title: Mathematical Investigations: A Primary Teacher Educator's Narrative Journey of Professional Awareness

authors: Bailey, Judy

subjects: mathematical investigations

abstract: Over a period of twenty months a mathematics teacher educator uses narrative inquiry, a form of story-telling, to investigate her professional practice in working alongside pre-service primary teachers. Two main themes emerge in this research. 

The first of these centres around the use of mathematical investigations as a vehicle for supporting pre-service primary teachers to consider what the learning and teaching of mathematics may entail. As part of this process the author personally undertook several mathematical investigations. This resulted in significant learning about previously unrecognised personal beliefs about the nature and learning of mathematics. These beliefs were discovered to include ideas that  'real' mathematicians solve problems quickly, do so on their own and do not get stuck. Surprisingly, all of these subconscious assumptions were contrary to what the author espoused in the classroom. 

A consequence of this learning included some changed beliefs and teaching practices. One such change has been moving from a conception of mathematics as a separate body of 'correct' mathematical ideas, and where the emphasis when doing mathematics was on attaining the correct answer, to now viewing mathematics as a sense-making activity involving discovering, doing and communicating in situations involving numbers, patterns, shape and space. Thus, mathematics is now perceived to primarily be found in the 'doing' rather than existing as a predetermined body of knowledge. As such one's interpretations of a mathematical problem are important to consider.

Changes in teaching include using mathematical investigations as a teaching approach with the belief that students can effectively learn mathematical ideas using this approach; an acceptance that this may involve periods of being 'stuck' and that this does not mean that the teacher needs to immediately support the students in becoming 'unstuck'; more in-depth interactions, including questioning, to support this mathematical learning; and an acceptance that mathematics can be learned by people working in a collaborative manner.

The second theme encountered in this narrative inquiry involves the exploration of narrative as a powerful means with which to pursue professional development. Narrative inquiry, including a mention of differing forms of narrative writing, is described. Issues also considered include the place of reflection in narrative; the notion of multiple perspectives that are encountered in qualitative research such as this; issues of validity and authenticity; a consideration of what the products of narrative research might be and who may benefit from such research; a brief mention of collaboration; and the place of emotion in qualitative research. 

The concept of change occurring within a narrative inquiry is not seen to imply an initial deficit position. Rather the research process is regarded as the building of a narrative layer that supports and grows alongside the writer's life as it occurs (Brown  Jones, 2001). Thus there is not a seeking of perfection or an ideal, but a greater awareness of one's professional practice. The results of narrative research therefore, are not definitive statements or generalisations about an aspect of that which is being researched (e.g., Winkler, 2003). As such, a definitive statement about how to be a teacher of pre-service students learning mathematics is not offered. Rather, a story is shared that may connect with the stories of the reader.

text: Mathematical Investigations: A Primary Teacher Educator's Narrative Journey of Professional Awareness Over a period of twenty months a mathematics teacher educator uses narrative inquiry, a form of story-telling, to investigate her professional practice in working alongside pre-service primary teachers. Two main themes emerge in this research. 

The first of these centres around the use of mathematical investigations as a vehicle for supporting pre-service primary teachers to consider what the learning and teaching of mathematics may entail. As part of this process the author personally undertook several mathematical investigations. This resulted in significant learning about previously unrecognised personal beliefs about the nature and learning of mathematics. These beliefs were discovered to include ideas that  'real' mathematicians solve problems quickly, do so on their own and do not get stuck. Surprisingly, all of these subconscious assumptions were contrary to what the author espoused in the classroom. 

A consequence of this learning included some changed beliefs and teaching practices. One such change has been moving from a conception of mathematics as a separate body of 'correct' mathematical ideas, and where the emphasis when doing mathematics was on attaining the correct answer, to now viewing mathematics as a sense-making activity involving discovering, doing and communicating in situations involving numbers, patterns, shape and space. Thus, mathematics is now perceived to primarily be found in the 'doing' rather than existing as a predetermined body of knowledge. As such one's interpretations of a mathematical problem are important to consider.

Changes in teaching include using mathematical investigations as a teaching approach with the belief that students can effectively learn mathematical ideas using this approach; an acceptance that this may involve periods of being 'stuck' and that this does not mean that the teacher needs to immediately support the students in becoming 'unstuck'; more in-depth interactions, including questioning, to support this mathematical learning; and an acceptance that mathematics can be learned by people working in a collaborative manner.

The second theme encountered in this narrative inquiry involves the exploration of narrative as a powerful means with which to pursue professional development. Narrative inquiry, including a mention of differing forms of narrative writing, is described. Issues also considered include the place of reflection in narrative; the notion of multiple perspectives that are encountered in qualitative research such as this; issues of validity and authenticity; a consideration of what the products of narrative research might be and who may benefit from such research; a brief mention of collaboration; and the place of emotion in qualitative research. 

The concept of change occurring within a narrative inquiry is not seen to imply an initial deficit position. Rather the research process is regarded as the building of a narrative layer that supports and grows alongside the writer's life as it occurs (Brown  Jones, 2001). Thus there is not a seeking of perfection or an ideal, but a greater awareness of one's professional practice. The results of narrative research therefore, are not definitive statements or generalisations about an aspect of that which is being researched (e.g., Winkler, 2003). As such, a definitive statement about how to be a teacher of pre-service students learning mathematics is not offered. Rather, a story is shared that may connect with the stories of the reader.

year: 2004

title: Key competencies: Views from the gym floor.

authors: Gillespie, Lorna B.

