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Many randomized controlled experiments in the classroom have found that mathematics learning is improved dramatically when practice problems of one kind are distributed across multiple assignments (spaced) and mixed with other kinds of problems (interleaved). In two studies, we investigated students' knowledge of spacing and interleaving. In Study 1, 193 undergraduates designed learning schedules for a hypothetical math class. In Study 2, 175 undergraduates selected from among five hypothetical schedules in response to a variety of questions, provided reasons for their selections, and rated the utility of spacing and interleaving. In both studies, most participants incorrectly judged schedules with minimal degrees of spacing and interleaving to be most effective. Also, schedules with more spacing and interleaving were perceived as more difficult, less enjoyable, and less common. Participants' ratings of utility revealed mixed perspectives on spacing and an underappreciation of interleaving. Altogether, these findings demonstrate that most students fail to recognize the benefits of spaced and interleaved practice. Further, by identifying specific ways in which their beliefs about spacing and interleaving fall short, we reveal opportunities to reshape students' beliefs to foster these effective learning techniques. [This is the in press version of a paper published in "Journal of Experimental Psychology: Applied."]

A typical mathematics assignment consists of a block of problems devoted to the same topic, yet several classroom-based randomized controlled trials have found that students obtain higher test scores when most practice problems are mixed with different kinds of problems -- a format known as interleaved practice. Interleaving prevents students from safely assuming that each practice problem relates to the same skill or concept as the previous problem, thus forcing them to choose an appropriate strategy on the basis of the problem itself. Yet despite the efficacy of interleaved practice, blocked practice predominates most mathematics textbooks. As an illustration, we examined 13,505 practice problems in six representative mathematics texts and found that only 9.7% of the problems were interleaved. This translates to only one or two interleaved problems per school day. In brief, strong evidence suggests that students benefit from heavy doses of interleaved practice, yet most mathematics texts provide scarcely any. [This paper was published in "Educational Psychology Review" v32 p873-883 2020 (EJ1263191).]

We report the results of a pre-registered, cluster randomized controlled trial of a mathematics learning intervention known as interleaved practice. Whereas most mathematics assignments consist of a block of problems devoted to the same skill or concept, an interleaved assignment is arranged so that no two consecutive problems require the same strategy. Previous small-scale studies found that practice assignments with a greater proportion of interleaved practice produced higher test scores. In the present study, we assessed the efficacy and feasibility of interleaved practice in a naturalistic setting with a large, diverse sample. Each of 54 seventh-grade mathematics classes periodically completed interleaved or blocked assignments over a period of four months, and then both groups completed an interleaved review assignment. One month later, students took an unannounced test, and the interleaved group outscored the blocked group, 61% vs. 38%, d = 0.83. Teachers were able to implement the intervention without training, and they later expressed support for interleaved practice in an anonymous survey they completed before they knew the results of the study. Although important caveats remain, the results suggest that interleaved mathematics practice is effective and feasible. [This is the online version of an article published in "Journal of Educational Psychology."]

High school freshmen in accelerated courses have known risk and resiliency factors that should be considered within systematic efforts to monitor and promote student academic and emotional well-being. This study created and evaluated a multi-method approach to identify students in Advanced Placement (AP) or International Baccalaureate (IB) courses with signs of risk mid-year in terms of stress, affective engagement, and academic performance. A total of 304 ninth grade students enrolled in AP/IB coursework and five AP/IB teachers at two public high schools in a Southeastern state took part in the screening. Using the researcher-developed screening approach, a total of 117 students (38.5%) met criteria for risk in at least one academic or emotional area. These results were compared to those obtained using a teacher nomination form, which had been developed collaboratively by the teachers and researchers, that specified signs of emotional and academic risk. The teacher nomination procedure resulted in the identification of 39.3% of the at-risk student population (average sensitivity rate = 35.7% across teachers). Sensitivity of teacher nominations was higher when identifying academic risk (average = 59.9%) as compared to emotional risk (average = 27.9% and 39.6% of students with low school satisfaction and high stress, respectively). Findings support the collection of data from students (surveys of stress and school satisfaction) and school records (course grades) when identifying AP/IB students to consider for targeted services within a multi-tiered system of supports. [This paper was published in "School Mental Health" v11 p210-227 2019 (EJ1229729).]

