Mathematics teaching – Teaching & Learning Research Initiative

Mathematical Reasoning and Knowledge in Initial Teacher Education (MARKITE)

Introduction The New Zealand Government’s goal is to have an education system that equips all learners with the knowledge, skills, and values needed to be successful citizens in the 21st century (New Zealand Government, 2011); government policy recognises that mathematical understanding is fundamental to effective participation in society, and delivers significant social and economic benefits (Tertiary Education Commission, 2012). Unfortunately, studies suggest that a significant proportion of the adult population does not have the level of mathematical thinking needed to function effectively in society (Alkema & Rean, 2014; Department of Education and Skills, 2011; Satherley, Lawes, & Sok, 2008). Mathematical thinking and reasoning skills are embedded in many of the activities

Capturing learning in undergraduate mathematics: a Learning in Undergraduate Mathematics: The Outcome Spectrum (LUMOS) report

Dedication Judy Paterson sadly passed away during this research project. However, her contribution was a major one, co-leading the design and grant application team, taking responsibility for the Team-Based Learning innovation, conducting interviews, and contributing strongly in several of the learning output observation groups. We dedicate this report to her memory. – Bill Overview of the project The LUMOS Project had two parts: the development of three innovative methods of undergraduate mathematics course delivery, and the identification and observation of a wide range of desired learning outcomes. This project sought to link these aspects. The research questions were: What practical, pedagogical, administrative and curricular barriers need to be overcome to establish

Enhancing teaching and learning of primary mathematics through the use of apps

1. Introduction How might enhancing teachers’ technological, pedagogical, and content knowledge (TPACK) influence the teaching and learning of primary school mathematics though using apps? The focus of this research project was on teaching and learning primary mathematics through the use of apps with mobile digital devices. Specifically, the project aimed to use the lens of teachers’ TPACK to advance and investigate the use of apps in primary mathematics classrooms, and their influence on students’ mathematical learning. Through co-inquiry based on a researcher–practitioner partnership, we co-constructed a framework to evaluate and inform teacher pedagogical decisions regarding the use of apps to enhance students’ conceptual understanding. A range of teachers across year levels

Learning the work of ambitious mathematics teaching

Introduction Seen by policy makers as both the cause of and a solution for education problems, teacher education is frequently criticised for not producing teachers of sufficient quality, while simultaneously being viewed as “an ideal site for increasing teacher quality, providing it is subject to reform” (Ell & Grudnoff, 2012, p. 79). Calls for reform (Education Workforce Report, 2010; NZTC, 2010) relate to newly qualified teachers’ capacity to respond to the needs of an increasingly diverse student body, alongside changing educational outcomes in terms of knowledge and competencies (Andretti & Major, 2010). Such calls are particularly pertinent to mathematics education. In New Zealand, too many students are disaffected with their mathematics

Teaching Algebra Conceptually in Years 9 and 10

Introduction Many students struggle with introductory algebra and teachers have little to guide them to assist their students learn this important component of mathematics. The project on teaching algebra conceptually (TAC) was designed to explore and create teaching approaches to assist students in Years 9 and 10 to develop a conceptual understanding of algebra. The effect of these teaching approaches was documented by use of a diagnostic tool that assessed and made students’ knowledge and strategic thinking in algebra explicit. Key findings Achievement in algebra can be enhanced by taking a structural perspective that provides high quality diagnostic assessment information to teachers. Effective teaching approaches that have an effect on student

Teaching undergraduate mathematics: Perspectives and interactions

The high demand for mathematics in undergraduate education means that large numbers of students enrol in the subject. Lecturing remains the prime delivery mode for teaching such courses. We addressed undergraduate mathematics’ lecturing through three components: lecturers and their development; student perspectives on mathematics; and interactions in the lecturing environment. We used theoretical frameworks from secondary contexts, developing them for tertiary application. This research aimed to improve the didactics of lecturing, and builds on studies on school/university transitions. Key findings Lecturer professional development based on Schoenfeld’s framework positively influenced lecturing practice in a way acceptable to lecturers. Students believe that learning mathematics involves natural ability; and that it is a subject

Learning to “friendly argue” in a community of mathematical inquiry

Introduction This project explored the sorts of culturally responsive pedagogy teachers can engage in to optimise equitable access for students to proficient forms of mathematical talk and activity. The project sought to further our knowledge of the effects on student achievement and mathematical disposition when a specific focus is placed on building a classroom culture of mathematical inquiry and argumentation. Key findings The teachers were able to create more opportunities for collaborative group activities focused on mathematical inquiry. The students’ role in inquiry mathematics learning activities required a dramatic change from passive receiver to active learner. Students developed new ways of thinking about mathematics and their relationship with mathematics, and came

Mathematical relationships and practices: A view into Year 9 mathematics classrooms.

While research has told us much about primary school mathematics classrooms, we know less about what happens at the secondary school level. Our Teaching and Learning Research Initiative project, a video study involving three Year 9 classes, enabled us to learn more about the mathematical relationships and practices in secondary classes. To date, our analysis has focused on the communities of practices, and the various ways in which teachers organise instructional activities. What we found was that, irrespective of school decile level, years of teachers’ experience, and proficiency level of students, teachers are highly focused on doing the best possible job for their students. Teachers work hard to enhance students’ confidence

Technology use and the teaching of mathematics in the secondary classroom

Mathematics teaching and learning is crucial to the future of New Zealand’s knowledge economy and deserves a special focus in education. One of the key synergisms of mathematics is with technology, and as technology advances it inevitably influences what happens in the mathematics classroom. However, with rapid advancements, teachers may be unprepared to take full advantage of new technology, with the types of technology use falling behind the learning possibilities demonstrated by international research studies (Thomas, Monaghan, & Pierce, 2004). In this study, we considered whether the National Certificate of Educational Achievement (NCEA) Levels 2 and 3 assessment standards had presented any challenges for teachers in terms of their use of

Te reo tataitai: Developing rich mathematical language in Māori immersion classrooms

1. Aims, objectives, and research questions Kō ta te rangatira kai he kōrero As described in the whakatauaki (proverb) above, language is the food of chiefs because fluency in it provides access to and control of learning. Khisty and Chval (2002) summarised the effect of this by stating, “[i]n essence, those with power are literate or in control of a discourse” (p. 167). Although Māori students who attend Māori immersion programmes do better than those attending mainstream schooling, generally they do not perform as well as other students in mathematics (Anthony & Walshaw, 2006 forthcoming). One of the reasons for this may be the difficulties Māori students have with the mathematics

Enhancing mathematics teaching and learning in early childhood settings

1. Aims, objectives, and research questions Aim The overall aim of the project was to engage early childhood teachers in investigating and improving their expertise in the teaching and learning of mathematics. The intention of the project was to develop a research environment through which researchers and kindergarten teachers worked collaboratively, using action research methodology, to explore means by which mathematical outcomes for children could be maximised. The research arose from the premise that within the field of mathematics education, while much has been written about mathematical experiences of both learners and teachers in the compulsory (school) sectors of education, very little is documented on mathematical learning and teaching in the