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There is a significant underrepresentation of women in many Science, Technology, Engineering, and Mathematics (STEM) majors and careers. Prior research has shown that self-efficacy can be a critical factor in student learning, and that there is a tendency for women to have lower self-efficacy than men in STEM disciplines. This study investigates gender differences in the relationship between engineering students' self-efficacy and course grades in foundational courses. By focusing on engineering students, we examined these gender differences simultaneously in four STEM disciplines (mathematics, engineering, physics, and chemistry) among the same population. Using survey data collected longitudinally at three time points and course grade data from five cohorts of engineering students at a large US-based research university, effect sizes of gender differences are calculated using Cohen's d on two measures: responses to survey items on discipline-specific self-efficacy and course grades in all first-year foundational courses and second-year mathematics courses. In engineering, physics, and mathematics courses, we find sizeable discrepancies between self-efficacy and performance, with men appearing significantly more confident than women despite small or reverse direction differences in grades. In chemistry, women earn higher grades and have higher self-efficacy. The patterns are consistent across courses within each discipline. All self-efficacy gender differences close by the fourth year except physics self-efficacy. The disconnect between self-efficacy and course grades across subjects provides useful clues for targeted interventions to promote equitable learning environments. The most extreme disconnect occurs in physics and may help explain the severe underrepresentation of women in "physics-heavy" engineering disciplines, highlighting the importance of such interventions., Comment: 31 pages, 9 figures, 2 tables

This paper describes three conceptual areas in physics that are particularly important targets for educational interventions in K-12 science. These conceptual areas are force and motion, conservation of energy, and geometrical optics, which were prominent in the US national and four US state standards that we examined. The four US state standards that were analyzed to explore the extent to which the K-12 science standards differ in different states were selected to include states in different geographic regions and of different sizes. The three conceptual areas that were common to all the four state standards are conceptual building blocks for other science concepts covered in the K-12 curriculum. Since these three areas have been found to be ripe with deep student misconceptions that are resilient to conventional physics instruction, the nature of difficulties in these areas is described in some depth, along with pointers towards approaches that have met with some success in each conceptual area., Comment: 27 pages, Keywords: Physics education research, Teaching, learning, pedagogy, Teacher preparation, k-12 education, force and motion, energy, optics, see http://www2.phy.ilstu.edu/~wenning/jpteo/issues/aut2009.html

