Research Articles
John A. Ross
Abstracts

Teacher Confidence

The Antecedents and Consequences of Teacher Efficacy

(No abstract. Introduction to Chapter provided)

Expectations are self-fulfilling prophecies. Teachers who believe that students will do well in school have been observed adjusting their behavior to make it so (Good & Brophy, 1990). One type of expectancy that has been consistently linked to teacher attributes, workplace conditions, instructional practice, and student outcomes is teacher efficacy. In this chapter I will identify the antecedent conditions associated with the waxing and waning of teacher efficacy, catalogue its influence on teacher actions and on student achievement, examine the results of interventions to enhance teacher efficacy, outline implications for practice, and suggest directions for further inquiry.

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Administrative Assignment of Teachers in Restructuring Secondary Schools: The Effect of Out of Field Course Responsibility on Teacher Efficacy.

Previous studies have treated teacher efficacy as a unitary trait without considering how teachers' expectations of their ability to produce student learning varies within teaching assignments. In this study, teachers in nine restructuring secondary schools in one district estimated their ability to perform common teaching tasks in four of the courses they expected to teach in the coming school year. Although the portion of the variance explained was small, the study found that teacher efficacy was lower for courses outside the teacher's subject. The effects of teaching outside one's area were greater than the effects of track and grade--two course characteristics that have been linked to teacher efficacy in previous research. This study also found that teacher efficacy was influenced by teacher leadership roles. Teachers who were expected to promote student learning across subjects had lower teacher efficacy than teachers in traditional positions of added responsibility (department heads) and teachers who were not in leadership positions.

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Prior Student Achievement, Collaborative School Processes, and Collective Teacher Efficacy

Collective teacher efficacy refers to teacher perceptions that they constitute an effective instructional team, capable of bringing about learning in students. Previous research demonstrates that a school staff with a strong sense of collective efficacy is likely to generate high student achievement. This study of 2,170 teachers in 141 elementary schools used structural equation modeling to examine the antecedents of collective teacher efficacy. The study found that prior student achievement in grade 6 mathematics predicted collective teacher efficacy, as expected by social cognition theory. The study also found that school processes that promoted teacher ownership of school directions (shared school goals, school-wide decision making, fit of plans with school needs, and empowering principal leadership) exerted an even stronger influence on collective teacher efficacy than prior student achievement. School cohesion and support contributed to collective teacher efficacy, but only in domains in which the school had control over its directions.

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Teacher self-assessment: A mechanism for facilitating professional growth

Self-assessment is a powerful technique for improving achievement. In this article we outline a theory of teacher change that links self-assessment by teachers to their professional growth. This theory provides avenues for peers and change agents to influence teacher practice. We apply the theory to change in mathematics teaching and report an explanatory case study in which use of the self-assessment tool, in combination with other elements, contributed to change in the instructional practice of a grade 8 mathematics teacher. Provision of a self-assessment tool contributed to teacher growth by: (1) influencing the teacher's definition of excellence in teaching and increasing his ability to recognize mastery experiences; (2) helping the teacher select improvement goals by providing him with clear standards of teaching, opportunities to find gaps between desired and actual practices, and a menu of options for action; (3) facilitating communication with the teacher's peer; and (4) increasing the influence of external change agents on teacher practice. The study argues that providing a self-assessment tool is a constructive strategy for improving the effectiveness of in-service provided it is bundled with other professional growth strategies: peer coaching, observation by external change agents, and focused input on teaching strategies.

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Professional Development Effects on Teacher Efficacy: Results of Randomized Field Trial

We designed a professional development (PD) program to increase the teacher efficacy of mathematics teachers. We randomly assigned 106 Grade 6 teachers in 1 school district to treatment and control conditions in a delayed-treatment design. The PD explicitly addressed 4 sources of teacher-efficacy information identified in social-cognition theory (Bandura, 1997). Treatment teachers outperformed control-group teachers on 3 measures of teacher efficacy, but results were statistically significant only for efficacy for classroom management. We attributed the teacher-efficacy effects of the PD (6% of the variance) to the priority given in the PD to management of classroom discussions and overt attempts by PD leaders to redefine teacher conceptions of classroom success.

