title: Promoting risk taking in mathematics classrooms: The importance of creating a safe learning environment

authors: Sharma, Sashi

abstract: Students beliefs and attitudes towards risk taking can impact on their mathematics learning and performance. However, at present, risk is not established in the field of mathematics education. The challenge for mathematics teachers in developing their students' risk taking dispositions is to choose appropriate activities and tools that match this concept and the learning needs of the students. This paper describes some research-based ideas for promoting risk taking behaviours in a mathematics classroom. It presents interactional pedagogical strategies from a design collaborative research conducted at one secondary school. As part of the learning activities, students critically evaluated statistical investigations undertaken by others. Students had to take risks: ask critical questions, construct statistical arguments and respond to others' arguments in face of criticisms. The findings are interpreted in relation to recent writing about students' abilities to take risks in mathematics classrooms. The final section considers the issues arising out of the paper and offers suggestions for meeting these challenges.

text: Promoting risk taking in mathematics classrooms: The importance of creating a safe learning environment Students beliefs and attitudes towards risk taking can impact on their mathematics learning and performance. However, at present, risk is not established in the field of mathematics education. The challenge for mathematics teachers in developing their students' risk taking dispositions is to choose appropriate activities and tools that match this concept and the learning needs of the students. This paper describes some research-based ideas for promoting risk taking behaviours in a mathematics classroom. It presents interactional pedagogical strategies from a design collaborative research conducted at one secondary school. As part of the learning activities, students critically evaluated statistical investigations undertaken by others. Students had to take risks: ask critical questions, construct statistical arguments and respond to others' arguments in face of criticisms. The findings are interpreted in relation to recent writing about students' abilities to take risks in mathematics classrooms. The final section considers the issues arising out of the paper and offers suggestions for meeting these challenges.

year: 2015-01-01

title: Modeling and simulation of the dynamic process in high energy ball milling of metal powders

authors: Wang, Wei

abstract: Mechanical alloying/mechanical grounding by using high-energy ball milling has been considered as a promising materials processing technique to synthesize materials. In this study, modeling simulation has been carried out to investigate the impacts, which are basic events in milling, as well as the milling dynamics in order to control and optimize this process. 

A 3-dimensional model has been developed to simulate the head-on impact process between two balls or between a ball and the vial wall with powder in between by considering the elastic deformation of impact objects, and the visco-plastic flow and elastic deformation of the powder compact. The comparison between the experimental results published in literature and the simulation outcome demonstrates that this model is the best to simulate the head-on impact process, which involves powder. Application of the model in high-energy ball milling shows that the ball-ball and ball-wall impacts do have some difference. It was also observed that the ball size, impact velocity and powder thickness all affect the impact pressure, and that the deformation of balls is substantial comparing to the powder thickness involved in an impact. 

3-dimensional models have also been developed to simulate the movement of balls considering the effects of powder, ball spinning and oblique impact of balls. The multi-ball impacts, which have been proved to occupy a substantial fraction among impacts, were also considered. Having realised the importance of knowing the volume of the powder involved in each impact, a model was also developed to estimate this volume. The prediction of the weight of powder involved in each impact made based on this model was in good agreement with the observation reported. 

A 3-dimensional global model has been developed for the SPEX-8000 Mixer/Mill based on the mechanics of the machine. By using this model, the motion of the vial was numerically determined. Then the global model was coupled with the models for the impacts in order to predict the dynamics of milling process. The simulation results revealed that the movement of balls after milling starts can be separated into two stages. The first stage is the unstable stage, which lasts for less than 0.3 second and involves mostly rolling and slipping of balls on the vial wall. The second stage is the stable stage, when the impact frequency, the mean impact velocity and mean spinning velocity of balls do not change significantly over time. Numerical experiments indicate that the frequency of impacts between balls and the vial wall is linearly proportional to the number of balls and the frequency of impacts between balls is nearly proportional to the square of the number of balls and the square of radius of balls. It is also shown that the majority of the impacts occur at low velocities of less than 4 m/s and with impact angles in the range of 15∼75°. The prediction of the impact frequency and impact angle distribution made from the simulation agrees well with the probability analysis. 

