This article was downloaded by: [University of Cambridge]On: 08 October 2014, At: 04:49Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T3JH, UK

Journal of Educational andPsychological ConsultationPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/hepc20

Teachers' Preferences forAcademic InterventionStrategies in Mathematics:Implications for InstructionalConsultationPaul B. de Mesquita & Alan ZollmanPublished online: 08 Jun 2010.

To cite this article: Paul B. de Mesquita & Alan Zollman (1995) Teachers'Preferences for Academic Intervention Strategies in Mathematics: Implications forInstructional Consultation, Journal of Educational and Psychological Consultation,6:2, 159-174, DOI: 10.1207/s1532768xjepc0602_5

To link to this article: http://dx.doi.org/10.1207/s1532768xjepc0602_5

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of allthe information (the “Content”) contained in the publications on ourplatform. However, Taylor & Francis, our agents, and our licensorsmake no representations or warranties whatsoever as to the accuracy,completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views ofthe authors, and are not the views of or endorsed by Taylor & Francis.The accuracy of the Content should not be relied upon and should beindependently verified with primary sources of information. Taylor andFrancis shall not be liable for any losses, actions, claims, proceedings,demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, inrelation to or arising out of the use of the Content.

This article may be used for research, teaching, and private studypurposes. Any substantial or systematic reproduction, redistribution,reselling, loan, sub-licensing, systematic supply, or distribution in any formto anyone is expressly forbidden. Terms & Conditions of access and usecan be found at http://www.tandfonline.com/page/terms-and-conditions

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

JOURNAL OF EDUCATIONAL AND PSYCHOLOGICAL CONSULTATION, 6(2), 159-174 Copyright 8 1995, Lawrence Erlbaum Associates, Inc.

Teachers' Preferences for Academic Intervention Strategies in

Mathematics: Implications for Instructional Consultation

Paul B. de Mesquita and Alan Zollman University of Kentucky

Primary school teachers were surveyed to investigate their preferences for three approaches to academic intervention when assisting students expe- riencing difficulty in mathematics. Sixty-two primary school teachers were presented with descriptions of two students experiencing difficulty on either a basic subtraction skills problem or an application skills problem involving money, For each problem, teachers rated their preferences for three instructional intervention approaches (cognitive, behavioral, and cooperative learning) as recommended by a school consultant. Results indicated significant differences between the more preferred cognitive and cooperative-learning approaches and the less preferred behavioral ap- proach, regardless of the problem type. Recognizing teacher preferences can enhance con~ultative compatibility between consultants and teachers and facilitate collaborative problem solving, particularly when developing academic interventions. Implications for instructional consultation with teachers are discrrssed.

Consultants previously focused most of their efforts on interventions to improve student misbehavior. Now they are being asked to provide more instructional consultation related to the remediation of academic problems. When academic difficulties underlie classroom discipline problems, instructional consultation approaches may provide the most appropriate solution alternatives. Instructional consultation has much in common with behavioral, mental health, and organizational consulta-

Requests for reprin& should be sent to Paul B. de Mesquita, University of Kentucky, 245 Dickey Hall-EDP, Lexington, KY 40506-0017.

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

tion models. One shared characteristic of consultation-collaborative problem solving-is a particularly important ingredient for successful instructional consultation, especially given the instructional expertise of the teacher and the academic nature of the problems (Rosenfield, 1987).

Collaborative problem solving requires a certain degree of consultative compatibility concerning both the content and process of academic intervention (Idol, 1990). In the case of instructional consultation, consultative compatibility means that enough common ground must be established between teacher and consultant so that the teacher's orien- tation to instruction is acknowledged and supported. Consultative incompatibility occurs when the theoretical perspective or instructional orientation of the teacher-consultee differs from that of the consultants. Such incompatibility is a potential barrier to developing a collaborative consultation relationship and reduces the likelihood of a successful outcome for teachers and their students.

When assisting with academic problems, consultants soon recognize that teachers' instructional preferences are an important factor influ- encing both the process and outcome of collaborative consultation. Compatibility or agreement between consultant and consultee has been found to be related to the use of and satisfaction with consultation services (Erchul, Hughes, Meyers, Hickman, & Braden, 1992). Further- more, the probability of a successful consultation outcome may increase when the consultant's approach and recommendations match the teach- er's thinking about a problem (Conoley, Conoley, Ivey, & Scheel, 1991; Hughes, 1992; Shavelson & Stern, 1981). However, the important role of the initial preferences of the consultee (e.g., Bardon, 1979; Caplan, 1970; Gallessich, 1974) has frequently been overlooked in the consultation research literature (Babcock & Pryzwansky, 1983). Research on the acceptability of classroom interventions would suggest that instructional consultation might be most effective when consultants set aside their theoretical perspective and acknowledge the attitudes, values, and instructional preferences of teachers (e.g., Witt & Elliott, 1985). Al- though teachers' acceptance of behavioral interventions has been inves- tigated, research about teachers' views toward various academic inter- ventions strategies recommended during consultation is lacking (Ringer, Doerr, Hollenshead, & Willis, 1989; Rosenfield, 1987).