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A Model for Increasing Reform Implementation and Teacher Efficacy: Teacher Peer Coaching in Grade 3 and 6 Mathematics

This study examined the effects of peer coaching on mathematics teaching practices and teacher beliefs about their capacity to impact student learning. Twelve teachers in grades 3 and 6 participated in a brief but intensive professional development program over six months. The program focused on effective math teaching strategies and peer coaching opportunities. Data sources included classroom observations, teacher self-assessments, interviews, and field notes. Data were analysed using a two level qualitative coding strategy with multiple interpreters. Findings showed that teachers implemented key strategies for effective math teaching, especially for facilitating student interaction and improving the quality of tasks assigned.

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The effects of sustained classroom-embedded teacher professional learning on teacher efficacy and related student achievement.

This paper reports on the impact of a classroom-embedded professional learning (PL) program for mathematics teaching in two contrasting districts in Canada, and investigates the relationship between teacher efficacy and student achievement. Before the PL, District A had lower teacher efficacy and student achievement than District B, but after the PL, this situation was reversed. Qualitative analysis revealed that the two districts reported learning very different things from the PL opportunity. The complexities of context, prior learning experiences, goal setting, and persistence of participants all factored into what and how teachers learned.

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Computers in the Classroom

Collateral Benefits of an Interactive Literacy Program

This study examined the collateral effects of WiggleWorks (1994-1996), an interactive literacy program, in two settings: a cohort study comparing random samples of Grade 1 and 2 students (N=452) before and after software implementation and a longitudinal sample tracing students from kindergarten to Grade 1 (N=126). WiggleWorks contributed to greater student use of computers, enhanced computer skills, computer self-efficacy, and (in Grade 1 only) enjoyment of computers. The univarieate effects were of small to medium size and were robust across grades and genders. Positive effects were observed regardless of whether the school received new hardware at the time of software delivery or used existing equipment of sufficient power acquired a year earlier. The study suggests that the high cost of adopting interactive literacy software may be warranted if the program has benefits beyond its contributions to reading and writing skills.

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Effects of Teacher Efficacy on Computer Skills and Computer Cognitions of K-3 Students

In this study of 387 students aged 6-9, we examined the effects of a change in teacher efficacy when students moved to a new grade. The effects of 4 dimensions of computer teacher efficacy on 3 types of student benefits (improved basic and advanced computer skills and increased computer self-efficacy) were investigated. Students in an upward trajectory (i.e., those who moved from a teacher with low computer confidence to a teacher with high computer confidence) benefited more from an infusion of technology than students in a downward trajectory (i.e., those who moved from a high- to a low-confidence teacher). Teacher efficacy on student outcomes was stronger when district in-service training was differientiated for individuals, distributed throughout the implementation period, established in-school networks, and was complemented by support focused on instructional rather than hardware issues.

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The Contribution of Technology to the Implementation of Mathematics Education Reform: Case Studies of Grade 1-3 Teachers

Previous research suggests that access to technology contributes to the implementation of mathematics education reform. This case study of three primary (grade 1-3) teachers investigated how access to computers and math teaching software influenced nine dimensions of reform. Teachers were selected on the basis of their commitment to math reform and their technological literacy. Interviews and observations over five months found that technology had its greatest impact by helping teachers expand the scope of their programs and by promoting positive attitudes toward math. Teachers adapted computer tasks to fit their off-line activities, heightening or depleting the contribution of technology to reform. The computer promoted equity of access to all forms and strands of mathematics but this did not necessarily ensure that all students had access to higher math. None of the teachers realized the potential of the computer to increase student-student construction of mathematical ideas, in part because of hardware problems but more because of their decision to assign students to individual computer tasks.

