Mathematics education – Teaching & Learning Research Initiative

Māku anō e hanga, i toku nei whare – I will build my own house

INTRODUCTION: The context of the project The proponents of Modern Learning Environments (MLE) or Innovative Learning Environments (ILE) are from largely non-indigenous backgrounds. In Aotearoa New Zealand, research about learning mathematics in an MLE is limited and focuses almost exclusively on English-Medium (EM) settings (Bisset, 2014; Murphy, 2016; Osborne, 2013). In contrast, this research sought to contribute to the literature and knowledge space about tamariki learning paangarau (mathematics) in a Maaori-medium MLE. It provided an opportunity to locate and explore Maaori-medium (MM) ways of knowing and doing and for MM kaiako to consider the MLE space and identify characteristics of an MLE appropriate for them and their aakonga. The research grew

Making mathematical thinking visible

1. Mathematical parts and wholes Of all the subjects in the New Zealand school curriculum, mathematics is perhaps the most strongly associated in students’ minds with expectations of conformity, accuracy, and rule-following. Yet mathematicians describe mathematics as a source of intense aesthetic pleasure, creativity, and play (Lockhart, 2009; Sinclair, 2004). Chevallard (as cited in Eisenberg & Dreyfus, 1991) attributes this difference to “didactical transposition”, a process whereby academic mathematical knowledge is broken down and sequentially ordered into atomistic units that are easy to teach and assess. As a result of this transposition, students often experience instructional mathematics as components or building blocks: small, explicitly presented pieces of knowledge and skills to

Using multiplication and division contexts to enhance young children’s part–whole thinking in mathematics

Project description This project built on previous research showing that insufficient numbers of children reach expected levels of achievement in mathematics. Māori, Pasifika, and students from lower decile schools are particularly disadvantaged. Young children should be given equitable opportunities to develop their mathematical thinking, particularly in all strategy domains of the New Zealand Number Framework. These include not only addition and subtraction (the predominant focus in junior classes), but also multiplication, division, and fractions. This project aimed to provide children with learning opportunities and challenges within the context of multiplication and division, with the goal of developing greater understanding of part–whole relationships in mathematics. Methodology The research question posed was: How

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

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

The transition from secondary to tertiary mathematics education

Introduction In recent years there has been a growing interest in the transition from school to university. Reports identify problems in transition as a significant factor in learning mathematics, with international concerns about decreasing numbers of students opting to study mathematics at university and their decreasing levels of competence (Smith, 2004). In addition, serious concern has been expressed around a lack of essential technical facility, a marked decline in analytical powers, and a changed perception of what mathematics is, especially with regard to the place of precision and proof. Although there have been some studies on possible causes of transition problems, the amount of research in mathematics education at the tertiary

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

Teachers Learning Mathematics: Professional development research

Introduction The issue of mathematical knowledge of teachers has been documented in New Zealand for 80 years, but no effective long-term solution has been found; indeed, the situation has worsened. For example, the 2004 New Zealand Ministry of Education Teacher Census (Ministry of Education, 2005) showed that 25 percent of secondary school mathematics teachers had no university mathematics qualification—a rise from 21 percent in 1977. This one-year research study, undertaken in 2007, aimed to investigate the development of teachers’ own mathematical knowledge for teaching. Seven secondary teachers used action research methodology to investigate, develop and evaluate some aspect of their mathematical knowledge, completing two cycles over the year. In addition, the

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

TLRI Mathematics Enhancement Project: Professional Development Research

1. Introduction The research project on professional development reported here was conducted within the context of the Mathematics Enhancement Project. The Mathematics Enhancement Project involves the Mathematics Education Unit of the Department of Mathematics, University of Auckland, working with senior mathematics teachers in low decile secondary schools in the Manukau region. It was the result of a needs analysis conducted in 1999–2000 and is an ongoing development and research endeavour that aims to enhance mathematics achievement at a time when students are making the transition from secondary school to tertiary education. The project works at the student level, at the teacher level, and at the school and parent community level. The

Teachers developing as researchers: teachers investigate their use of questions in mathematics

1. Introduction In this research project, a group of teachers developed their research capability through their investigation of the use of questioning to facilitate students’ learning in mathematics. Eight teacher researchers worked in partnership with two research team leaders to analyse their own practice in order to identify aspects of questioning behaviour. During this one-year project, the teacher researchers had significant input into the shape and direction of the research. It was intended that this research project would build understanding by adding the teachers’ perspectives of the strengths and weaknesses of current pedagogical practice to the existing body of research. The project was closely aligned with the following principles of the