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This study describes an online method of measuring individual students' collaborative problem-solving abilities using four interactive mathematics-based tasks, with students working in pairs. Process stream data were captured from 3,000 students who completed the tasks in the United States, Australia, Canada, Costa Rica, Singapore, and Finland. The data were transformed into indicators of collaborative problem-solving ability and were analyzed using item response modeling. The assessments employed in this study can be used as a teaching tool for introduction to algebraic concepts and as a measurement instrument for collaborative problem-solving ability. The paper describes the construction, calibration, and reliability of the tasks and considers validation issues, such as fairness between assessments for both partners and avoidance of cultural biases. Investigations into the dependencies between student scores provide evidence for convergent and discriminant validity.

As a component of the ongoing development of the mathematics curriculum in China, we compare the country's high school mathematics textbooks with those of several other countries. We base our analysis on the assumption that textbooks, as primary printed teaching resources, are key tools for interpreting educational policy. In this paper, we compare what content is selected and how that content is presented in series of high school textbooks from China, France, Germany, Japan, Russia, the United Kingdom, and the United States according to four core domains: algebra, geometry, statistics and probability, and calculus. We then discuss the implications of the analysis for the reform of the high school mathematics curriculum in China, particularly as it applies to the development of textbooks within that process of reform. The comparative results provide us with the opportunity to recognise the distinguishing features of the content and presentation of the Chinese mathematics curriculum and lead to some suggestions for future curriculum development.

This paper compares sections on functions and linear functions from two Korean textbooks and an American standards-based textbook (University of Chicago School Mathematics Project [UCSMP] Algebra) to understand differences and similarities among these textbooks through horizontal and vertical analyses. We found that these textbooks provide different opportunities to learn (OTL). UCSMP Algebra places strong emphasis on real-life applications of linear functions rather than on pure mathematics and mathematical algorithms. Also, compared to Korean textbooks, UCSMP Algebra offers more OTL for students to solve, explain, and reason about higher level cognitively demanding mathematics problems than Korean secondary textbooks. Contradictory results, compared to previous studies about East Asian mathematics textbooks indicate the need for further study to compare secondary textbooks from more East Asian countries. Also, with the results of this study, we need to understand the results of international assessments more carefully.

The algebra classroom in urban public high schools in the United States is a complex space, ripe with many challenges and opportunities. In this paper I introduce the notion of a heart-centered stance for the teacher and the educator and a method of engaging in creative expression for reflection and introspection toward individual change in the rich context of the high school algebra classroom. My evolving relationships with two high school algebra teachers, observations of their classrooms, as well as my own self-study and professional growth, are incorporated into this paper as I introduce and exemplify two tenets of a heart-centered stance: multidimensionality of experience and receptivity to relatedness. This study suggests the possibility of using creative artistic expression and a self-study approach to support the transformation of educators’ perspectives toward research, creative activities, and outreach that are receptive to the mathematical experiences of teachers and students in our local communities. [ABSTRACT FROM AUTHOR]

In this exploratory case study, the researchers conducted a descriptive, qualitative microanalysis of the tutoring of two eighth grade students with learning disabilities while solving algebra problems. The researchers analyzed the participants' problem solving tendencies and interventions that helped the students succeed. One of the students, Nicole, demonstrated considerable capability at supporting her memory and processing by carefully and neatly writing out her steps for solving equations on paper. The other participant, Rachel, struggled at times to organize her thinking processes on paper and solve equations due to poor handwriting legibility, math anxiety and issues of confidence as a learner of mathematics that all seemed to be inter‐related. Both students demonstrated success with solving algebra equations, but Rachel required intensive intervention for addressing her difficulties with math anxiety and visual‐motor integration, while Nicole mostly required mathematics instruction designed to capitalise on her success at creating useful visual representations of her thought processes. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of computing all possible order ideals and also sets connected to 1, and the corresponding border bases, for the vanishing ideal of a given finite set of points. In this context, two different approaches are discussed: based on the Buchberger–Möller Algorithm [H. M. Möller and B. Buchberger, The construction of multivariate polynomials with preassigned zeros, EUROCAM '82 Conf., Computer Algebra, Marseille/France 1982, Lect. Notes Comput. Sci. 144, (1982), pp. 24–31], we first propose a new algorithm to compute all possible order ideals and the corresponding border bases for an ideal of points. The second approach involves adapting the Farr–Gao Algorithm [J. B. Farr and S. Gao, Computing Gröbner bases for vanishing ideals of finite sets of points, in 16th Int. Symp. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC-16, Las Vegas, NV, USA (Springer, Berlin, 2006), pp. 118–127] for finding all sets connected to 1, as well as the corresponding border bases, for an ideal of points. It should be noted that our algorithms are term ordering free. Therefore, they can compute successfully all border bases for an ideal of points. Both proposed algorithms have been implemented and their efficiency is discussed via a set of benchmarks. [ABSTRACT FROM AUTHOR]