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Conditions for Effective Use of Interactive On-line Learning Objects: The Case of a Fractions Computer-based Learning Sequence

Students are challenged when learning fractions and problems often persist into adulthood. Teachers may find it difficult to remediate student misconceptions in the busy classroom, particularly when the concept is as challenging as fractions has proven to be. We theorized that a technology-based learning resource could provide the sequencing and scaffolding teachers might have difficulty providing. A development team of teachers, researchers and educational software programmers designed five sets of fractions activities in the form of learning objects, called CLIPS. As part of a larger mixed-methods study, 36 observations as well as interviews were conducted in four classrooms, grades 7-10. Four students were selected by their teachers for CLIPS use from each of these four classrooms because the students were experiencing difficulty with fractions concepts. CLIPS use contributed to student achievement, provided the conditions enabled an effective learning environment and students experienced the full sequence of tasks in the CLIPS. In this article we describe the conditions that enabled student success. Three interacting contexts affected successful use of CLIPS: technological contexts (such as access to computers with audio), teaching contexts (such as introductory activities that prepared students for the CLIPS activities) and student contexts (such as the level of student confidence and opportunities to communicate to a peer). The study illustrates how a research-based set of learning objects can be effective and provides guidelines to consider when using learning objects to enhance mathematics programs.

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Student Achievement Effects of Technology-Supported Remediation of Understanding of Fractions

Students have difficulty learning fractions and problems in understanding fractions persist into adulthood, with moderate to severe consequences for everyday and occupational decision-making. Remediation of student misconceptions is hampered by deficiencies in teachers’ knowledge of the discipline and pedagogical content knowledge. We theorized that a technology resource could provide the sequencing and scaffolding that teachers might have difficulty providing. Five sets of learning objects, called CLIPS, were developed to provide remediation on fraction concepts.

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Characteristics of students assigned to technology-based instruction

Previous research has examined factors influencing teacher decisions to integrate technology using between-teacher designs. This study used a within-teacher design to compare students who were assigned multi-media learning objects for learning fractions with students taught by the same teachers who were not assigned to the technology. There were two conditions: (1) teachers were asked to limit the number of assigned students to 25% of their class (N=375 grade 7-10 students) and (2) teachers could assign as many students as they wanted (N=149 grade 7 students). In the constrained decision setting, students assigned to the technology were more likely than students not assigned to score lower on a fractions achievement test, have dysfunctional attitudes toward mathematics learning, have low self-efficacy, exert low effort, and be male. In the unconstrained decision setting 70% of students were assigned the technology and the only statistically significant predictor was prior achievement. Teachers’ criteria were intuitively sensible and congruent with research identifying correlates of mathematics achievement and comfort with technology. The results indicate that the technology contributed to teachers’ ability to differentiate instruction, with the important proviso that teachers appeared to be unaware of the opportunity cost of their decisions.

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Sequencing computer-assisted learning of transformations of trigonometric functions

Studies incorporating technology into the teaching of trigonometry, although sparse, have demonstrated positive effects on student achievement. The optimal sequence for integrating technology with teacher-led mathematics instruction has not been determined. Our research investigated whether technology has a greater impact on student achievement and attitudes if it is implemented before or after whole class teaching. The curriculum context of the study was a set of learning objects (CLIPS: Trig) designed to support student learning of transformations of trigonometric functions. The software includes functional features identified in prior research: it relieves students of the tedium of creating graphs by hand; sliders give students control of the simulations within program parameters; there are easy transitions between algebraic and graphic representations; the environment is dynamic; animation and visualization are included with graphing functions.

Twenty Canadian classrooms (N=489 grade 11-12 students, aged 17-18 years) were randomly assigned to two instructional sequences: CLIPS: Trig followed by whole class teaching (CLIPS early treatment) and whole class teaching followed by CLIPS: Trig (CLIPS late treatment). We found that in the pre test to post test comparisons, students who experienced CLIPS: Trig after whole class teaching of core concepts learned more than students who began the unit with technology-supported simulations. However, there were no statistically significant differences in the pre test to delayed post comparisons. Beginning the trigonometry unit with CLIPS: Trig enhanced the impact of whole class teaching, while beginning with whole class teaching enriched students’ technology experience. The findings suggest that a tight integration of whole class and technology-assisted instruction is preferable.

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School Improvement

Building Change Capacity Within Secondary Schools Thorough Goal-driven and Living Organizations

Restructuring and reculturing secondary schools within one Ontario school district began in 1994 when Government policy towards subject integration made it difficult to assign traditional department head responsibilities. Site-based decision making provided for very different organisational structures within the schools. This article examines change capacity from the notions of chaos theory and a living organisation. Longitudinal quantitative and qualitative data were collected over a five-year period to understand the irnpact of organisational change on the whole school. Our findings suggest that school leadership teams worked differently based on contextual conditions that fostered change capacity and reculturing. Consequently, schools functioned as living organisations with evolving and emerging organisational structures that were responsive to school goals.

