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In the United States, students with mild intellectual disability (MID) are expected to access the general education curriculum and some of these students are required to pass the same high-stakes exams as students without disabilities. Research supports that students with MID can demonstrate success with mathematics after receiving interventions that emphasize the strategic use of visual representations. In this qualitative case study, the researchers describe the teaching methods of a seventh grade, special education teacher who heavily emphasized visuals, such as diagrams and gestures, in her instructional approach. In her classroom, two students with MID demonstrated the ability to solve and discuss algebra problems that required use of the distributive property and to solve word problems of the same structure. [ABSTRACT FROM AUTHOR]

This paper examines the relationship of the policies and practices employed by 3 high school reform models – Early College High Schools, Redesigned High Schools, and High Schools That Work – with student success in college preparatory mathematics courses by the end of the 10th grade. Data on policies and practices collected through a survey of school principals in North Carolina are combined with administrative data on student course-taking and performance. The examined policies include course-taking requirements, rigorous instruction, academic support, personalization, and relevance. Results show that implementation of these policies varies across models and that higher levels of implementation of combinations of these policies are associated with improved outcomes. [ABSTRACT FROM PUBLISHER]

Saurabh Bansal and James S. Dyer study a common problem in the commercial agribusiness market, where farmers have a preference for a farm input such as a seed based on a fit with their geographical location but are also willing to accept a closely related substitute. Such consumer-driven choices may not be adequately represented by traditional models that maximize the profit of a firm that seeks to make substitutions while maximizing its profit. They use a set of recent results for evaluations of moments over polyhedra to determine the exact inventory levels a firm should keep of substitutable products. Using proprietary data from a large firm in this domain, they highlight the role of geographical and climate-related factors that affect product substitution in the agribusiness industry and identify specific regions in the United States where product substitution is a source of substantial revenue for firms. In this paper, we consider the problem in which a firm offers a portfolio of products (agricultural seeds) to multiple customer segments comprising farmers under aggressive fill-rate constraints, and some, but not all, customers will accept a substitute to their preferred choice. This business situation is not adequately represented by traditional inventory-management models, where a firm initiates a substitution based on its monetary considerations. By exploiting some recent results on polyhedral expectations, we develop a decomposition-based approach to determine optimal inventory levels for the firm's seed portfolio under aggressive fill-rate targets. The approach provides an exact solution that is implementable in managerial-friendly environments and permits a what-if analysis for real-time decision support. Subsequently we extend the technical development to establish: (i) a simple computable bound on the value of substitution, (ii) a procedure for determining implied penalty costs for substitutable products, and (iii) comparative static results for the product portfolio. We also discuss the implementation of the technical development at a Fortune 100 firm that has resulted in significant monetary savings. Finally, we provide geography- and climate-specific managerial insights for managing seed substitution by end-users. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses topics within the issue including advances in the research area of self-belief in educational settings; relationships between American adolescents' self-efficacy in mathematics and science; and analysis of school-level differences.

For over forty years, demographers have worked intensely to develop methods that assess a gain in life expectancy from a reduction in mortality, either hypothetical or observed. This considerable body of research was motivated by assessing the gains in life expectancy when mortality declined in a particular manner and determining the contribution of a cause of death in observed changes in life expectancy over time. As yet, there has been no framework unifying this important demographic work. In this paper, we provide a unifying framework for assessing the change in life expectancy given a change in age- and cause-specific mortality. We consider both conceptualizations of mortality change-counterfactual assessment of a hypothetical change and a retrospective assessment of an observed change. We apply our methodology to violent deaths, the leading cause of death among young adults, and show that realistic targeted reductions could have important impacts on life expectancy., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Atherosclerosis, the leading death in the United State, is a disease in which a plaque builds up inside the arteries. As the plaque continues to grow, the shear force of the blood flow through the decreasing cross section of the lumen increases. This force may eventually cause rupture of the plaque, resulting in the formation of thrombus, and possibly heart attack. It has long been recognized that the formation of a plaque relates to the cholesterol concentration in the blood. For example, individuals with LDL above 190 mg/dL and HDL below 40 mg/dL are at high risk, while individuals with LDL below 100 mg/dL and HDL above 50 mg/dL are at no risk. In this paper, we developed a mathematical model of the formation of a plaque, which includes the following key variables: LDL and HDL, free radicals and oxidized LDL, MMP and TIMP, cytockines: MCP-1, IFN-γ, IL-12 and PDGF, and cells: macrophages, foam cells, T cells and smooth muscle cells. The model is given by a system of partial differential equations with in evolving plaque. Simulations of the model show how the combination of the concentrations of LDL and HDL in the blood determine whether a plaque will grow or disappear. More precisely, we create a map, showing the risk of plaque development for any pair of values (LDL,HDL). [ABSTRACT FROM AUTHOR]

