Teacher Actions to Maximize Mathematics Learning Opportunities in Heterogeneous Classrooms

The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11–12) class.     

Constructing Neonarratives: A Pluralistic Approach to Research

Practitioners in the visual arts and education can find researching their field a tricky business. They are often caught within the debate about the values of qualitative vs quantitative research, as well as the need to reflect the reality of visual arts practices in a changing world. The selection of an approporiate research method is no easy task. This paper presents a way of approaching research in art and education using a narratological approach to develop neonarratives. Such a method can satisfy calls for rigour while offering contemporary views of the issues under investigation.     

Classroom Competencies and Marginal Positionings

In this paper we examine the way students are positioned in classrooms in terms of the binary power/powerlessness and its relation to other binaries such as teacher/student, white/black and competent/incompetent student. We show how those positioned in the marked non‐ascendant pair of each binary are assumed, from the perspective of ‘teaching‐as‐usual’ to be choosing (irrationally) their lesser status. We show how this can be read quite differently from a poststructuralist perspective and how such a reading makes visible the ways in which power and ascendant positionings are discursively achieved not only as ‘normal’ but as the way things really are and should be. It further makes visible the ways in which such discursive achievements are dependent on those who are positioned as the necessary other/outsider to the ascendant order.     

TEACHING FOR STATISTICAL LITERACY: UTILISING AFFORDANCES IN REAL-WORLD DATA

It is widely held that context is important in teaching mathematics and statistics. Consideration of context is central to statistical thinking, and any teaching of statistics must incorporate this aspect. Indeed, it has been advocated that real-world data sets can motivate the learning of statistical principles. It is not, however, a straightforward task to take a real-world example and incorporate it into a lesson that will teach important statistical principles. This paper considers issues involved in using real data to exemplify statistical ideas and examines pre-service teachers’ attempts to design teaching activities using such data. Pre-service teachers were supplied with a topical data set and asked to plan lessons that would teach some key statistical idea to year 6 students. The lessons were analysed using a hierarchy for teaching statistical literacy, and great variation was found in the level of statistical thinking demanded in the planned lessons. Teachers who had completed a preliminary activity helping them to think carefully about what might be taught from real data in general produced lessons with stronger statistical content. A key requirement for having lessons with deep consideration of statistical ideas is to identify the actual affordances for teaching contained within a data set; the planning process then benefits from explicit attention to making that content evident in the teaching activities.     

Revealing educationally critical aspects of rate

Rate (of change) is an important but complicated mathematical concept describing a ratio comparing two different numeric, measurable quantities. Research referring to students’ difficulties with this concept spans more than 20 years. It suggests that problems experienced by some calculus students are likely a result of pre-existing limited or incorrect conceptions of rate. This study investigated 20 Australian Year 10 students’ understanding of rate as revealed by phenomenographic analysis of interviews. Eight conceptions of rate emerged, leading to the identification of four educationally critical aspects of the concept which address gaps in students’ thinking. In addition, the employment of phenomenography, to reveal conceptions of rate, is described in detail.     

Costabile,Angela & Spears,Barbara A ed (2012) The impact of technology on relationships in educational settings David Fulton (Routledge,Abingdon UK & New York) isbn 978‐0‐415‐61008‐7 217 pp £29.99 http://www.routledge.com/books/details/9780415610087/

Teachers interested in harnessing the internet for positive purposes will enjoy this book—it lays bare some myths, challenges perceptions, and provides evidence of interventions which hold great promise for ameliorating negative misuse, such as cyber‐bullying. Case studies from European, American and Australian practitioners highlight the work being done to harness the positive power of social networking and connectedness. If the content of this book is likely to be relevant to you, I recommend that you arrange to borrow a copy for a while. Robyn Smyth