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In a recent paper Engle et al. (Commun Math Phys 354:231–246, 2017) showed that there is a unique state on the reduced holonomy–flux ∗ -algebra of homogeneous isotropic loop quantum cosmology, that is invariant under residual diffeomorphims. This result has been claimed to be true both for the Ashtekar–Bojowald–Lewandowski framework and for that introduced by the present author. Unfortunately, the uniqueness proof relies on an incorrect argument which spoils the second case. In our short note, we are going to patch this issue, this way keeping the nice uniqueness result in both cases. Moreover, we will even extend the underlying operator algebraic statements as this might help later for studying higher-dimensional models. [ABSTRACT FROM AUTHOR]

This paper discusses issues centered around three topics related to studying textbooks in an information age. First considered are the multiple roles of textbooks, from a source of content and questions to a vehicle for changing the curriculum. Second are some of the lessons we have learned from studies comparing student performance with different textbooks within the United States, including the recognition that a common test given to students using two different curricula cannot cover the differences between the curricula and still be fair to all the students. Third is the consideration of textbooks as a delivery system and their comparison with electronic delivery of curriculum, including a discussion of the overt nature of textbooks as compared to the covert nature of electronic systems. We distinguish this use of electronic devices from the use of computers and calculators to do mathematics. Finally, predictions are given regarding the future of textbooks in an age of electronic delivery systems. The perspective of this paper is from the United States and based on the author's four decades of experience directing studies of instruction and student performance with different mathematics textbooks. [ABSTRACT FROM AUTHOR]

This paper focuses on commonalities and differences of three approaches to large-scale professional development (PD) in mathematics education, based on two studies from Germany and one from the United States of America. All three initiatives break new ground in improving PD targeted at educating 'multipliers,' and in all three cases specific design principles for successful PD are defined, implemented, and discussed. All three teams systematically investigate the success of their PD activity and thereby discuss their theoretical assumptions, research questions, methods, and results. Given the goal of scaling up, the initiatives are pilot projects due to the relatively small number of participants. The paper highlights the diversity of approaches, each including various specific strengths but also some limitations. This is done by analyzing the three studies regarding the features 'large-scale PD and scientific knowledge on it', 'goals and design of PD', 'research design and methods', and 'research results and implications'. Overall, the studies help to understand the enormous challenges of the field when aiming at large-scale PD and systematically investigating and reflecting its impact. One prominent challenge is teacher educators' double role of intervening and investigating. All three studies recommend a continued or even stronger focus on participants' practice and its challenges. It makes sense to assume that the focus on participants' practice and strengths is even more important when starting further cascades. [ABSTRACT FROM AUTHOR]

Research universities in the United States have larger mathematics faculties outside their mathematics departments than inside. Members of this 'extensive' faculty conduct most mathematics research, their interests are the most heavily published areas of mathematics, and they teach this mathematics in upper division courses independent of mathematics departments. The existence of this de facto faculty challenges the pertinence of institutional and national policies for higher education in mathematics, and of philosophical and sociological studies of mathematics that are limited to mathematics departments alone. [ABSTRACT FROM AUTHOR]

Objectives: A large body of research exists on families and their impact on children's developmental outcomes. Fewer studies examine family processes within different family structures and their impact on adolescents. This study extends prior work by evaluating associations between family structure (two biological parents, single-parent—mother only, and blended families with a step parent), family functioning (communication, cohesion and flexibility) and adolescents' logic and reasoning skills and math performance. Methods: A convenience sample of 269 African American adolescents was recruited from a university-based summer enrichment program. The sample was mostly female (63%), with a mean age of 16.34 years. Data were derived from the baseline assessment during which participants completed the Family Adaptability and Cohesion Evaluation Scales (FACES IV), a computer-administered test of cognitive skills, and a paper-based math performance test. Results: Families with different structures varied in their family functioning (Wilks' ʌ = 0.942, F(6, 496) = 2.486, p = 0.022, η2 = 0.835). Families differed on the dimensions of cohesion (F(2, 250) = 5.80, p = 0.003, η2 = 0.044), flexibility (F(2, 250) = 5.48, p = 0.005, η2 = 0.042) and communication (F(2, 250) = 5.80, p = 0.003, η2 = 0.047). Different dimensions of family functioning significantly predicted both logic and reasoning skills (F(7, 244) = 2.14, p = 0.040, R2 = 0.06) and math outcomes (F(7, 142) = 3.16, p = 0.004, R2 = 0.14). Conclusions: Families with different household structures differ in their functioning, including in their levels of cohesion, flexibility and communication. Family functioning is more important than family structure in predicting African American adolescents' reasoning skills and math performance. [ABSTRACT FROM AUTHOR]

When asked to estimate how much their state or nation has contributed to history, people typically provide unreasonably large estimates, claiming that their group has contributed much more to history than nongroup members would estimate, demonstrating collective overclaiming. Why does such overclaiming occur? In the current study we examined factors that might predict collective overclaiming. Participants from 12 U.S. states estimated how much their home state contributed to U.S. history, completed measures of collective narcissism and numeracy, and rated the importance of 60 specific historical events. There was a positive relationship between collective overclaiming and collective narcissism, a negative relationship between collective overclaiming and numeracy, and a positive relationship between collective overclaiming and the importance ratings of the specific events. Together, these results indicate that overclaiming is partially and positively related to collective narcissism and negatively related to people's ability to work with numbers. We conclude that collective overclaiming is likely determined by several factors, including the availability heuristic and ego protection mechanisms, in addition to collective narcissism and relative innumeracy. [ABSTRACT FROM AUTHOR]