PREVIOUS RESEARCH

Much of the literature on classroom interventions has examined the use of behavioral approaches designed to improve student conduct by either reducing the frequency of undesirable behavior or increasing the fre-

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

MATHEMATICS INTERVENTIONS 161

quency of desirable behavior (Kazdin, 1980; Rosenfield, 1987). Similarly, much of the research on consultation has concentrated on behavioral consultation that incorporates the use of behavioral interventions. Although behavioral consultation frequently targets classroom misbe- havior and employs interventions based on principles of contingent reinforcement and punishment, behavioral consultation also can lead to interventions that focus on other important curriculum and instructional variables (Gutkin & Curtis, 1990). A behavioral orientation to consulta- tion, and its accompanying empirical data-based approach to problem solving (Bergan, 1990), may offer a useful framework for developing instructional interventions (Bergan & Schnaps, 1983).

However, before either behavioral or instructional interventions are implemented, teachers must view them not only as effective but also as acceptable (Elliott & Shapiro, 1990). Research related to teacher prefer- ences for interventions has shown that teachers were less resistant, and viewed behavioral interventions as more acceptable, when the interven- tions were considered to be effective, easily implemented, and required little extra time or training (e.g., Witt, 1986; Witt & Elliott, 1985; Witt, Martens, & Elliott, 1984). When asked to compare consultation ap- proaches, teachers preferred behavioral and collaborative models of consultation (Babcock & Pryzwansky, 1983; West & Idol, 1990) over other approaches. Therefore, to maximize the probability that instruc- tional interventions will be implemented successfully, teachers must feel involved and view the intervention as acceptable. For example, consult- ants can collaborate by providing a general intervention strategy and then requesting teachers to provide the specific implementation details of the intervention (Bergan, 1977, 1990).

Numerous studies have been reported on teachers1 views concerning the selection and use of behavioral interventions in the classroom (e.g., Elliott, 1988; Elliott, Witt, & Kratochwill, 1991; Skinner & Hales, 1982). For example, previous investigations examined the theoretical orienta- tion and perceived acceptability of interventions (Hall & Wahrman, 1987), the kinds of information teachers consider useful (Thurlow & Ysseldyke, 1982), the impact of a collaborative or individual intervention development prooess (Kutsick, Gutkin, & Witt, 1991), teacher percep- tions of collaboration with consulting reading specialists during "pull- in" programs (Meyers, Gelzheiser, & Yelich, 1991), and teacher views toward interventions and behavioral consultation (Gutkin & Hickman, 1990; Martens, Peterson, Witt, & Cirone, 1986; Rhoades & Kratochwill, 1992). Overall, these studies share a common concern for recognizing the importance of teachers1 orientations and perceptions as either potential barriers or facilitators of collaborative consultation. However, concerning various academic intervention strategies, more research is

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

162 DE MESQUITA AND ZOLLMAN

needed to understand the perspective of the teacher-consultee (Rosenfield, 1987). More specifically, research has not been reported on teachers' preferences for consultant-recommended instructional strate- gies for remediating academic problems in specific subject domains (reading, math, science, etc.).

FOCUS ON MATHEMATICS INSTRUCTION

Coinciding with the need for more instructional consultation research is a growing need to improve the academic performance of students in mathematics (National Council of Teachers of Mathematics, 1989,1991), including the math skills of mainstreamed children with mild learning disabilities (Cawley & Parmar, 1991). Mastery of basic computational skills and the application of those skills to real-world problems are two common difficulties of students leading teachers to request instructional consultation (Shapiro, 1989). Contingent reinforcement and feedback strategies are used frequently to improve basic skills (Johnston & McLaughlin, 1982; Luiselli & Downing, 1980), whereas strategy training and self-instruction are useful methods for improving not only basic skills and algorithmic procedures but also problem-solving processes (Cullinan, Lloyd, & Epstein, 1981; Fox & Kendall, 1983). However, consultants responsible for assisting teachers in developing academic interventions may have little information regarding teachers' knowledge of and attitudes toward the use of these methods with specific student problems. The purpose of this article, therefore, was to investigate the preferences of teachers for instructional intervention strategies as might be suggested by instructional consultants to improve the performance of students experien4ing specific difficulties in mathematics.

