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Drawing on data from the Republic of Cyprus, this paper uncovers elementary teachers' epistemological beliefs about mathematics. Twenty-two experienced teachers were invited to individual semi-structured interviews. Thematic data-driven analyses identified three themes and eight sub-themes, which I discuss, taking their socio-cultural context into consideration. This study suggests that applying predetermined frameworks directly taken from the literature when examining teachers’ epistemological beliefs in mathematics can be problematic, as they might hinder other culturally specific beliefs from emerging. In closing, this paper presents some implications for the results on teacher education and professional development, as well as ideas for future research. [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]

Students make sense of mathematical ideas using a variety of representations including physical models, pictures, diagrams, spoken words, and mathematical symbols. As students’ understanding of mathematical ideas becomes more general and abstract, there is a need to express these ideas using mathematical notation. This paper describes students’ movement from model building and personal notations to elegant use of mathematical symbols that show their understanding of advanced counting ideas. Specifically, this paper shows how earlier ideas from investigations of specific combinatorics problems (questions about making pizzas with different toppings and using cubes to build towers) are retrieved and built upon using the formal mathematical register to explain the meaning of Pascal's Identity, the addition rule of Pascal's Triangle. This analysis also shows the power of shared communication in mathematical problem solving. [ABSTRACT FROM AUTHOR]

• First study investigating causal inference of a math remedial program in Germany. • Microanalysis of a math remedial program with detailed information of the sample. • Semester-long remedial courses can be helpful compensating missing math skills. Almost all German universities complain that the math skills of students entering the higher education system do not meet the level demanded by universities. This is a major problem, particularly in math-related study programs such as economics, engineering or science. To bridge the gap, almost all universities offer some remedial math courses. However, there is only weak empirical evidence for the effectiveness of these courses in Germany. This paper aims to fill this gap by evaluating a remedial math course given within the Economics Department of a German university. A key finding: taking a math remedial course on a regular basis will enhance students' math skills and increase the probability of passing the final math exam by 35 percent. [ABSTRACT FROM AUTHOR]