Ratio (and associated topics such as fractions and proportion) is known to be an area of mathematics that students find difficult. Multiplicative thinking is necessary, and students benefit from a wide range of strategies and representations for interpreting ratio. This study examined aspects of teachers' pedagogical content knowledge for teaching…

This study examined the types of mathematical connections established by four secondary school students while constructing concept maps on transformations of the parabola. The use of concepts maps revealed students' understandings--including some misconceptions--of transformations of the parabola and confirmed the usefulness of a model for…

In this paper, the SOLO taxonomy is used to identify different levels of student understanding of the statistical concepts associated with sampling distribution. This study was part of a research project investigating students' conceptual understanding of concepts of hypothesis testing taught with the support of simulation learning activities. The…

This study reports on a professional learning (PL) initiative aimed at establishing a community of practice, through teacher working groups in which teachers can explore and develop their algebraic pedagogical content knowledge (PCK). Here we report on teachers' solutions to three differently represented algebraic problems and explore what the…

Pedagogical Content Knowledge (PCK) is a powerful construct for examining the complexity of teacher knowledge. Together with teachers' moment-by-moment choices of action, it provides insight into teachers' knowledge and its influence on student learning. This paper investigates the PCK experienced by a senior secondary mathematics class during a…

The idea of variation is a foundation of statistical reasoning, and many curriculum documents, including the "Australian Curriculum", include variation in the learning required for the primary years. In this paper, we consider the design of activities that can exemplify the idea of variation for young students and investigate how…

Pedagogical content knowledge is widely considered an essential and complex facet of mathematics teacher knowledge, but little research has focused on PCK at the senior secondary level. This study explores some of the complexities of PCK in a teacher's lesson for senior secondary students by analysing data from lesson observation, the teacher's…

Mathematical knowledge in classrooms is mediated through the use of both technical and informal language. This paper is a report of a study of the language use of teachers as they examine students' work and discuss teaching for the topic of fraction operations. This provides a window on their pedagogical content knowledge and also on the way in…

Teacher knowledge, including Pedagogical Content Knowledge (PCK), continues to be the focus of research, with the general consensus being that PCK impacts upon teaching and learning. Much of the current research has focused on pre-service teachers and practicing primary teachers, with few studies focused on studying senior secondary teachers' PCK.…

The "flipped classroom" is gaining popularity in a number of settings, including secondary schools, reflecting a belief that the approach is more engaging and effective for students. This paper reports on a senior secondary mathematics class's experience with adopting a flipped classroom approach. The findings indicate that the teacher…

This paper presents a framework for examining the Pedagogical Content Knowledge (PCK) required of mathematics teacher "educators" as they endeavour to build the PCK for teaching mathematics that is required of the pre-service teachers with whom they work. The framework builds on existing research into PCK, and provides a series of…

Slope is a mathematical concept that is both fundamental to the study of advanced calculus and commonly perceived in everyday life. The measurement of steepness of terrain as a ratio is an example of an everyday application the concept of slope. In this study, a group of pre-service teachers were tested for their capacity to mathematize the…

Teachers now require high levels of statistical literacy in order to take advantage of the many statistical reports analysing assessment data that are provided by system authorities. In this report 16 items from the Attitudes and Statistical Literacy Instrument (ASLI) are used with 704 teachers to provide a hierarchical scale of teacher ability to…

This paper analyses the responses of 247 middle school students to items requiring the concept of average in three different contexts: a city's weather reported in maximum daily temperature, the number of children in a family, and the price of houses. The mixed but overall disappointing performance on the six items in the three contexts indicates…