The present stuqy investigated the preferences of primary teachers on three types of recpmmended instructional interventions for assisting students experiencing difficulty with mathematics. It addressed the following questions: Are there differences among teachers' preferences for cognitive, behavioral, and cooperative approaches to consultant- recommended instructional interventions? Does the type of instruc- tional problem (basic skills vs. application) influence teachers1 views about instructional interventions?

METHOD

Participants

The participants were 62 primary school teachers from kindergarten through fourth grade, representing both rural and urban schools from

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

an educational cooperative consisting of 18 member school districts located in the central region of a midwestern state. Participants were recruited from two groups: 41 teachers were enrolled in an advanced graduate course in mathematics instruction and 58 teachers were attending a professional development workshop on developmentally appropriate instructional practices for primary students. Overall, the 62 participants represented 65% of the 95 teachers who were invited to participate. The group of participating teachers comprised all 41 teachers enrolled in the graduate course and 21 of the 58 teachers present at the workshop (39%). Based on years experience, classroom assignments, and instructional interests, the participating teachers appeared to be representative of the larger group of teachers invited to volunteer. In general, the participants were typical of elementary teachers teaching in the primary grades. They were all female, and their years of classroom experience ranged from 2 to 31 years (M = 14.65, SD = 6.95). The sample included only teachers who were responsible for mathematics instruction in the primary grades.

Procedures

Teachers were invited to participate in the study, and they voluntarily completed a survey following either a graduate class or an inservice workshop. The procedures resembled the analog methodology initially reported by Kazdin (1980) and subsequently developed by Witt and colleagues (e.g., Witt, Elliott, & Martens, 1984; Witt & Martens, 1983). This analog approach, combined with intervention rating measures, has been used in a number of treatment acceptability studies and is reported to be a reliable and valid methodology (Elliott & Treuting, 1991; Miltonberger, 1990; Reirners, Wacker, & Koeppl, 1987; Witt & Martens, 1983). In the present study, teachers first read a description of a student experiencing difficulty with a basic skills mathematics problem and then rated the three recommended intervention approaches: cognitive, be- havioral, and cooperative-peer learning. The same procedure was followed for a second problem that described a student experiencing difficulty with solving an application word problem using money (see Appendix for descriptions of problems and interventions). Both the basic skills and application problems were described as persistent and unresponsive to standard classroom instruction. To control the potential influence of racial or gender biases (Leder, 1992; Secada, 1992) on the teachers' responses, the problem descriptions mentioned only students' initials rather than names.

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

TABLE 1 Instructional Intervention Survey Items

1. I consider this an acceptable intervention strategy for this child's math problem. 2. This is an effective intervention strategy for solving this child's math problem. 3. I would use this instructional intervention strategy in my classroom. 4. The intervention strategy is impractical and requires too much time to implement. 5. The intervention strategy requires too much technical skill or training for me to use. 6. The intervention strategy would be difficult to implement and still assist other

children in my classroo& with their math lessons:

Survey

Teacher preferences were measured using survey items adapted from the Intervention Rating Profile (IRP) used in previous research investi- gating treatment acceptability of behavioral interventions (Martens, Witt, Elliott, & Darveaux, 1985; Witt & Martens, 1983). Reliability of the IRP has been reported as r = .91 for internal consistency using Cronbach's alpha (Witt & Martens, 1983). Because the IRP was designed to determine the acceptability of behavioral treatments for behavior problems, the original measure was considered less applicable for judging the preferences of teachers for academic interventions, The survey employed in this study consisted of six items representing factors considered to influence the acceptability of classroom interventions as measured by the IRP: overall acceptance, effectiveness, willingness to use, practicality, training required, and difficulty of implementation. The six items were rated on a 6-point Likert scale, ranging from 3 (strongly agree) to - 3 (strongly disagree). To discourage a response set bias, three of the items were worded positively and three were worded negatively. Because three of the six items were stated negatively, their scale scores were reverse scored for purposes of statistical analysis. The six items are listed in Table 1.

RESULTS

To determine teachers' overall preferences, responses for each of the six items were summed for each of the three intervention approaches on each problem. This resulted in six total scores, representing all possible combinations of problem and intervention types. Positive or negative sums indicated positive or negative preferences. Means and standard deviations for total scores presented for each of the three interventions and the two problem types are found in Table 2. None of the mean total ratings were negative, suggesting that teachers generally felt positive

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

MATHEMATICS INTERVENTIONS 165

TABLE 2 Means and Standard Deviations for Teachers' Ratings by Problem and Intervention Types