This paper introduces an analytic framework that can be used to assess the relationships between individual movement differentials and place characteristics, on the one hand, and aggregate mobility levels and city-suburb population change (in size or composition), on the other. Application of this framework using census data for individual metropolitan areas allows the analyst to decompose population changes due to net migration into contributing mobility streams and their component rates which are subject to unique community and individual influences. The paper provides both theoretical and empirical rationale for the framework, illustrates its use with 1970 census data, and discusses its implications for empirical research on city-suburb population redistribution. [ABSTRACT FROM AUTHOR]

This paper deals with a further analysis of the stable equivalent population for human populations. It first shows that the arithmetic difference between the size of the stable equivalent population and the actual population captures the total prospective contribution of age composition to the growth of the present population" if fertility and mortality rates are held constant at their current levels. The second part of the paper examined Fisher's reproductive value function and investigates the location of maxima in relation to alternative values of the intrinsic growth rate. One conclusion which follows from this analysis is that, contrary to what has been discovered by others in specific examples, the reproductive value function can possess a global maximum in the first one or two years of life, provided the intrinsic rate of population growth is sufficiently negative. This principle is illustrated by reference to reproductive value functions calculated from the recent experience of U.S. females. [ABSTRACT FROM AUTHOR]

This work studies mathematics word problems' use in a classroom of recent immigrants, or newcomers, to a United States public elementary school. I study how word problems foster the recontextualization of mathematical concepts in a lived reality experienced by newcomer students in their new cultural and educational setting. In this study's setting language plays a significant role in the process of meaning-making. I describe how language use in word problems remains intertwined with mathematics instruction. This opens a space for questioning word problems' purpose and role in multilingual classrooms, and I highlight how the creative process of co-constructing problems' meaning in this context can expand notions of genre applied to word problems. Throughout I adopt a theorization of translanguaging as a language practice and apply it in problem discussion. This helps probe how language use impacts students' ways of understanding and utilizing mathematical concepts. [ABSTRACT FROM AUTHOR]

Place-of-birth-by-residence data, tabulated by age and sex for the same areal units in two successive censuses, have been used to estimate intercensal net migration flows. However, a fuller use of the same data permits the estimation of place-to-place flows. This paper describes a method for estimating intercensal migration streams from place-of-birth- by-residence data and illustrates its application with data on the white female native population of the United States. [ABSTRACT FROM AUTHOR]

Despite widespread agreement that proof should be central to all students' mathematical experiences, many students demonstrate poor ability with it. The curriculum can play an important role in enhancing students' proof capabilities: teachers' decisions about what to implement in their classrooms, and how to implement it, are mediated through the curriculum materials they use. Yet, little research has focused on how proof is promoted in mathematics curriculum materials and, more specifically, on the guidance that curriculum materials offer to teachers to enact the proof opportunities designed in the curriculum. This paper presents an analytic approach that can be used in the examination of the guidance curriculum materials offer to teachers to implement in their classrooms the proof opportunities designed in the curriculum. Also, it presents findings obtained from application of this approach to an analysis of a popular US reform-based mathematics curriculum. Implications for curriculum design and research are discussed. [ABSTRACT FROM AUTHOR]

Explores the work of Nicolas Rashevsky, a Russian émigré theoretical physicist who developed a program in mathematical biophysics at the University of Chicago in Illinois during the 1930s. Resistance of experimental biologists to mathematical biology during the time of Rashevsky; Claims of Rashevsky that methods of theoretical physics were needed to simplify complex biological processes; Gap between the physicist's idealizations and work.

This study assessed whether the links between early maternal employment and children's school readiness have changed over time. Research has examined mothers' labor force participation and its associations with children's well-being. As maternal employment has become more normative, these associations may have changed, particularly among subgroups of families. Data come from two large, longitudinal samples of children born in the U.S. in 1991 (N = 1042) and in 2001 (N = 7850). OLS regression models estimated changes between cohorts in the associations between early maternal employment and children's reading/language skills, math skills, and conduct problems at age 4 and school entry. Despite similar prevalence rates of maternal employment by 9 months between the 1991 and 2001 samples, there were differences in the demographic characteristics of mothers in each employment pattern over the decade. Examining associations between the early maternal employment patterns and children's school readiness, results revealed that full time employment by 9 months in comparison to non-employment shifted to having more positive associations with reading/language skills at age 4 and school entry from 1991 to 2001. However, full time maternal employment by 9 months was associated with children's higher conduct problems at school entry in 1991 and 2001, and by 2001, part time employment had similar repercussions. The results differed by family income. There have been small changes in the associations between early maternal employment and children's school readiness over time. Highlights: Full time employment by 9 months shifted to having more positive links with reading/language skills from 1991 to 2001. Full time maternal employment by 9 months was associated with children's higher conduct problems in 1991 and 2001. Changes in the associations between maternal employment and school readiness differed by family income. [ABSTRACT FROM AUTHOR]

