Affordances of spreadsheets in mathematical investigation: Potentialities for learning

This article, is concerned with the ways learning is shaped when mathematics problems are investigated in spreadsheet environments. It considers how the opportunities and constraints the digital media affords influenced the decisions the students made, and the direction of their enquiry pathway. How might the leraning trajectory unfold, and the learning process and mathematical understanding emerge? Will the spreadsheet, as the pedagogical medium, evoke learning in a distinctive manner? The article reports on an aspect of an ongoing study involving students as they engage mathematical investigative tasks through digital media, the spreadsheet in particular. In considers the affordances of this learning environment for primary-aged students

Visual perturbances in digital pedagogical media

Several studies have investigated how the formation of informal conjectures, and the dialogue they evoke, might influence young children’s learning trajectories, and enhance their mathematical thinking. In a digital environment, the visual output and its distinctive qualities can lead to interpretation and response of a particular nature. In this paper the notion of visual perturbance is explored, and situated within the data obtained, when ten-year-old children engaged in number investigations in a spreadsheet environment

Processing mathematics through digital technologies: A reorganisation of student thinking?

This article reports on aspects of an ongoing study examining the use of digital media in mathematics education. In particular, it is concerned with how understanding evolves when mathematical tasks are engaged through digital pedagogical media in primary school settings. While there has been a growing body of research into software and other digital media that enhances geometric, algebraic, and statistical thinking in secondary schools, research of these aspects in primary school mathematics is still limited, and emerging intermittently. The affordances of digital technology that allow dynamic, visual interaction with mathematical tasks, the rapid manipulation of large amounts of data, and instant feedback to input, have already been identified as ways mathematical ideas can be engaged in alternative ways. How might these, and other opportunities digital media afford, transform the learning experience and the ways mathematical ideas are understood? Using an interpretive methodology, the researcher examined how mathematical thinking can be seen as a function of the pedagogical media through which the mathematics is encountered. The article gives an account of how working in a spreadsheet environment framed learners' patterns of social interaction, and how this interaction, in conjunction with other influences, mediated the understanding of mathematical ideas, through framing the students' learning pathways and facilitating risk taking

Making mathematics meaningful: Using student-initiated problems to situate mathematics

Mathematics is everywhere-from the minute we open our eyes to check the alarm clock and calculate how many minutes extra we can afford to lie in bed, to measuring out our cereal for breakfast and estimating if we have enough petrol to make the 18 kilometre journey to work. As teachers of mathematics. we must ask ourselves if the way we teach reflects the real-life problem-solving situations our students will experience within their everyday world

Processing mathematical thinking through digital pedagogical media: the spreadsheet

Abstract This study is concerned with the ways mathematical understanding emerges when mathematical phenomena are encountered through digital pedagogical media, the spreadsheet, in particular. Central to this, was an examination of the affordances digital technologies offer, and how the affordances associated with investigating mathematical tasks in the spreadsheet environment, shaped the learning trajectories of the participants. Two categories of participating students were involved, ten-year-old primary school pupils, and pre-service teachers. An eclectic approach to data collection, including qualitative and quantitative methods, was initially undertaken, but as my research perspective evolved, a moderate hermeneutic frame emerged as the most productive way in which to examine the research questions. A hermeneutic process transformed the research methodology, as well as the manner in which the data were interpreted. The initial analysis and evolving methodology not only informed this transition to a moderate hermeneutic lens, they were constitutive of the ongoing research perspectives and their associated interpretations. The data, and some that was subsequently collected, were then reconsidered from this modified position. The findings indicated that engaging mathematical tasks through the pedagogical medium of the spreadsheet, influenced the nature of the investigative process in particular ways. As a consequence, the interpretations of the interactions, and the understandings this evoked, also differed. The students created and made connections between alternative models of the situations, while the visual, tabular structuring of the environment, in conjunction with its propensity to instantly manage large amounts of output accurately, facilitated their observation of patterns. They frequently investigated the visual nature of these patterns, and used visual referents in their interpretations and explanations. It also allowed them to pose and test their informal conjectures and generalisations in non-threatening circumstances, to reset investigative sub-goals easily, hence fostering risk taking in their approach. At times, the learning trajectory evolved in unexpected ways, and the data illustrated various alternative ways in which unexpected, visual output stimulated discussion and extended the boundaries of, or reorganised, their interaction and mathematical thinking. An examination of the visual perturbations, and other elements of learning as hermeneutic processes also revealed alternative understandings and explanations. Viewing the data and the research process through hermeneutic filters enhanced the connectivity between the emergence of individual mathematical understanding, and the cultural formation of mathematics. It permitted consideration of the ways this process influences the evolution of mathematics education research. While interpretive approaches are inevitably imbued with the researcher perspective in the analysis of what gets noticed, the research gave fresh insights into the ways learning emerges through digital pedagogical media, and the potential of this engagement to change the nature of mathematics education

The Solomon Islands mathematics: Pedagogy in transition?

