion for statistical significance, there was not a statistically significant difference between poor strategy use and poor motivation self-regulatory styles. Table 3 presents the z scores and effect sizes pertaining to teacher personal efficacy (teacher confidence) and outcome expectancy (teacher effort and expectation regarding student performance) and the level of instructional support expected with respect to the three self-regulatory styles. See issue's website <http://rapidintellect.com/AEQweb/sum02.htm>

Friedman's nonparametric matched-sample test (Marascuilo & McSweeney, 1977) indicated a statistically significant difference in teachers' ratings of the seven grouping strategies in response to both poor strategy use and poor motivation. (All effect sizes were very large.) In contrast, teachers' ratings of grouping strategies did not differ statistically significantly in response to self-regulatory style associated with efficient motivation/strategy use (i.e., baseline self-regulatory style). Interestingly, Friedman's nonparametric matched sample test indicated a statistically significant difference in teachers' ratings of the seven grouping strategies in response to self-regulatory style associated with efficient motivation/strategy use only. In contrast, no statistically significant difference in teachers' ratings of grouping strategies was noted with respect to poor strategy use and poor motivation self-regulatory styles. Table 4 presents the chi-square statistics and Cramer's V statistics (i.e., [] W/n) that were utilized as measures of effect size. See issue's website <http://rapidintellect.com/AEQweb/sum02.htm>

Discussion

This study investigated the degree to which teacher personal efficacy and outcome expectancy is mediated by self-regulatory styles (i.e., poor strategy use vs. poor motivation vs. efficient motivation/strategy use) of students. Results indicated that teachers expressed less confidence in their efficacy (i.e., personal efficacy) at addressing students with poor motivation and poor strategy use in contrast to baseline students. In addition, teachers perceived that they would have to expend a higher degree of instructional effort (i.e., outcome expectancy) in order for students with poor motivation to reach grade level expectation in mathematics. Similarly, teachers had lower expectations of student performance (i.e., outcome expectancy) for learning styles characterized as poor strategy use and poor motivation in contrast to baseline learning styles.

These preceding findings support the conclusions of Collins and Gerber (2001) regarding teachers' efficacy beliefs in addressing diversity of student learning in practice. Results of both studies indicate consistently that teachers report relatively low personal efficacy and outcome expectancy when confronted with scenarios in which students exhibited learning styles associated with LD (i.e., poor strategy use and poor motivation). This present inquiry also examined the degree to which teachers' perceptions of the effectiveness and practicality of grouping strategies, as a measure of classroom practice, is influenced by students' self-regulatory styles. Teachers' responses indicated that self-regulatory learning styles is a mitigating variable influencing their perceptions regarding effectiveness of instructional strategies, specifically related to grouping strategies. However, results also indicated that despite the apparent difference in teachers' beliefs regarding the effectiveness and practicality of the reform recommendations and reported lower levels of personal efficacy and outcome expectancy for students who exhibit learning styles associated with LD, teachers do not pragmatically recognize students' self-regulatory learning styles and respond by adapting grouping strategies. A question that arises based on this result is why did teachers recognize baseline learning styles in practically adapting grouping strategies, yet, they did not adapt grouping strategies in response to students' self-regulatory styles? Future research should include open-ended questions asking respondents to provide a reason for each of their responses to students' self-regulatory styles.

However, the responses of this cohort of teachers is identical to that of the control group in the earlier study (i.e., Collins & Gerber, 2001) who did not participate in the inservice training. This current finding highlights the importance of addressing teachers' levels of self-efficacy beliefs by providing explicit guidelines about "how" teachers may implement instructional techniques aligned to reform recommendations and concurrently accommodate student diversity in classroom instruction. Thus, replications of the present study are needed utilizing mixed methodological techniques, larger samples of teachers, and open-ended questions asking respondents to provide a reason for each of their responses to students' self-regulatory styles.

References

Ashton, P.T., & Webb, R.B. (1982, March). Teachers' sense of efficacy: Toward an ecological model. Paper presented at the annual meeting of the American Educational Research Association, New York, N.Y.

Bandura, A. (1977a). Social learning theory. Englewood Cliffs, NJ: Prentice-Hall.

Bandura, A. (1977b). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84, 191-215.

Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs, NJ: Prentice Hall.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New York: John Wiley.

Collins, K.M.T., & Gerber, M.M. (2001). Teachers' beliefs about mathematics reform: Instructional implications for students with learning disabilities. Research in the Schools, 8(2), 59-70.

Gibson, S., & Dembo, M.H. (1984). Teacher efficacy: A construct validation. Journal of Educational Psychology, 76(4), 569-582.

Hofmeister, A. M. (1993). Elitism and reform in special education. Remedial and Special Education, 14(6), 8-13.

Jones, E.D. Wilson, R., & Bhojwani. S. (1997). Mathematics instruction for secondary students with learning disabilities. Journal of Learning Disabilities, 30(2), 151-163.

Kameenui, E. J., Chard, D.J., & Carnine, D.W. (1996). Response: The new school mathematics and the age-old dilemma of diversity: Cutting or untying the gordian knot. In M.C. Pugach & C.L. Warger (Eds), Curriculum trends, special education, and reform refocusing the conversation (pp. 68-83). New York, NY: Teachers College Press.

Marascuilo, L. A., & McSweeney, M. (1977). Nonparametric and distribution-free methods for the social sciences. Monterey, CA: Brooks/Cole.

McDonnell, L.M., McLaughlin, M.J. & Morison, P. (1997). Educating one and all: Students with disabilities and standards-based reform. Washington, DC: National Academy Press.

Mercer, C. D., Harris, C. A., & Miller, S. P.(1993). First invited response: Reforming reforms in mathematics. Remedial and Special Education, 14(6), 14-19.

Miller, S., & Mercer, C.D. (1997). Educational aspects of mathematics disabilities. Journal of Learning Disabilities, 30(1), 47-56..

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (1995). Assessment standards for teaching mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (1998). Principles and standards for school mathematics: Discussion draft. Reston, VA: Author.

Onwuegbuzie, A.J., & Daniel, L.G. (in press-a). Typology of analytical and interpretational errors in quantitative and qualitative educational research. Current Issues in Education.

Onwuegbuzie, A.J., & Daniel, L.G. (in press-b). Uses and misuses of the correlation coefficient. Research in the Schools.

Rivera, D. M. (1993). Third invited response: Examining mathematics reform and the implications for students with mathematical disabilities. Remedial and Special Education, 14(6), 24-27.

Rivera, D.M. (1997). Mathematics education and students with learning disabilities: Introduction to the special series. Journal of Learning Disabilities, 30 (1), 2-19.

Schumn, J.S., & Vaughn, S. (1991). Making adaptations for mainstreamed students: Regular classroom teachers' perspectives. Remedial and Special Education, 12(4), 18-27.

Scott, B. J., Vitale, R., & Masten, W.G. (Mar/Apr. 1998). Implementing instructional adaptations for students with disabilities in inclusive classrooms: A literature review. Remedial and Special Education, 19(2), 106-19.

U. S. Department of Education. (1997). Nineteenth annual report to Congress on the implementation of the Individuals with Disabilities Education Act. Washington, DC.

Kathleen M. T. Collins is an Assistant Professor and Anthony J. Onwuegbuzie is an Associate Professor. Address correspondence regarding this article to Kathleen M. T. Collins, Saint Mary's University of Minnesota, 2500 Park Ave. Minneapolis, MN 55404.
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Author:Onwuegbuzie, Anthony J.
Publication:Academic Exchange Quarterly
Geographic Code:1USA
Date:Jun 22, 2002
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