The mathematics education community has been widely recognized as a leader in the standards-based reform movement. Despite the widespread interest and attention that reform documents such as the NCTM Standards have generated. what has yet to he fully understood is the impact of these types of reform documents on the preservice teacher preparation process. This paper examines the state of the standards-based reform effort in mathematics teacher education by presenting the results of a three-year study of six cohorts of secondary mathematics student teachers (n = 63). Examined in particular are the ways in which these student teachers' professed beliefs about and knowledge of the NCTM Standards contrast with their teaching practices. Possible explanations for the mismatch between belief and knowledge statements and teaching practices are examined, along with other implications for mathematics teacher preparation. [ABSTRACT FROM AUTHOR]

Lifetime and age-conditional risk estimates of developing cancer provide a useful summary to the public of the current cancer risk and how this risk compares with earlier periods and among select subgroups of society. These reported estimates, commonly quoted in the popular press, have the potential to promote early detection efforts, to increase cancer awareness, and to serve as an aid in study planning. However, they can also be easily misunderstood and frightening to the general public. The Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute and the American Cancer Society have recently begun including in annual reports lifetime and age-conditional risk estimates of developing cancer. These risk estimates are based on incidence rates that reflect new cases of the cancer in a population free of the cancer. To compute these estimates involves a cancer prevalence adjustment that is computed cross-sectionally from current incidence and mortality data derived within a multiple decrement life table. This paper presents a detailed description of the methodology for deriving lifetime and age-conditional risk estimates of developing cancer. In addition, an extension is made which, using a triple decrement life table, adjusts for a surgical procedure that removes individuals from the risk of developing a given cancer. Two important results which provide insights into the basic methodology are included in the discussion. First, the lifetime risk estimate does not depend on the cancer prevalence adjustment, although this is not the case for age-conditional risk estimates. Second, the lifetime risk estimate is always smaller when it is corrected for a surgical procedure that takes people out of the risk pool to develop the cancer. The methodology is applied to corpus and uterus NOS cancers, with a correction made for hysterectomy prevalence. The interpretation and limitations of risk estimates are also discussed. [ABSTRACT FROM AUTHOR]

To influence the number of children ever born to a woman, socioeconomic variables must operate through behavioral and biological mechanisms such as the age at marriage, the level of fertility in the absence of deliberate fertility control, and the level of control exerted to reduce fertility within marriage. In this paper, we propose a new measure of cumulative fertility which is standardized for the age-fecundity relationship and for exposure to the risk of conception associated with duration of marriage. A simple model of fertility behavior which incorporates some of the mechanisms through which socioeconomic factors may affect fertility is developed and applied to data from the United States to demonstrate the properties of alternative measures of family size. The results indicate that use of the new measure allows more precise estimates of socioeconomic fertility relationships than would be obtained with children ever born or by sample stratification. [ABSTRACT FROM AUTHOR]

Several authors have argued that increased work opportunities for women have helped to produce a reduction in the average age at marriage in the United States. This paper tests this proposition on data for the 100 largest SMSA's in 1960. Using ordinary least-squares regression, we find that areas of relatively attractive female employment opportunities had relatively low proportions of women ever married in the age interval 22-24. Other variables significantly related to the proportion married in an SMSA are its sex ratio, percent Catholic, and number of inhabitants. A decline in the sex ratio and improvements in female employment opportunities appear to have been equally influential in producing declines in proportions married between 1960 and 1970. [ABSTRACT FROM AUTHOR]

If the pattern of fertility, mortality and interregional migration exhibited by the United States population during 1950-60 were to continue in the future, the proportions of persons in the various age groups and regions would fluctuate from decade to decade. These fluctuations would become less marked with time, however, and eventually all the proportions would stabilize at certain fixed values. This collection of values may be called a stable age by region composition corresponding to the given schedule of fertility, mortality and migration. The same phenomenon may be observed when individuals move between socioeconomic categories as, for example, socioeconomic status or educational attainment levels. The substantial differences between these various situations conceal remarkable similarities. In each case the continued operation of schedules of fertility, mortality and mobility between categories may result in a stable composition. The purpose of this paper is to shed some light on the nature of these stable compositions, on the interrelation between their various components, and on their relation to the patterns of fertility, mortality and mobility which generate them. [ABSTRACT FROM AUTHOR]

We examined the relationships between different aspects of mathematics engagement for 285 students in their first year of high school in the United States. Path Analyses were used to trace the relationships between students' self-reported prior motivation and appraisals of control and value of mathematics, perceptions of teacher support and peer support. These variables and observed teacher and peer support as coded from video by researchers, were examined as potentially impacting students' self-reported in-the moment affect and task-level control and value appraisals Our results showed three key contributions. First, significant paths corresponded to relationships predicted by Control Value Theory (CVT) across a particularly robust set of variables and over the course of their first semester in high school. Second, results added further nuance by considering the objects that students' in-the-moment emotions were directed toward, showing distinctions between positive and negative emotions directed at the mathematics task, students' teachers and peers, and selves. Third, results more closely considered the impact of both observed and perceived aspect of support from peers and teachers in the classroom, in both its academic and social forms. Implications are discussed for theory and practice. [ABSTRACT FROM AUTHOR]

