title: Connecting the Points: An Investigation into Student Learning about Decimal Numbers

authors: Moody, Bruce David

subjects: Decimals

abstract: The purpose of this research project was to investigate the effects of a short-term teaching experiment on the learning of decimal numbers by primary students. The literature describes this area of mathematics as highly problematic for students. 
The content first covered student understanding of decimal symbols, and how this impacted upon their ability to order decimal numbers and carry out additive operations. It was then extended to cover the density of number property, and the application of multiplicative operations to situations involving decimals. In doing so, three areas of cognitive conflict were encountered by students, the belief that longer decimal numbers are larger than shorter ones (irrespective of the actual digits), that multiplication always makes numbers bigger, and that division always makes numbers smaller. 
The use of a microgenetic approach yielded data was able to be presented that provides details of the environment surrounding the moments where new learning was constructed. The characteristics of this environment include the use of physical artifacts and situational contexts involving measurement that precipitate student discussion and reflection. 
The methodology allowed for the collection of evidence regarding the highly complex nature of the learning, with evidence of 'folding back' to earlier schema and the co-existence of competing schema.   The discussion presents reasons as to why the pedagogical approach that was employed facilitated learning. 
One of the main findings was that the use of challenging problems situated in measurement contexts that involved direct student participation promoted the extension and/or re-organization of student schema with regard to decimal numbers. 
The study has important implications for teachers at the upper primary level wanting to support student learning about the decimal numbers system.

text: Connecting the Points: An Investigation into Student Learning about Decimal Numbers The purpose of this research project was to investigate the effects of a short-term teaching experiment on the learning of decimal numbers by primary students. The literature describes this area of mathematics as highly problematic for students. 
The content first covered student understanding of decimal symbols, and how this impacted upon their ability to order decimal numbers and carry out additive operations. It was then extended to cover the density of number property, and the application of multiplicative operations to situations involving decimals. In doing so, three areas of cognitive conflict were encountered by students, the belief that longer decimal numbers are larger than shorter ones (irrespective of the actual digits), that multiplication always makes numbers bigger, and that division always makes numbers smaller. 
The use of a microgenetic approach yielded data was able to be presented that provides details of the environment surrounding the moments where new learning was constructed. The characteristics of this environment include the use of physical artifacts and situational contexts involving measurement that precipitate student discussion and reflection. 
The methodology allowed for the collection of evidence regarding the highly complex nature of the learning, with evidence of 'folding back' to earlier schema and the co-existence of competing schema.   The discussion presents reasons as to why the pedagogical approach that was employed facilitated learning. 
One of the main findings was that the use of challenging problems situated in measurement contexts that involved direct student participation promoted the extension and/or re-organization of student schema with regard to decimal numbers. 
The study has important implications for teachers at the upper primary level wanting to support student learning about the decimal numbers system.

year: 2008

title: Decolouring bloodmeal: Consumption and potential recycling of peracetic acid

authors: Hicks, Talia

abstract: A method of deodorizing and decolouring bloodmeal using an equilibrium mixture of peracetic acid, hydrogen peroxide, acetic acid and water has been developed to improve its marketability as a source of protein for bioplastics.
The objective of this study was to determine what quantity of peracetic acid is required to give reasonable bleaching of the bloodmeal and determine whether there is potential for the wastewater to be recycled. This was carried out by measuring the quantity of chemical species in the initial equilibrium mixture and the resulting wastewater upon bleaching using volumetric analysis. Bleaching efficacy was determined after exposing 100 g bloodmeal to 1.1, 2.5, 3.6, 4.5 and 5.6 wt% peracetic acid solutions as either 300 g total solution or a constant molar equivalent of 2.2 mmol peracetic acid/g bloodmeal and using a chromameter to measure colour change.
Addition of 300 g 5.6 wt% peracetic acid solution resulted in effective bleaching. This represented a ratio of 2.20 mmol peracetic acid/g bloodmeal of which 1.4 mmol peracetic acid/g bloodmeal was consumed (63%). If 300 g <2.5 wt% peracetic acid solution was used, there was insufficient bleaching. If >300 g of <2.5 wt% solution is added such that there is still 2.2 mmol peracetic acid/g bloodmeal, bleaching is still insufficient.
These results suggest that an excess of peracetic is required for bleaching to occur, and that its concentration is paramount to bleaching efficacy. Due to the excess of peracetic acid used in the bleaching process, there is potential for wastewater recycling to be carried out provided that the wastewater is not diluted.

