Number lines and area models are both used pervasively in teaching fractions. Prior studies found that second and third graders demonstrated better magnitude knowledge of proper fractions after a 15-minute training using the number line as compared to using the area model. The current study aimed to extend these findings to improper fractions. We randomly assigned fourth and fifth graders to a number line training, an area model training, or a non-numerical control condition. The number line and area model trainings involved both proper and improper fractions and were closely modeled on the training procedures in prior studies. Fraction training with the area model produced improvements in children's area model estimation of proper and improper fractions. However, contrary to our expectations, training with the number line did not improve number line estimation, and neither training led to improvements in transfer tasks assessing fraction magnitude knowledge. These findings suggest that children can develop the skill to represent improper fractions on area models with brief training. Nevertheless, it is unclear whether this skill enhances a comprehensive understanding of fraction magnitudes.

Pre-algebra mathematical competencies were assessed for a large and diverse sample of sixth graders (n = 1,926), including whole number and fractions arithmetic, conceptual understanding of equality and fractions magnitudes, and the fractions number line. The goal was to determine if there were clusters of students with similar patterns of pre-algebra strengths and weaknesses and if variation between clusters was related to mathematics attitudes, anxiety, or for a subsample (n = 342) some combination of intelligence, working memory, or spatial abilities. Critically, strengths and weaknesses were not uniform across the three identified clusters. Lower-performing students had pronounced deficits in their understanding of mathematical equality, fractions magnitudes, and the fractions number line. Higher-performing students had particular advantages in whole number and fractions arithmetic, and the fractions number line. Students could be reliably placed into clusters based on their mathematics self-efficacy and a combination of intelligence and spatial abilities. The results contribute to our understanding of key aspects of students' mathematical development, highlight areas in need of intervention for at-risk students, and identify cognitive areas in which scaffolds might be incorporated into these interventions.

The growth mindset or the belief that intelligence is malleable has garnered significant attention for its positive association with academic success. Several recent randomized trials, including the National Study of Learning Mindsets (NSLM), have been conducted to understand why, for whom, and under what contexts a growth mindset intervention can promote beneficial achievement outcomes during critical educational transitions. Prior research suggests that the NSLM intervention was particularly effective in improving low-achieving 9th graders’ GPA, while the impact varied across schools. In this study, we investigated the underlying causal mediation mechanism that might explain this impact and how the mechanism varied across different types of schools. By extending a recently developed weighting method for multisite causal mediation analysis, the analysis enhances the external and internal validity of the results. We found that challenge-seeking behavior played a significant mediating role, only in medium-achieving schools, which may partly explain the reason why the intervention worked differently across schools. We conclude by discussing implications for designing interventions that not only promote students’ growth mindsets but also foster supportive learning environments under different school contexts. © 2021 Taylor & Francis Group, LLC.

A dominant paradigm for research on teacher professional development has centred teacher learning as created in and through practice. Critical scholars argue for the need to grapple productively with the complexities of teaching in the power-laden contexts of schooling. This involves continual reflection on the ways that teaching reinforces structural inequalities. We articulate the notion of historical self to describe noticing as ground in both personal and social histories that are situated in hierarchies of power and dominant ideologies. We draw on data from a three year, multi-site project that engaged teachers, community members, and researchers in co-developing a noticing for re-humanising framework. Through the narrative of Shannon, a project participant-researcher, we illuminate as part of the historical self: (1) the interconnectedness of both personal and social histories in and through moment-to-moment interactions and their relation to what and how we notice; (2) the vulnerability embedded in rupturing embedded assumptions in these histories, and (3) the importance of understanding what we do not notice, as tied to our privilege.

Equity-related issues are a critical contemporary concern in mathematics education, and one specific area that has been taken up deals with equitable instructional modalities. However, the focus of many of these discussions, meetings, and publications is on K–12 mathematics education. This study reports on one aspect of an ongoing, equity issue in undergraduate mathematics education–face-to-face versus online mathematics instruction. In so doing, it investigates this issue surrounding online mathematics learning with African American (Both African American and Black are used interchangeably throughout this article, and these terms refer to students who were born and completed their schooling in the United States.) male Science, Technology, Engineering, and Mathematics (STEM) majors who have successfully completed the Calculus sequence using a critical race perspective. Findings show that these Black men did not prefer online mathematics instruction. Recommendations are shared to deal with the qualms and quarrels of online mathematics and ultimately better prepare African American male students for STEM majors. © 2020 Research Council on Mathematics Learning.

Mathematics teachers make a number of decisions that shape their lessons, which therein impact their students’ opportunity to learn mathematics. Past research has often focused on teachers, students and the mathematical content as key classroom elements that drive teachers’ decisions. In this article, we propose that a fourth element–the curriculum–along with teachers’ curricular reasoning also hold considerable influence on teachers’ decisions. Using data collected from middle grades teachers’ curricular decisions, we share the Instructional Pyramid model for Curricular Reasoning to organize the interactions among these four key classroom elements and to delineate aspects of curricular reasoning. This model serves as a multi-dimensional framework to make sense of teachers’ curricular decisions. © 2021 Research Council on Mathematics Learning.