Little research has examined the associations between perceived inclusivity within informal science learning sites, youth program belonging and perceptions of program career preparation. This study explored relations between these factors at three timepoints (T1 = start of program, T2 = 3 months and T3 = 12 months after start). Participants were a diverse sample of 209 adolescents participating in STEM youth programs within informal science learning sites situated in the United States and United Kingdom (70% females: Mage = 15.27, SDage = 1.60), with 53.1% British and 64.1% non-White. Path analysis revealed that only perceptions of inclusivity for own social identity group (i.e., gender, ethnicity) at T1 were associated with T2 STEM youth program belonging. There was a significant indirect effect of T1 perceptions of inclusivity for one's own social identity groups on T3 perceptions of program career preparation via T2 program belonging. This study highlights that, over time, perceptions of inclusivity around youth's own social identity groups (i.e., gender and ethnicity/culture) are related to a sense of youth program belonging, which in turn is later associated with perceptions of program career preparation. [ABSTRACT FROM AUTHOR]

Background: Implementing research-based teaching practices has been repeatedly cited as an important factor for student success in university mathematics courses. Many research-based practices increase the amount of student–student and/or student–instructor interaction. However, some instructors are hesitant to implement such practices because they anticipate their students reacting negatively to experiencing an interactive classroom. As part of a larger project studying introductory undergraduate mathematics courses in the United States, we investigated students' perceptions of the helpfulness of various classroom characteristics, particularly those that require interaction. Results: From analyzing quantitative student data, we found that students reported interactive classroom characteristics (e.g., group work) as less prevalent than other classroom characteristics (e.g., lecture). Moreover, the students tended to regard characteristics that they reported experiencing often as helpful for their learning. From analyzing qualitative data from student focus groups, we found that students considered several indicators when identifying if a characteristic was helpful for their learning. In particular, students suggested that they can identify a characteristic as helpful for their learning when it supported them in solving assigned problems and understanding why the procedures work, earning good grades, building on their knowledge or applying it in different contexts, and teaching others. Conclusions: The key finding from our work is that students are likely to view classroom characteristics that they experience more often as more helpful for their learning and are less likely to view characteristics that they rarely experience as helpful for their learning. Students view the characteristics that they regularly experience as helping them to solve problems and understand why the procedures work, earn good grades, build on their knowledge or apply it in different contexts, and teach others. We discuss important implications for practice, policy, and research as it relates to both student and instructor buy-in for increasing interactions in class. [ABSTRACT FROM AUTHOR]

Background: Active learning used in science, technology, engineering, and mathematics (STEM) courses has been shown to improve student outcomes. Nevertheless, traditional lecture-orientated approaches endure in these courses. The implementation of teaching practices is a result of many interrelated factors including disciplinary norms, classroom context, and beliefs about learning. Although factors influencing uptake of active learning are known, no study to date has had the statistical power to empirically test the relative association of these factors with active learning when considered collectively. Prior studies have been limited to a single or small number of evaluated factors; in addition, such studies did not capture the nested nature of institutional contexts. We present the results of a multi-institution, large-scale (N = 2382 instructors; N = 1405 departments; N = 749 institutions) survey-based study in the United States to evaluate 17 malleable factors (i.e., influenceable and changeable) that are associated with the amount of time an instructor spends lecturing, a proxy for implementation of active learning strategies, in introductory postsecondary chemistry, mathematics, and physics courses. Results: Regression analyses, using multilevel modeling to account for the nested nature of the data, indicate several evaluated contextual factors, personal factors, and teacher thinking factors were significantly associated with percent of class time lecturing when controlling for other factors used in this study. Quantitative results corroborate prior research in indicating that large class sizes are associated with increased percent time lecturing. Other contextual factors (e.g., classroom setup for small group work) and personal contexts (e.g., participation in scholarship of teaching and learning activities) are associated with a decrease in percent time lecturing. Conclusions: Given the malleable nature of the factors, we offer tangible implications for instructors and administrators to influence the adoption of more active learning strategies in introductory STEM courses. [ABSTRACT FROM AUTHOR]

Brief experimental analysis (BEA) can be used to specify intervention characteristics that produce positive learning gains for individual students. A key challenge to the use of BEA for intervention planning is the identification of performance indicators (including topography of the skill, measurement characteristics, and decision criteria) that meaningfully relate to longer term success in the learning environment. This study investigates the utility of various curriculum-based assessment and measurement estimates of mathematics performance for predicting functional outcomes (i.e., retention of learned skills over time and faster learning of related content in the future). All children in grades 2–5 at the participating school participated in protocol-based computational fluency-building intervention 4 days per week for an entire school year. Specific criteria were applied each week to systematically increase intervention difficulty classwide according to a pre-established sequence of computational skill objectives. Three measurements were routinely obtained. Each week children completed a timed probe of the skill for which intervention was currently occurring and a timed probe of previously mastered skills from the sequence of computational skill objectives. Each month, all children completed a timed probe of mathematics skills representing computational skills that students were expected to master by year’s end at each grade level. At all grade levels, learning a skill that appeared early in the hierarchy or sequence of skills related positively to learning of future related and more complex computational skills. Fluency criteria were specified that predicted retention of the skill over several months. [ABSTRACT FROM AUTHOR]

In Baumann (American Philosophical Quarterly 42: 71–79, 2005) I argued that reflections on a variation of the Monty Hall problem throws a very general skeptical light on the idea of single-case probabilities. Levy (Synthese, forthcoming, 2007) puts forward some interesting objections which I answer here. [ABSTRACT FROM AUTHOR]