Problem

Cognitive Behavioral Cooperative

M SD M SD M SD

Basic skills 1. Acceptance 2.29 0.78 0.18 1.92 1.80 0.93 2. Effectiveness 2.05 0.97 -0.29 1.79 1.66 1.06 3. Willingness to use 1.95 1.06 -0.08 1.88 1.77 1.07 4. Impractical 1.59 1.36 1.27 1.57 2.03 0.82 5. Requires training 2.23 0.86 2.02 1.03 1.92 1.22 6. Difficult 1.46 1.48 1.05 1.80 1.98 1.01 7. Total 11.56 5.13 4.16 7.58 11.20 4.25

Application 1. Acceptance 2.46 0.92 -0.31 1.94 1.87 0.94 2. Effectiveness 2.42 0.92 -0.48 1.95 1.62 1.16 3.Willingnesstouse 2.33 0.94 -0.49 1.89 1.82 1.07 4. Impractical 1.87 1.27 1.34 1.47 1.93 0.85 5. Requires training 2.18 0.92 1.87 1.02 2.00 1.02 6. Difficult 1.92 1.23 1.23 1.63 1.95 1.04 7. Total 13.16 4.62 3.16 7.20 11.20 4.48

about all three of the recommended intervention approaches. However, they were considerably more positive about the cognitive and cooperative-peer approaches than about the behavioral approach.

An examination of the means for each of the individual items shows that cognitive and cooperative-peer intervention approaches were con- sistently rated as more positive than the behavioral approach on five of the six items: acceptance, effectiveness with specific problem, willing- ness to use, impractical, and difficult to individualize. However, the similarities across all three intervention types on Item 5 suggest that, regardless of the problem type, teachers shared similar positive views of their technical skill and saw little need for additional training to implement any of these intervention approaches.

To test for possible differences between the teachers enrolled in the graduate mathematics education course and the teachers attending the professional development inservice workshop, univariate analyses of variance (ANOVAs) were conducted for each of the six total scores. Results produced F(1, 59) values ranging from .13 to .77, ns. Therefore, the remaining analyses are reported for one group consisting of the total sample of teachers.

Hypotheses of mean differences were tested using a 3 (cognitive vs. behavioral vs. cooperative interventions) x 2 (basic vs. application problems) ANOVA with repeated measures on both problem type and intervention type. Results showed that there was no sigruficant main

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

166 DE MESQUrrA AND ZOLLMAN

TABLE 3 Mean Differences for Painvise Comparisons Between Total Ratings for All

Combinations of Problems and Interventions - --

Mean Differences

Problem i- Intervention M I 2 3 4 5 6

1. Application + Behavioral 3.16 0.00 1.00 8.04* 8.04* 8.40* 10.00* 2. Basic + Behavioral 4.16 0.00 7.04* 7.04* 7.40* 9.00* 3. Basic + Cooperative 11.20 0.00 0.00 0.36 1.96 4. Application + Cooperative 11.20 0.00 0.36 1.96 5. Basic + Cognitive 11.56 0.00 1.60 6. Application + Cognitive 13.16 0.00

Note. Tukey honesty significant difference = 3.07. * p < .01.

effect for problem type, F(1, 58) = .40, p < 33. However, significant effects were present for intervention type, F(2, 116) = 62.60, p < .0001, and for the Problem x Intervention interaction, F(2, 116) = 4.51, p < .01.

To determine which of the mean differences were significant, pairwise comparisons of the means of the six possible Problem x Intervention combinations were made according to Tukey's (1949) Honestly Signifi- cant Difference (HSD) method. As suggested by the discrepancies between mean scores, the cognitive and cooperative-peer learning approaches were rated significantly more positively than the behavioral approaches for both types of problems (Tukey HSD = 3.07, p < .01). Table 3 presents the mean differences for all pairwise comparisons.

Although the teachers generally agreed most strongly with the cognitive interventions, no significant differences were noted between the cognitive and cooperative-peer learning approaches. Cognitive and cooperative-peer learning strategies were preferred similarly over be- havioral approaches to instruction, regardless of the problem.

DISCUSSION

Overall, the results indicated that cognitive, behavioral, and coopera- tive-peer intervention approaches were viewed positively. Teacher preferences for the intervention approaches were consistent regardless of whether the instructional problem involved basic mathematics skills or applied problem solving using money. However, cognitive learning strategies employed to teach students how to solve application problems received the highest ratings. Generally, cognitive learning strategies and

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

cooperative-peer strategies were rated similarly. Although viewed pos- itively, behavioral approaches to instructional interventions were rated lowest and preferred least.

