Tracking informal fraction knowledge and its correlates across first grade.

Young children have informal knowledge of fractions before learning about fraction symbols in school. In the current study, we followed 103 children in the Mid-Atlantic United States from the fall to the spring of first grade to characterize the development of individual differences in early informal fraction knowledge, as well as its relation to other mathematical and cognitive skills. Most children in our sample showed some early fraction knowledge at the beginning of first grade, especially with nonsymbolic fractions and halving, and this knowledge improved over the school year without explicit instruction in fractions. However, there were large individual differences in early fraction knowledge at the start of first grade, which explained significant variance in math achievement at the end of first grade, even when controlling for whole number knowledge and a variety of cognitive skills. Start-of-year whole number knowledge, but not spatial scaling or proportional reasoning, also predicted early end-of-year fraction knowledge. These data can inform activities for learning in the early years to foster both early fraction and integer knowledge in parallel, which may better prepare students for later formal instruction in fractions. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Parents' and Experts' Awareness of Learning Opportunities in Children's Museum Exhibits.

Informal learning outside of school are crucial for a child's development. Children's museums, in particular, are environments conducive to this sort of learning, especially when parents guide children's exploration. However, research suggests a gap between parents' and experts' perceptions of the value of informal learning. In Study 1, we asked groups of parents and experts (i.e., individuals in the community connected with the field of education or those with training in child growth and development) to rate the presence of learning opportunities available in two museum exhibits, finding that parents consistently provided lower ratings. In Study 2, we explored whether signage aimed at orienting parents toward the learning potential in these exhibits would have an impact on their ratings. Results suggested that signage made parents' ratings look more like those of experts. Taken together, these studies show that a simple intervention can help parents perceive the learning opportunities in children's museum exhibits as experts do.

Using analogy to learn about phenomena at scales outside human perception.

Understanding and reasoning about phenomena at scales outside human perception (for example, geologic time) is critical across science, technology, engineering, and mathematics. Thus, devising strong methods to support acquisition of reasoning at such scales is an important goal in science, technology, engineering, and mathematics education. In two experiments, we examine the use of analogical principles in learning about geologic time. Across both experiments we find that using a spatial analogy (for example, a time line) to make multiple alignments, and keeping all unrelated components of the analogy held constant (for example, keep the time line the same length), leads to better understanding of the magnitude of geologic time. Effective approaches also include hierarchically and progressively aligning scale information (Experiment 1) and active prediction in making alignments paired with immediate feedback (Experiments 1 and 2).

Dealing with Big Numbers: Representation and Understanding of Magnitudes Outside of Human Experience.

Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception (e.g., nanoseconds, geologic time). This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the effectiveness of hierarchical alignment in improving estimations, and transfer across dimensions. The activity was successful in increasing accuracy for temporal and spatial magnitudes, and learning transferred to the estimation of numeric magnitudes associated with events and objects. However, there were also a number of informative differences in performance on temporal, spatial, and numeric magnitude measures, suggesting that participants possess different categorical information for these scales. Educational implications are discussed.

Delaware Longitudinal Study of Fraction Learning: Implications for Helping Children With Mathematics Difficulties.

The goal of the present article is to synthesize findings to date from the Delaware Longitudinal Study of Fraction Learning. The study followed a large cohort of children ( N = 536) between Grades 3 and 6. The findings showed that many students, especially those with diagnosed learning disabilities, made minimal growth in fraction knowledge and that some showed only a basic grasp of the meaning of a fraction even after several years of instruction. Children with low growth in fraction knowledge during the intermediate grades were much more likely to fail to meet state standards on a broad mathematics measure at the end of Grade 6. Although a range of general and mathematics-specific competencies predicted fraction outcomes, the ability to estimate numerical magnitudes on a number line was a uniquely important marker of fraction success. Many children with mathematics difficulties have deep-seated problems related to whole number magnitude representations that are complicated by the introduction of fractions into the curriculum. Implications for helping students with mathematics difficulties are discussed.

Magnitude, numerosity, and development of number: Implications for mathematics disabilities.

Leibovich et al. challenge the prevailing view that non-symbolic number sense (e.g., sensing number the same way one might sense color) is innate, that detection of numerosity is distinct from detection of continuous magnitude. In the present commentary, the authors' viewpoint is discussed in light of the integrative theory of numerical development along with implications for understanding mathematics disabilities.

Pathways to fraction learning: Numerical abilities mediate the relation between early cognitive competencies and later fraction knowledge.

The current study investigated the mediating role of number-related skills in the developmental relationship between early cognitive competencies and later fraction knowledge using structural equation modeling. Fifth-grade numerical skills (i.e., whole number line estimation, non-symbolic proportional reasoning, multiplication, and long division skills) mapped onto two distinct factors: magnitude reasoning and calculation. Controlling for participants' (N=536) demographic characteristics, these two factors fully mediated relationships between third-grade general cognitive competencies (attentive behavior, verbal and nonverbal intellectual abilities, and working memory) and sixth-grade fraction knowledge (concepts and procedures combined). However, specific developmental pathways differed by type of fraction knowledge. Magnitude reasoning ability fully mediated paths from all four cognitive competencies to knowledge of fraction concepts, whereas calculation ability fully mediated paths from attentive behavior and verbal ability to knowledge of fraction procedures (all with medium to large effect sizes). These findings suggest that there are partly overlapping, yet distinct, developmental pathways from cognitive competencies to general fraction knowledge, fraction concepts, and fraction procedures.

Developmental growth trajectories in understanding of fraction magnitude from fourth through sixth grade.