This study explored how adaptive help seeking was related to academic self-efficacy, perfectionism (maladaptive and adaptive), attitudes towards help seeking (perceived benefits and perceived threats), and teacher emotional support among 311 grade 9 students in Advanced Placement and International Baccalaureate classes. Significant bivariate links emerged between adaptive help-seeking and all six potential correlates. Regression analyses indicated that teacher emotional support, adaptive perfectionism (high personal standards), and perceived benefits were significant, positive predictors of adaptive help seeking. Gender also was a significant predictor, as boys had lower levels of adaptive help seeking compared to girls. Furthermore, gender moderated the association between perceived benefits and adaptive help-seeking; perceived benefits were particularly highly associated with boys' adaptive help seeking from classroom teachers. Strategies for explicating the benefits of adaptive help seeking, promoting adaptive perfectionism, and fostering teacher emotional support are provided, as well as limitations and future directions for research. [This paper was published in "Psychology in the Schools" v56 n5 p652-669 2019 (EJ1211093).]

In two studies (ns = 312 and 1149) with 9-12 grade students in pre-International Baccalaureate (IB) and IB Diploma programs, we evaluated the reliability, factor structure, measurement invariance, and criterion-related validity of the scores from the School Attitude Assessment Survey-Revised (SAAS-R; McCoach & Siegle, 2003a). Reliabilities of the five SAAS-R subscale scores were good (as > 0.80) for pre-IB (grades 9-10) and IB students (grades 11-12). Study 1 model fit indices for the five-factor SAAS-R model from confirmatory factor analyses showed greater misfit than those previously reported by McCoach and Siegle. In contrast, Study 2 fit indices for the five-factor model with pre-IB and IB students were similar to values reported by McCoach and Siegle. Tests of measurement invariance in Study 2 using multigroup confirmatory factor analysis identified three items within the Motivation/Self-Regulation subscale that differed in their item intercepts (i.e., uniform differential item functioning) with pre-IB students endorsing these items more strongly compared to IB students. Based on these results along with evidence of criterion-related validity as reflected in the moderate statistical relations between the SAAS-R subscales and students' GPAs, the SAAS-R shows promise as a research tool that can be used to examine the psychological factors associated with pre-IB and IB students' academic achievement. [This paper was published in "Gifted Child Quarterly" v59 n1 p38-54 2015 (EJ1047515).]

Successful coping with academic demands is important given the inverse relationship between stress and positive adjustment in adolescents. The Coping with Academic Demands Scale (CADS) is a new measure of coping appropriate for students pursuing advanced high school curricula, specifically Advanced Placement (AP) classes and the International Baccalaureate (IB) program. We developed the CADS in parallel with a new measure of stress designed for this same population (Suldo, Dedrick, Shaunessy-Dedrick, Roth, & Ferron, in press). We generated an initial item pool using multiple sources including focus groups and individual interviews with 177 students, 72 teachers, and 47 parents. Multiple iterations of expert review and item analyses resulted in 120 items, which were completed by 727 high school students in six schools (312 IB, 415 not in IB but taking at least one AP class). Exploratory factor analyses and additional item review indicated a 16-factor solution with 58 items. Cronbach's alpha reliabilities for the factors ranged from 0.53 to 0.90, with 11 factors exceeding 0.70. All 16 factors had test-retest reliabilities greater than 0.70. Support for the construct validity of the CADS scores was provided using a nomological network, which specified relationships between the CADS and broader dimensions of school-related coping dimensions (task, avoidance, and emotion-oriented), as well as indicators of achievement (GPA) and mental health (life satisfaction). An additional seven items that were not part of the 16-factor CADS, but which were identified as relevant in different phases of instrument development, are provided as a resource for researchers. [This paper was published in "Journal of Psychoeducational Assessment" v33 n4 p357-374 2015 (EJ1063635).]

A typical mathematics assignment consists primarily of practice problems requiring the strategy introduced in the immediately preceding lesson (e.g., a dozen problems that are solved by using the Pythagorean Theorem). This means that students know which strategy is needed to solve each problem before they read the problem. In an alternative approach known as "interleaved practice," problems from the course are rearranged so that a portion of each assignment includes different kinds of problems in an interleaved order. Interleaved practice requires students to choose a strategy on the basis of the problem itself, as they must do when they encounter a problem during a comprehensive examination or subsequent course. In the experiment reported here, 126 seventh-grade students received the same practice problems over a three-month period, but the problems were arranged so that skills were learned by interleaved practice or by the usual blocked approach. The practice phase concluded with a review session, followed 1 or 30 days later by an unannounced test. Compared to blocked practice, interleaved practice produced higher scores on both the immediate and delayed tests (Cohen's d = 0.42 and 0.79, respectively). Two appendices include: (1) Serial Position of Each Graph and Slope Problem in the Assignments (table); and (2) Frequency of Responses of Three Teachers to Statements About Interleaved Practice (table). [Note: This article was "in press" at the time of submission. No citation information is available at this time.]