This paper examines the redesign of evaluation components for a teacher professional development project funded by the National Science Foundation. It focuses on aligning evaluation instrumentation and strategies with program goals, research goals and program evaluation best practices. The study identifies weaknesses in the original (year 1) program evaluation design and implementation, develops strategies and tracks changes for year 2 implementation, and then reports enhancement of findings and recommendations for year 3. It includes lessons learned about assessment and evaluation over the project lifespan, with implications for research and evaluation of a range of related programs. This study functions as a classic illustration of how critical it is to observe first principles of assessment and evaluation for funded programs, the risks that arise when they are ignored, and the benefits that accrue when they are systematically observed., (Copyright (c) 2009. Published by Elsevier Ltd.)

Excellence in reading and math enable children entry to all of the professions. This is especially true for the nursing profession. Therefore, the purpose of this paper is to provide background information on the national crisis in reading and math achievement among school children, present the methodology of the Saturday School church-based approach to enhance reading and math skills, and the seven year outcomes.

Background: Low literacy and numeracy skills are common. Adequate numeracy skills are crucial in the management of diabetes. Diabetes patients use numeracy skills to interpret glucose meters, administer medications, follow dietary guidelines and other tasks. Existing literacy scales may not be adequate to assess numeracy skills. This paper describes the development and psychometric properties of the Diabetes Numeracy Test (DNT), the first scale to specifically measure numeracy skills used in diabetes., Methods: The items of the DNT were developed by an expert panel and refined using cognitive response interviews with potential respondents. The final version of the DNT (43 items) and other relevant measures were administered to a convenience sample of 398 patients with diabetes. Internal reliability was determined by the Kuder-Richardson coefficient (KR-20). An a priori hypothetical model was developed to determine construct validity. A shortened 15-item version, the DNT15, was created through split sample analysis., Results: The DNT had excellent internal reliability (KR-20 = 0.95). The DNT was significantly correlated (p < 0.05) with education, income, literacy and math skills, and diabetes knowledge, supporting excellent construct validity. The mean score on the DNT was 61% and took an average of 33 minutes to complete. The DNT15 also had good internal reliability (KR-20 = 0.90 and 0.89). In split sample analysis, correlations of the DNT-15 with the full DNT in both sub-samples was high (rho = 0.96 and 0.97, respectively)., Conclusion: The DNT is a reliable and valid measure of diabetes related numeracy skills. An equally adequate but more time-efficient version of the DNT, the DNT15, can be used for research and clinical purposes to evaluate diabetes related numeracy.

Background: Basic numeracy skills are necessary before patients can understand the risks of medical treatments. Previous research has used objective measures, similar to mathematics tests, to evaluate numeracy., Objectives: To design a subjective measure (i.e., self-assessment) of quantitative ability that distinguishes low- and high-numerate individuals yet is less aversive, quicker to administer, and more usable for telephone and Internet surveys than existing numeracy measures., Research Design: Paper-and-pencil questionnaires., Subjects: The general public (N = 703) surveyed at 2 hospitals., Measures: Forty-nine subjective numeracy questions were compared to measures of objective numeracy., Results: An 8-item measure, the Subjective Numeracy Scale (SNS), was developed through several rounds of testing. Four items measure people's beliefs about their skill in performing various mathematical operations, and 4 measure people's preferences regarding the presentation of numerical information. The SNS was significantly correlated with Lipkus and others' objective numeracy scale (correlations: 0.63-0.68) yet was completed in less time (24 s/item v. 31 s/item, P < 0.05) and was perceived as less stressful (1.62 v. 2.69, P < 0.01) and less frustrating (1.92 v. 2.88, P < 0.01). Fifty percent of participants who completed the SNS volunteered to participate in another study, whereas only 8% of those who completed the Lipkus and others scale similarly volunteered (odds ratio = 11.00, 95% confidence interval = 2.14-56.65)., Conclusions: The SNS correlates well with mathematical test measures of objective numeracy but can be administered in less time and with less burden. In addition, it is much more likely to leave participants willing to participate in additional research and shows much lower rates of missing or incomplete data.

