Danielle N. Dupuis

What Does Research Suggest About the Teaching and Learning of Introductory Statistics at the College Level? A Review of the Literature

Since the first studies on the teaching and learning of statistics appeared in the research literature, the scholarship in this area has grown dramatically. Given the diversity of disciplines, methodology, and orientation of the studies that may be classified as “statistics education research,” summarizing and critiquing this body of work for teachers of statistics is a challenging and important endeavor. In this paper, a representative subset of studies related to the teaching and learning of statistics in introductory, non-calculus based college courses is reviewed. As a result of this review, and in an effort to improve the teaching and learning of statistics at the introductory college level, some guidelines to help advance future research in statistics education are offered.

Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students’ Proportional Reasoning: A Randomized Experiment

Abstract This study examined the effect of schema-based instruction (SBI) on 7th-grade students’ mathematical problem-solving performance. SBI is an instructional intervention that emphasizes the role of mathematical structure in word problems and also provides students with a heuristic to self-monitor and aid problem solving. Using a pretest-intervention–posttest-retention test design, the study compared the learning outcomes for 1,163 students in 42 classrooms who were randomly assigned to treatment (SBI) or control condition. After 6 weeks of instruction, results of multilevel modeling indicated significant differences favoring the SBI condition in proportion problem solving involving ratios/rates and percents on an immediate posttest (g = 1.24) and on a 6-week retention test (g = 1.27). No significant difference between conditions was found for a test of transfer. These results demonstrate that SBI was more effective than students’ regular mathematics instruction.

A Randomized Controlled Trial of the Impact of Schema-Based Instruction on Mathematical Outcomes for Third-Grade Students with Mathematics Difficulties

This study compared the effects of delivering a supplemental, small-group tutoring intervention on the mathematics outcomes of third-grade students at risk for mathematics difficulties (MD) who were randomly assigned to either a schema-based instruction (SBI) or control group. SBI emphasized the underlying mathematical structure of additive problems. All students at risk for MD identified through screening received a mathematics intervention in groups of 2–4 for 12 weeks across the school year. Results revealed that students in the SBI group outperformed students in the control group on a word problem solving (WPS) posttest (g = 0.46). The effect of SBI proved to be equivalent for students in both high and low at-risk subgroups. On a district-administered mathematics achievement test, SBI students scored significantly higher than control students (g = 0.34); however, there were no significant effects on the WPS retention test (8 weeks later).

Student and high-school characteristics related to completing a science, technology, engineering or mathematics (STEM) major in college

Background: The importance of increasing the number of US college students completing degrees in science, technology, engineering or mathematics (STEM) has prompted calls for research to provide a better understanding of factors related to student participation in these majors, including the impact of a student’s high-school mathematics curriculum. Purpose: This study examines the relationship between various student and high-school characteristics and completion of a STEM major in college. Of specific interest is the influence of a student’s high-school mathematics curriculum on the completion of a STEM major in college. Sample: The sample consisted of approximately 3500 students from 229 high schools. Students were predominantly Caucasian (80%), with slightly more males than females (52% vs 48%). Design and method: A quasi-experimental design with archival data was used for students who enrolled in, and graduated from, a post-secondary institution in the upper Midwest. To be included in the sample, students needed to have completed at least three years of high-school mathematics. A generalized linear mixed model was used with students nested within high schools. The data were cross-sectional. Results: High-school predictors were not found to have a significant impact on the completion of a STEM major. Significant student-level predictors included ACT mathematics score, gender and high-school mathematics GPA. Conclusions: The results provide evidence that on average students are equally prepared for the rigorous mathematics coursework regardless of the high-school mathematics curriculum they completed.

The Role of the ACCUPLACER Mathematics Placement Test on a Student's First College Mathematics Course.

The first college mathematics course a student enrolls in is often affected by performance on a college mathematics placement test. Yet validity evidence of mathematics placement tests remains limited, even for nationally standardized placement tests, and when it is available usually consists of examining a student’s subsequent performance in mathematics courses. This study expands on existing literature by considering whether a nationally standardized college mathematics placement test (ACCUPLACER) contributes to the prediction of enrollment and success in developmental and nondevelopmental mathematics courses above and beyond prediction associated with the ACT mathematics test. Results for a sample of more than 1,300 students from 20 postsecondary institutions suggest that ACCUPLACER does not contribute to either the prediction of enrollment or subsequent success in such courses, and that comparable information is provided by using the ACT mathematics score alone. Implications of these findings are discussed.

