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 A mere hope, based upon no direct provision, promise, or trust. An expectancy is the possibility of receiving a thing, rather than having a vested interest in it. The term has been applied to situations where an individual hopes and expects to receive something, generally , according to according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. Bandura's (1977a, 1977b, 1986) theory of self-efficacy, when confronted with scenarios in which students displayed learning styles associated with learning disabilities. ********** The curricula promulgated prom·ul·gate tr.v. prom·ul·gat·ed, prom·ul·gat·ing, prom·ul·gates 1. To make known (a decree, for example) by public declaration; announce officially. See Synonyms at announce. 2. in most standards-based reform documents, as guided by NCTM NCTM National Council of Teachers of Mathematics NCTM Nationally Certified Teacher of Music NCTM North Carolina Transportation Museum NCTM National Capital Trolley Museum NCTM Nationally Certified in Therapeutic Massage 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 per·tain intr.v. per·tained, per·tain·ing, per·tains 1. To have reference; relate: evidence that pertains to the accident. 2. 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 mer·cer n. Chiefly British A dealer in textiles, especially silks. [Middle English, from Old French mercier, trader, from merz, merchandise, from Latin merx , 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 United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. (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 ap·a·thet·ic adj. Lacking interest or concern; indifferent. ap  a·thet 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 ex·pend tr.v. ex·pend·ed, ex·pend·ing, ex·pends 1. To lay out; spend: expending tax revenues on government operations. See Synonyms at spend. 2. (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 rep·li·cate v. 1. To duplicate, copy, reproduce, or repeat. 2. To reproduce or make an exact copy or copies of genetic material, a cell, or an organism. n. A repetition of an experiment or a procedure. 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 me·di·ate v. me·di·at·ed, me·di·at·ing, me·di·ates v.tr. 1. To resolve or settle (differences) by working with all the conflicting parties: 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 elementary school: see school. 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 The attributes of people in a particular geographic area. Used for marketing purposes, population, ethnic origins, religion, spoken language, income and age range are examples of demographic data. 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 Vignette A symbol or pictorial representation of the corporation on a stock certificate. Usually a complicated and artistic design, it is meant to make the counterfeiting of stock certificates as difficult as possible. , the hypothetical Hypothetical is an adjective, meaning of or pertaining to a hypothesis. See:
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 coefficient /co·ef·fi·cient/ (ko?ah-fish´int) 1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities. 2. 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 seat·work n. Lessons assigned to be done by students at their desks in the classroom. ; (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 In statistics, the average amount a number varies from the average number in a series of numbers. (statistics) standard deviation - (SD) A measure of the range of values in a set of numbers. 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 cohen or kohen (Hebrew: “priest”) Jewish priest descended from Zadok (a descendant of Aaron), priest at the First Temple of Jerusalem. The biblical priesthood was hereditary and male. , 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 char·ac·ter·ize tr.v. character·ized, character·iz·ing, character·iz·es 1. To describe the qualities or peculiarities of: characterized the warden as ruthless. 2. 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 mit·i·gate v. mit·i·gat·ed, mit·i·gat·ing, mit·i·gates v.tr. To moderate (a quality or condition) in force or intensity; alleviate. See Synonyms at relieve. v.intr. To become milder. 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 A closed-ended question is a form of question, which normally can be answered with a simple "yes/no" dichotomous question, a specific simple piece of information, or a selection from multiple choices (multiple-choice question), if one excludes such non-answer responses as dodging a asking respondents In the context of marketing research, a representative sample drawn from a larger population of people from whom information is collected and used to develop or confirm marketing strategy. to provide a reason for each of their responses to students' self-regulatory styles. However, the responses of this cohort cohort /co·hort/ (ko´hort) 1. in epidemiology, a group of individuals sharing a common characteristic and observed over time in the group. 2. 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 guidelines, n.pl a set of standards, criteria, or specifications to be used or followed in the performance of certain tasks. 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 The American Educational Research Association, or AERA, was founded in 1916 as a professional organization representing educational researchers in the United States and around the world. , New York New York, state, United States New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of , N.Y. Bandura ban`dur´a n. 1. A traditional Ukrainian stringed musical instrument shaped like a lute, having many strings. , 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 Social Cognitive Theory utilized both in Psychology and Communications posits that portions of an individual's knowledge acquisition can be directly related to observing others within the context of social interactions, experiences, and outside media influences. . Englewood Cliffs, NJ: Prentice Hall Prentice Hall is a leading educational publisher. It is an imprint of Pearson Education, Inc., based in Upper Saddle River, New Jersey, USA. Prentice Hall publishes print and digital content for the 6-12 and higher education market. History In 1913, law professor Dr. . Cohen, J. (1988). Statistical power analysis for the behavioral sciences behavioral sciences, n.pl those sciences devoted to the study of human and animal behavior. (2nd ed.). New York: John Wiley John Wiley may refer to:
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 See validate. validation - The stage in the software life-cycle at the end of the development process where software is evaluated to ensure that it complies with the requirements. . Journal of Educational Psychology, 76(4), 569-582. Hofmeister, A. M. (1993). Elitism e·lit·ism or é·lit·ism n. 1. The belief that certain persons or members of certain classes or groups deserve favored treatment by virtue of their perceived superiority, as in intellect, social status, or financial resources. and reform in special education. Remedial REMEDIAL. That which affords a remedy; as, a remedial statute, or one which is made to supply some defects or abridge some superfluities of the common law. 1 131. Com. 86. The term remedial statute is also applied to those acts which give a new remedy. Esp. Pen. Act. 1. 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 Gordian knot: see Gordius. . In M.C. Pugach & C.L. Warger (Eds), Curriculum trends, special education, and reform refocusing Noun 1. refocusing - focusing again focalisation, focalization, focusing - the act of bringing into focus 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 The National Council of Teachers of Mathematics (NCTM) was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally. . (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 Principles and Standards for School Mathematics was a document produced by the National Council of Teachers of Mathematics [1] in 2000 to set forth a national vision for precollege mathematics education in the US and Canada. : Discussion draft. Reston, VA: Author. Onwuegbuzie, A.J., & Daniel, L.G. (in press-a). Typology typology /ty·pol·o·gy/ (ti-pol´ah-je) the study of types; the science of classifying, as bacteria according to type. typology the study of types; the science of classifying, as bacteria according to type. 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 Correlation Coefficient A measure that determines the degree to which two variable's movements are associated. The correlation coefficient is calculated as: . 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  Some statements may be disputed, incorrect, , biased or otherwise objectionable. 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 See also
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