Examination of the teacher responses on individual items provides some insight into their views on specific aspects of the interventions. Teachers found the recommended cognitive and cooperative-peer learning strategies to be more acceptable, more effective, and more time-efficient than the recommended behavioral strategies. Teachers also indicated they would be more willing to use these two approaches over the recommended reinforcement-only behavioral approach. Fur- thermore, teachers agreed that behavioral approaches would take more time to implement. They also felt that behavioral approaches would be difficult to implement and still assist the other children in the classroom. Interestingly, the similarity among ratings on the technical skill or additional training item suggested that teachers are confident in their ability to implement any of the three intervention strategies.

There are two possible explanations for the lower preference for behavioral approaches to academic intervention. First, previous re- search on the treatment acceptability of interventions used with class- room behavior problems has suggested that, despite the effectiveness of certain interventions, teachers may hold negative attitudes toward behaviorally described methods, may view behavioral approaches as less acceptable, or may be unfamiliar with behavioral principles (Abidin, 1975; Axelrod, Moyer, & Berry, 1990; Elliott & Shapiro, 1990; Skinner & Hales, 1992; Witt & Elliott, 1985; Witt, Moe, Gutkin, & Andrews, 1984; Woolfolk, Woolfolk, & Wilson, 1977). Second, teachers' responses may have been influenced by recent educational reform trends that empha- size cooperative and cognitive learning methods.

Limitations and Future Research

Results of this survey must be interpreted cautiously due to limitations in the sample and design. Additional research with larger samples is needed in which randomly selected teachers can be randomly assigned to groups represeriting combinations of problem type and instructional intervention. More research is needed on the relation between teachers' preferences for instructional interventions and their actual classroom practices within the context of school consultation. Furthermore, be- cause each approach included several strategies or instructional tech- niques, this study did not determine the specific methods within each approach that teachers found more or less acceptable. In addition, the three sets of intervention strategies were presented in the same order to all participants, possibly creating an order effect. Presenting the strate-

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

gies in a counterbalanced manner would overcome this limitation in future studies. Moreover, rather than using only one method at the exclusion of all others, as was presented in the intervention descrip- tions, teachers might use a wider variety of instructional intervention approaches, or some combination of the three approaches under actual classroom conditions.

Because this study focused on math problems, research is needed to assess teacher views concerning instructional interventions in other subject areas such as reading, language arts, science, and social studies. Future research also could investigate the instructional approach of teachers when solving the academic problems of children of different genders and ethnicity. In turn, children's preferences for various approaches to instructional interventions might better inform both teachers and school consultants when developing intervention plans. Finally, although previous research has addressed teachers' views toward behavioral treatments, reliable and valid means are needed for assessing their acceptance of academic instructional interventions.

Implications for Instructional Consultation

When consulting with teachers about instructional problems, particu- larly in mathematics, there are several implications for school consult- ants that are consistent with previous research. First, before allowing a theoretical orientation to limit the range of intervention possibilities, consultants should consider the values and attitudes of the teachers with whom they consult mitt & Elliott, 1985). During the entry stages of consultation, consultants should also take into account teachers' expectations and preferences for various models of consultation (Babcock & Pryzwansky, 1983).

Second, along with respecting teachers' theoretical perspectives and preferences for consultation, consultants should assess teachers' views toward specific instructional approaches, particularly when the focus of consultation is an academic problem. Teachers' perceptions of the amount of technical skill and training needed for implementing recom- mended academic interventions appears to be another important factor deserving careful consideration. Although these teachers felt equally skilled in using any of the three recommended approaches, feelings of competence for less experienced teacher-consultees may depend on the approach advocated by the consultant and their nature of their experi- ence. For example, less experienced teachers might be more knowledge- able about newer approaches to instruction and feel they need less technical training. In contrast, more experienced teachers, who may be

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

less knowledgeable of current instructional research, may feel they require more training and technical guidance.

Consultants should guard against teachers1 passive acceptance of recommended strategies and their subsequent failure to implement an agreed-upon intervention. Teachers may view all recommended inter- vention approaches positively, simply because of the "expert" status bestowed upon a consultant (French & Raven, 1959; Martin, 1978). In this case, teachers who relinquish their collaborative role, and who may seem cooperative and agreeable during the initial stages of consultation, may become less willing to follow through with intervention plans that were not developed collaboratively.

Finally, the results of this survey may remind consulting school psychologists of the importance of consultation as an interpersonal process (Hughes, 1992). Ultimately, the effectiveness of the consultant's strategy is enhanced by important interpersonal factors that are at the heart of the consultation process (Meyers, Parsons, & Martin, 1979). Each consultation problem involves a teacher with unique views toward the various possible interventions. Therefore, finding a unique solution requires recognition of the teacher's perceptions and incorporation of the recommended intervention strategy into the teacher's way of thinking (Medway, 1989).