subjects: physical education

abstract: The release of The New Zealand Curriculum (2007) will inevitably yield challenges and possibilities for teachers of Physical Education in both primary and secondary schools. In this paper I describe the vision and key competencies embedded in this new curriculum and discuss their relationship to Physical Education. Drawing on the voices of secondary school students, I interrogate the opportunities that students envisage for developing key competencies in Physical Education. I propose that students can, and do, afford significant insight into how teachers may enact key competencies in curriculum learning and that it is critical thinking that will enable both students and teachers to understand and relate to the movement culture in meaningful and relevant ways.

text: Key competencies: Views from the gym floor. The release of The New Zealand Curriculum (2007) will inevitably yield challenges and possibilities for teachers of Physical Education in both primary and secondary schools. In this paper I describe the vision and key competencies embedded in this new curriculum and discuss their relationship to Physical Education. Drawing on the voices of secondary school students, I interrogate the opportunities that students envisage for developing key competencies in Physical Education. I propose that students can, and do, afford significant insight into how teachers may enact key competencies in curriculum learning and that it is critical thinking that will enable both students and teachers to understand and relate to the movement culture in meaningful and relevant ways.

year: 2008

title: Do two rights fix a wrong? A study of employee and organizational responses to abusive supervision in New Zealand

authors: de Fluiter, Alida Jane

subjects: Abusive supervision

abstract: Organizational justice theories suggest that employees who are abused by their supervisor are likely to respond with lower job and personal outcomes. However, an under-explored area has been the influence of support perceptions. The present study suggests that perceived supervisor support (PSS) and perceived organizational support (POS) may moderate the influence of abusive supervision, and this was tested with three-way interactions. Data was collected from two samples: (1) 100 blue-collar workers in construction and (2) 218 random Maori employees from a variety of industries and professions. Structural equation modeling confirmed the unique constructs of the study measures towards abusive supervision and PSS and POS. Direct effects showed abusive supervision was significant and negative in both samples towards life satisfaction, job satisfaction, and organizational-based self-esteem (OBSE), and significant and positive in both samples towards turnover intentions, anxiety, depression, and insomnia. The results indicated that abusive supervision accounted for large amounts of variance towards all outcomes, with the exception of life satisfaction in study two (7%), and insomnia (8% in study one, and 4% in study two), ranging from 13%-32% variance. Significant three-way interactions were found for all outcomes except turnover intentions and insomnia. The three-way interaction towards life satisfaction in study one indicated that under abusive supervision, respondents with high PSS and high POS experienced the greatest levels of life satisfaction. Similar relationships were found toward depression (study one and two) and anxiety (study one), showing that respondents who experienced high abusive supervision, high PSS, and high POS had the lowest levels of negative mental health outcomes amongst all abused respondents. This suggested a potentially cumulative effect of multiple sources of support. Furthermore, towards job satisfaction in study two, findings show respondents with high abusive supervision and high POS reported the highest job satisfaction, irrespective of levels of PSS. A similar relationship was found toward OBSE in study two, suggesting that of the support variables examined, POS may have greater effect on outcomes, thereby supporting research of Dawley, Andrews and Bucklew (2008) who found POS to be the best predictor of organizational outcomes. Overall, this paper supports the notion that perceptions of support may moderate the influence of abusive supervision perceptions on employee’s work and personal outcomes. The findings show that while abusive supervision can play a dominant role on outcomes, this can be somewhat nullified by greater support from the organization. This has strong implications for firms dealing with problem supervisors, signaling the importance of establishing POS, and emphasizing that creating a supportive organization may be the first step to enabling employees to develop positive work and individual outcomes.

text: Do two rights fix a wrong? A study of employee and organizational responses to abusive supervision in New Zealand Organizational justice theories suggest that employees who are abused by their supervisor are likely to respond with lower job and personal outcomes. However, an under-explored area has been the influence of support perceptions. The present study suggests that perceived supervisor support (PSS) and perceived organizational support (POS) may moderate the influence of abusive supervision, and this was tested with three-way interactions. Data was collected from two samples: (1) 100 blue-collar workers in construction and (2) 218 random Maori employees from a variety of industries and professions. Structural equation modeling confirmed the unique constructs of the study measures towards abusive supervision and PSS and POS. Direct effects showed abusive supervision was significant and negative in both samples towards life satisfaction, job satisfaction, and organizational-based self-esteem (OBSE), and significant and positive in both samples towards turnover intentions, anxiety, depression, and insomnia. The results indicated that abusive supervision accounted for large amounts of variance towards all outcomes, with the exception of life satisfaction in study two (7%), and insomnia (8% in study one, and 4% in study two), ranging from 13%-32% variance. Significant three-way interactions were found for all outcomes except turnover intentions and insomnia. The three-way interaction towards life satisfaction in study one indicated that under abusive supervision, respondents with high PSS and high POS experienced the greatest levels of life satisfaction. Similar relationships were found toward depression (study one and two) and anxiety (study one), showing that respondents who experienced high abusive supervision, high PSS, and high POS had the lowest levels of negative mental health outcomes amongst all abused respondents. This suggested a potentially cumulative effect of multiple sources of support. Furthermore, towards job satisfaction in study two, findings show respondents with high abusive supervision and high POS reported the highest job satisfaction, irrespective of levels of PSS. A similar relationship was found toward OBSE in study two, suggesting that of the support variables examined, POS may have greater effect on outcomes, thereby supporting research of Dawley, Andrews and Bucklew (2008) who found POS to be the best predictor of organizational outcomes. Overall, this paper supports the notion that perceptions of support may moderate the influence of abusive supervision perceptions on employee’s work and personal outcomes. The findings show that while abusive supervision can play a dominant role on outcomes, this can be somewhat nullified by greater support from the organization. This has strong implications for firms dealing with problem supervisors, signaling the importance of establishing POS, and emphasizing that creating a supportive organization may be the first step to enabling employees to develop positive work and individual outcomes.

year: 2011