This paper reports the results of the National Survey of Accommodations and Alternate Assessments for Students who are Deaf or Hard of Hearing in the United States (National Survey). This study focused on the use of accommodations and alternate assessments in statewide assessments used with students who are deaf or hard of hearing. A total of 258 participants responded to the survey, including 32 representing schools for the deaf, 168 from districtwide/school programs, and 58 from mainstreamed settings. These schools and programs served a total of nearly 12,000 students who are deaf or hard of hearing nationwide. The most prevalent accommodations used in 2003-2004 statewide standardized assessments in mathematics and reading were extended time, an interpreter for directions, and a separate room for test administration. Read aloud and signed question-response accommodations were often prevalent, used more often for mathematics than in reading assessments. Participants from mainstreamed settings reported a more frequent use of accommodations than those in schools for the deaf or districtwide/school programs. In contrast, schools for the deaf were most likely to have students participate in alternate assessments. The top three alternate assessment formats used across all settings were out-of-level testing, work samples, and portfolios. Using the National Survey results as a starting point, future research will need to investigate the validity of accommodations used with students who are deaf or hard of hearing. In the context of the No Child Left Behind Act of 2001 accountability policies, the accommodations and alternate assessment formats used with students who are deaf or hard of hearing may result in restrictions in how scores are integrated into state accountability frameworks.

There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better QS than at any time in the past. Ways in which mathematics and science academics are working together to build the QS of their undergraduate science students, together with the mathematics and statistics needed or desired in a science degree, are reported on in this paper. The emphasis is on the life sciences. Forty-eight academics from eleven Australian and two USA universities were interviewed about QS in science. Information is presented on: what QS academics want in their undergraduate science students; who is teaching QS; how mathematics and science departments work together to build QS in science and implications for building the QS of science students. This information leads to suggestions for improvement in QS within a science curriculum. [ABSTRACT FROM PUBLISHER]

Data extracted from the Atomic Data and Nuclear Data Tables [S. Raman et al., At. Data Nucl. Data Tables 78, 1 (2001)] are used for the calculation of magnetic moments of atomic nuclei. However, in October 2018, the author discovered that when nuclear theorists use Raman's table, an incorrect math procedure is applied when calculating the magnetic moments for exotic excited even Z = N nuclei. Obviously, it is mandatory for nuclear theorists to ascertain the repercussions of such an error in nuclear physics. [ABSTRACT FROM AUTHOR]

Within-class ability grouping (WCAG) is widely used in elementary mathematics instruction in the United States, yet it has drawn criticism on the grounds that it can inequitably limit the learning opportunities of some students, not least because of its connection to between-class ability grouping (BCAG) that is more common in middle or secondary schooling. Meanwhile, some high achieving countries use relatively little ability grouping in elementary school in comparison to the United States. In this paper, we draw on qualitative data from a series of assignments in four sections of an elementary mathematics methods course in the beginning teacher education programme at a United States university. These assignments were designed to explore the potential of using preservice teachers' (PSTs') memories of and experiences with ability grouping in their own schooling to support critical reflection about the possible negative consequences of within-class ability grouping practices. We found that while many PSTs reported negative personal experiences with ability grouping in mathematics, they often remained uncritical when reflecting on the use of ability grouping in the elementary classes they visited as part of their teacher education programme. [ABSTRACT FROM AUTHOR]

• We examine the relationship between teacher meanings and conventions. • Teachers often do not dissociate conventions from logico-mathematical operations. • We provide implications for teaching in relation to conventions of graphing. In this paper, we use relevant literature and data to motivate a more detailed look into relationships between what we perceive to be conventions common to United States (U.S.) school mathematics and individuals' meanings for graphs and related topics. Specifically, we draw on data from pre-service (PST) and in-service (IST) teachers to characterize such relationships. We use PSTs' responses during clinical interviews to illustrate three themes: (a) some PSTs' responses implied practices we perceive to be conventions of U.S. school mathematics were instead inherent aspects of PSTs' meanings; (b) some PSTs' responses implied they understood certain practices in U.S. school mathematics as customary choices not necessary to represent particular mathematical ideas; and (c) some PSTs' responses exhibited what we or they perceived to be contradictory actions and claims. We then compare our PST findings to data collected with ISTs. [ABSTRACT FROM AUTHOR]

The article offers information on the efforts being made by American universities to improve their teaching methods for science, technology, engineering, and mathematics (STEM) at all levels of the U.S. educational system. Association of American Universities (AAU), a group of 59 public and private research universities, has launched a five year plan to develop new methodologies for teaching. INSET: An observatory that comes home every morning.