With the increasing emphasis on educational reform and mathematics education (National Research Council, 1989), teachers may rely more often on school psychologists for instructional consultation and assis- tance with academic problems in the classroom (McKellar, 1983; McKellar & Hartshorne, 1986). Within this context, effective consultants will be those who recognize the importance of assessing the instruc- tional preferences of teachers and who achieve a level of consultative compatibility that facilitates a collaborative consultation process.

REFERENCES

Abidin, Jr., R. R. (1975). Negative effects of behavioral consultation: "I know I ought to, but it hurts too much." Journal of School Psychology, 13, 51-57.

Axelrod, S., Moyer, L., & Berry, B. (1990). Why teachers do not use behavioral modification procedures. Journal of Educational and Psychol~'ca1 Consultation, 1,309-320.

Babcock, N . L., & Pryzwansky, W. B. (1983). Models of consultation: Preferences of educational professional at five stages of service. Journal of School Psychology, 21, 359-366.

Bardon, J. (1979). The consultee in consultation: Preparation and training. HAVAT Da'AT [Israeli Journal of Psychology and Counseling in Education], 10, 5-7.

Bergan, J. R. (1977). Behavioml consultation, Columbus, OH: Merrill. Bergan, J. R. (1990). Contributions of behavioral psychology to school psychology. In T. B.

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

1 70 DE MESQUITA AND ZOLLMAN

Gutkin & C. R. Reynolds (Eds.), The handbmk of school psychology (2nd ed., pp. 126-142). New York: Wiey.

Bergan, J. R., & Schnaps, A. (1983). A model for instructional consultation. In J. Alpert & J. Meyers (Eds.), Training in consultation (pp. 104-119). Springfield, IL: Thomas.

Caplan, G. (1970). The theory and practice of mental health consultation. New York: Basic Books.

Cawley, J. F., & Parmar, R. S. (1991). Maximizing mathematics success in the regular classroom. In G. Stoner, M. R. Shinn, & H. M. Walker (Eds.), Intementions for achievement and behavior problems (pp. 415-438). Silver Spring, MD: National Association of School Psychologists.

Conoley, C. W., Conoley, 1. C., Ivey, D. C., & Scheel, M. J. (1991). Enhancing consultation by matching the consultee's perspective. Journal of Counseling and Development, 69, 546-549.

Cullinan, D., Lloyd, J., & Epstein, M. H. (1981). Strategy training: A structured approach to arithmetic instruction. Exceptional Education Quarterly, 2, 4149.

Elliott, S. N. (1988). Acceptability of behavioral treatments: Review of variables that influence treatment selection. Professional Psychology: Research and Practice, 19, 68-80.

Elliott, S. N., & Shapiro, E. S. (1990). Intervention techniques and programs for academic performance problems. In T. B. Gutkin & C. R. Reynolds (Eds.), The handbook of school psychology (2nd ed., pp. 635-660). New York: Wiley.

Elliott, S. N., & Treuting, M. V. B. (1991). The Behavior Intervention Rating Scale: Development and validation of a pretreatment acceptability and effectiveness measure. Journal of School Psychology, 29, 43-51.

Elliott, S. N., Witt, J. C., & Kratochwill, T. R. (1991). Selecting, implementing, and evaluating classroom interventions. In G. Stone, M. R. Shinn, & H. Walker (Eds.), Intmentions for achieaement and behavior problems (pp. 99-135). Silver Spring, MD: National Association of School Psychologists.

Erchul, W. W., Hughes, J. N., Meyers, J., Hickman, J. A., & Braden, J. P. (1992). Dyadic agreement concerning the consultation process and its relationship to outcome. Journal of Educational and Psychological Consultation, 3, 119-132.

Fox, D. E. C., & Kendall, P. C. (1983). Thinking through academic problems: Applications of cognitive behavior therapy to learning. In T. R. Kratochwill (Ed.), Advances in school psychology (Vol. 3, pp. 269-301). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

French, J. R., & Raven, B. H. (1959). The bases of social power. In D. Cartwright (Ed.), Studies in social power (pp. 150-167). Ann Arbor: University of Michigan Institute of Social Research.

Gallessich, J. (1974). Training the school psychologist for consultation. Journal of School Psychology, 12, 138-149.

Gutkin, T. B., & Curtis, M. J. (1990). School-based consultation: Theory, techniques, and research. In T. B. Gutkin & C. R. Reynolds (Eds.), The handbook of school psychology (pp. 577-611). New York: Wiley.

Gutkii, T. B., & Hickman, J. A. (1990). The relationship of consultant, consultee, and organizational characteristics to consultee resistance to school-based consultation: An empirical analysis. Journal of Educational and Psychological Consultation, 1, 111-122.