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Transformational Leadership and Teacher Commitment to Organizational Values: The Mediating Effects of Collective Teacher Efficacy

Transformational leadership researchers have given little attention to teacher expectations that mediate between goals and actions. The most important of these expectations, teacher efficacy, refers to teacher beliefs that they will be able to bring about student learning. This study examined the mediating effects of teacher efficacy by comparing two models derived from Bandura’s social-cognitive theory. Model A hypothesized that transformational leadership would contribute to teacher commitment to organizational values exclusively through collective teacher efficacy. Model B hypothesized that leadership would have direct effects on teacher commitment and indirect effects through teacher efficacy. Data from 3,074 teachers in 218 elementary schools in a cross-validation sample design provided greater support for Model B than Model A. Transformational leadership had an impact on the collective teacher efficacy of the school; teacher efficacy alone predicted teacher commitment to community partnerships; and transformational leadership had direct and indirect effects on teacher commitment to school mission and commitment to professional learning community.

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School Leadership and Student Achievement: The Mediating Effects of Teacher Beliefs

Principals are held accountable for student achievement even though most studies find that principals have no direct effect on it. This study tested a model hypothesizing that principals contribute to student achievement indirectly, through teacher commitment and teacher beliefs about their collective capacity. Path analysis of data from 205 elementary schools supported the hypothesis. Schools with higher levels of transformational leadership had higher collective teacher efficacy, greater teacher commitment to school mission, school community, and to school-community partnerships, and higher student achievement. Increasing the transformational leadership practices in schools by one standard deviation would increase student achievement in grade 3 and 6 Reading, Writing, and Mathematics by .22 standard deviations.

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Participatory Needs Assessment

Needs assessments are typically conducted exclusively by practitioners at the cost of quality or entirely by external evaluators at the cost of relevance. This paper makes a case for participatory needs assessment, which we define as a systematic approach to setting organizational priorities in which trained evaluators and program stakeholders share responsibility for all substantive and procedural decisions. We outline potential advantages and three critical challenges: enlisting genuine participation by program staff, reducing time demands on stakeholders, and maintaining evaluation quality. We conducted a case study in which 81 stakeholders worked with an external evaluator to identify and prioritize needs in one school district. The district developed nine strategies for dealing with the challenges of participatory needs assessment. The result was a needs assessment that reached relatively high levels of utilization (support for discrete decisions, conceptual use and process use) and moderately high levels of quality, particularly with regard to credibility with users. We argue that participatory needs assessment is an appropriate extension of participatory approaches to program evaluation.

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Evaluations that Consider the Cost of Educational Programs: The Contribution of High Quality Studies

Cost studies are program evaluations that judge program worth by relating program costs to program benefits. There are three sets of strategies: cost-benefit, cost-effectiveness, and cost-utility analysis, although the last appears infrequently. We searched relevant databases to identify 103 cost studies in education and then reduced the set to 31 using eight criteria: one set focused on rigor in determining program effects and the other set focused on assessment of costs. We found that cost studies (1) provide evidence of the worth of educational spending at the macro and individual program levels, information that is not provided by other evaluation approaches; (2) they provide direction for program improvement that differs from recommendations based solely on effect sizes; and (3) they contribute to knowledge development by constructing and testing models that link spending to student learning.

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Cost-utility Analysis in Educational Needs Assessment

Educational needs assessments (hereafter NAs) are inattentive to cost considerations and are frequently dominated by elite stakeholder groups. In this article I make a case for adopting a cost-utility approach, illustrating the argument with data generated in a NA of central library services in a Canadian school district. Using survey data from eight stakeholder groups, I found that (1) NAs based on the service preferences of a single stakeholder group can be misleading; (2) service preferences can be integrated into a single set of priorities, even when there are disagreements, by using the stakeholder group as the unit of analysis and assigning weights that privilege input from knowledgeable respondents; (3) that the ranking of service operations produced by user preferences was not significantly correlated with the ranking produced by integrating preferences with costs. Cost-utility analysis would be more helpful if the utilities represented rigorously determined benefits of the services assessed, as well as stakeholder perceptions of the value of these benefits. Cost-utility analysis in NA will not reach its potential until cost considerations are routinely included in educational program evaluations.

