Showing papers in "Mathematics Education Research Group of Australasia in 2018"

Characteristics of spatial visualisation: Perspectives from area of composite shapes

Abstract: This paper attempted to make explicit some of the underlying characteristics of spatial visualisation using the concept of area of composite shapes. By engaging students with metric-free tasks, we identify the type of perceptual and visual/spatial manoeuvres that they deploy in such situations. Interview data collected from three students in Grade 7, 8, and 9 are used to exemplify three key constituents of spatial visualisation: figure-ground perception, global and local perception, and gesturing. An observable discontinuity was discovered in coordinating different pieces of spatial information after disembedding the parts that constitute the whole. This paper concludes with pedagogical implications.

Exploring Mathematical Fluency: Teachers' Conceptions and Descriptions of Students.

Abstract: Interviews can provide a window into what teachers think. This paper reports on findings from an exploratory study into teachers’ conceptions of mathematical fluency. Focusing on stage two of the study, I discuss 3 of 17 teachers interviewed, analysing their conceptions and descriptions of students. Teachers spoke of students having understanding and multiple ways of thinking, and their ability to work through errors and transfer knowledge. This suggested fluency in mathematics as more than carrying out procedures. Viewing fluency as the result of having conceptual understanding, strategic competence and adaptive reasoning, would make it synonymous with mathematical proficiency.

Using Apps for Teaching and Learning Mathematics: A Sociotechnological Assemblage.

Abstract: This paper reports on an aspect of a research project that examined the use of apps in primary school mathematics programmes. It reports teacher and student perspectives on how they used a range of digital tools within the apps to solve problems. We consider the interplay between the affordances of the mobile technologies, including multirepresentation and haptic, with other social and pedagogical aspects, and how the assemblage of social and technological entities influences the ways that teachers might integrate apps into their mathematics programmes.

Teachers’ perceptions of obstacles to incorporating a problem solving style of mathematics into their teaching.

Abstract: Despite recommendations to incorporate mathematical problem solving into the practice of primary teachers there is little evidence of the widespread acceptance of such advice by Early Years teachers. Understanding teachers’ perceptions of the obstacles they encounter when incorporating mathematical problem solving into their teaching can shed light on the matter. Survey responses of 22 teachers of Foundation and Year 1 across three Victorian schools indicated that the initial obstacles teachers perceived were those concerning children, teaching pedagogy, planning, resources, tasks and time.

What can be learned from teachers assessing mathematical reasoning: a case study

Abstract: Recently, mathematical reasoning has grown in prominence in curriculum documents and professional learning programs. However, the assessment of reasoning actions continues to be an elusive task for many teachers. Research has shown that many primary teachers focus only on explaining. This case study examines the salient behaviours of two Year 6 primary teachers employing the Assessing Mathematical Reasoning Rubric. Results indicated the teachers gained deeper insights into the diverse nature of reasoning through the employment of rubric. Therefore, it provides teachers with a vehicle for a more nuanced examination of reasoning beyond explaining and is a launching pad for lesson planning.

Developing a Rubric for Assessing Mathematical Reasoning: A Design-Based Research Study in Primary Classrooms.

Abstract: Despite mathematical reasoning being a proficiency included in mathematics curricula around the world, research has found that primary teachers struggle to understand, teach, and assess mathematical reasoning. A detailed rubric involving the three reasoning actions of analysing, generalising and justifying at five proficiency levels was refined according to feedback from teachers. At different stages of the study, teachers used the rubric to assess their students’ reasoning and provided feedback about its usefulness.

Free-Response Tasks in Primary Mathematics: A Window on Students' Thinking.

Abstract: We administered specially-designed, free-response mathematics tasks to primary students (N = 583, ages five to 12 years old). Our focus was on whether (i) the children’s responses could be reliably assessed, and (ii) the responses could provide insights into children’s mathematical thinking. We used a contemporary comparative judgement technique, interviews with four teachers, and analysed a sample of six responses to make inferences about the students’ mathematical thinking. We found that the sampled responses’ scores, interviewees’ comments and qualitative features of the sampled responses led to consistent insights on the children’s mathematical thinking. We argue that free-response tasks should supplement traditional assessments in primary mathematics.

The Beliefs about Mathematics, Its Teaching and Learning of Those Involved in Secondary Mathematics Pre-Service Teacher Education.