This article examines the transition of the Solomon Islands School of Education's primary and secondary mathematics education programme from a focus on content knowledge and teacher transmission, to a more activity-based, problem-solving, learner-centred approach. The ways the development team co-constructed that change so that it incorporated current mathematics education pedagogy, the Solomon Islands' Mathematics Curriculum document, and elements of Solomon Islands mathematics are described. How the team attempted to manage the dilemma between local educational imperatives and the globalisation of mathematics education is considered. Central to this are comparisons with international research on mathematics education pedagogy, while giving recognition to the situating of these within localised contexts. The article describes the ways the transition evolved, and how issues related to the change process, such as trust, culture, pedagogy and power, were engaged with, both proactively and incidentally. It will also consider lecturer/student reflection on the programme and the ways the changes may have influenced teaching. This article contends that change that is co-constructed and hinged to respectful partner relationships, will lead to greater participant autonomy and enhance the sustainability of the change. Finally, it poses questions that require subsequent examination for the transition to be sustainable

Representing the one left over: A social semiotic perspective of students’ use of screen casting

This paper examines the potential of using screen casting with an iPad to enhance learning in mathematics. Data are presented from two seven-year-old students as they use the Explain Everything app to solve a division with remainder problem (DWR). A social semiotic perspective was used to interpret students’ use of multiple modes as they represented the mathematical ideas within the context of the problem. We consider how a social semiotic perspective has the potential to draw attention to the students’ interests and emerging expressions in representing mathematical relationships. We further consider how the use of representations in the app might relate to student learning

How might the use of apps influence students' learning experiences? Exploring a socio-technological assemblage

In this paper, we report on primary-school students’ views of their learning experiences when they engaged with mathematical phenomena through apps. The students commented on how they used a range of digital tools within the apps to solve problems, and we consider how the affordances of the mobile technologies, including multi-representation, dynamic and haptic, might influence the learning experiences. In particular, we focus on the interplay between the affordances of the mobile technologies with other social and pedagogical aspects, and ask how the assemblage of social and technological entities might influence mathematical learning experiences

Using scratch to facilitate mathematical thinking

This article reports on a research project that examined the ways that 10-year-old students, who were using Scratch for coding, engaged with mathematical ideas. Interactive software is emerging that has cross-curricula implications and facilitates thinking in rich, problem-solving environments. Scratch, a free-to-use graphical programming environment provides opportunities for creative problem solving. When students process mathematics through digital technologies, the digital pedagogical media influences the learning process and students’ understanding emerges in distinctive ways. The children used Scratch to create mathematical digital learning objects, including games. An interpretive approach was undertaken, with the data collected over a two-week research period. The students wrote daily blogs articulating their progress and reflections. Students and the teacher were interviewed, and classroom observations (both written and photographic) were recorded. The findings suggest that mathematical thinking, including geometry and problem-solving processes, was facilitated through this process. Together, these findings indicate that teachers should not only use Scratch in primary school classroom programmes to develop coding skills but also be aware of its potential to facilitate thinking in other related areas

Tauira Rangatahi Numeracy and Literacy Programme: Apps in Numeracy and Literacy Research

A key aspect of tertiary education undertaken by Te Wananga o Aotearoa (TWoA) is re-establishing engagement and success in the rangatahi space through meeting the literacy and numeracy demands for programmes at levels 1–3. TWoA has Youth Guarantee programmes that deliver introductory Sport and Leisure and Contemporary Māori Arts programmes with embedded literacy and numeracy. The purpose of this research project was to investigate tauira rangatahi attitudes towards literacy and numeracy development through the application of appropriate cultural capital in conjunction with contemporary digital technologies. The research examined the influence of iPad apps on the beliefs and attitudes of Youth Guarantee tauira towards numeracy and literacy