An effective model has been developed for the first time to calculate the time needed for mechanical milling based on probability analysis. This model can be used once the effective impact frequency and the fraction of powder effectively mechanically milled powder are known. The latter can be achieved through modeling. The milling efficiency corresponding to various ball numbers and sizes have been evaluated. The results show that there is an optimum number for the best milling efficiency for a given size of balls. 

Global models for the milling process in a planetary mill and an attritor mill have also been developed. Preliminary simulation experiments have been conducted.

text: Modeling and simulation of the dynamic process in high energy ball milling of metal powders Mechanical alloying/mechanical grounding by using high-energy ball milling has been considered as a promising materials processing technique to synthesize materials. In this study, modeling simulation has been carried out to investigate the impacts, which are basic events in milling, as well as the milling dynamics in order to control and optimize this process. 

A 3-dimensional model has been developed to simulate the head-on impact process between two balls or between a ball and the vial wall with powder in between by considering the elastic deformation of impact objects, and the visco-plastic flow and elastic deformation of the powder compact. The comparison between the experimental results published in literature and the simulation outcome demonstrates that this model is the best to simulate the head-on impact process, which involves powder. Application of the model in high-energy ball milling shows that the ball-ball and ball-wall impacts do have some difference. It was also observed that the ball size, impact velocity and powder thickness all affect the impact pressure, and that the deformation of balls is substantial comparing to the powder thickness involved in an impact. 

3-dimensional models have also been developed to simulate the movement of balls considering the effects of powder, ball spinning and oblique impact of balls. The multi-ball impacts, which have been proved to occupy a substantial fraction among impacts, were also considered. Having realised the importance of knowing the volume of the powder involved in each impact, a model was also developed to estimate this volume. The prediction of the weight of powder involved in each impact made based on this model was in good agreement with the observation reported. 

A 3-dimensional global model has been developed for the SPEX-8000 Mixer/Mill based on the mechanics of the machine. By using this model, the motion of the vial was numerically determined. Then the global model was coupled with the models for the impacts in order to predict the dynamics of milling process. The simulation results revealed that the movement of balls after milling starts can be separated into two stages. The first stage is the unstable stage, which lasts for less than 0.3 second and involves mostly rolling and slipping of balls on the vial wall. The second stage is the stable stage, when the impact frequency, the mean impact velocity and mean spinning velocity of balls do not change significantly over time. Numerical experiments indicate that the frequency of impacts between balls and the vial wall is linearly proportional to the number of balls and the frequency of impacts between balls is nearly proportional to the square of the number of balls and the square of radius of balls. It is also shown that the majority of the impacts occur at low velocities of less than 4 m/s and with impact angles in the range of 15∼75°. The prediction of the impact frequency and impact angle distribution made from the simulation agrees well with the probability analysis. 

An effective model has been developed for the first time to calculate the time needed for mechanical milling based on probability analysis. This model can be used once the effective impact frequency and the fraction of powder effectively mechanically milled powder are known. The latter can be achieved through modeling. The milling efficiency corresponding to various ball numbers and sizes have been evaluated. The results show that there is an optimum number for the best milling efficiency for a given size of balls. 

Global models for the milling process in a planetary mill and an attritor mill have also been developed. Preliminary simulation experiments have been conducted.

year: 2000

title: Weaving Mana Wahine and Masi methodology: Centring the embodied experiences of young Māori and Pasifika wāhine in physical activity and everyday life

authors: Nemani, Mihi Joy

subjects: Aotearoa New Zealand

abstract: Young Indigenous Māori and Pasifika wāhine (women) in Aotearoa New Zealand (hereafter Aotearoa) have too often been framed as vulnerable, ‘at risk’ and problematic in the media, policy and research. This thesis moves beyond these deficit framings and uses an Indigenous feminist, strengths-based approach by centring the voices and lived experiences of young Māori and Pasifika wāhine who are agentic in their everyday lives, celebrate their strong brown bodies and are physically active. 

Being an Indigenous feminist early career researcher of Māori-Samoan ancestry, I intentionally weave Mana Wahine (Māori) and Masi (Pasifika) methodologies throughout all aspects of this research. Employing wānanga (focus group discussions), individual interviews and digital methods, I gather knowledge from a total of 31 young Māori and Pasifika wāhine residing in two low socio-economic urban regions (Porirua and South Auckland) in Te Ika-a-Maui, the North Island of Aotearoa. Centring their voices and lived experiences, I examine how the young wāhine embrace and weave their intersectional identities with culture, body image and physical activity. 