Abstract: Secondary mathematics pre-service teachers often have different experiences of mathematics and its teaching and learning during their initial teacher education. This paper documents the beliefs about mathematics, its teaching, and its learning, of mathematicians and mathematics educators who teach secondary mathematics pre-service teachers. The beliefs of the surveyed sample of eighty-two academics and differences between groups were characterised using descriptive statistics and one-way comparisons between groups ANOVA. Generally, respondents had a Problem-solving view of mathematics and those with education backgrounds were more in agreement with that method of teaching.;

Dialogic Practices in the Mathematics Classroom

Abstract: Teaching mathematics involves a lot of talking, and dialogic practices are central to most pedagogical practices in mathematics classrooms. Furthermore, for mathematical processes such as ‘reasoning’, ‘explaining’ and ‘mathematical thinking’ to be developed, there is a need for rich and robust dialogic interactions in the classroom. In this paper we investigate the dialogue in a typical Year 5 mathematics lesson by analysing the transcript using two different analytical frameworks. While the analysis showed that there were many interactions with nearly half being student turns, it was also evident that almost all the exchanges followed an Initiation-Response-Feedback pattern, with a high degree of teacher control. Furthermore, there was little evidence that the dialogic pedagogies of the lesson promoted student development in the mathematical processes. Thus, we content that there is a need to understand the dialogue of mathematics pedagogy, and its impact on students’ broader mathematical learning.

Measuring Mental Computational Fluency with Addition: A Novel Approach.

Abstract: Measuring computational fluency, an aspect of procedural fluency, is complex. Many attempts to measure this construct have emphasised accuracy and efficiency at the expense of flexibility and appropriate strategy choice. Efforts to account for these latter constructs through assessing children’s computational reasoning using structured interviews (e.g., MAI), are necessarily time-intensive. In this paper, we introduce a novel measure of Mental Computational Fluency with Addition (MCF-A) that attempts to incorporate these aspects by requiring children to reason from the perspective of another child. We describe results of a pilot study using the MCF-A with 169 Year 3 and 4 students.

Using Technology in Mathematics: Professional Development for Teachers.

Abstract: The Ghanaian mathematics curriculum expects teachers to adopt technologies as an instructional tool to assist students to learn mathematics relationally. Teachers’ dispositions (knowledge, beliefs, and attitudes) towards technology are critical in translating the curriculum intention into practice. This paper presents teachers’ initial dispositions related to technology integration and their views about a professional development model. In this model, they worked in teams to develop and enact GeoGebra-based mathematics lessons with support from expert, exemplary materials, and demonstration lessons. The results indicate that the model of professional development is promising in engaging teachers in technology integration.

Mathematics Anxiety: Year 7 and 8 Student Perceptions.

Abstract: Studies, such as Programme for International Student Assessment 2012, indicate that there are gender based differences in measures of mathematics anxiety, self-concept and selfefficacy among students. In this study we explore self-efficacy, self-concept and mathematics anxiety in a sample of Year 7 and 8 South Australian students to examine if these differences still exist. The findings indicate that high levels of mathematics anxiety is present among Year 7 and 8 students and that gender based differences are also evident in both self-efficacy and anxiety.

Verification and validation: what do we mean?

Abstract: Verification and validation are essential aspects of mathematics and beyond in STEM, but these constructs are not consistently defined in research nor in curricula documents. In this theoretical paper, we argue that verification and validation are largely characterized as binary judgments by teachers and researchers about what students do. We then present empirical examples of student work to show this view does not account for students’ thinking as they resolve problems. We conclude that in order to foster learners who are confident and capable in STEM fields, it is necessary to revisit how verifying and validating activities are conceptualised and developed across years of schooling.

The Experiences of Homeschooling Parents When Teaching Mathematics.

Abstract: This paper compares and contrasts the experiences of two parents who have chosen to homeschool their children in mathematics despite having difficulties with mathematics at school themselves. It describes the strategies these two parents used to overcome their lack of content knowledge and/or mathematics anxiety and are illustrative examples of how these deficits can be overcome with sufficient motivation.

Generating ideas for numeracy tasks across the curriculum

Abstract: The purpose of this article is to provide insight into how teachers identify initial ideas for the design of numeracy tasks. A design-based research approach was employed utilising classroom observations, video-stimulated recall techniques and semi-structured teacher interviews. Data collection and analysis were informed by a rich model of numeracy as well as generic principals of task design synthesised from relevant literature. Data analysis indicated that there were at least two approaches to generating ideas for numeracy tasks both of which were compatible with the principles of task design employed in this study.

Speaking Spatially: Implications for Remote Indigenous Learners.