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Equity and leadership: Research-based strategies for school leaders.

Principals are required by policy, regulation, legislation and democratic discourse to promote equity of outcomes. This integrated review investigates research on equity issues facing five student groups: special needs students; religious, cultural and racial minorities; groups disadvantaged by socioeconomic status; gender groups; and students differentiated by their sexual orientations. Sixteen research-based strategies for reducing the gap in achievement between advantaged and disadvantaged students are generated, the strategies being organised within four domains of principal influence: curriculum interpretation, instruction, assessment, and community involvement.

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Principal perspectives on special education needs.

This study investigated principal perspectives on special education needs in one Ontario school district (N=69 schools). The authors found substantial discrepancies between district records and principals in terms of whether the number of students with particular exceptionalities was increasing or decreasing. Support for a re-alignment of resources toward students with behaviour and autism exceptionalities was greatest for principals working in schools serving disadvantaged student populations, in schools with a history of relatively high achievement, who had more experience as principals, and who had not obtained special education qualifications. The authors attributed these findings to the principal's twin mandate to raise the bar (i.e., increase the proportion of students in the school reaching the provincial standard on mandated assessments) and reduce the gap (i.e., bring low achieving groups closer to the level reached by high achieving groups). The practical implications are that districts need to 1) reconcile their special education identification records with the practices of schools; (2) clarify what it means to raise the bar for the school while reducing the gap between high and low achieving students; and (3) invest in principal training on special education issues.

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The role of external diagnosis in school improvement in an Ontario school district.

External diagnosis is recommended when schools lack the capacity to assess their needs. This qualitative study of one Ontario district compared 33 elementary schools that conducted external diagnosis to 47 schools using internal diagnosis. External diagnosis created pressure for change, helped schools develop a plan that included previously neglected needs, promoted consistency within- and between-schools, contributed to the improvement culture of the school, and encouraged shared instructional leadership. It also depressed teacher efficacy and commitment to school improvement. Positive effects of external diagnosis were facilitated and negative effects mitigated by principals who adopted shared instructional leadership strategies.

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The student achievement effects of comprehensive school reform: A Canadian case study.

We conducted a third party study of the student achievement effects of Struggling Schools, a user generated approach to Comprehensive School Reform (CSR). The design was quasi-experimental, pre-post matched sample (N=180) with school as unit of analysis, drawing on two years of achievement data from standardized external assessments. Struggling Schools had a statistically significant positive effect on Grade 3 Reading achievement; ES=.48 in 2005-06 and .60 in 2006-07. There were enduring achievement effects two years after exit from the program. The outcomes indicate that CSR approaches based on capacity building, partnerships with an external agency, and accountability enhance student learning.

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Student Assessment

Student Self-evaluation in Grade 5-6 Mathematics: Effects on Problem Solving Achievement

We examined the effects of self-evaluation training on mathematics achievement. When Grade 5-6 students self-evaluated for 12 weeks (N = 259 treatment, 257 control) treatment students outperformed control students (ES = .40). The findings contribute to the consequential validity argument for self-evaluation. Considered in the context of previous research, these results indicate that subject moderates the effects of self-evaluation on achievement.

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Influences on Student Cognitions About Evaluation

Interviews on two occasions with 71 Grade 2, 4 and 6 students in a multi-ethnic setting in Toronto, Canada, found that student cognitions about evaluation mediated the relationship between evaluation and achievement. Parents, peers and student characteristics influenced student cognitions about evaluation. Parents identified the evaluation dimensions their children should attend to, raised student aspirations, stated how well student work attained standards and recommended actions children should take in response to the evaluation. Peer interpretations influenced whether a given performance was viewed as superior or inferior. Older student peers focused attention, to a greater extent than parents, on specific aspects of student performance that could be ameliorated through self-remediation. Children became more sophisticated evaluation consumers as they grew older. Females processed evaluation data more productively than males. There were few cultural differences in response to evaluation. Students responded to traditional and alternate evaluation in very similar ways.