This is a PhD with publication. It begins with an introductory chapter and a literature review chapter that locates the project in the context of Aotearoa and the local and international literature. In the methods chapter, which is a published article, I focus on the importance of creating culturally safe and supportive spaces for young wāhine to participate in research that feels meaningful to them. The empirical chapters are presented in three different manuscripts. Chapter Four contains a manuscript (currently under review) that focuses on the intersectional identities of the young wāhine. It is structured using three key themes, including 1) ethnic and cultural identities, 2) navigating, and 3) how they embrace cultural pride, particularly through family values, customs and responsibilities. Chapter Five is a published manuscript that explores body image through an intersectional Indigenous feminist lens. This publication examines cultural perspectives that influence their views on body image and provides insights into how the young wāhine navigate body image stereotypes. Chapter six is the final empirical manuscript (currently under review) that evaluates the motivations the young wāhine have for participation in physical activity. It examines the types of activities they enjoy and provides insights into how and why they use cultural knowledge as a motivator for participation.

This research contributes to international literature conducted with, for and by Indigenous feminist scholars on young women’s identities, body image and physical activity. It responds to the limited academic scholarship that explores the lived experiences of young Māori and Pasifika wāhine in Aotearoa and their nuanced cultural knowledge of their bodies. In so doing, this research offers insights and new ways of understanding the complex lives of young Māori and Pasifika wāhine, and highlights the importance of intersectional approaches and localized Indigenous methods that listen to, and amplify the voices of young wāhine.

text: Weaving Mana Wahine and Masi methodology: Centring the embodied experiences of young Māori and Pasifika wāhine in physical activity and everyday life Young Indigenous Māori and Pasifika wāhine (women) in Aotearoa New Zealand (hereafter Aotearoa) have too often been framed as vulnerable, ‘at risk’ and problematic in the media, policy and research. This thesis moves beyond these deficit framings and uses an Indigenous feminist, strengths-based approach by centring the voices and lived experiences of young Māori and Pasifika wāhine who are agentic in their everyday lives, celebrate their strong brown bodies and are physically active. 

Being an Indigenous feminist early career researcher of Māori-Samoan ancestry, I intentionally weave Mana Wahine (Māori) and Masi (Pasifika) methodologies throughout all aspects of this research. Employing wānanga (focus group discussions), individual interviews and digital methods, I gather knowledge from a total of 31 young Māori and Pasifika wāhine residing in two low socio-economic urban regions (Porirua and South Auckland) in Te Ika-a-Maui, the North Island of Aotearoa. Centring their voices and lived experiences, I examine how the young wāhine embrace and weave their intersectional identities with culture, body image and physical activity. 

This is a PhD with publication. It begins with an introductory chapter and a literature review chapter that locates the project in the context of Aotearoa and the local and international literature. In the methods chapter, which is a published article, I focus on the importance of creating culturally safe and supportive spaces for young wāhine to participate in research that feels meaningful to them. The empirical chapters are presented in three different manuscripts. Chapter Four contains a manuscript (currently under review) that focuses on the intersectional identities of the young wāhine. It is structured using three key themes, including 1) ethnic and cultural identities, 2) navigating, and 3) how they embrace cultural pride, particularly through family values, customs and responsibilities. Chapter Five is a published manuscript that explores body image through an intersectional Indigenous feminist lens. This publication examines cultural perspectives that influence their views on body image and provides insights into how the young wāhine navigate body image stereotypes. Chapter six is the final empirical manuscript (currently under review) that evaluates the motivations the young wāhine have for participation in physical activity. It examines the types of activities they enjoy and provides insights into how and why they use cultural knowledge as a motivator for participation.

This research contributes to international literature conducted with, for and by Indigenous feminist scholars on young women’s identities, body image and physical activity. It responds to the limited academic scholarship that explores the lived experiences of young Māori and Pasifika wāhine in Aotearoa and their nuanced cultural knowledge of their bodies. In so doing, this research offers insights and new ways of understanding the complex lives of young Māori and Pasifika wāhine, and highlights the importance of intersectional approaches and localized Indigenous methods that listen to, and amplify the voices of young wāhine.

year: 2024-10-20