This paper presents a Takagi-Sugeno fuzzy model-based approach to modeling, controlling, and stabilizing an aircraft in both normal and damaged conditions. The major contributions of this paper are as follows. First, it introduces the Takagi-Sugeno modeling and the parallel distributed compensation control approach. Then, it demonstrates how the approach can be applied to aircraft in a systematic manner. Finally, the approach is applied to the modified NASA F-15 number 837 nonlinear model, and preliminary simulation results are presented. The benefits of using a Takagi-Sugeno model-based parallel distributed compensation control approach include a systematic controller design procedure, mathematical proof of stability for classes of failures, and intuitive insight into damage effects on an aircraft. This work is the first to present this control approach as applied to aircraft. [ABSTRACT FROM AUTHOR]

The focus of this paper is on detailing the decisions made when we created, implemented and studied a mathematics professional development (PD) program in low-performing, urban schools. Our program held many characteristics espoused by researchers as critical for effectiveness. We begin by reviewing the characteristics of quality PD programs that guided our work. For each, we detail our interpretation and how that interpretation played out in the design and implementation of the PD. We also evaluate our level of success with respect to using that characteristic to positively impact teachers' learning experiences and, where possible, the subsequent learning experiences of their students. We close with suggestions for the development of PD programs. [ABSTRACT FROM AUTHOR]

The American government set new standards mandating States to demonstrate adequate yearly progress for all students with the inception of the No Child Left Behind Act. To be eligible for the more recent Race to the Top funds, states must show, in part, a commitment to "building data systems that measure student growth and success, and inform teachers and principals how to improve instruction" (DOE, 2009, p.2). This sweeping education reform focuses on the need for formative data collection systems. Many states are meeting this challenge by implementing a Responsiveness to Intervention (RtI) model. As such, the demand for effective progress monitoring systems and powerful instructional interventions has never been greater. This paper illustrates how a multi-level assessment system assessment aligns annual normative measures with daily frequency building practice and curriculum-based measurement probes within an RtI framework to drive academic outcomes. [ABSTRACT FROM AUTHOR]

This paper generalizes Benders decomposition to maximize a nonconcave objective function and uses that decomposition to solve an "electric power grid interdiction problem." Under one empirically verified assumption, the solution to this bilevel optimization problem identifies a set of components, limited by cardinality or "interdiction resource," whose destruction maximizes economic losses to customers (and can thereby guide defensive measures). The decomposition subproblem typically incorporates a set of dc optimal power-flow models that cover various states of repair after an attack, along with a load-duration curve. Test problems describe a regional power grid in the United States with approximately 5000 buses, 6000 lines, and 500 generators. Solution time on a 2-GHz personal computer is approximately one hour. [ABSTRACT FROM AUTHOR]

The two studies examined in this paper compare the different mathematical opportunities provided in preschool classrooms in China, Japan, and the United States, with an emphasis on mathematical-themed books in classroom libraries. Study one presents the results of an online survey to examining the content of preschool classroom libraries in China (N = 134), Japan (N = 168), and the United States (N = 291). Study two presents data obtained from semi-structured interviews of teachers in China (N = 8), Japan (N = 8), and the United States (N = 8). The interviews examined teacher perceptions of how they teach mathematics, the importance of teaching mathematics, and the use of the classroom library as a venue for mathematics. Study one results indicated that teachers from all three countries encourage classroom library use; however, teachers from China reported more mathematics storybooks than their Japanese or United States counterparts. Study two results indicated that teachers from all three countries viewed mathematics as important and provided various mathematics learning opportunities to children throughout the school day. Chinese teachers reported providing the most mathematics learning opportunities using whole group instruction, mathematics centers, and free play. Japanese teachers reported few whole group forms of instruction other than circle time but reported providing opportunities for using mathematics during free play and other embedded activities. United States teachers indicated that mathematics learning occurred using whole group instruction and mathematics centers. [ABSTRACT FROM AUTHOR]

A biography of professor Glenn F. Webb in the U.S. is presented. Webb was born in Cleveland, Ohio. He studied chemical engineering at the Georgia Institute of Technology, however, decided to took up mathematics where he enrolled graduate studies at Emory University. Webb has written several papers related to mathematics, including sine and cosine operators, infinite dimensional systems and mathematical biology.