Creative cognition has been consistently associated with functional connectivity between frontoparietal control and default networks. However, recent research identified distinct connectivity dynamics for subnetworks within the larger frontoparietal system-one subnetwork (FPCNa) shows positive coupling with the default network and another subnetwork (FPCNb) shows negative default coupling-raising questions about how these networks interact during creative cognition. Here we examine frontoparietal subnetwork functional connectivity in a large sample of participants (n=171) who completed a divergent creative thinking task and a resting-state scan during fMRI. We replicated recent findings on functional connectivity of frontoparietal subnetworks at rest: FPCNa positively correlated with the default network and FPCNb negatively correlated with the default network. Critically, we found that divergent thinking evoked functional connectivity between both frontoparietal subnetworks and the default network, but in different ways. Using community detection, we found that FPCNa regions showed greater co-assignment to a default network community. However, FPCNb showed overall stronger functional connectivity with the default network-reflecting a reversal of negative connectivity at rest-and the strength of FPCNb-default network connectivity correlated with individual creative ability. These findings provide novel evidence of a behavioral benefit to the cooperation of typically anticorrelated brain networks.

The Conceptual Survey of Electricity and Magnetism (CSEM) is a widely used multiple-choice instrument measuring a student's conceptual understanding of electricity and magnetism. This study applied modified module analysis (MMA) and modified module analysis-partial (MMA-P), network analytic methods that identify groups of correlated responses, to CSEM data from two institutions (N = 2538 and 3595). In module analysis, groups of correlated responses are called communities. As in previous applications of MMA and MMA-P to mechanics conceptual inventories, a number of communities related to physics concepts and some communities related to the structure of blocked items in the inventory were identified. An item block is a set of items all referring to each other or to a common stem. Many blocked communities involved responses where the response to the later item would be correct if the response to the earlier item was correct. This suggests a modified scoring rubric for the CSEM is needed to account for these connections between items. A modified scoring rubric is proposed; however, the modified overall average scores changed by less than 1%. The communities of incorrect responses to the CSEM related to physical concepts had varied explanations. These explanations ranged from seemingly straightforward errors (the electric field pointing to higher potential or reversing the right-hand rule), to misconceptions about Newton's 2nd and 3rd laws carried over from mechanics, to naive reasoning conflating general topics in electricity and magnetism. The identification of incorrect communities allowed the computation of misconception scores showing how prevalent the misconceptions were in the classes studied.

This study examined the mediation and moderation of membership in a demographic group underrepresented in physics classes on course outcomes measured by course grades and Force and Motion Conceptual Evaluation (FMCE) post-test scores. The study used a large dataset (N=4490) of course grades, SAT and ACT mathematics scores (ACTM), and matched FMCE pretest and post-test scores to investigate differences by gender, underrepresented ethnic or racial minority (UERM) status, and status as a first-generation college student (FGCS). For UERM and FGCS students, ACTM and pretest scores significantly mediated the relation of membership in the demographic group and both course grade and post-test score. Differences between minority and majority members of these groups were largely removed by controlling for ACTM and pretest scores. The overwhelming majority of the effect acted through ACTM for course grade (60% and 45%, respectively), while more of the effect acted through pretest score for the post-test (36% and 48%, respectively). As such, for these groups prior preparation measures predict physics outcomes (course grades or post-test scores) differently. The mediational relations for gender were dramatically different. No mediation was detected for the relation of gender to course grade because no significant difference in course grade existed. Sixty percent of the effect of gender on post-test score was not explained by either ACTM or pretest score; pretest score accounted for 38% of the effect. As such, the majority of the difference in post-test scores between men and women was not explained by either ACTM or pretest scores. Significant moderation was also detected showing that the relation of these variables was not consistent for members of all demographic groups. © 2021 authors. Published by the American Physical Society.

Purpose This paper aims to analyze the median price for existing single-family housing units in Las Cruces, New Mexico. The proposed theoretical model accounts for the interplay between supply and demand sides of a metropolitan housing market. Design/methodology/approach This study analyzes the median price for existing single-family housing units in Las Cruces, New Mexico. The proposed theoretical model accounts for the interplay between supply and demand sides of a metropolitan housing market. Explanatory variables used in the analysis are real per capita income, the housing stock, real mortgage rates, real apartment rents and the median real price of single-family units in the USA. Annual frequency data are collected for a 1971-2017 sample period. Parameter estimation is completed using two-stage generalized least squares. Empirical results confirm several, but not all, of the hypotheses associated with the underlying analytical model. In particular, Las Cruces housing prices are found to be reliably correlated with local income and national housing prices. Findings Empirical results confirm several of the hypotheses associated with the underlying analytical model. In particular, Las Cruces housing prices are found to be reliably correlated with local income and national housing prices. Research limitations/implications Results obtained support only a subset of the hypothetical relationships associated with the theoretical model. Additional testing for other small and/or medium sized is required to clarify whether these outcomes are unique to Las Cruces. Practical implications Local income fluctuations and national housing price fluctuations appear to be reliably related to housing price fluctuations for this metropolitan economy. Originality/value Comparatively little housing market research has been conducted for small and medium size urban economies. There is no guarantee that results obtained for large metropolitan housing markets are representative of smaller regional housing markets. The model developed has fairly moderate data requirements and may be applicable to other small and medium size economies such as Las Cruces.