This article provides an initial comparison of the Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics by examining the fundamental notion of slope. Each set of standards is analyzed using eleven previously identified conceptualizations of slope. Both sets of standards emphasize Functional Property,…

Pat was a 19-year-old attending a Special School for the Intellectually Disabled in Indonesia. She was interviewed by the first author regarding her mental calculation strategies when solving 1- and 2-digit addition and subtraction problems. Results indicate that she was able to see ten as a unit composed of ten ones and was facile in using…

Declining participation rates in advanced mathematics courses and STEM-related occupations has been an issue in Australia for some time, particularly for females. As students continue to disengage with mathematics and complain about its usefulness, it is important to explore what we can do to stem the tide of departing students. One area worthy of…

In this essay, the authors share some of their journey as they seek to make sense of what it might mean to prepare secondary mathematics preservice teachers to teach mathematics for social justice. The focus on how to prepare mathematics teachers to critically consider the world around them and to further develop the dispositions to become agents…

This article describes a part of a large scale study which helped to gain understanding of the high school mathematics teachers' perceptions related to the integration of history of mathematics into instruction. There is obvious lack of correspondence between general perception about possible benefits of students learning the history of…

Despite compulsory mathematics throughout primary and junior secondary schooling, many schools across Australia continue in their struggle to achieve satisfactory numeracy levels. Numeracy is not a distinct subject in school curriculum, and in fact appears as a general capability in the Australian Curriculum, wherein all teachers across all…

What "is" mathematics? What does it mean to "do" mathematics? The answers to these two questions critically influence the ways in which learners respond to a mathematical problem. On the other hand, if they see questions as having only one correct answer and as needing to be solved in one particular way, they will be prone to…

In this paper we aim to contribute to the process of networking between theoretical frames in mathematics education by means of forging connections between Constructionism and Instrumental Theory to discuss a design for instrumentalisation. We specifically focus on instrumentalisation, i.e. the ways in which students make changes to digital…

Principles and Standards for School Mathematics (NCTM 2000) states, "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning." The focus on reasoning and sense making with technology in the lesson presented in this article will enable students to do more…

Statistical studies are referenced in the news every day, so frequently that people are sometimes skeptical of reported results. Often, no matter how large a sample size researchers use in their studies, people believe that the sample size is too small to make broad generalizations. The tasks presented in this article use simulations of repeated…

A picture is worth a thousand words. This statement is especially true in mathematics teaching and learning. Visual representations such as pictures, diagrams, charts, and tables can illuminate ideas that can be elusive when displayed in symbolic form only. The prevalence of representation as a mathematical process in such documents as…

This article reports the findings of a comparative study of pedagogy in lower-secondary school mathematics in Denmark and England. Lesson observations and interviews identified the range of goals towards which teachers in each country worked and the actions these prompted. These were clustered using the lens of Bernstein's pedagogic discourse to…

This article looks at how social and participatory media can be used to strengthen interdisciplinary literacy and connects the multimodality of social environments with Middle-Years Mathematics curriculum and delivery. The article reports on part of an eighteen months action research study in an Australian public high school within the author's…

Some of mathematics teaching is routine, like an exercise from a textbook for which you have received instruction and already know what to do. On other occasions, however, teaching mathematics is challenging, involving problems of teaching for which the solutions may not be readily apparent. These situations require the application of mathematical…

This research examines secondary mathematics teachers' use of textbook curriculum materials within "typical" cycles of planning and teaching in a school year. The curriculum use of four teachers from the western US was examined before and after engagement in a form of professional development focused on more purposeful and flexible…