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Student Assessment Practices in Cooperative Learning

Student assessment in Cooperative Learning [CL] constitutes a substantial challenge for instructors. Teachers who have evaluated students as isolated learners have to figure out how to evaluate students working in groups, at a time when standards for appraisal are escalating. Guidelines for giving students feedback on group work abound in CL manuals but little is known about the effectiveness of these strategies. In this chapter we will review previous research on student assessment in CL, with particular attention to the practical issues that teachers face. We will reframe the practical issue as a set of research questions and report the results of research. Finally, we will suggest practical actions teachers might take based on the research findings.

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Effects of Running Records Assessment on Early Literacy Achievement

Recent research on effective schools (e.g., Pressley et al., 2001 identified consistent associations between students' literacy achievement and teacher practice. In this study, the author extended those correlational findings by conducting a controlled experiment to test the claims about 1 practice recommended by recent effective school research, systematic classroom assessment, represented here as the use of running records for planning instruction. Students in schools assigned to the running records treatment outperformed students in schools assigned to a near-treatment condition (action research). After controlling for prior school achievement and collective teacher efficacy, the running records intervention accounted for 12% of the between-school variance in reading and 7% in writing, confirming the correlational finding from effective schools research..

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Student Assessment in Online Courses: Research and Practice, 1993-2004

Research on student assessment in online environments has not been extensive, although manuals for instructors provide broad guidelines and specific procedures. In this article we review the most frequently reported approaches to online assessment in postsecondary settings, giving particular attention to systems for assessing the quality of student participation. We also extrapolate from research on assessment in face-to-face courses to identify strategies that could be usefully adapted to online assessment. Research on the reliability and validity of online assessment methods is mixed and there is not much of it. We suggest to online instructors that there appears to be a disjunction between assessment methods and instructional ideologies and suggest to researchers there is an urgent need to investigate the consequential validity of online assessment.

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Needs Assessment for the Development of Learning Objects.

In a review of 125 needs assessments conducted in educational settings, Witkin (1994) identified multiple deficiencies: mono-method bias (use of a single data source to identify needs), confusion between solutions (instructional actions) and needs (gaps in student performance), use of unsystematic procedures, and over-reliance on data from a single group. We attempted to avoid these problems in selecting the focus for CLIPS being developed for lower achieving mathematics students in grades 7-10. In our study, CLIPS (Critical Learning Instructional Paths Support) are learning objects—short multimedia programs focused on specific learning objectives. In this research note we describe how we applied systematic needs assessment procedures (Witkin & Altschuld, 1995) to focus five CLIPS.

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Self-Assessment in a Technology Supported Environment: The Case of Grade 9 Geography

We investigated the impact of self-assessment training on student achievement and on computer self-efficacy in a technology-supported learning environment (grade 9 students using Global Information Systems software). We found that self-assessment had a positive effect on student achievement, accounting for 25% of the variance across three measures. The treatment effect was as large for females as for males and for those with low initial self-efficacy as it was for those with higher scores. In addition, self-efficacy increased more in the control than in the treatment group. We interpreted the self-efficacy results to be a positive outcome of the treatment: teachers may have used self-assessment training to depress the inflated self-perceptions of some teenagers.

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Alignment of Scores on Large Scale Assessments and Report Card Grades

We examined how much agreement there was between scores from large scale, mandated assessments and report card grades for 14,776 students in grades 3, 6 and 9 of a district in which conditions were conducive to alignment of assessments. We found significant mean differences between internal and external assessments: effect sizes were .29 to .63 in grades 3-6 and .10 to.30 in grade 9. Spearman correlations were in the .32 to .59 range. Chance-adjusted agreement was low. Report card grades were consistently higher than external assessments for grade 3 and 6 students and consistently lower for grade 9 students.

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Mathematics Teaching and Learning

Research on Reform in Mathematics Education, 1993-2000

Proponents and opponents of reform of mathematics education all cite the research base in support of their positions. This article reports the results of a review of studies that contained empirical evidence of the effects of reform or the difficulty of implementing reform that were published between 1993 and 2000. The studies reviewed indicate that implementation of math reform contributes to student achievement, but evidence abounds of superficial implementation and barriers to enactment. There are well-documented strategies for reducing these barriers, the most promising strategies being inservice that simultaneously focuses on teachers' practice and their cognition about mathematics teaching.