Most mathematics assignments consist of a group of problems requiring the same strategy. For example, a lesson on the quadratic formula is typically followed by a block of problems requiring students to use the quadratic formula, which means that students know the appropriate strategy before they read each problem. In an alternative approach, different kinds of problems appear in an interleaved order, which requires students to choose the strategy on the basis of the problem itself. In the classroom-based experiment reported here, grade seven students (n = 140) received blocked or interleaved practice over a nine-week period, followed two weeks later by an unannounced test. Mean test scores were greater for material learned by interleaved practice rather than by blocked practice (72% vs. 38%, d = 1.05). This interleaving effect was observed even though the different kinds of problems were superficially dissimilar from each other, whereas previous interleaved mathematics studies required students to learn nearly identical kinds of problems. We conclude that interleaving improves mathematics learning not only by improving discrimination between different kinds of problems but also by strengthening the association between each kind of problem and its corresponding strategy. [This article was published in: "Psychonomic Bulletin & Review" v21 n5 p1323-1330 Oct 2014; http://dx.doi.org/ 10.3758/s13423-014-0588-3.]

In a typical mathematics course, the material is divided into many lessons, and each lesson is followed by an assignment consisting of practice problems. Most commonly, each assignment consists solely of problems on the preceding lesson. For example, a lesson on ratios might be followed by an assignment with 12 problems on ratios. In other words, problems of the same kind are arranged in blocks. In this study, "blocked assignments" served as the control. In an alternative approach that is the intervention of interest, problems within the course are rearranged so that most of the problems within each assignment are based on previous lessons and arranged in an "interleaved" order. For example, after a lesson on ratios, an interleaved assignment might include a small block of four ratio problems and one problem from each of eight previous lessons. The remaining eight ratio problems are distributed across future assignments. Researchers conducted the study at a large public middle school in Tampa, Florida. Three middle school mathematics teachers and 140 of their seventh grade students participated. Students received 10 assignments over an 8-week period. All students received the same practice problems, but the problems were rearranged to produce two versions of each assignment. Across all assignments, students received 12 problems on each of four different kinds of problems. The study used a counterbalanced crossover design. For each assignment, researchers provided teachers with a slide presentation with solved examples and solutions to each problem. Teachers presented the examples before distributing the assignment. On the following school day, teachers presented the solutions while encouraging students to make any necessary corrections to their own solutions, and then collected the assignments. Within two days of each assignment's due date, at least one of the authors visited the school and scored the assignments. The Final Test was given to students during their regular classroom period and proctored by both the teacher and one author. Final test scores revealed that interleaved assignments were nearly twice as effective as blocked assignments. This finding suggests that interleaved mathematics assignments might be feasible and effective. This intervention could be implemented at all levels of mathematics instruction, and creators of mathematics texts and other instructional media can provide interleaved practice by simply rearranging practice problems.

Method effects associated with item wording have been explored in a variety of instruments and found that the practice of using positively- and negatively- worded items may introduce systematic measurement errors that disrupt analyses and interpretations of the results. Therefore, the first purpose in the present study was to explore if method effects were present in a Chinese general self-concept scale, originally developed in Chinese. The second purpose was to determine if the factor structure of the method effects, if present, differed for third and sixth grade students. The third purpose was to determine if the observed method effects were related to other substantively meaningful variables. Results from a series of CFAs support the presence of method effects associated with the negatively and positively worded items and method effects were largest for the negatively worded items. The results from multigroup model comparisons indicate that the factorial structure of these method effects was not significantly different for third and sixth graders. Three demographic variables, including student gender, student grade level, and students' overall performance ratings provided by teachers, were used to examine the relationships with negative method effects. The results of path analysis indicated that students who were rated lower by their teachers were more likely to endorse negative statements about themselves. Furthermore, students in grade 3 were significantly more likely to endorse negative statements compared to students in grade 6. But gender was not significantly related to the negative method factor. (Contains 8 figures and 6 tables.)

The purpose of this study was to develop and gather initial validity evidence for a scale designed to assess teacher knowledge and practice regarding statistics anxiety and negative attitudes toward statistics. A secondary purpose was to assess the levels of encouragement, knowledge of statistics anxiety, and current teaching practices of respondents as baselines to evaluate the need for training in encouragement of students with statistics anxiety. The study was undertaken in the context of the development of EncStat, a multimedia program to address student statistics anxiety. Responses to a developed instrument were received from 42 statistics educators, who completed self-report surveys. Results suggest that the proposed instrument holds promise for providing valid measures of critical aspects related to teaching statistics, although substantial development work remains. Estimates of consistency for the Assessment, Scaffolding, and Supplementary Teaching Materials section were low, suggesting that special attention must be given to expanding items for these areas of teacher practice. (Contains 7 tables and 11 references.) (SLD)