A novel technique of functional Feynman-Kac equations is developed for the probability distribution of the limit lognormal multifractal process introduced by Mandelbrot [in Statistical Models and Turbulence, M. Rosenblatt and C. Van Atta, eds., Springer, New York (1972)] and constructed explicitly by Bacry, Delour, and Muzy [ Phys. Rev. E 64:026103 (2001)]. The distribution of the process is known to be determined by the complicated stochastic dependence structure of its increments (SDSI). It is shown that the SDSI has two separate layers of complexity that can be captured in a precise way by a pair of functional Feynman-Kac equations for the Laplace transform. Exact solutions are obtained as power series expansions in the intermittency parameter using a novel intermittency differentiation rule. The expansion of the moments gives a new representation of the Selberg integral. [ABSTRACT FROM AUTHOR]

The article features the conference "Renaissance Banff: Mathematics, Music, Art, Culture" that was held on July 30 to August 3, 2005. The conference was the first interdisciplinary conference on mathematics and the arts to be held at the famed Banff Centre and brought a diverse group of about 200 participants from the United States, Canada, and abroad. Several activities are detailed.

This paper offers for discussion and critique a conceptual framework that applies a situative perspective on learning to the study of learning to teach mathematics. From this perspective, such learning occurs in many different situations -- mathematics and teacher preparation courses, pre-service field experiences, and schools of employment. By participating over time in these varied contexts, mathematics teachers refine their conceptions about their craft -- the big ideas of mathematics, mathematics-specific pedagogy, and sense of self as a mathematics teacher. This framework guides a research project that traces the learning trajectories of teachers from two reform-based teacher preparation programs into their early teaching careers. We provide two examples from this research to illustrate how this framework has helped us understand the process of learning to teach. [ABSTRACT FROM AUTHOR]

Background: Motivation is critical for supporting persistence and achievement in science, technology, engineering, and mathematics (STEM) disciplines. In this study, we focus on the assessment of mathematics motivation among secondary school students. We provide validity and reliability evidence for the Mathematics Motivation Questionnaire (MMQ)—adapted from the Science Motivation Questionnaire designed for college students—using data from 2551 secondary students from seven states across the United States. Results: Exploratory and confirmatory factor analyses confirmed five latent factors of the MMQ indicated by 19 items: intrinsic value, self-regulation, self-efficacy, utility value, and test anxiety. The nonlinear SEM reliability coefficients of the five constructs ranged from 0.76 to 0.91. To assess criterion validity, analyses using a subset of the data that included students' mathematics standardized scores (n = 536) indicated that intrinsic value, self-regulation, and self-efficacy were significantly positively correlated with mathematics achievement, whereas test anxiety was significantly negatively correlated with mathematics achievement. Conclusions: The MMQ provides a reliable, valid, and feasible measure of the specific factors underlying mathematics motivation among secondary students. [ABSTRACT FROM AUTHOR]

Early math success in the PreK classroom is recognized as a strong predictor of later academic success. However, many early childhood teachers report they lack the content knowledge, confidence and beliefs to deliver high quality math experiences in their classrooms. Professional development opportunities to gain and expand these skills are often difficult for early childhood educators to access. The purpose of this article is to examine the professional development opportunities available to early childhood educators in the United States and to present a model of professional development that is accessible and effective. This article provides a description of the importance of math in the early years and reveals the need for early math professional development opportunities for early childhood teachers. A portrait of the current state of professional development opportunities for early childhood teachers in the United States is presented along with a presentation of a successful online early math professional development program that was developed to meet the need of early childhood educators. The article ends with implications for current professional development opportunities and ideas for future directions. [ABSTRACT FROM AUTHOR]

Assessment data from the United States and international reports of student achievement indicate that upper elementary students are failing to meet basic levels of proficiency in fractions and writing, and that this is particularly prevalent with students with or at-risk for learning disabilities in mathematics. Proficiency with fractions has been identified as foundational for learning higher-level mathematics but remains one of the most difficult skills for students to learn. In addition, students' difficulty with fractions is exacerbated because of increased chances of comorbidity with language learning problems, particularly difficulties constructing arguments and communicating using writing. We describe FACT + R2C2, a language-based, metacognitive instructional intervention that was designed using the Self-Regulated Strategy Development model (SRSD) for teaching foundational concepts of fractions. The results from two studies in which the intervention was administered to upper elementary students who exhibit mathematics difficulties indicated selected increases in students' computational accuracy, quality of mathematical reasoning, number of rhetorical elements, and total words. With evidence of improved performance in these areas, FACT + R2C2 holds promise for helping these students become proficient self-regulated learners. [ABSTRACT FROM AUTHOR]

Writing is recognized as a critical skill in science, technology, engineering, and mathematical fields, as it provides opportunities for individuals to think critically about learned information, integrate knowledge, communicate understanding, and contribute new information to the field. Requirements for applying mathematical knowledge to writing require a seamless blend of content-specific knowledge, domain-specific vocabulary, and an understanding of written expression. Relatively, little is known about how mathematics writing is currently being assessed in K-12 classrooms to promote the acquisition and growth of students' writing. This exploratory survey research sought to evaluate how undergraduate students across various career majors, at a large university in the USA, perceive the writing quality of elementary mathematics writing samples. Research determined that respondents valued accuracy of the mathematics, logical explanation, effort of the response, as well as organization/mechanics of the writing. The extremes of mathematical writing had the most reliable scores, bringing attention to the need to develop quality assessments (e.g., rubrics) that address subjectivity of writing quality indicators and explicitly communicate expectations of mathematics writing. Implications for practice and future research are presented. [ABSTRACT FROM AUTHOR]

