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: Time-varying risk premia in the term structure of interest rates in New Zealand

authors: Margaritis, Daimitri

subjects: New Zealand

abstract: An empirical analysis of the term structure of interest rates in New Zealand during the post-1985 financial liberalization period is presented. Particular emphasis is placed upon the effect of time-varying risk premia in the term structure equation. The risk premium is assumed to depend on the time-varying conditional variance of the excess holding yield. The results indicate that the expectations theory cannot be rejected at the short end of the term structure provided that account is taken of the volatility clustering in interest rate data. There is also support for the expectations theory in the term structure relationship between long-term and short-term interest rates. The results do not indicate excess over- or under-sensitivity of long rates to current short rates. Initial statistical evidence suggests that excess returns on long-term bonds can be explained by their lagged values and macroeconomic variables. However, this return predictability is removed once the effects of changing real and nominal uncertainty are accounted for in the term structure equation. The latter result suggests that a monetary policy of low and stable inflation can affect the risk characteristics of long-term bonds. The presence of varying real uncertainty in bond returns indicates that the slope of the yield curve may not be a reliable indicator for assessing inflationary pressures in the economy when compared to a situation where the variation in bond returns was solely driven by nominal uncertainty.

text: Time-varying risk premia in the term structure of interest rates in New Zealand An empirical analysis of the term structure of interest rates in New Zealand during the post-1985 financial liberalization period is presented. Particular emphasis is placed upon the effect of time-varying risk premia in the term structure equation. The risk premium is assumed to depend on the time-varying conditional variance of the excess holding yield. The results indicate that the expectations theory cannot be rejected at the short end of the term structure provided that account is taken of the volatility clustering in interest rate data. There is also support for the expectations theory in the term structure relationship between long-term and short-term interest rates. The results do not indicate excess over- or under-sensitivity of long rates to current short rates. Initial statistical evidence suggests that excess returns on long-term bonds can be explained by their lagged values and macroeconomic variables. However, this return predictability is removed once the effects of changing real and nominal uncertainty are accounted for in the term structure equation. The latter result suggests that a monetary policy of low and stable inflation can affect the risk characteristics of long-term bonds. The presence of varying real uncertainty in bond returns indicates that the slope of the yield curve may not be a reliable indicator for assessing inflationary pressures in the economy when compared to a situation where the variation in bond returns was solely driven by nominal uncertainty.

year: 1994

title: Testing a suicidal ideation-to-action framework among Queer and Takatāpui people in Aotearoa New Zealand: An examination of the three-step theory

authors: Schimanski, Irie

abstract: The three-step theory (3ST) of suicide is well-established in the general population and shows promise for explaining suicidal ideation among Queer samples. This study examined the applicability of the 3ST using data from 250 Queer (n = 213) and Takatāpui (n = 37) people aged 18-74 living in Aotearoa New Zealand. The analytic approach entailed hierarchical multiple regression, ANOVA, t-tests, and logistic regression. Step-one was partially supported, with discrimination and hopelessness independently associated with suicidal ideation, but not their interaction. Step-two was fully supported, showing social support associated with lower suicidal ideation when social support exceeded discrimination, compared with the inverse. Full support for step-three was observed, finding higher self-harm among participants with histories of attempted suicide than those who had never attempted. An adapted version of the 3ST for Queer and Takatāpui people is presented, offering novel approaches to testing the ideation-to-action framework with these communities.

text: Testing a suicidal ideation-to-action framework among Queer and Takatāpui people in Aotearoa New Zealand: An examination of the three-step theory The three-step theory (3ST) of suicide is well-established in the general population and shows promise for explaining suicidal ideation among Queer samples. This study examined the applicability of the 3ST using data from 250 Queer (n = 213) and Takatāpui (n = 37) people aged 18-74 living in Aotearoa New Zealand. The analytic approach entailed hierarchical multiple regression, ANOVA, t-tests, and logistic regression. Step-one was partially supported, with discrimination and hopelessness independently associated with suicidal ideation, but not their interaction. Step-two was fully supported, showing social support associated with lower suicidal ideation when social support exceeded discrimination, compared with the inverse. Full support for step-three was observed, finding higher self-harm among participants with histories of attempted suicide than those who had never attempted. An adapted version of the 3ST for Queer and Takatāpui people is presented, offering novel approaches to testing the ideation-to-action framework with these communities.

year: 2025-08-01