This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

This theoretical paper explores the decision-making process involved in modelling and mathematizing situations during problem solving. Specifically, it focuses on the authority behind these choices (i.e., what or who determines the chosen mathematical models). We show that different types of situations involve different sources of authority,…

There is much to be learned and pondered by reading "Proofs and Refutations" by Imre Lakatos (Lakatos, 1976). It highlights the importance of mathematical definitions, and how definitions evolve to capture the essence of the object they are defining. It also provides an exhilarating encounter with the ups and downs of the mathematical reasoning…

Through professional development activities involving action research, middle-grades teachers at this author's school learned how to honor students' prior knowledge and experience by finding out about their K-5 computational development. Rather than complaining about what their students did not know, they learned to appreciate results from their…

"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

Many empirical investigations concerning the use of computer algebra systems (CAS) and symbolic calculators (SC) are restricted to a period of only a few weeks. They do not show long-term effects on students understanding. Therefore, a long term project (2003-2012) was started to test the use of symbolic calculators in Bavarian…

An nth-term problem involves a sequence. Students must determine which expression will allow them to calculate the nth position of the sequence. To solve such problems, students are to find "a rule that determines the number of elements in a step from the step number." These types of problems help students develop concepts of functions, variables,…

Many American students begin their high school mathematics study with the algebra 1-geometry-algebra 2 sequence. After algebra 2, then, students with average or below-average mathematical ability face a dilemma in choosing their next mathematics course. For students to succeed in higher mathematics, understanding the concept of functions is…

The mathematics of information processing and the Internet can be organized around four fundamental themes: (1) access (finding information easily); (2) security (keeping information confidential); (3) accuracy (ensuring accurate information); and (4) efficiency (data compression). In this article, the author discusses each theme with reference to…

Making constructions with paper is called "origami" and is considered an art. The objective for many fans of origami is to design new figures never constructed before. From the point of view of mathematics education, origami is an interesting didactic activity. In this article, the authors propose to help High School students understand new…

Fraction division is generally introduced in sixth or seventh grade with this rule: "Invert and multiply." The authors examined current commercial curricula and found that few textbooks use context as a way to build meaning for the division of fractions. When context is used, the connection between the invert-and-multiply rule and the context is…

This article analyzes the experiences of prospective secondary mathematics teachers during a teaching methods course, offered prior to their student teaching, but involving actual teaching and reflexive analysis of this teaching. The study focuses on the pedagogical difficulties that arose during their teaching, in which prospective teachers…

This article reports on a quantitative study carried out into the influence of affective variables, the role of conceptions of mathematics and approaches to learning on students in the transition to Service mathematics at the University of Limerick (UL). Questionnaires were distributed to three groups of first year students on Service mathematics…

Interpreting graphs found in various content areas is an important skill for students, especially in light of high-stakes testing. In addition, reading and understanding graphs is an important part of numeracy, or numeric literacy, a skill necessary for informed citizenry. This article explores the different categories of graphs, provides…