title: Processing mathematical thinking through digital pedagogical media: the spreadsheet

authors: Calder, Nigel Stuart

subjects: mathematics education

abstract: 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.

text: 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.

year: 2008

title: Lower-Limb Passive Heat Maintenance Combined With Pre-cooling Improves Repeated Sprint Ability

authors: Beaven, Christopher Martyn

subjects: Science & Technology

abstract: Pre-conditioning strategies to potentiate performance are a common feature of pre-competition routines. The elevation of muscle temperature is seen as a vital component of preparing for physical performance, while pre-cooling strategies have been adopted to offset fatigue during repeated efforts. We investigated the individual and combined effects of a passive heat maintenance strategy and the ingestion of an ice-water slurry on repeated sprint performance. In a random cross-over design, 12 professional male athletes performed 5 × 40 m maximal running sprints under one of four conditions following a standardized warm-up: 15-min passive rest (Control); wearing a lower-body survival garment (HEAT); consuming a 500 mL ice slushy (COLD); or wearing the survival garment and consuming the slushy (H+C). Measures of sprint speed, fatigue, heart rate, and rectal temperature were collected. Compared to COLD: HEAT improved Sprint 1 (ES: 0.84; p = 0.05), but negatively impacted Sprint 4 (ES: -0.87; p = 0.08), and Sprint 5 (ES: -1.57; p = 0.002). H+C was faster than Control for every sprint (ES: 0.28 to 0.66), clearly faster than COLD on Sprints 1–3 (ES: 0.73 to 0.54), and clearly faster than HEAT on Sprints 4 and 5 (ES: 1.31 and 1.87). Fatigue was greatest after the HEAT intervention with a large correlation between fatigue and rectal temperature (r = 0.66; p = 0.0204). While there are undoubtedly peripheral effects of cooling and heating on various aspects of muscle function and fatigue, understanding the integration of psychophysiological homeostatic feedback loops relating to a combined warming and cooling intervention may benefit sports in which repeat sprints are performed.

text: Lower-Limb Passive Heat Maintenance Combined With Pre-cooling Improves Repeated Sprint Ability Pre-conditioning strategies to potentiate performance are a common feature of pre-competition routines. The elevation of muscle temperature is seen as a vital component of preparing for physical performance, while pre-cooling strategies have been adopted to offset fatigue during repeated efforts. We investigated the individual and combined effects of a passive heat maintenance strategy and the ingestion of an ice-water slurry on repeated sprint performance. In a random cross-over design, 12 professional male athletes performed 5 × 40 m maximal running sprints under one of four conditions following a standardized warm-up: 15-min passive rest (Control); wearing a lower-body survival garment (HEAT); consuming a 500 mL ice slushy (COLD); or wearing the survival garment and consuming the slushy (H+C). Measures of sprint speed, fatigue, heart rate, and rectal temperature were collected. Compared to COLD: HEAT improved Sprint 1 (ES: 0.84; p = 0.05), but negatively impacted Sprint 4 (ES: -0.87; p = 0.08), and Sprint 5 (ES: -1.57; p = 0.002). H+C was faster than Control for every sprint (ES: 0.28 to 0.66), clearly faster than COLD on Sprints 1–3 (ES: 0.73 to 0.54), and clearly faster than HEAT on Sprints 4 and 5 (ES: 1.31 and 1.87). Fatigue was greatest after the HEAT intervention with a large correlation between fatigue and rectal temperature (r = 0.66; p = 0.0204). While there are undoubtedly peripheral effects of cooling and heating on various aspects of muscle function and fatigue, understanding the integration of psychophysiological homeostatic feedback loops relating to a combined warming and cooling intervention may benefit sports in which repeat sprints are performed.

year: 2018

title: The science-society relationship in Aotearoa: practicing responsible innovation in the New Zealand research and innovation system

authors: Finlay-Smits, Susanna

subjects: Responsible innovation

abstract: Reports on Aotearoa New Zealand’s research, science, and innovation (RSI) system suggest the sector could improve its social responsibility and create more social value. However, researchers and innovators within the sector find this challenging. Through qualitative interviews and a national survey of RSI system participants, this study explores the current perceptions, practices enacted, and support given around responsible research and innovation practices. Findings indicate that researchers and innovators have diverse understandings of what responsible research and innovation entails, viewing anticipation and reflexivity-aligned practices as the most important aspects of responsible research and innovation. Participants feel most supported by research organisations and funding bodies to enact such aspects of responsible practice. However, they perceive a discrepancy, across all dimensions explored, between what researchers and innovators should do, and what they actually do in terms of enacting responsible practices. Thus, significant room for improvement is identified, particularly regarding practices that align with researchers’ and innovators’ obligations under Te Tiriti o Waitangi, and requirements under Vision Mātauranga.

text: The science-society relationship in Aotearoa: practicing responsible innovation in the New Zealand research and innovation system Reports on Aotearoa New Zealand’s research, science, and innovation (RSI) system suggest the sector could improve its social responsibility and create more social value. However, researchers and innovators within the sector find this challenging. Through qualitative interviews and a national survey of RSI system participants, this study explores the current perceptions, practices enacted, and support given around responsible research and innovation practices. Findings indicate that researchers and innovators have diverse understandings of what responsible research and innovation entails, viewing anticipation and reflexivity-aligned practices as the most important aspects of responsible research and innovation. Participants feel most supported by research organisations and funding bodies to enact such aspects of responsible practice. However, they perceive a discrepancy, across all dimensions explored, between what researchers and innovators should do, and what they actually do in terms of enacting responsible practices. Thus, significant room for improvement is identified, particularly regarding practices that align with researchers’ and innovators’ obligations under Te Tiriti o Waitangi, and requirements under Vision Mātauranga.

year: 2023-05-17