Analogous thinking has been commonly discussed as being an inherent and distinguishing characteristic of human cognition (e.g., Gentner, 2010; Goldstone, Day, & Son, 2010; Holyoak, in press; Rittle-Johnson & Star, in press). Gentner (2003) has argued that as part of the human cognitive toolbox, comparison accompanied by the relational language to support it has rocketed humanity to the top of the natural hierarchy. As a way of appropriating this informal, experiential learning that is at least partly driven by analogous thinking (e.g., categorization; Gentner & Holyoak, 1997), numerous formal learning situations have been designed with case comparisons to teach more traditional subject matter within classrooms (e.g., Gadgil & Nokes, 2009; Gentner, Loewenstein, Thompson, & Forbus, 2009; Mason, 2004; Michael, Klee, Bransford, & Warren, 1993; Nagarajan & Hmelo-Silver, 2006; Rittle-Johnson & Star, in press; Schwartz & Bransford, 1998; etc.). Analogous thinking in the form of learning tasks requiring case comparisons is arguably a form of scaffolded constructivism that is more than merely active (Chi, 2009) because it demands from the learner a level of engagement that goes beyond the learning materials in order to notice the underlying connections between them. The appreciation of those underlying connections potentially leads to learning (Gentner, 2010). In terms of the learning environments outlined by Chi, a learning task of case comparisons is not only active but also constructive (e.g., structural alignment, role-based relational processing, etc.; Gentner, 2010; Holyoak, in press, respectively) because it provides learners with two instances and asks them to construct their own understanding that serves to bridge the cases in the most consistent way. Within the case comparisons literature, there is a great variety in the ways in which cases are instantiated and tested both in laboratory and classroom settings. Some of these variables can be considered process variables because they are related to the learners' processions through learning tasks. Process variables include the following: the qualities of cases, the types of instructions that introduce learners to the tasks, the scaffolds in place to assist learners, etc. Other variables can be considered generalizability variables: the domain of the subject matter (e.g., math, science, etc.), the age and experience levels of participants, etc. Thus, when considering the efficacy of case comparisons and the variety of methodologies that have previously investigated them, a meta-analysis seemed appropriate to get a better of sense of where the field is, how well the authors' model of this learning process fits the patterns observed, and how future investigations could be designed best to answer remaining questions. This current meta-analysis focuses on the following three questions: (1) Overall, are case comparisons a method of instruction that leads to outcomes that are superior to other forms of instruction? (2) To what extent are such findings generalizable to all learners in all domains and situations? (3) What characterizes better case comparisons learning tasks and which conditions of the authors' process variables fall short? Furthermore, the current study presents a new methodology for investigating potential moderators through meta-analytic techniques by investigating to what extent general trends are maintained across levels of other correlated variables. The sample includes studies of learners of all ages and experience-levels and both age and experience were included as potential moderators. Analyses indicated that the effects are largely generalizable. Although few studies investigated adolescent-aged learners, within this sample case comparisons seems beneficial to learners of all ages and of all levels of experience. The marginal difference found between the effect sizes in math and science do not hold up under all circumstances. In studies published in second-tier journals, effect sizes in math and science are functionally equivalent. Effect sizes in the math, science, and other domain are all equivalent when the instructional design is brief and when learners are familiar with the subject matter. Effects also seem consistent in both laboratory and classroom settings but the former tend to be brief in duration and the latter tend to be long (i.e., strongly correlated with duration). When the authors consider the findings for their process variables, several features of case comparisons tasks stand out. Learners benefit most when they are asked only to find the similarities between cases, when they are provided with the features of at least one of the two cases, and when the principle is provided after the case comparisons task. Finding only the similarities helps learners to align the cases (Gentner, 2010) potentially because doing so is the most focused form of case comparisons. Learners can easily be distracted by differences and not have the same amount of study time to appreciate fully the shared common system. Moreover, having the features of at least one case provided, potentially acts as scaffolding for the learner who might otherwise be uncertain as to how to align the two cases. Presenting the principle after the task helps to confirm the learner's potentially tentative understanding (Holyoak, in press). In a related pattern, the more immediate the testing, the better performances are but it is not only the forgetting curve at work (Ebbinghaus, 1913). It seems that the tentative nature of learners' abstractions also factor in because there is no effect of the lag in testing when the authors only analyzed the tasks that included the presentation of the principle after. Such findings support claims made within the preparation-for-future learning (PFL; Bransford & Schwartz 1999; Schwartz & Bransford, 1998) literature. Overall, case comparisons tasks seem to be a promising way to get learners to be constructive and consequently, to learn. (Contains 5 tables, 1 figure and 2 footnotes.)

The aim of this study was to test a training program intended to fine-tune the mental representations of double-digit numbers, thus increasing the discriminability of such numbers. The authors' assumption was that increased fluency in math could be achieved by improving the analogic representations of numbers. The study was completed in the University of Pittsburgh and was a behavioral as well as imaging lab study. Only the behavioral part is reported here. Forty participants (20 male) completed the experiment in return for $230 base pay plus performance bonuses for a mean total pay of $317. All participants were college students or recent graduates, 18 to 25-years-of-age with English as their first language. Participants were screened to be non-experts in math (math SAT between 600 and 700), and to not have a math-connected discipline as their major. Twenty participants (10 male) were assigned to the experimental group. The remaining participants, each matched in gender and math SAT score to an experimental participant, were assigned to the control group. The results show an advantage of the training program over control training. The selective advantages of the Arithmetic training were widespread and included gains on SAT-like complex math questions, automatic addition, math facts retrieval, and representational change of numbers. This pattern of results suggested that when engaged in a training program that emphasizes fast processing of double-digit numbers, participants enhanced a variety of skills and representations that together comprise the basis for skilled numerical processing. Rather than merely increasing the ability to retrieve math facts from memory, the training program also increased automatic arithmetical proficiency and the precision of representations of double-digit numbers. (Contains 1 table and 1 figure.)