Behavioral and Social Cognitive Processes in Preschool Children's Social Dominance

This longitudinal, naturalistic study addressed behavioral and social cognitive processes implicated in preschool childrens social dominance. In the first objective, we examined the degree to which peer aggression, affiliation, and postaggression reconciliation predicted social dominance across a school year. Consistent with predictions, all three predicted dominance early in the year while only affiliation predicted dominance later in the year, suggesting that aggression, affiliation, and reconciliation were used to establish social dominance where affiliation was used to maintain it. In the second, exploratory, objective we tested the relative importance of social dominance and reconciliation (the Machiavellian and Vygotskian intelligence hypotheses, respectively) in predicting theory of mind/false belief. Results indicated that social dominance accounted for significant variance, beyond that related to reconciliation and affiliation, in predicting theory of mind/false belief status. Results are discussed in terms of specific behavioral and social cognitive processes employed in establishing and maintaining social dominance.

The Effects of Schema-Based Instruction on the Proportional Thinking of Students With Mathematics Difficulties With and Without Reading Difficulties

This study examined the effect of schema-based instruction (SBI) on the proportional problem-solving performance of students with mathematics difficulties only (MD) and students with mathematics and reading difficulties (MDRD). Specifically, we examined the responsiveness of 260 seventh grade students identified as MD or MDRD to a 6-week treatment (SBI) on measures of proportional problem solving. Results indicated that students in the SBI condition significantly outperformed students in the control condition on a measure of proportional problem solving administered at posttest (g = 0.40) and again 6 weeks later (g = 0.42). The interaction between treatment group and students’ difficulty status was not significant, which indicates that SBI was equally effective for both students with MD and those with MDRD. Further analyses revealed that SBI was particularly effective at improving students’ performance on items related to percents. Finally, students with MD significantly outperformed students with MDRD on all measures of proportional problem solving. These findings suggest that interventions designed to include effective instructional features (e.g., SBI) promote student understanding of mathematical ideas.

A longitudinal study of preschool children's (Homo sapiens) sex segregation

In this 2-year longitudinal study, we hypothesized that sex of the human child (Homo sapiens), differences in physical activity, and time of the year would interact to influence preschool childrens sex segregation. We also hypothesized that activity would differentially relate to peer rejection for boys and girls. Consistent with the first hypothesis, high-activity girls started off as the most integrated group but became more segregated with time, whereas high-activity boys remained the most segregated group across the duration of the study. The second hypothesis was also supported: For girls only, activity was significantly related to peer rejection during Year 1 only, the time when high-activity girls also interacted frequently with boys. Results are discussed in terms of sexual selection theory and gender boundary violations.

A Randomized Trial of the Effects of Schema-Based Instruction on Proportional Problem-Solving for Students With Mathematics Problem-Solving Difficulties

This article reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and their students in the larger study were randomly assigned to an SBI or control condition and teachers in both conditions then provided instruction on the topics of ratio, proportion, and percent. We found that students with MD-PS in SBI classrooms scored on average higher than their counterparts in control classrooms on a posttest and delayed posttest administered 9 weeks later. Given students’ difficulties with proportional problem-solving and the consequences of these difficulties, an important contribution of this research is the finding that when provided with appropriate instruction, students with MD-PS are capable of enhanced proportional problem-solving performance.

Curriculum-Based Measurement and Standards-Based Mathematics: Monitoring the Arithmetic Word Problem-Solving Performance of Third-Grade Students at Risk for Mathematics Difficulties.

This purpose of this study was to examine the reliability and validity of a curriculum-based measure of word problem solving (CBM-WPS) as an indicator of performance and progress in a sample of 136 third-grade students at risk for mathematics difficulties (MDs) instructed in a standards-based mathematics curriculum. Students completed the CBM-WPS measure every 2 weeks across 12 school weeks. Results indicated that the CBM-WPS measure was reliable and significantly correlated with measures of arithmetic WPS, number combinations fluency, and a standardized test of mathematics achievement. Results of growth modeling indicated that students showed significant growth on the CBM-WPS measure, with an average increase of 0.33 problems correct per week. Additional analyses revealed that students identified as high at-risk demonstrated similar growth as students identified as low at-risk. Furthermore, the CBM-WPS growth slopes were a significant predictor of students’ spring performance on a standardized test of mathematics achievement, demonstrating their predictive validity. Implications for practice and future research for assessing mathematics skill development are discussed.