HIV incidence estimates are used to monitor HIV-1 infection in the United States. Use of laboratory biomarkers that distinguish recent from longstanding infection to quantify HIV incidence rely on having accurate knowledge of the average time that individuals spend in a transient state of recent infection between seroconversion and reaching a specified biomarker cutoff value. This paper describes five estimation procedures from two general statistical approaches, a survival time approach and an approach that fits binomial models of the probability of being classified as recently infected, as a function of time since seroconversion. We compare these procedures for estimating the mean duration of recent infection (MDRI) for two biomarkers used by the U.S. National HIV Surveillance System for determination of HIV incidence, the Aware BED EIA HIV-1 incidence test (BED) and the avidity-based, modified Bio-Rad HIV-1/HIV-2 plus O ELISA (BRAI) assay. Collectively, 953 specimens from 220 HIV-1 subtype B seroconverters, taken from 5 cohorts, were tested with a biomarker assay. Estimates of MDRI using the non-parametric survival approach were 198.4 days (SD 13.0) for BED and 239.6 days (SD 13.9) for BRAI using cutoff values of 0.8 normalized optical density and 30%, respectively. The probability of remaining in the recent state as a function of time since seroconversion, based upon this revised statistical approach, can be applied in the calculation of annual incidence in the United States. [ABSTRACT FROM AUTHOR]

The number of students who leave U.S. schools mathematically underprepared has prompted widespread concern. Low achieving students, many of whom have been turned off mathematics, are often placed in low tracks and given remedial, skills-oriented work. This study examines a different approach wherein heterogeneous groups of students were given responsibility and agency and asked to engage in a range of mathematical practices collaboratively. The teaching intervention, which was introduced in the first paper, took place as part of a summer class on algebra, and it gave students the opportunity to participate with mathematics in changed ways. This paper will report evidence that the vast majority responded with increased engagement, achievement, and enjoyment. The students chose collaboration and agency as critical to their improved relationships with mathematics. [ABSTRACT FROM AUTHOR]

Breweries across the country are investing in energy efficient and low-carbon brewing practices. Drawing insights from the sustainable consumption and ecological economics literature, this analysis evaluates whether consumers are willing to pay more for sustainable beer and what predicts the value of the premium. Based on a survey of beer consumers from across the U.S. that contained one of two willingness-to-pay exercises, we evaluate what respondent attributes are associated with a higher willingness-to-pay for sustainably brewed beer. We find that the majority of beer consumers are willing to pay more for sustainable beer. Consumers who are prepared to pay a premium tend to already pay more per unit of beer, are more aware of their purchasing behavior and the manner in which their consumption patterns may affect the environment, and pursue lifestyles based on professional advancement, helping the environment, and helping other causes. [ABSTRACT FROM AUTHOR]

This study’s objective was to describe long-term trends and patterns in first cigarette use (cigarette initiation) and daily cigarette use (daily initiation) among youth and young adults in the U.S. We used cross-sectional survey data from the National Survey on Drug Use and Health, 2002–2015, to estimate annual incidence of first cigarette use (N = 270,556) and first daily cigarette use (N = 373,464) for each year by age groups, race/ethnicity and gender, examining trends over time and the average annual change in initiation for each group. Several clear patterns emerged: 1) cigarette initiation and daily initiation significantly decreased over time among those aged 12–14 and 15–17 and these trends were consistent among nearly all racial/ethnic and gender subgroups; 2) among 18–21 year olds, cigarette initiation sharply increased through 2009, surpassing rates among 15–17 year olds, and sharply declined through 2015 while remaining higher than rates among the younger group, and this trend was consistent for almost all racial/ethnic subgroups; 3) daily initiation for those aged 18–21 significantly declined, and this was significant among most subgroups 4) there was no change in cigarette initiation and daily initiation for 22–25 year olds overall and most subgroups; 5) there was a significant increase in cigarette initiation for 22–25 year old Hispanics males and daily initiation for 22–25 year old males. This study provides a comprehensive look at trends in cigarette and daily initiation among U.S. youth and young adults. Despite notable declines in smoking initiation among youth and young adult populations over the last two decades, targeted prevention and policy efforts are needed for subgroups at higher risk, including young adults and Hispanic males. [ABSTRACT FROM AUTHOR]

Students hold many misconceptions as they transition from arithmetic to algebraic thinking, and these misconceptions can hinder their performance and learning in the subject. To identify the errors in Algebra I which are most persistent and pernicious in terms of predicting student difficulty on standardized test items, the present study assessed algebraic misconceptions using an in-depth error analysis on algebra students' problem solving efforts at different points in the school year. Results indicate that different types of errors become more prominent with different content at different points in the year, and that there are certain types of errors that, when made during different levels of content, are indicative of math achievement difficulties. Recommendations for the necessity and timing of intervention on particular errors are discussed. [ABSTRACT FROM AUTHOR]