Problem Statement: The acquisition of certain mathematical skills is part of many curricula around the world. These skills involve problem-solving, effective use of mathematics in daily life, thinking logically and systematically, taking risks and making decisions. The US National Council of Teachers of Mathematics ([NCTM], 1991) relates these skills to mathematical power. Knowledge construction and abstraction might have an impact on mathematical power. In this paper, the primary concern is with the construction of new knowledge structures rather than with consolidation or abstraction for that matter. Recognizing, Building-with, and Constructing (RBC hereafter) theory of abstraction provides a particularly useful framework in achieving a detailed examination of the new mathematical constructions through epistemic actions. Therefore, this paper, with reference to the RBC epistemic actions, examines the knowledge construction process of students with different mathematical power. Purpose of Study: The purpose of the study is to explain the similarities and differences between the knowledge construction processes of 6th grade students with different mathematical power. Methods: A case study was used as the main research approach. The mathematical power scale was applied to 282 students. The case study was conducted with four students who were chosen purposefully among them. The RBC theory of abstraction was used as an analytical tool. The patterns noticed in the case study were determined and interpreted. Findings and Results: According to findings, it was seen that the students with low mathematical power, whose knowledge constructing processes were examined, could recognize structures while they could not building with and constructing. When observing that the students with low mathematical power have low communication, connection and reasoning skills, in general, it can be said that for building-with and constructing, it is important to have these three skills. The students who reflected themselves and used the feedback to continue had high mathematical power. They also were able to construct mathematical knowledge more quickly. Conclusions and Recommendations: The RBC theory of abstraction can be useful in explaining the relationship between the components of mathematical power and other mental activities. For this purpose, the usage of the RBC theory of abstraction in the mathematical knowledge construction process in the classroom can be proposed as a new study. [ABSTRACT FROM AUTHOR]

Research on modelprocedure selection has focused on selecting a single model globally. In many applications, especially for high-dimensional or complex data, however, the relative performance of the candidate procedures typically depends on the location, and the globally best procedure can often be improved when selection of a model is allowed to depend on location. We consider localized model selection methods and derive their theoretical properties.This research was supported by U.S. National Science Foundation CAREER Grant DMS0094323. We thank three referees and the editors for helpful comments on improving the paper. [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]

Background/Context: The theoretical framework of the paper comes from research on problem solving, considered by many to be the essence of mathematics; research on the importance of oral language in learning mathematics; and on the importance of the teacher as the primary instrument of learning mathematics for most students. As a nation, we are not doing well enough in teaching our students mathematics, and need to look to new perspectives about why this is happening. Purpose: This paper looks at a promising tool for enabling students who are not skilled readers to approach problem solving tasks. But in sharing its usefulness with teachers in professional development, the instrument uncovered specific and serious gaps in teacher content knowledge. Group discussion, using the protocol helped to clarify some of those gaps. Setting: All three problem-probing sessions occurred during professional development activities for New York City Public School mathematics teacher leaders. The facilitator was Academic Director of a New Visions for Public Schools' Middle School Mathematics Standards project, (MS)2, funded by. NSF. The sessions were part of a variety of ongoing professional development activities, and occurred during the third year of a five year study. Therefore, the 12 to 20 participants of each session, though different from each other, all knew the facilitator. Research Design: The research design was qualitative. Teachers were presented with a written problem and directed not to solve it. The discourse that followed flowed of its own accord, with participants speaking as they thought and responded to the facilitator and/or the other participants. Records of speakers' words were transcribed in one case hand, and in two other cases by audio tapes. The discourse was then analyzed by the researcher from two perspectives: what mathematical misconceptions mere revealed and how the talk helped to clarify them. Conclusions/recommendations: From preliminary, explorations, the protocol seems an accessible and effective instrument for decoding and analyzing mathematics word problems by teachers who were not able to approach such tasks before. Also suggested was its potential value as an assessment instrument for teachers' content knowledge. Further study is needed to determine what kinds of in-class supports teachers need to internalize the process and use this instrument on a regular basis with their students. Background/Context: A of the literature demonstrates that schools are frequently called upon to improve, by developing high levels of teacher collaboration. At the same time, there a paucity of research investigating the extent to which teachers' collaborative school improvement practices are related to student achievement. Purpose: The purpose of study to was to review the literature and empirically test the relationship between a theoretically driven measure of teacher collaboration for school improvement and student achievement. Setting: The data for this study were drawn from students and teachers in a large urban school district located in the midwestern United States. Population: The population for this study came from the elementary schools in one large midwestern school district. Survey data were drawn from a sample of 47 elementary schools with 452 teachers and 2,536 fourth-grade students. Research Design: Hierarchical linear modeling (HLM) was the primary analytic method. Survey data were collected approximately 2 months before students took the mandatory state assessments, which provided the scale scores that served as dependent variables in this research. HLM accounted for the nested nature of the data (students nested in schools).… [ABSTRACT FROM AUTHOR]