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Self-Evaluation in Grade 11 Mathematics: Effects on Achievement and Student Beliefs About Ability

Assessment practices affect student outcomes. At the simplest level, increasing the frequency of testing to at least once per week contributes to higher achievement (Bangert-Drowns, Kulik & Kulik,1991). Recent research has focused on the effects of alternative assessment on student cognitions and achievement. For example, Herman, Klein, and Wakai (1997) reported that students describe performance assessments as more challenging than multiple-choice items and try harder on the former because they have to explain more of their thinking. In this article we continue this line of research by reporting a case study of a grade 11 mathematics classroom in which training in self-evaluation processes was introduced as a stimulus to higher achievement.

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A Survey Measuring Implementation of Mathematics Education Reform by Elementary Teachers

Intensive case study is an expensive tool for measuring teachers’ instructional practice. Previous research suggests that teacher self-report surveys provide a low cost and relatively accurate picture of classroom practice. To estimate the extent to which teachers are implementing mathematics education reform, we developed a 20-item survey based on nine dimensions of Standards-based teaching. We provide evidence of the reliability (internal consistency) and validity of the instrument. The evidence consists of correlations of survey scores with a mandated performance assessment in grade 6 mathematics, congruence with classroom observations of a small sample of teachers, and demonstrations that teachers who are similar in their claims about using a Standards-based text series differ in how they use the text, in ways predicted by the survey.

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The Impact of a Professional Development Program on Student Achievement in Grade 6 Mathematics

Grade 6 teachers (N=106) in one school district were randomly assigned to early or late professional development (PD) groups. The program incorporated principles of effective PD recommended by researchers, although the duration of the treatment was modest (one full day and four after school sessions over a ten-week period). At the posttest, there were no statistically significant differences in student achievement. Although it could be argued that the result demonstrates that PD resources should be redirected to more intensive PD delivered over longer periods, we claimed that the PD was assessed prematurely. After the completion of the study, the external assessments administered by the province showed a significant increase in student achievement from one year to the next involving both the early and late treatment groups, an increase that was not found for the same students in other subjects. The study had high ecological validity: it was delivered by district curriculum staff to all grade 6 teachers, volunteers and conscripts alike. The cost to the district, less than CAN$14 [9 euros] per student, was comparable to the modest expenditures typically available for professional development in Canadian school districts.

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The Effects of Standards-based Mathematics Teaching on Low Achieving Grade 7 and 8 Mathematics Students

Previous research (e.g., Woodward & Baxter, 1997) found that Standards-based mathematics teaching provides marginal or no benefits for low achievers, in contrast with positive effects for middle and high ability students. A randomized quasi-experiment in 52 Canadian schools found that low achieving grade 7 and 8 students who received support consisting of placement on a learning continuum, instruction focused on their specific learning needs, and concrete materials to represent mathematical constructs, benefited from teaching that emphasized construction over transmission of knowledge. Treatment students showed small but statistically significant improvements over controls in student achievement, and controversially, in mathematical beliefs, and attitudes. The latter finding raised issues of the appropriate balance between Type I and Type II error in educational research.

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The gender confidence gap in junior high school mathematics: Gender differences in student belief-achievement relationships

Recent research demonstrates that in many countries gender differences in mathematics achievement have virtually disappeared. Social cognition theory predicts that if gender differences in achievement have declined there should be a similar decline in gender differences in self-beliefs. Extant literature is equivocal: there are studies indicating that the male over female advantage in self-efficacy and beliefs about math learning is as strong as ever and there are studies reporting an absence of gender differences in belief. Using data from 996 grades 7-10 Canadian students, we found that gender differences in beliefs continued, even though gender differences in achievement were near zero. Gender differences, favoring males, were larger for self-beliefs (math self-efficacy and fear of failure) and weaker for functional and dysfunctional beliefs about math learning. There were also gender differences in the structure of a model linking beliefs about math, beliefs about self and achievement.

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Updated: April 1, 2009