Family food routines are important contexts through which children develop math knowledge and skills. The Food For Thought (FFT) program teaches Latino parents strategies to develop their kindergarten children's math abilities during family food routines such as grocery shopping and cooking. We examined whether attendance to FFT was related to children's math outcomes at post-test (right after program completion). Sixty-eight low-income Latino parents and their kindergarten children (M = 71 months) participated in the four-week program taking place in schools. Children's math skills (counting, numeral recognition and cardinal understanding) were assessed at pre- and post-test. The association between parents' attendance to FFT meetings and children′s math outcomes at post-test depended on children's initial levels of math skills (i.e., math skills at pre-test). Children with lower initial math skills whose parents attended more FFT meetings had more advanced math outcomes at post-test, than children with lower initial math skills whose parents attended fewer FFT meetings. The effect size of this interaction was moderate, d = 0.46. Limitations and future directions of this early math intervention targeting Latino families are discussed. [ABSTRACT FROM AUTHOR]

Although women have made progress in entering scientific careers in biology, they remain underrepresented in mathematically intensive fields such as physics. We investigated whether gender differences in mathematics motivation and socialisers' perceptions impacted choices for diverse STEM careers of varying mathematical intensity. Drawing on expectancy-value theory, we tested structural equation models in which adolescents' preferred careers related to each of physics, biology, chemistry, and mathematics were predicted by prior mathematical performance, motivations, and mothers' perceptions. We explored potential differences in gendered processes of influence using multigroup models. Samples were 331 Australian adolescents followed from 9th to 11th grade in 1998 and 277 U.S. adolescents from 9th to 12th grade in 2009-10. In both samples female adolescents preferred biological careers more than males did; male adolescents preferred physics-related careers and also mathematical careers in the Australian sample. Mothers' perceptions were important to female and male adolescents' mathematics motivations; gendered motivations were more evident in the Australian sample. Mathematics interest played the strongest role in male adolescents' preferred careers, whereas actual or perceived mathematical achievements were most important for females, demonstrating the impacts of mathematical motivations on preferences for diverse STEM careers. [ABSTRACT FROM AUTHOR]

Mathematics motivation declines for many adolescents, which limits future educational and career options. The present study sought to identify predictors of this decline by examining whether implicit theories assessed in ninth grade (incremental/entity) predicted course-taking behaviors and utility value in college. The study integrated implicit theory with variables from expectancy-value theory to examine potential moderators and mediators of the association of implicit theories with college mathematics outcomes. Implicit theories and expectancy-value variables were assessed in 165 American high school students (47 % female; 92 % White), who were then followed into their college years, at which time mathematics courses taken, course-taking intentions, and utility value were assessed. Implicit theories predicted course-taking intentions and utility value, but only self-concept of ability predicted courses taken, course-taking intentions, and utility value after controlling for prior mathematics achievement and baseline values. Expectancy for success in mathematics mediated associations between self-concept of ability and college outcomes. This research identifies self-concept of ability as a stronger predictor than implicit theories of mathematics motivation and behavior across several years: math self-concept is critical to sustained engagement in mathematics. [ABSTRACT FROM AUTHOR]

Using data from a well-executed randomized experiment, I examine the effects of gender composition and peer achievement on high school students' outcomes in disadvantaged neighborhoods. Results show that having a higher proportion of female peers in the classroom improves girls' math test scores only in less-advanced courses. For male students, the estimated gender peer effects are positive but less precisely estimated. I also find no effect of average classroom achievement on female math test scores. Males, on the other hand, seem to benefit from a higher-achieving classroom. I propose mechanisms relating to lower gender stereotype influences and gender-specific attitudes toward competition as potential explanations for peer effects findings. Finally, having a higher proportion of female students in the classroom decreases student absenteeism among male students but has no impact on female attendance. [ABSTRACT FROM AUTHOR]

Using a nationally representative sample of 1,189 immigrant youth in American high schools, we examine whether the quality of education in their country of origin is related to post-migration math achievement in the 9th grade. To measure the quality of their education in the country of origin, we use country-specific average test scores from two international assessments: the Programme for International Student Assessment (PISA) and the Trends in International Mathematics and Science Study (TIMSS). We find that the average PISA or TIMSS scores for immigrant youth's country of origin are positively associated with their performance on the 9th grade post-migration math assessment. We also find that each year spent in the United States is positively associated with performance on the 9th grade post-migration math assessment, but this effect is strongest for immigrants from countries with low PISA/TIMSS scores. [ABSTRACT FROM AUTHOR]