This paper traces the international evolution of mathematical theory and construction processes that affected the design, construction, and use of continuous truss bridges in the United States. It covers the evolution from intuitive designs in wood and iron of the early 19th century to the mathematically rigorous designs of long-span continuous steel trusses in the late 19th and early 20th centuries. [ABSTRACT FROM AUTHOR]

This paper compares two methods of analyzing aggregate data that is classified by period and age. Because there is a linear relationship among age, period, and cohort, it is not possible to distinguish the separate effects without employing an identifying assumption. The first method, which is applied in the economics literature, assumes that period effects are orthogonal to a linear time trend. The second method, which is applied in the statistics literature, assumes that the effect parameters change gradually. Simulation results suggest that the performances of both methods are comparable. The results of applying the second method to household saving rates suggest that period effects had a negligible influence in the United States but considerable influence in Japan. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In recent years, US curriculum policy has emphasized standards‐based conceptions of curricula in mathematics and science. This paper explores the data from the Third International Mathematics and Science Study (TIMSS) to argue that the presence of content standards is not sufficient to guarantee curricula that lead to high‐quality instruction and achievement. An examination of the content topics covered in each grade of a group of six of the highest‐achieving TIMSS countries in mathematics and science shows a pattern in which new topics are gradually introduced, are a part of instruction for a few grades, and then often leave the curriculum as separate topics. This contrasts sharply with mapping of topics in the various US national standards in mathematics and science. Topics enter and linger, so that each grade typically devotes instructional attention to many more topics than is typical of the six high‐achieving countries; in addition, each topic stays in the curriculum for more grades than in the high‐achieving countries. An examination of mathematics and science content standards from 21 states and 50 districts in the US shows a pattern more like that of the US national standards than those of the high‐achieving TIMSS countries. While content standards have become integral to US curriculum development and reform, they have yet to reflect the coherence that is typical of countries that achieved significantly better than the US in the TIMSS study. [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.

Three levels of prevention and intervention in the area of mathematics are addressed: (a) primary prevention focusing on universal design, (b) secondary prevention focusing on adaptations, and (c) tertiary prevention focusing on intensive and explicit contextualization of skills-based instruction. The purpose of this paper is to identify and discuss principles of prevention and intervention in the area of mathematics. First, we identify research-based principles associated with primary prevention. Second, we turn our attention to secondary prevention, with a focus on prereferral intervention. We identify principles that serve to differentiate primary and secondary prevention and specify instructional variables that are promising for use within a secondary prevention mode. Finally, we discuss intervention. We identify principles of effective intervention, which include individually referenced decision making, instructional intensity, and deliberate contextualization of skills-based instruction. [ABSTRACT FROM AUTHOR]

