Web-based mathematics : some 'dos' and 'don’ts'

This case study describes an “out of field” teacher’s use of the Internet to teach a range of mathematical topics in a modified Year 8 mathematics class. It highlights the importance of three factors for implementing a discernible web-based teaching strategy: appropriate choice of web objects,effective “virtual” pedagogy, and technical support and expertise. Based on these findings, a framework is suggested for constructing an effective teaching strategy to support the use of virtual resources in the actual mathematics classroom.

Sex differences in achievement in year 12 mathematics and non-routine problem solving

In 1991 all Victorian year 12 students undertook the new Victorian Certificate of Education Mathematics Study designed by the Victorian Curriculum and Assessment Board. This paper presents the results of a study into sex difference in achievement in the new VCE Mathematics study in Victoria. An important goal of the study designers was to encourage more equal participation in senior secondary mathematics by females and males and to include assessment of mathematical skills previously not assessed in a year 12 course in Victoria. These new tasks could conceivably change the degree and direction of sex difference in achievement in senior secondary mathematics.

Geeks and nerds : computers, gender and the mathematics classroom

This paper presents some of the findings of a pilot study concerning gender differences in behaviour in a Year 10 co- educational secondary mathematics classroom that used computers. Analysis of interactions between students and the teacher and engagement with the task, the computer and the mathematics suggest some evidence of gender difference. A number of factors were hypothesised as relating to behaviour and this paper discusses the preliminary findings in relation to students' experience with computers and their style of interaction with computers.

The "strugglers" in selected computer based mathematics classrooms

In this paper, the experiences of lower achieving mathematics students in two secondary mathematics classrooms in which computers were regularly used are described. A year 8 and a year 9 mathematics class from one secondary school participated in the ethnographic study. The results show that in these two classrooms the learning relationships and power relationships did not, in general, support the learning and engagement of lower achievers in mathematics. Research into computer based teaching methods that engage low achieving students in computer based mathematics is needed.

Equity and technology : a case study

I am researching equitable and socially just teaching practices when using technology for the mathematical learning of disadvantaged and marginalised students in junior secondary school. Using data gathered from teacher interviews and a meeting of teachers, I present a case study of one teachers’ practice. The case suggests that there are some equity considerations for the use of an integrated project approach to teaching mathematics and that whole class problem solving with technology can provide access to mathematical ideas when students have limited access or skills with technology.

Teaching and aligning upper level mathematics classes to Michigan high school content expectations in an alternative education setting : approaches and issues

After teaching regular education secondary mathematics for seven years, I accepted a position in an alternative education high school. Over the next four years, the State of Michigan adopted new graduation requirements phasing in a mandate for all students to complete Geometry and Algebra 2 courses. Since many of my students were already struggling in Algebra 1, getting them through Geometry and Algebra 2 seemed like a daunting task. To better instruct my students, I wanted to know how other teachers in similar situations were addressing the new High School Content Expectations (HSCEs) in upper level mathematics. This study examines how thoroughly alternative education teachers in Michigan are addressing the HSCEs in their courses, what approaches they have found most effective, and what issues are preventing teachers and schools from successfully implementing the HSCEs. Twenty-six alternative high school educators completed an online survey that included a variety of questions regarding school characteristics, curriculum alignment, implementation approaches and issues. Follow-up phone interviews were conducted with four of these participants. The survey responses were used to categorize schools as successful, unsuccessful, and neutral schools in terms of meeting the HSCEs. Responses from schools in each category were compared to identify common approaches and issues among them and to identify significant differences between school groups. Data analysis showed that successful schools taught more of the HSCEs through a variety of instructional approaches, with an emphasis on varying the ways students learned the material. Individualized instruction was frequently mentioned by successful schools and was strikingly absent from unsuccessful school responses. The main obstacle to successful implementation of the HSCEs identified in the study was gaps in student knowledge. This caused pace of instruction to also be a significant issue. School representatives were fairly united against the belief that the Algebra 2 graduation requirement was appropriate for all alternative education students. Possible implications of these findings are discussed.

Development of prospective mathematics teachers’ professional noticing in a specific domain: proportional reasoning

The aim of this research is to identify aspects that support the development of prospective mathematics teachers’ professional noticing in a b-learning context. The study presented here investigates the extent to which prospective secondary mathematics teachers attend and interpret secondary school students’ proportional reasoning and decide how to respond. Results show that interactions in an on-line discussion improve prospective mathematics teachers’ ability to identify and interpret important aspects of secondary school students’ mathematical thinking.

Why do we study mathematics: a philosophical and historical retrospect ...

"Address delivered before the Secondary mathematics section of the National education association, Boston, July 8, 1910."

Learning mathematics in a classroom community of inquiry

This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal development (ZPD) is invoked as a fundamental framework for explaining learning as increasing participation in a community of practice characterized by mathematical inquiry. The analysis draws on classroom observation and interviews with students and the teacher to show how the teacher established norms and practices that emphasized mathematical sense-making and justification of ideas and arguments and to illustrate the learning practices that students developed in response to these expectations.

Lesson study - Could it work for you?