Hall, C. W., & Wahrman, E. (1987). Theoretical orientations and perceived acceptability of intervention strategies applied to acting-out behavior. Journal of School Psychology, 26, 195-198.

Hughes, J. N. (1992). Social psychology foundations of consultation. In F. J. Medway & T. P. Cafferty (Eds.), School psychology: A social psychological perspective (pp. 269-303). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Idol, L. (1990). The scientific art of classroom consultation. Journal of Educational and Psychological Consultation, 1, 3-22.

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

MATHEMATICS INTERVENTIONS 1 71

Johnston, M. B., & McLaughlin, T. F. (1982). The effects of free time on assignment completion and accuracy in arithmetic: A case study. Education and Treatment ofchildren, 5, 35-40.

&din, A. E. (1980). Acceptability of alternative treatments for deviant child behavior. Journal of Applied Behavior Analysis, 13,259-273.

Kutsick, K. A., Gutkin, T. B., & Witt, J. C. (1991). The impact of treatment development process, intervention type, and problem severity on treatment acceptability as judged by classroom teachers. Psychology in the Schools, 28, 325-331.

Leder, G. C. (1992). Mathematics and gender: Changing perspective. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 597-622). New York: Macmillan.

Luiselli, J. K., &Downing, J. N. (1980). Improving a student's arithmetic performance using feedback and reinforcement procedures. Education and Treatment of Children, 3, 45-49.

Martens, B. K., Peterson, R. L., Witt, J. C., & Cirone, S. (1986). Teacher perceptions of school-based intervention: Ratings of intervention effectiveness, ease of use, and frequency of use. Extqfional Children, 53, 213-223.

Martens, B. K., Witt, J. C., Elliott, S. M., & Darveaux, D. K. (1985). Teacher judgments concerning the acceptabiity of school-based interventions. Professional Psychology: Research and Practice, 16, 191-198.

Martin, R. (1978). Expert and referent power: A framework for understanding and maximizing consultation effectiveness. Journal o f School Psychology, 16, 44-59.

McKellar, N. A. (1983, April). Instructional consultation. Paper presented at the National Association of School Psychologists Convention, Detroit.

McKellar, N. A., & Hartshorne, T. S. (1986, April). Information desired by teachers in instructional wnsultatim. Paper presented at the National Association of School Psychol- ogists Convention, Hollywood, FL.

Medway, F. J. (1989). Further considerations on a cognitive problem-solving perspective on school consultation. Professional School Psychology, 4, 21-27.

Meyers, J., Gelzheiser, L. M., & Yelich, G. (1991). Do pull-in programs foster teacher collaboration? Remedhl and Special Education, 12(2), 7-15.

Meyers, J., Parsons, R. D., &Martin, R. (1979). Mental health consultation in the schools. San Francisco: Jossey-Bass.

Miltonberger, R. G. (1990). Assessment of treatment acceptability: A review of the literature. Topics in Early Childhood Special Education, 10(3), 24-38.

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

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

National Research Coupcil. (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington, DC: National Academy Press.

Reimers, T. M., WaclCer, D. P., & Koeppl, G. (1987). Acceptability of behavioral treatments: A review of the literature. School Psychology Review, 16, 212-227.

Rhoades, M. M., & Kratochwill, T. R. (1992). Teacher reactions to behavioral consultation: An analysis of language and involvement. School Psychology Quarterly, 7, 47-59.

Ringer, M. M., Doerr, P, F., Hollenshead, J. H., &Wills, G. (1989). Current behavioral and academic interventions in use by classroom teachers: Implications for school psychol- ogists. Tminers' Forum, 9(3), 1-6.

Rosenfield, S. A. (19817). Instructional consultation. Hiusdale, NJ: Lawrence Erlbaum Associates, Inc.

Secada, W. G. (1992). Race, ethnicity, social class, languages, and achievement in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 623-660). New York: Macmillan.

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

Shapiro, E. S. (1989). Academic skills problems: Direct assessment and intervention. New York: Guilford.

Shavelson, R. J., & Stern, P. (1981). Research on teachers' pedagogical thoughts judg- ments, decisions, and behavior. Revim of Educational Research, 51, 455-498.

Skinner, M. E., & Hales, M. R. (1992). Classroom teachers' "explanations" of student behavior: One possible barrier to the acceptance and use of applied behavior analysis procedures in the schools. Journal of Educational and Psychological Consultation, 3, 219-232.

Thurlow, M. L., & Ysseldyke, J. E. (1982). Instructional planning: Information collected by school psychologists vs. information considered useful by teachers. Journal of School Psychology, 20, 3-10.

Tukey, J. W. (1949). Comparing individual means in the analysis of variance. Biometries, 5, 99-114.