Development of fraction number line estimation was assessed longitudinally over 5 time points between 4th and 6th grades. Although students showed positive linear growth overall, latent class growth analyses revealed 3 distinct growth trajectory classes: Students who were highly accurate from the start and became even more accurate (n = 154); students who started inaccurate but showed steep growth (n = 121); and students who started inaccurate and showed minimal growth (n = 197). Younger and minimal growth students typically estimated both proper and improper fractions as being less than 1, failing to base estimates on the relation between the numerator and denominator. Class membership was highly predictive of performance on a statewide-standardized mathematics test as well as on a general fraction knowledge measure at the end of 6th grade, even after controlling for mathematic-specific abilities, domain-general cognitive abilities, and demographic variables. Multiplication fluency, classroom attention, and whole number line estimation acuity at the start of the study predicted class membership. The findings reveal that fraction magnitude understanding is central to mathematical development. (PsycINFO Database Record

Seeing Like a Geologist: Bayesian Use of Expert Categories in Location Memory.

Memory for spatial location is typically biased, with errors trending toward the center of a surrounding region. According to the category adjustment model (CAM), this bias reflects the optimal, Bayesian combination of fine-grained and categorical representations of a location. However, there is disagreement about whether categories are malleable. For instance, can categories be redefined based on expert-level conceptual knowledge? Furthermore, if expert knowledge is used, does it dominate other information sources, or is it used adaptively so as to minimize overall error, as predicted by a Bayesian framework? We address these questions using images of geological interest. The participants were experts in structural geology, organic chemistry, or English literature. Our data indicate that expertise-based categories influence estimates of location memory-particularly when these categories better constrain errors than alternative ("novice") categories. Results are discussed with respect to the CAM.

Breaking new ground in the mind: an initial study of mental brittle transformation and mental rigid rotation in science experts.

The current study examines the spatial skills employed in different spatial reasoning tasks, by asking how science experts who are practiced in different types of visualizations perform on different spatial tasks. Specifically, the current study examines the varieties of mental transformations. We hypothesize that there may be two broad classes of mental transformations: rigid body mental transformations and non-rigid mental transformations. We focus on the disciplines of geology and organic chemistry because different types of transformations are central to the two disciplines: While geologists and organic chemists may both confront rotation in the practice of their profession, only geologists confront brittle transformations. A new instrument was developed to measure mental brittle transformation (visualizing breaking). Geologists and organic chemists performed similarly on a measure of mental rotation, while geologists outperformed organic chemists on the mental brittle transformation test. The differential pattern of skill on the two tests for the two groups of experts suggests that mental brittle transformation and mental rotation are different spatial skills. The roles of domain general cognitive resources (attentional control, spatial working memory, and perceptual filling in) and strategy in completing mental brittle transformation are discussed. The current study illustrates how ecological and interdisciplinary approaches complement traditional cognitive science to offer a comprehensive approach to understanding the nature of spatial thinking.

Health worker attitudes toward peer workers in hepatitis C prevention.

Attitudes toward people who inject drugs (PWID) and attitudes toward peer workers among a cross-section of 101 Australian hepatitis C health workers were assessed. A survey consisting of Likert-type questions and one open-ended question regarding training was used. Bivariate and regression analyses demonstrated that health workers' attitudes toward peer workers were associated with their attitudes toward PWID, independent of type of organization or time in the hepatitis C sector. Qualitative analysis revealed four training areas suggested by health workers for peer workers. Implications of these findings for staff and peer training are discussed and future research directions suggested.

Perceptions of discriminatory treatment by staff as predictors of drug treatment completion: utility of a mixed methods approach.

INTRODUCTION AND AIMS: Staff interactions with their clients are an important factor in the quality of care that is provided to people in drug treatment. Yet there is very little research that addresses staff attitudes or clients' perceptions of discrimination and prejudice by staff with regard to treatment outcomes. This research aimed to assess whether perceptions of discrimination by staff predict drug treatment completion. DESIGN AND METHODS: The study used a mixed methods approach. Ninety-two clients in residential rehabilitation facilities in Sydney were administered a series of quantitative measures assessing drug history, severity of drug use, treatment history, perceptions of staff discrimination and treatment motivation. Clients were followed up regularly until an outcome (dropout or completion) was obtained for the full sample. RESULTS: Perceptions of discrimination were a significant predictor of treatment completion, with greater perceived discrimination associated with increased dropout. Qualitative interviews with 13 clients and eight health-care workers from these treatment services were then conducted to gain insight into how perceived discrimination may impact on treatment experiences. Clients and staff discussed how they would address the issue of perceived discrimination during the current treatment experience. DISCUSSION AND CONCLUSIONS: Adopting a mixed methods approach facilitated exploration of the impact of perceived discrimination on treatment from both clients' and health-care workers' perspectives. This methodology may also enhance interpretation and utilisation of these findings in drug treatment.

Exploring the role of consumer participation in drug treatment.

Despite recognition of the benefits of involving consumers in their own treatment, there is little research on consumer participation in drug treatment. This paper focuses on clients who use illicit substances and the role of consumer participation in their self-reported satisfaction with their drug treatment and sense of goal achievement in that treatment. As part of a secondary analysis, the data from 492 participants who had previously or who were currently engaged in drug treatment were analysed to assess the importance of consumer participation in drug treatment. Participants who had a history of opiate or psychostimulant use were recruited at various treatment services and health care facilities for drug users located in five urban and rural/regional sites in Australia. They were asked to complete an interviewer-assisted questionnaire assessing a range of variables including five questions about consumer participation. Findings from this study illustrate that clients' opportunity to participate in drug treatment is independently associated with greater satisfaction with drug treatment and a greater sense of achievement of treatment goals. This research provides evidence to support the importance of consumer activity in drug treatment and should encourage drug treatment programs to afford clients appropriate levels of consumer participation.