Abstract: As part of a much larger study where spatial reasoning is the focus, this paper draws on the language aspects of this strand of the curriculum. The quarantined part of the project discussed in this presentation is based in remote Indigenous schools. We draw on the challenges of the concept of symmetry and where the language of instruction (and mathematics) is a foreign language. We pose questions of the nuanced, and often complex, language of spatial reasoning and the impact this has on the performance of Indigenous learners when applied to the enacted practices in school mathematics. We conclude by raising concerns and directions of the subsequent phases of the project.

Variations on a Theme: Pre-Service Mathematics Teacher Reflections Using an Affect-Based Critical Moment Protocol.

Abstract: Examining critical incidents in the mathematics classroom is a useful way for pre-service teachers to understand the experience of teaching. This paper examines the development and trialling of variations of a novel affect-based critical moment protocol that enables preservice mathematics teachers to reflect on their teaching performance. The emotions experienced in these moments were examined using self and group reflection, considering the thoughts and actions occurring immediately prior to, or during those moments. The four case studies presented report on trialled variations of this reflection process in a range of programs and delivery modes in four regional Australian universities.

Preservice Teacher Mathematics Education: Online vs. Blended vs. Face to Face! Is this the whole story?

Abstract: Negative experiences of university mathematics education are often laid at the feet of online or blended learning. However, data collected as part of a five-year project at two universities suggests that there is much more to consider in determining the quality of preservice teacher mathematics education courses. This paper outlines a methodology that investigates the experiences of pre-service education teachers (PSTs) in relation to their journey of learning how to teach primary mathematics delivered via a variety of modes. Results indicated that the mode of delivery is not the critical factor as course design, teacher knowledge, and building rapport seem to be more influential in student success.

Fluency with number facts – Responding to the Australian Curriculum: Mathematics

Abstract: This paper reports on results of a targeted and extended (two school terms) program for building Grade 3 and Grade 4 students’ facility with number facts and application for mental computation. As part of a larger project, this paper reports results from two schools. Results indicated strong gains in number fact recall and mental computation for both cohorts at both schools. The similar gains in outcomes at both schools suggests the power of a targeted and extended program to build basic fact fluency for mental computation.;

Maintaining Productive Patterns of Teacher-Student Interactions in Mathematics Classrooms.

Abstract: In preparing to study teacher-student interactions in mathematics classrooms in Iran, this paper as a literature review considers relevant mathematics education literature. I explore which aspects of classroom environments orient researchers to judge patterns of classroom interactions as productive. I examine patterns of classroom interactions that were empirically linked to student understanding. This paper highlights the importance of productive patterns of teacher-student interactions in promoting student learning, examining authoritative and dialogic teaching as two opposing approaches.

Engaging Pre-Service Non-Specialist Teachers in Teaching Mathematics Using Embodied Technology Tools.

Abstract: We report on an initial analysis of survey data that was generated through a collaboration between the schools of Education and Information Technology in exploring pathways through which future teachers could envision mathematics as engaging and creative subject, while also enhancing their awareness of, and skills in, using digital technologies in teaching mathematics. We specifically share insights generated into students' attitudes towards, current understandings of, and expectations for uses of technology in teaching and learning mathematics in schools. We bring attention to a mismatch between pre-service teachers views of technology and those of technology educators.

A Comparison of STEM and Non-STEM Teachers' Confidence in and Attitudes towards Numeracy.

Abstract: This study reports initial results of a larger study examining teacher practices in numeracy in the secondary sector. Survey data examined STEM teachers’ confidence in mathematics topics and attitudes towards numeracy in everyday life, and the responses were compared to teachers trained in non-STEM areas. The data indicate that teachers’ specialist backgrounds influence certain aspects of their numeracy. Similarities between groups highlight the contribution made by all teachers to secondary school numeracy education.

The R in the ELR Process: Reflection and the Emotions of PreService Teachers. A Case Study

Abstract: Reflective practice in mathematical teaching improves teaching skills and confidence. This paper investigates affect-based critical moments as a reflective practice for pre-service teaching. An embedded case study is presented by one regional university as a discovery into the reflective phase of the Enhancement-Learning-Reflection process to uncover the types of emotions and themes from student chosen critical moments. An analysis of these critical moments found students’ expressed mainly positive emotions combined with the negative emotion of anxiety. Themes emerged around pedagogical content knowledge: teaching strategies; student thinking; and appropriate mathematical content knowledge.