Evidence-based interventions are being disseminated broadly in schools across the USA, but the implementation levels achieved in community settings vary considerably. The current study examined the extent to which teacher and school factors were associated with implementation dosage and quality of the PAX Good Behavior Game (PAX GBG), a universal classroom-based preventive intervention designed to improve student social-emotional competence and behavior. Specifically, dosage (i.e., number of games and duration of games) across the school year and quality (i.e., how well the game is delivered) of PAX GBG implementation across four time points in a school year were examined. Hierarchical linear modeling was used to examine the association between teacher-level factors (e.g., demographics, self-reports of personal resources, attitudes toward the intervention, and workplace perceptions) and longitudinal implementation data. We also accounted for school-level factors, including demographic characteristics of the students and ratings of the schools' organizational health. Findings indicated that only a few teacher-level factors were significantly related to variation in implementation. Teacher perceptions (e.g., fit with teaching style, emotional exhaustion) were generally related to dosage, whereas demographic factors (e.g., teachers' age) were related to quality. These findings highlight the importance of school contextual and proximal teacher factors on the implementation of classroom-based programs. [ABSTRACT FROM AUTHOR]

This study examined the difference between children with autism spectrum disorders (ASD) and children with typical development (TD) in mathematical word problem solving ability and the factors associated with these children's word problem-solving ability. A total of 20 children with ASD and 20 children with TD participated in this study. Independent sample t tests and Spearman's rho correlations were used for data analysis. This study found: (a) Children with TD had higher word problem solving ability than did children with ASD; (b) Sentence comprehension, math vocabulary, computation, and everyday mathematical knowledge were associated with word problem solving ability of children with ASD and children with TD; and (c) Children with TD had higher everyday mathematical knowledge than did children with ASD. [ABSTRACT FROM AUTHOR]

The present work investigates the validation of a newly developed instrument, the attributional bias instrument, based on achievement attribution theories that distinguish between effort and ability explanations of behavior. The instrument further incorporates the distinction between explanations for success versus failure in academic performance. An important characteristic of the instrument is that it can be used to assess biased attributions. For instance, attributional gender bias is the tendency to generate different attributions (explanations) for female versus male students' performance in math. Whereas boys' successes in math are attributed to ability, girls' successes are attributed to effort; conversely, boys' failures in math are attributed to a lack of effort and girls' failures to a lack of ability. Previous research has shown this bias to be committed by teachers, parents, and students themselves. In the present study, high school students in Mexico were administered the instrument and asked to generate attributions for their successes and failures in math. Findings revealed: (1) a factor analysis confirmed the proposed structure of the instrument, (2) boys and girls committed the attributional gender bias, replicating effects in U.S. samples, and (3) additional analyses involving related measures further supported valid use of the instrument. [ABSTRACT FROM AUTHOR]

In previous work with a nationally representative sample of over 1,400 monozygotic and dizygotic twins born in the US, Tucker-Drob et al. (Psychological Science, 22, 125-133, ) uncovered a gene × environment interaction on scores on the Bayley Short Form test of mental ability (MA) at 2 years of age-higher socioeconomic status (SES) was associated not only with higher MA, but also with larger genetic contributions to individual differences in MA. The current study examined gene × SES interactions in mathematics skill and reading skill at 4 years of age (preschool age) in the same sample of twins, and further examined whether interactions detected at 4 years could be attributed to the persistence of the interaction previously observed at 2 years. For early mathematics skill but not early reading skill, genetic influences were more pronounced at higher levels of SES. This interaction was not accounted for by the interaction observed at 2 years. These findings indicate that SES moderates the etiological influences on certain cognitive functions at multiple stages of child development. [ABSTRACT FROM AUTHOR]

The author expresses concern about the math standards of the Common Core Curriculum in relation to young children. The editorial cites others who share concerns about how the global community uses standards. She suggests caution in implementation because the overemphasis on the standards may overlook the investment needed in effective curriculum development and professional development for teachers. The editorial concludes with the revisions will be neccesary to the current version of the Common Core Standards given the concern. [ABSTRACT FROM AUTHOR]

Over the past decade the U.S. Environmental Protection Agency (EPA) and the states have partnered in developing a web-based information sharing initiative that provides state environmental agencies easy access to federal environmental monitoring data and to the environmental data of other states, and gives the EPA access to data from state sources. The Environmental Information Exchange Network (EIEN) has established basic data exchange nodes in each of the states. Using multiple regression analysis we investigate the factors that account for the number and development stage of the data exchanges in which the states participate as of 2009. Overall, we find that administrative factors, especially the EPA's grant program, are more important than political or environmental conditions. Participation in the exchanges is important not only as a way to reduce costs for data reporting and communication, but also as a precursor to greater eventual interstate environmental collaboration. Though clear evidence of a transition to collaboration is not yet seen here, there are some indications it may emerge in time. [ABSTRACT FROM AUTHOR]

Given the large investment in teacher professional development (PD), further understanding of the factors that impact PD success is needed. In a previous study, the authors established a framework for categorizing PD projects using the notion of orientations. A PD orientation is comprised of project characteristics that drive the PD design and implementation for that project. In this study, we applied this orientation framework to 14 science and mathematics PD projects and examined the relationship between projects of differing orientations and PD outcomes (e.g. perceived improvement in teaching practices). The results provide support for the value of the framework and demonstrate that PD projects with different orientations exhibit differing participant outcomes. This study also provides evidence of the value of this research framework for understanding how PD implementation characteristics are related to PD outcomes, as well as points to the value of a 'balanced' orientation where both content and pedagogy are addressed in equal parts. [ABSTRACT FROM AUTHOR]

