Creativity is one of keys to success in the evolving global economy and also be a fundamental skill that is absolutely necessary in the 21st century. Also in mathematics, creativity or thinking creatively is important to be developed because creativity is an integral part of mathematics. However, limiting the use of creativity in the classroom…

Students often struggle with concepts from abstract algebra. Typical classes incorporate few ways to make the concepts concrete. Using a set of woven paper artifacts, this paper proposes a way to visualize and explore concepts (symmetries, groups, permutations, subgroups, etc.). The set of artifacts used to illustrate these concepts is derived…

This article documents the classroom mathematical practices observed in a collegiate level teacher education course related to the circle topic. The course, which was prepared as design research, utilized a dynamic geometry environment which influenced the type and nature of the evolved mathematical practices. The study uses emergent perspective…

This article is based on data from two major research projects that investigated students involved in mathematically demanding courses during their transition through college and into university. It explores the nature of modelling as a mathematical practice in this important transition phase for students. Theoretical considerations are informed…

This paper presents the outcomes of the work of the ICME 13 Survey Team on "Conceptualisation and the role of competencies, knowing and knowledge in mathematics education research". It surveys a variety of historical and contemporary views and conceptualisations of what it means to master mathematics, focusing on notions such as…

The adoption of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) has caused a shift in the expectations for student learning, with implications for teaching. It has also introduced a new kind of standard focused on the way that students think about content in the form of the Standards for Mathematical Practice (SMP). The SMP…

The creation of crowd-sourced content in learning systems is a powerful method for adapting learning systems to the needs of a range of teachers in a range of domains, but the quality of this content can vary. This study explores linguistic differences in teacher-created problem content in ASSISTments using a combination of discovery with models…

The creation of crowd-sourced content in learning systems is a powerful method for adapting learning systems to the needs of a range of teachers in a range of domains, but the quality of this content can vary. This study explores linguistic differences in teacher-created problem content in ASSISTments using a combination of discovery with models…

This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…

This "Activity for Students" article presents a taxicab geometry problem that engages students in plotting points and observing surprising shapes and underlining reasons for the appearance of figures when working with street grids. With this activity, teachers can provide an extra challenge by writing additional problems introducing a…

The notion of linearity is perhaps the most fundamental idea in algebraic thinking. It sets the transition to functions and culminates with the instantaneous rate of change in calculus. Despite its simplicity, this concept poses complexities to a considerable number of first semester college algebra students. The purpose of this observational…

Teaching students how to use and interpret various representations of functions remains an enduring challenge for educators. Providing students access to such representations is a key feature of providing them access to mathematical participation and communication. This study is based on a teaching experiment, which aims to provide students access…

The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…

The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…