This article examines what constitutes a 'good' mathematical problem and proposes to conceptualize the notion of "collective mathematical problems" as phenomena that arise through and by way of the inter-actions enabled by the collective itself. The author examines how these collective mathematical problems can emerge in the classroom…

In this paper, we explored the type of mathematical connections Grade 11 learners make when solving two-dimensional (2D) trigonometric problems in an Activity-Based Learning (ABL) environment. We followed a qualitative case study design within an interpretive paradigm. Convenience sampling was used to select a whole class of 45 Grade 11 learners…

There exist many studies on modeling competencies and their promotion; however, there is a need to investigate what modeling competencies are and how they vary in lower and higher-achieving groups of students in mathematics within the current modeling literature domain. This study examined how mathematical modeling competencies were displayed in…

This article aims to describe the mathematical identity of elementary school students during studying mathematics. When studying mathematics, the students often face difficulties in understanding the concepts which results the decrease in their learning motivation. It will lead to the lack of development of their mathematical identity. The…

Mathematics classrooms have reflected little change over the past century, consisting of the learning of inert, disjoint procedures with few connections between mathematics concepts and students' everyday experiences. However, problem posing, that is, the reformatting of existing problems and the generation of new ones, has been promoted by the…

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. I contribute to these efforts by expanding the constructs in Cobb and Yackel's (1996) interpretive framework that allow for coordinating social and individual perspectives. This expansion involves four…

About half of students attending community colleges leave school before finishing their intended goals. To increase students' retention and to prevent the multiple-repeater problem, Queensborough Community College (QCC) offered a short-term workshop for remedial-mathematics students. This was another chance to exit remediation instead of repeating…

Perceptual characteristics of mathematical equations may influence solvers' problem solving. For example, in a study of equations involving addition and multiplication, Landy and Goldstone (2010) showed that participants tended to perform narrowly spaced operations first, suggesting that spacing affects how symbols are grouped for problem solving.…

Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…

Being situated within a course at the applied end of the spectrum of maths degrees, the pure mathematics modules at Sheffield Hallam University have an applied spin. Pure topics are taught through consideration of practical examples such as knots, cryptography and automata. Rubik's cubes are used to teach group theory within a final year pure…

Persevering in problem solving and constructing and critiquing mathematical arguments are some of the mathematical practices included in the Common Core State Standards for Mathematics (CCSSI 2010). To solve unfamiliar problems, students must make sense of the situation and apply current knowledge. Teachers can present such opportunities by…

In the international literature, increasing numbers of articles and books are published about teaching and learning, with the brain in mind. For a long time, I have been sceptical about this question. However, seeing many unresolved issues in the teaching and learning of mathematics, I slowly started to study the relevant literature and have…

Crime Scene for Mathematics Investigation (CSMI) was created as a small group, cooperative, self-selective grouping strategy to allow students to explore mathematics based on their own understanding and perceived readiness, much like the concept and application of literature circles in language arts. In essence, these self-chosen small groups met…

In a statistics course for bachelor students in econometrics a new format was adopted in which students were encouraged to study more actively and in which cooperative learning and peer teaching was implemented. Students had to work in groups of two or three students where each group had to perform certain tasks. One of these tasks was: explaining…

This activity involves students investigating the mathematics of packaging and exploring various concepts in geometry, including area and the Pythagorean theorem. Mathematics comes out of the discussion of packaging cans into six-packs and focuses on the cost-effectiveness of the horizontal storage area used. Students learn how knowledge of…