Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning…

This paper investigates students' mathematical modeling activity in data-rich modeling tasks. It aims at gaining insight into how students develop meaning when modeling data-rich situations and the mathematical models produced. A tendency to model a particular dataset, rather than the phenomenon that the dataset is a particular instance of, has…

Surveys are commonly used to determine how people feel about a specific issue. The increasing availability of the internet and popularity of social networking sites have opened up new possibilities for conducting surveys and, with limited additional costs, enlarge the pool of volunteer respondents with the desired background, experience, or…

The numeracy capabilities of pre-service teachers are a recent focus in the Australian educational system. In this article, we discuss findings from an analysis of data from the Literacy and Numeracy Test for Initial Teacher Education Students (LANTITE), which is administered by the Australian Council for Educational Research. In our analysis, we…

This paper provides a set of five indicators of CAS use, which provide a means to analyse a student's written solution to determine whether they used CAS for solving a given problem. These indicators provide a way for researchers and teachers to determine CAS use without requiring classroom observation or the explicit recording of extra…

It seems that calculators continue to be misunderstood as devices solely for calculation, although the likely contributions to learning mathematics with modern calculators arise from other characteristics. A four-part model to understand the educational significance of calculators underpins this paper. Each of the four components (representation,…

At the turn of this century, expectations for learning mathematics by students with Down syndrome were low. Research and practice continued to indicate considerable difficulty with number and calculation (Bird & Buckley, 2001). Unfortunately, most authors extrapolated difficulty with number to difficulty with mathematics in general, even…

Two decades ago, in an award-winning paper, Dan Kennedy (1995) likened learning mathematics to climbing a tree, for which there was only one way to climb: up a large and solid trunk. In the limited time that is available, many students give up the climb, impede others, fall off the trunk, or fail to climb the tree sufficiently well. In the case of…

The introduction of linear functions is the turning point where many students decide if mathematics is useful or not. This means the role of parameters and variables in linear functions could be considered to be "threshold concepts". There is recognition that linear functions can be taught in context through the exploration of linear…

Logarithms continue to play an important role in mathematics (most significantly in calculus), science, and engineering. It is therefore important for students to understand logarithms as real numbers as well as the characteristics of logarithmic functions. Exploration of challenges in understanding logarithms as real numbers and logarithmic…

Since the 1990s, computer algebra systems (CAS) have been available in Australia as hand-held devices designed for students with the expectation that they will be used in the mathematics classroom. The data discussed in this paper was collected as part of a pilot study that investigated first year university mathematics and statistics students'…

Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one…

In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about…

In 2009, four mathematics subjects were offered at the year 12 level in the Victorian Certificate of Education (VCE). The two subjects at the intermediate level--Mathematical Methods and Mathematical Methods CAS--run in parallel, that is, a student can be enrolled in only one or the other, the choice being made at the school level. The curricular…

In this paper, the relationships between students' beliefs about knowing and learning mathematics, and how they engage with calculators, are investigated. An online survey was conducted for 964 Singaporean and 176 Victorian senior secondary students. Students' "connected knowing-deep approach" conception of mathematics was found to be…