In this study, we investigated students' thinking about the use of letters in algebra. Responses from over 1,400 Australian secondary school students to a set of three algebra items were analysed to determine the prevalence of the "letter as object" misconception. We estimate that 50% to 80% of Year 7 students bring this misconception to…

Getting students adopt the habits of mind specific to many disciplines can be seen as an anchor that will support them to solve the problems in their daily lives. Starting from this premise, a new subject, featuring the habits of mind and how to use and improve them in educational environments seems to worth thinking on. This article describes an…

Quantifier Elimination is a procedure that allows simplification of logical formulas that contain quantifiers. Many mathematical concepts are defined in terms of quantifiers and especially in calculus their use has been identified as an obstacle in the learning process. The automatic deduction provided by quantifier elimination thus allows…

Many students with learning disabilities (LD) in mathematics receive their mathematics education in general education inclusive classes; therefore, these students must be capable of learning algebraic concepts, including developing algebraic thinking abilities, that are part of the general education curriculum. To help students develop algebraic…

Patterns are a ubiquitous phenomenon. They exist in nature's plant species emerging as a complete order from truncated matter. Patterns are also present in the fine arts where the aesthetic properties of form exist and conjugate through paintings and sculptures. Mathematical patterns, the focus of this position paper, dominate financial scenarios,…

In this research, I set out to elucidate the relationships that might exist between students' conceptual understanding upon which they draw in their proof activity. I explore these relationships using data from individual interviews with three students from a junior-level Modern Algebra course. Each phase of analysis was iterative, consisting of…

Many students with learning disabilities (LD) in mathematics receive their mathematics education in general education inclusive classes; therefore, these students must be capable of learning algebraic concepts, including developing algebraic thinking abilities, that are part of the general education curriculum. To help students develop algebraic…

This study posed and studied a solution to a prevailing tension in online education: the online medium is fundamentally connective and yet students often report feelings of social isolation. The study compared two online interventions -- both into a student's fluency in the language of functions and graphs, a major focus of a student's transition…

The article discusses three empirical examples of Computer Algebra System (CAS) use in a Danish upper secondary school mathematics class that had experienced a recent change of teacher. All examples lead to didactical problems surrounding the situation and unclear expectations between teacher and students, involving loss of students' mathematical…

Fully online courses can provide teachers fresh opportunities to expand their mathematical conceptions and infuse technology into their classroom teaching. In this article, the authors share the experience of two classroom teachers (Hornbein and Bryson) who participated in a fully online mathematics education course--Expanding Conceptions of…

Most word processors, including Google Docs™ and Microsoft® Word, include an equation editor. These are great tools for the occasional homework problem or project assignment. Getting the mathematics to display correctly means making decisions about exactly which elements of an expression go where. The feedback is immediate: Students can see…

In a classroom teaching experiment, we explored fifth graders' ability to identify relationships in and between two patterns--what we may refer to as functional relationships. Conventional functions curricula are dominated by defining relationships between two patterns via a rule, describing how to find y or f(x) given a particular value for x…

Assessment and instruction are interwoven in mathematically rich formative assessment tasks, so employing these tasks in the classrooms is an exciting and time-efficient opportunity. To provide a window into how these tasks work in the classroom, this article analyzes summaries of student work on such a task and considers several students'…

Admittedly, the study of Complex Analysis (CA) requires of the student considerable mental effort characterized by the mobilization of a related thought to the complex mathematical concepts. Thus, with the aid of the dynamic system Geogebra, we discuss in this paper a particular concept in CA. In fact, the notion of winding number v[f(gamma),P] =…

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…