Introduction: Informational graphics and data representations (e.g., charts and figures) are critical for accessing educational content. Novel technologies, such as the multimodal touchscreen which displays audio, haptic, and visual information, are promising for being platforms of diverse means to access digital content. This work evaluated educational graphics rendered on a touchscreen compared to the current standard for accessing graphical content. Method: Three bar charts and geometry figures were evaluated on student (N = 20) ability to orient to and extract information from the touchscreen and print. Participants explored the graphics and then were administered a set of questions (11–12 depending on graphic group). In addition, participants' attitudes using the mediums were assessed. Results: Participants performed statistically significantly better on questions assessing information orientation using the touchscreen than print for both bar chart and geometry figures. No statistically significant difference in information extraction ability was found between mediums on either graphic type. Participants responded significantly more favorably to the touchscreen than the print graphics, indicating them as more helpful, interesting, fun, and less confusing. Discussion: Accessing and orienting to information was highly successful by participants using the touchscreen, and was the preferred means of accessing graphical information when compared to the print image for both geometry figures and bar charts. This study highlights challenges in presenting graphics both on touchscreens and in print. Implications for Practitioners: This study offers preliminary support for the use of multimodal, touchscreen tablets as educational tools. Student ability using touchscreen-based graphics seems to be comparable to traditional types of graphics (large print and embossed, tactile graphics), although further investigation may be necessary for tactile graphic users. In summary, educators of students with blindness and visual impairments should consider ways to utilize new technologies, such as touchscreens, to provide more diverse access to graphical information. [ABSTRACT FROM AUTHOR]

Introduction: In 2016, the United States transitioned to two new braille codes for science, technology, engineering, and mathematics (STEM). Little is known about the experiences of teachers of students with visual impairments in learning and supporting their students in learning these new braille codes: Nemeth Code within Unified English Braille (UEB) Contexts and UEB Technical. Methods: Thirteen certified teachers of students with visual impairments participated in one of three focus groups during the spring of 2020. The audio files were transcribed and then analyzed. Results: Some participants reported that they were still in the process of transitioning to Nemeth Code within UEB Contexts or UEB Technical. The majority of participants learned a new code through self-study and were introducing the symbols incrementally to their students. The participants reported that their students had been successful in learning Nemeth Code within UEB Contexts or UEB Technical, but there were challenges, including inadequate lead time, in supporting their students in STEM classes. Discussion: Affordable training and professional development for learning a new code were needed. Additional resources, including grade-level charts and curricula for K-12 students, should be created for both codes. Implications for Practitioners: Teachers of students with visual impairments are an essential part of the STEM educational team for students who read braille. Supporting student learning requires specialized knowledge of the braille codes used in STEM courses and technologies for producing tactile materials. Sharing of instructional materials, existing resources, and teacher expertise throughout mentorship would benefit the field of visual impairment. [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]

Children learn math concepts long before they enter school. Across all cultures, children are exposed to number and spatial language to varying degrees during everyday home routines. Yet most studies of math talk occur in the lab and target non-Hispanic, English-speaking families. We expanded inquiry to the spontaneous math language (i.e., number and spatial language) of Spanish-speaking mothers and their 1- to 2-year-olds (N = 50) during home activities. Mothers varied enormously in their use of math language, and mother math language related to toddler math language, whereas mother non-math language did not. Children's math language both preceded and followed mother math talk, suggesting imitation and reinforcement as important processes in children's math language learning. Children also produced math language outside the context of mother input. Findings advance an understanding of children's early math language in natural settings and have implications for interventions aimed at promoting math skills in toddlers from diverse backgrounds. [ABSTRACT FROM AUTHOR]

Mathematical creativity is among the most intriguing research fields in the world. This is plausible because research on mathematical creativity, particularly in the field of education, has a positive impact on many dimensions of life. Even though numerous studies have been conducted on this topic, there are still many aspects that have not been examined. Using bibliometric analysis, the authors of this study evaluated scientific articles on mathematical creativity from 2002 to 2022 that were indexed in Scopus using Biblioshiny and VOSviewer. The authors analyzed 162 publications in terms of document distribution patterns and growth trends, contributions and impacts from countries, institutions, authors, and journals, patterns of development and evolution of the theme of mathematical creativity, and future research opportunities. Despite a decrease in the average number of citations per document, the results suggest a significant increase in the number of publications between 2002 and 2022. The United States and the University of Haifa are the nations and institutions with the highest publication output, ZDMMathematics Education has the highest impact, and Bicer is a core author who is extremely productive and influential. "Creativity" has been the most popular keyword over the past two decades, but it is not the only one. This study encourages future research on mathematical creativity in mathematics education to not only focus on the theme of discipline-specific instructional practices, but also on the theme of general instructional practices involving more person, process, product, and press/environment creativity. [ABSTRACT FROM AUTHOR]