text: Decolouring bloodmeal: Consumption and potential recycling of peracetic acid A method of deodorizing and decolouring bloodmeal using an equilibrium mixture of peracetic acid, hydrogen peroxide, acetic acid and water has been developed to improve its marketability as a source of protein for bioplastics.
The objective of this study was to determine what quantity of peracetic acid is required to give reasonable bleaching of the bloodmeal and determine whether there is potential for the wastewater to be recycled. This was carried out by measuring the quantity of chemical species in the initial equilibrium mixture and the resulting wastewater upon bleaching using volumetric analysis. Bleaching efficacy was determined after exposing 100 g bloodmeal to 1.1, 2.5, 3.6, 4.5 and 5.6 wt% peracetic acid solutions as either 300 g total solution or a constant molar equivalent of 2.2 mmol peracetic acid/g bloodmeal and using a chromameter to measure colour change.
Addition of 300 g 5.6 wt% peracetic acid solution resulted in effective bleaching. This represented a ratio of 2.20 mmol peracetic acid/g bloodmeal of which 1.4 mmol peracetic acid/g bloodmeal was consumed (63%). If 300 g <2.5 wt% peracetic acid solution was used, there was insufficient bleaching. If >300 g of <2.5 wt% solution is added such that there is still 2.2 mmol peracetic acid/g bloodmeal, bleaching is still insufficient.
These results suggest that an excess of peracetic is required for bleaching to occur, and that its concentration is paramount to bleaching efficacy. Due to the excess of peracetic acid used in the bleaching process, there is potential for wastewater recycling to be carried out provided that the wastewater is not diluted.

year: 2012

title: Harakeke: Enhancing Māori Student Engagement and Achievement in a Mainstream Primary School

authors: Anderson, Diana

subjects: Harakeke

abstract: Ministry of Education research indicates that the inclusion of culture and te reo
Māori in teaching can help improve Māori student education. If students can find
the links between what is being taught and the relevance to their own lives then
information will be easier to retain. Research has also shown that environmental
education provides relevant learning that can connect students to their world.
Māori indigenous knowledge (IK) and environmental education (EE) share many
commonalities. One such similarity is the relationship between tangata (people)
and nature. While the sometimes destructive nature of this relationship has lead to
global environmental issues, this study explores the combination of IK and EE to
enhance Māori student engagement and achievement in a mainstream primary
school.
An intervention unit based on harakeke was designed delivered in a Year 5/6
boys' only class in a suburban mainstream primary school, over a 10 week period.
The environmental and socio-cultural significance of harakeke enabled a range of
kaupapa (themes) to be included in the unit. This included; eeling and how to
make and use a hinaki (eel/fish trap), karakia (prayer) and the relevance when
harvesting kai (food) and resources. Each kaupapa also provided the opportunity
for students to increase their te reo Māori vocabulary, with the introduction of
kaupapa specific words. The Māori kaupapa also enabled the students to view EE
from a Māori perspective, including the introduction of rahui - a form of
conservation.
The findings indicated that the incorporation of a Māori kaupapa strengthened
student engagement, improved student use of te reo Māori, improved the selfesteem
and confidence for some students, increased students' awareness of
harakeke and the value and versatility of the plant, and increased their awareness
from a Māori perspective on sustainable harvesting.
Bringing Māori kaupapa into the classroom allowed the classroom teacher, who
was Māori, the opportunity to share her own lived experiences of IK, as these are
passed down from generation to generation, and people are born into them. The
Page | iii
familiarity of whanau offered the teacher the opportunity to bring this concept into
the classroom and teach values that could flow into all curriculum areas while
strengthening relationships between the teacher and student, student and student
and teacher and student whanau.
This study has shown that both IK and EE, while each complex in their own right,
have the ability to provide a holistic curriculum approach that can lead to
engagement and achievement by Māori students in a mainstream school.

text: Harakeke: Enhancing Māori Student Engagement and Achievement in a Mainstream Primary School Ministry of Education research indicates that the inclusion of culture and te reo
Māori in teaching can help improve Māori student education. If students can find
the links between what is being taught and the relevance to their own lives then
information will be easier to retain. Research has also shown that environmental
education provides relevant learning that can connect students to their world.
Māori indigenous knowledge (IK) and environmental education (EE) share many
commonalities. One such similarity is the relationship between tangata (people)
and nature. While the sometimes destructive nature of this relationship has lead to
global environmental issues, this study explores the combination of IK and EE to
enhance Māori student engagement and achievement in a mainstream primary
school.
An intervention unit based on harakeke was designed delivered in a Year 5/6
boys' only class in a suburban mainstream primary school, over a 10 week period.
The environmental and socio-cultural significance of harakeke enabled a range of
kaupapa (themes) to be included in the unit. This included; eeling and how to
make and use a hinaki (eel/fish trap), karakia (prayer) and the relevance when
harvesting kai (food) and resources. Each kaupapa also provided the opportunity
for students to increase their te reo Māori vocabulary, with the introduction of
kaupapa specific words. The Māori kaupapa also enabled the students to view EE
from a Māori perspective, including the introduction of rahui - a form of
conservation.
The findings indicated that the incorporation of a Māori kaupapa strengthened
student engagement, improved student use of te reo Māori, improved the selfesteem
and confidence for some students, increased students' awareness of
harakeke and the value and versatility of the plant, and increased their awareness
from a Māori perspective on sustainable harvesting.
Bringing Māori kaupapa into the classroom allowed the classroom teacher, who
was Māori, the opportunity to share her own lived experiences of IK, as these are
passed down from generation to generation, and people are born into them. The
Page | iii
familiarity of whanau offered the teacher the opportunity to bring this concept into
the classroom and teach values that could flow into all curriculum areas while
strengthening relationships between the teacher and student, student and student
and teacher and student whanau.
This study has shown that both IK and EE, while each complex in their own right,
have the ability to provide a holistic curriculum approach that can lead to
engagement and achievement by Māori students in a mainstream school.

year: 2009