Mathematics education is a critical part of the curriculum for students worldwide. The foundation for understanding mathematical concepts related to number sense begins early in life, and early childhood classrooms can provide the seeds for mathematical skills that will be needed later in life. In this article, the authors make a case for meaningful and developmentally appropriate mathematics experiences for young children in diverse early learning settings. Instructional and curricular methods inspired by the Reggio Emilia Approach are described as effective ways to teach number concepts to young children from preschool through primary age. Strategies for teachers of young learners are presented in order to strengthen the mathematics curriculum in contemporary early learning settings. The authors' analysis and recommendations are informed by their extensive experiences including studies in Reggio Emilia early childhood settings (infant toddler, preschool, and primary schools) and their work in early childhood teacher education at their respective universities. [ABSTRACT FROM AUTHOR]

Different forms of curriculum determine what is taught and learned in US classrooms and have been used to stimulate school improvement and to hold school systems accountable for progress. For example, the intended curriculum reflected in standards or learning expectations increasingly influences how instructional time is spent in classrooms. Curriculum materials such as textbooks, instructional units, and computer software constitute the textbook curriculum, which continues to play a dominant role in teachers' instructional decisions. These decisions influence the actual implemented curriculum in classrooms. Various curriculum policies, including mandated end-of-course assessments (the assessed curriculum) and requirements for all students to complete particular courses (e.g., year-long courses in algebra, geometry, and advanced algebra or equivalent integrated mathematics courses) are also being implemented in increasing numbers of states. The wide variation across states in their intended curriculum documents and requirements has led to a historic and precedent-setting effort by the Council of Chief State School Officers and the National Governors Association Council for Best Practices to assist states in the development and adoption of common College and Career Readiness Standards for Mathematics. Also under development by this coalition is a set of common core state mathematics standards for grades K-12. These sets of standards, together with advances in information technologies, may have a significant influence on the textbook curriculum, the implemented curriculum, and the assessed curriculum in US classrooms in the near future. [ABSTRACT FROM AUTHOR]

This article describes a study in which measures of mathematical knowledge for teaching developed in the United States were adapted to measure mathematical knowledge for teaching in Ireland. When adapting the measures it was not assumed that the mathematical knowledge used by Irish and U.S. teachers is the same. Instead psychometric and interview-based methods were used to determine a correspondence between the constructs being measured, and ensure the integrity of item performance in the Irish context. The study found overlap between the knowledge that is used to teach in both Ireland and the United States, and that the items tapped into this knowledge. However, specific findings confirm the usefulness of conducting extensive checks on the validity of items used in cross-national contexts. The process of adaptation is described to provide guidance for others interested in using the items to measure mathematical knowledge for teaching outside the United States. The process also enabled the authors to raise questions about the assumptions that lie behind the practice-based construct of mathematical knowledge for teaching. [ABSTRACT FROM AUTHOR]

Parents often become frustrated when their perception of their child’s talent in mathematics differs from that held by the school. Yet for the young child, research suggests parents have a much deeper insight into the interests and talents of their child. Failure to recognize talent can result in lost opportunities for the child as well as a loss to society. This article evaluates the development of an instrument designed to assess parent perceptions of mathematical talent. Parental perceptions and family demographics were collected for third grade students participating in Project M3: Mentoring Mathematical Minds, a research program conducted collaboratively by the University of Connecticut, Northern Kentucky University and Boston University, and for second grade students under consideration for the program. The data were correlated with other identification tools used for the identification of talented second graders for Project M3 to explore a research-based means of parent identification of mathematical talent. [ABSTRACT FROM AUTHOR]

Affiliation with substance using peers is one of the strongest predictors of adolescent alcohol use. This association is typically interpreted causally: peers who drink incite their friends to drink. This association may be complicated by uncontrolled genetic and environmental confounds because teens with familial predispositions for adolescent substance use may be more likely to select into social networks where drinking is common. We test this alternative hypothesis using a sample of 1,820 twin and sibling pairs, and their same-sex best friends, from three waves of the National Longitudinal Study of Adolescent Health. Across all three waves, peer report of substance use did not influence adolescent alcohol use when genetic and shared environmental predispositions for drinking were considered. The association between alcohol use and peer behavior may be a spurious association attributable to a shared genetic liability to drink alcohol and associate with peers who drink alcohol. [ABSTRACT FROM AUTHOR]

The Third International Mathematics and Science Study (TIMSS) reports that the mathematics teaching in Japan is distinctly different from that found in the United States. They attribute part of that difference to the professional development practice of Lesson Study. However, is the pre-service preparation of Japanese mathematics teachers also different? In an effort to understand the Japanese secondary mathematics student teaching process better, the author spent two weeks in Japan at three different universities and their affiliated junior high schools observing student teachers as they interacted with their cooperating teachers. This article is a description of that process as seen through the eyes of an American mathematics teacher educator. The author found that the main focus of student teaching at the observed junior high schools is on the preparation, teaching and reflection on the lesson itself. [ABSTRACT FROM AUTHOR]

It is useful to consider the WKB method on the phase space via the global FBI transformation. It enables us to avoid the difficulty arising from caustics. As an application, the Bohr-Sommerfeld quantization condition is obtained. [ABSTRACT FROM AUTHOR]