The poor mathematics performance of children in the United States has become a topic of national concern. Numerous studies have shown that American children consistently perform worse than their counterparts in many parts of the world. In contrast, children in China, Japan, Taiwan, and other Asian countries consistently perform at or near the top in international comparisons. This paper examines possible causes of the poor performance of American children and the excellent performance of Asian children. Contrary to the beliefs of many Americans, the East Asian advantage in mathematics is probably not due to a genetically-based advantage in mathematics. Instead, differences in beliefs about the role of genetics may be partly responsible. Asians strongly believe that effort plays a key role in determining a child's level of achievement, whereas Americans believe that innate ability is most important. In addition, despite the relatively poor performance of their children, American parents are substantially more satisfied with their children's performance than Asian parents. The American emphasis on the role of innate ability may have several consequences for children's achievement. For example, it may lead children to fear making errors and to expend less effort on mathematics than their Asian counterparts. As research on genetic influences on behavior, traits, and abilities increases scientists should be careful to ensure that the public understands that genetics does not directly determine the exact level of a child's potential achievement.

The arithmetical competencies of more than 200 Chinese or American kindergarten, first-, second-, or third-grade children were assessed toward the beginning and toward the end of the U.S. school year. All children were administered a paper-and-pencil test of addition skills, a digit span measure, and an addition strategy assessment. The addition strategy assessment provided information on the types of strategies the children used to solve simple addition problems as well as information on the speed and accuracy of their strategy use. Information on the number of math instruction periods across times of measurement was also obtained for each of the first-, second-, and third-grade children. The pattern of arithmetical development across the academic year and across the Chinese and American children suggests that a mix of cultural and maturational factors influence the emergence of early arithmetical competencies and that the Chinese advantage in early mathematical development is related to a combination of language- and school-related factors.

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]

This paper reports selected findings from a study of number sense proficiency of students aged 8 to 14 years in Australia, Sweden, United States, and Taiwan. It comments on the meaning and importance of number sense, the development of the assessment instruments, and student responses to the items. Some implications for classrooms of the findings are then 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]

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]

Contemporary reforms in the US urge deep changes in mathematics teaching and learning and yet classroom practice continues, in many places, to be as conventional as ever. This paper examines how one mid-sized urban district marshalled resources for instruction in mathematics. We appraise the resources afforded by the district to mathematics and offer an argument for why the resource patterns look as they do. In contrast with literacy where staff, experience, and concern were extensive, mathematics lacked parallel resources. We argue that this pattern of resource allocation significantly affected the possibilities for change in the district's elementary mathematics programme. The magnitude of the changes envisioned by the current mathematics reforms, set against an analysis of the key district players' ideas, understandings, and agendas, leads us to argue that there is a paradoxical inversion of resources needed to support the kinds of improvements promoted by the mathematics reforms. [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]

A model for the placement of n detection stations for optimum coverage of an arbitrary plane area is described. The stations are assumed to be identical and to have a probability of detection that is a function only of the distance between the station and the event to be detected. Furthermore, the stations are assumed to operate independently of each other. It is also assumed that the enemy has complete knowledge of the station locations and effectiveness and is interested only in eluding detection by the detection stations. Thus, the situation is reduced to the minimax problem of placing the stations so that the maximum probability of not detecting an enemy event is minimized. A hill climbing iterative technique for finding the optimum locations is described in some detail. This technique is illustrated for the problem of locating detection stations within the United States and Soviet Union. The results of these applications are presented and discussed. The paper concludes with some remarks on how this model can be made more descriptive of the real world situations being modeled. [ABSTRACT FROM AUTHOR]

Adults with learning disabilities (LD) face educational and employment challenges and may also have other disabilities and health conditions. Little is known about these adults' numeracy skills and how they use numeracy at work or home. The article's objective was to investigate numeracy skills and skill use for U.S. adults with LD. The author conducted descriptive and regression analyses of the data from the 2012/2014/2017 U.S. Program for the International Assessment of Adult Competencies (PIAAC). Findings are presented on assessed numeracy skills and skill use, relationships of use and skills, and skill use among seven groups of adults with LD. Compared with the general population, adults with LD have lower mean numeracy scores. Skill use at home adds to the variance explained in numeracy skills, which suggests that using numeracy skills matters in gaining skills. Knowing the relationships of assessed numeracy skills with skill use helps educators implement strategies to support adult program completion. Implications of findings are discussed for adult educators and policymakers. [ABSTRACT FROM AUTHOR]

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]