West, J. F., & Idol, L. (1990). Collaborative consultation in the education of mildly handicapped and at-risk students. Remedial and Special Education, 11(1), 22-31.

Witt, J. C. (1986). Teacher's resistance to the use of school-based interventions. Journal of School Psychology, 24, 37-44.

Witt, J. C., &Elliott, S. N. (1985). Acceptability of classroominterventions strategies. In T. Kratochwill (Ed.), Advances in school psychology (Vol. 4, pp. 251-288). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Witt, J. C., Elliott, S. N., & Martens, B. K. (1984). Acceptability of behavioral interventions used in classrooms: The influence of teacher time, severity of behavior problem, and type of instruction. Behavioral Disorders, 10, 95-104.

Witt, J. C., & Martens, B. K. (1983). Assessing the acceptability of behavioral interventions used in the classroom. Psychology in the Schools, 20, 510-517.

Witt, J. C., Martens, B. K., & Elliott, S. N. (1984). Factors affecting teachers' judgments of the acceptability of behavioral interventions: Time involvement, behavior problem severity, type of intervention. Behavior Therapy, 15, 204-209.

Witt, J. C., Moe, G., Gutkin, T. B., & Andrews, L. (1984). The effect of saying the same thing in different ways: The problem of language and jargon in school-based consul- tation. Journal of School Psychology, 22, 361-367.

Woolfolk, A. E., Woolfolk, R. C., & Wilson, G. T. (1977). A rose by any other name . . .: Labeling bias and attitudes toward behavior modification. Journal of Consulting and Clinical Psychology, 45, 1&&191.

APPENDIX

Descriptions of Math Problems and Consultant-Recommended Strategies

Descriptions of Math Problems

Basic Math Facts Problem

J.C., a student in your third-grade class, is having difficulty correctly solving problems requiring basic addition and subtraction facts. You have observed that this student experiences difficulty on problems such as :

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

MATHEMATICS INTERVENTIONS 1 73

17 13 -8 and -5 - -

J.C. has had similar trouble with addition facts. These difficulties have persisted since first grade, and you have decided to request the help of a school consultant for instructional recommendations.

Math Application Problem

B. J., a student in your third-grade class, demonstrates good basic facts and algorithm skills in addition and subtraction. However, B.J. experi- ences difficulty when asked to apply those skills to solve real world problems involving money such as:

"If juice costs 33 cents, how much change should you receive from 50 cents?" and 'You earned 75 cents raking leaves. If you buy juice for 33 cents and buy gum for 26 cents, how much change will you have?"

You have tried to teach B.J. how to apply his basic math skills, but B. J. is still unsuccessful.

Descriptions of Consultant-Recommended Strategies

The school consultant suggested a cognitive learning strategy ap- proach. As the teacher you could use one or more of the following methods for improving B.J.'s difficulty with math application problems:

PROBLEM REPRESENTATION (e.g., using manipulatives to rep- resent the problem in various ways). ACTIVATE EXISTING KNOWLEDGE (e.g., recall previous expe- riences or problems). CREATE MEANINGFUL CONTEXTS (e.g., use authentic situa- tions and real world items such as coins). ACTIVE LEARNING (e.g., play "store" and acting out the prob- lem). METACOGNITION (e.g., talking yourself through step-by-step, "what do I do Ist, now, what's 2nd?", etc.).

The school consultant suggested a behavioral learning approach. As .the teacher you would improve B.J.'s basic math application skills by using drill and practice, rewarding B. J.'s correct answers to application problems, with one or more of the following methods:

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014

1 74 DE MESQUITA AND ZOLLMAN

TANGIBLE REINFORCEMENT (e.g., use cookies, pens, pencils, drinks, and toys). TOKEN REINFORCEMENT (e-g., achievement charts, award cer- tificates, checks, points, stars). REINFORCING ACTIVITIES (e.g., games, early dismissal, extra recess, leadership roles and responsibilities). SOCIAL REINFORCERS (e.g., class recognition, work displayed, verbal praise).

The school consultant has suggested you use a cooperativelpeer learning approach. As the teacher you could improve B.J.'s basic math application skills by having B.J. work on application problems with other students in one or more of the following arrangements:

MIXED ABILITY GROUP (e.g., mix students into groups of high, average, and low math abilities). COOPERATIVE SKILLS BUILDING (e. g., group members learn helping, tutoring, and sharing). GROUP EVALUATION (e-g., base grades and evaluations on group products). BUDDY SYSTEM (e.g., a skilled student partners an unskilled classmates for one-one tutoring).

Dow

nloa

ded

by [

Uni

vers

ity o

f C

ambr

idge

] at

04:

49 0

8 O

ctob

er 2

014