1. Introduction Japanese Lesson Study first came to world-wide attention through Makoto Yoshida’s doctoral dissertation (Yoshida, 1999; Fernandez & Yoshida, 2004) and Stigler and Hiebert’s (1999) accounts of Lesson Study based on the Third International Mathematics and Science Study (TIMSS). By 2004, Lesson Study was taking place in the USA in at least 32 states and 150 lesson study clusters.Lewis (2002) describes the Lesson Study Cycle as having four phases: goal-setting and planning – including the development of the Lesson Plan; teaching the “research lesson” – enabling the lesson observation; the post-lesson discussion; and the resulting consolidation of learning, which has many far-reaching consequences (see, for example, Lewis & Tsuchida, 1998). It could be said that research lessons make participants and observers think quite profoundly about specific and general aspects of teaching.In Japan, Lesson Study occurs across many curriculum areas, mainly at the elementary school level, and to a lesser extent junior secondary. In mathematics, the research lesson usually follows the typical lesson pattern for a Japanese “structured problem solving lesson”.Major characteristics of such lessons include: the hatsumon – the thought-provoking question or problem that students engage with and that is the key to students’ mathematical development and mathematical connections; kikan-shido – sometimes referred to as the “purposeful scanning” that takes place while students are working individually or in groups, which allows teachers not only to monitor students’ strategies but also to orchestrate their reports on their solutions in the neriage phase of the lesson; neriage – the “kneading” stage of alesson that allows students to compare, polish and refine solutions through the teacher’s orchestration and probing of student solutions; and matome — the summing up and careful review of students’ discussion in order to guide them to higher levels of mathematical sophistication (see, for example, Shimizu, 1999).

Accelerating mathematics learners : what counts?

This article elaborates on my statements quoted in The Age October 2014 article 'More students take on VCE mathematics subject early'. (http://theage.com.au/victoria/more-students-take-on-vce-subjects-early-20141024-11b4rv.html). This article was about accelerating mathematics students by allowing them to take year 11 Mathematics subjects in year 10, and year 12 Mathematics subjects in year 11. My statements were 'Although 'taking on Year 12 subjects early could help students prepare for the workload once they reach their final year ... based on my research and teaching experience, you don't take on early those subjects that are going to be key to your university studies' because 'going early means you are going to rely much more heavily on learning things faster.

Contesting lost ground for the middle years in Australia : using the case study of Queensland

Over the past twenty years Australia has witnessed an extraordinary rise of the middle year’s movement. In more recent years, however, there is concern that middle years has fallen from the mainstream education agenda (Australian Research Alliance for Children and Youth, 2011). At a national level, evidence of this fall can be seen in the new national curriculum frameworks where reference to middle years is significantly absent, such as The Shape of the Australian Curriculum Version 2.0, (Australian Curriculum, Assessment and Reporting Authority, 2010). Evidence of the fall at a state level can be seen in Queensland Government’s 2015 commencement of junior secondary, rather than middle years, as outlined in A Flying Start for Queensland children: Why year 7 will be part of high school from 2015 (Queensland Government, 2011a). This announcement came after the Queensland government had undertaken an extensive consultation period exploring the possible uptake of middle years at a systemic level. While some may argue that middle years practices can be seen to be embedded in both the national curriculum and the junior secondary reform – it is the fact that middle years practices and philosophies are implicitly embedded (hidden) rather than being made explicitly and systematically mainstreamed (broadly accepted), that causes us grave concern. As such, we argue that this is clear indication that the middle years are being marginalized from the overarching educational agendas in Australia.

Teaching reading comprehension across the national curriculum with EAL/D learners : are we brave enough to really take it on?

Teaching English to EAL/D learners as a cross-curricula priority, not just the purview of the English classroom or language specialist, is now officially endorsed in the national curriculum. Yet many teachers, including subject English teachers, feel ill-equipped for this task. This paper presents an action research project conducted with a teacher of junior secondary English and Geography. The focus of the project was developing metacognitive reading strategies among EAL/D learners to enable them to access content area information more effectively and more independently. We discuss the particular strategies that were beneficial for students at the Emerging level of English and present a range of research-based reading strategies that teachers can embed in regular teaching in order to enhance reading comprehension. Examples from Geography and English lessons will be provided to show how the teaching of explicit ‘second language’ reading strategies can position EAL/D learners as valuable members of the classroom.

Responding to literature : accessible texts for reluctant readers

The Australian Curriculum: English 5.2 states, across all year level descriptions, that “students engage with a variety of texts for enjoyment”, with the level types of texts and levels of understanding developing over time (ACARA, 2014a). Problems arise when students are unable or unwilling to enjoy texts, and are reluctant to read, view, interpret, and evaluate written texts. This in turn impedes their ability to perform these texts for assessment purposes. The literacy abilities of students can vary widely within a single classroom, and it is a challenge for teachers to source and present texts which are accessible across the spectrum of reading abilities, as well as reflecting themes that are relevant and engaging for students, in addition to being consistent with the General Capabilities and Cross-Curriculum Priorities of the AC:E. In senior English also, the mainstream Qld Senior Syllabus (QSA, 2010, p. 6) requires that students have learning experiences developed through 15-20 literary texts, including the in-depth study of a complete novel. In the leisure context of English Communications, students may also “write stories, poems, or song lyrics” (QSA, 2004, p. 14). Since students’ responses to literature often take the form of other imaginative text creation we address this in this paper. We start by offering synopses of some accessible texts and strategies for teachers with these students who are unwilling or low literacy readers in junior secondary and senior level English. This paper canvases some easily read novels and some films with companion text suggestions which may serve as models for students responses. For the junior secondary texts, we identify how these align with the architecture of the Australian Curriculum’s General Capabilities and Cross Curriculum Priorities. Then, we will outline some suitable imaginative responses as possible assessment outcomes, such as short stories and digital stories.