What Do Culturally Diverse Students in New Zealand Value Most for Their Mathematics Learning

Abstract: Classrooms around the world are becoming increasingly diverse. A major challenge faced by educators is achieving equity for all mathematics learners. To achieve equity, educators need to acknowledge and cater for this increasing diversity which includes attending to values of their students. Drawing on survey responses and individual interviews, this paper explores the mathematics education values espoused by 227 middle school students in New Zealand, including Pākehā/European, East Asian, Māori and Pāsifika learners. Results from this study provide insight into what is valued in the mathematics classroom and may assist teachers to develop pedagogy and classroom culture which aligns with students’ values.

Disciplinary Literacy in the Mathematics Classroom.

Abstract: Nationally and internationally, teachers are being held increasingly accountable for student achievement, particularly in light of high stakes literacy and numeracy tests. Policies have been implemented that are designed to improve educational outcomes through raising student literacy levels across all school years in all subject areas. This has resulted in all teachers being seen as teachers of literacy. Research around the teaching of literacy in mathematics supports the view that focusing on the language of mathematics will assist students to move from the concrete to the more abstract understandings required in the older year levels (Schleppergrell, 2007). However, this can be challenging for teachers who might be subject, but not language, specialists. In this paper, we report on a case study that investigated literacy teaching practices in a Year 7 mathematics classroom and specifically, the practices around teaching mathematical reportwriting and the conditions that might have enabled or constrained them. Findings suggest that while teaching the general writing required in mathematics might be part of teaching practice, if practices are to change, school leaders need to provide both time and money to enable teachers to develop their knowledge of specific disciplinary writing practices.

Examining a Teacher's Use of Multiple Representations in the Teaching of Percentages: A Commognitive Perspective.

Abstract: Learning Mathematics in Primary Schools is often mediated through the use of multiple representations. However, teachers may not pay enough attention to the way they use these representations. Given that the translations among representations may not always be smooth, it may be insightful to examine how teachers mediate learning through the use of multiple representations. In this paper, I will share key ideas in commognition before I present a case study of how Hannah, a teacher, mediate learning of percentages in her class. I will also introduce the idea of a ‘Mediation Flowchart’ and demonstrate how it can be used to describe and analyse a teacher’s use of multiple representations.

Insights into a Year 4 Student's Spatial Reasoning and Conceptual Knowledge of Rectangular Prisms.

Abstract: While spatial reasoning skills have been found to predict mathematical achievement, little is known about how primary students’ conceptual understanding of three-dimensional objects develops. This paper reports insights into a Year 4 student’s spatial reasoning when constructing and describing the properties of rectangular prisms, using Froebel’s Gifts, in an interview. Categories of the van Hiele framework were used to analyse student responses in conjunction with a specially designed analysis tool. The findings highlight the benefit of using a one-to-one interview to shed light on one student’s spatial reasoning and conceptual knowledge of rectangular prisms.

The Distinction Between Mathematics and Spatial Reasoning in Assessment: Do STEM Educators and Cognitive Psychologists Agree?

Abstract: Mathematics in Australia specifies spatial reasoning as a general capability within the curriculum. However, psychological research to date limits spatial assessment to psychometric tests leaving little room for a well-defined spatial curriculum. Although there are clear relationships between mathematics and spatial thinking, the independence in the measurement of the two constructs in research literature is rarely explored. In the present study, professionals in the fields of STEM Education and Cognitive Psychology evaluated mathematics and spatial assessment items. The results show evidence for a distinction between the two constructs in the content of the items, however with a caveat that thoughtful selection of assessment items is crucial to ensure independence in the measures.

Sense-making in mathematics: Towards a dialogical framing

Abstract: This paper presents a new theoretical viewpoint blended from the perspectives that mathematical meaning is extracted (from objects falling under a particular concept) and that mathematical meaning is given (to objects that an individual interacts with). It is elaborated that neither uni-directional framing (whether involving extracting meaning or giving meaning) provides a comprehensive account of the complex emergence of evolving forms of meaning. It is argued for a framing that construes sense-making in mathematics as dialogical: where what meaning one extracts is a function of what meaning is given to, and vice versa.

Orchestrating Mathematics Lessons: Beyond the Use of a Single Rich Task.

Abstract: Teachers have several challenges when designing and implementing mathematically-rich tasks, and hence, these tasks are not prevalent in many mathematics classrooms. Instead, teachers often use typical problems, such as standard textbook tasks and examination questions, to develop students’ procedural fluency. This begs the question of whether, and if so, how teachers can think about, and use these typical problems differently to develop conceptual understanding. In this paper, we report findings drawn from a two-year designbased research project and highlight two teaching vignettes to illustrate how typical problems were used to orchestrate instructional activities. Our findings suggest three important principles for teachers to consider when using typical problems.