title: Exploring the transition into Year 3 of Year 2 students who use counting on to solve mathematics problems

authors: Matthews, Muirean Johanna (Jo)

subjects: Counting on

abstract: This research project examined how five Year 2 students, at stage 4 on the Number Framework (counting on), experienced mathematics as they transitioned into a Year 3 and 4 classroom. It investigated the support structures put in place to shift students from counting on to part-whole thinking, as part of the Numeracy Development Projects (NDP) approach to teaching mathematics. An additional transition of two teachers into Year 3 and 4 (one up from Year 2 and one down from Year 5 and 6) provided evidence of teacher transition experiences when shifting teaching levels. The setting, role of the teacher, and external influences were examined. 
This research was a qualitative investigation framed within a case study approach. The main source of data was classroom observations and semi-structured interviews. The teachers’ interviews focused on their approach to teaching and learning, attitude, student ability, assessment, and knowledge of the mathematics curriculum from Level 1 to Level 2. The combination of classroom observation and student interviews demonstrated the current level students were operating at and any signs of shift in their knowledge, as well as attitude towards mathematical learning. 
The thesis illustrates how classroom practices and teaching approaches encouraged students to count on instead of shifting into part-whole thinking. The findings highlight possible barriers, student experience, the importance of teacher knowledge and understanding, and the impact of teaching practices that support and undermine the shift. The findings also show that teachers are still following the NDP material very closely, without a full understanding of the pedagogy of number knowledge which can bridge Level 1 to Level 2 of the New Zealand Curriculum. 
The findings also indicate that the NDP teaching model is not being fully incorporated into classroom teaching, with a decrease of manipulatives used over the transition, a limited use of visualisation through diagrams and pictures, and students experiencing abstract representations without a full understanding of their meaning. The findings also show that the current reform in mathematics is only operating at a surface level. Teacher practices reflected an instrumental, procedurally-based approach to the teaching and learning of mathematics.
The evidence contained within this thesis points to the link between knowledge and strategy not being made explicit, with limited experiences of exploring relationships between numbers and quantity. It considers a critical aspect of student understanding is to develop a full understanding of number relationships through the concept of subitising, part-whole relationships, and more-and-less relationships. Continuing Professional Learning and Development is needed for teachers to develop a deeper understanding of these relationships and how they support student shift from ‘counting on’ to part-whole thinking.

text: Exploring the transition into Year 3 of Year 2 students who use counting on to solve mathematics problems This research project examined how five Year 2 students, at stage 4 on the Number Framework (counting on), experienced mathematics as they transitioned into a Year 3 and 4 classroom. It investigated the support structures put in place to shift students from counting on to part-whole thinking, as part of the Numeracy Development Projects (NDP) approach to teaching mathematics. An additional transition of two teachers into Year 3 and 4 (one up from Year 2 and one down from Year 5 and 6) provided evidence of teacher transition experiences when shifting teaching levels. The setting, role of the teacher, and external influences were examined. 
This research was a qualitative investigation framed within a case study approach. The main source of data was classroom observations and semi-structured interviews. The teachers’ interviews focused on their approach to teaching and learning, attitude, student ability, assessment, and knowledge of the mathematics curriculum from Level 1 to Level 2. The combination of classroom observation and student interviews demonstrated the current level students were operating at and any signs of shift in their knowledge, as well as attitude towards mathematical learning. 
The thesis illustrates how classroom practices and teaching approaches encouraged students to count on instead of shifting into part-whole thinking. The findings highlight possible barriers, student experience, the importance of teacher knowledge and understanding, and the impact of teaching practices that support and undermine the shift. The findings also show that teachers are still following the NDP material very closely, without a full understanding of the pedagogy of number knowledge which can bridge Level 1 to Level 2 of the New Zealand Curriculum. 
The findings also indicate that the NDP teaching model is not being fully incorporated into classroom teaching, with a decrease of manipulatives used over the transition, a limited use of visualisation through diagrams and pictures, and students experiencing abstract representations without a full understanding of their meaning. The findings also show that the current reform in mathematics is only operating at a surface level. Teacher practices reflected an instrumental, procedurally-based approach to the teaching and learning of mathematics.
The evidence contained within this thesis points to the link between knowledge and strategy not being made explicit, with limited experiences of exploring relationships between numbers and quantity. It considers a critical aspect of student understanding is to develop a full understanding of number relationships through the concept of subitising, part-whole relationships, and more-and-less relationships. Continuing Professional Learning and Development is needed for teachers to develop a deeper understanding of these relationships and how they support student shift from ‘counting on’ to part-whole thinking.

year: 2014

title: Benthic nutrient release from Auckland dune lakes

authors: Özkundakci, Deniz

abstract: New Zealand’s freshwater lakes are under pressure from land use intensification, discharge of nutrient contaminants and over-allocation of groundwater resources. Dune lakes are comparatively rare ecosystems formed by wind-blown sand which creates depressions or water impoundments. Often isolated and diversity depauperate, their geomorphological features can make them particularly vulnerable to anthropogenic eutrophication. Ecological models provide a tool for assessing potential strategies for remediation of lake eutrophication. However, they require an understanding of the drivers of water quality decline, including external and internal nutrient loading. The University of Waikato was contracted by Auckland Council to assess lake littoral groundwater infiltration rates and sediment nutrient release rates in seven dune lakes to support the development of ecological models for the lakes.  

Littoral groundwater infiltration was measured using custom moulded clear acrylic domes fitted with valves which allowed water passage into an attached collection bag. The chambers were deployed in the winter and of late spring of 2023. Depending on lake size and site suitability, between one and four chambers were deployed in the littoral zone (generally ~0.5m depth) of each lake and left in place for 24 hours. Net groundwater efflux was not detected by any of the chambers, while groundwater infiltration rates ranged from 1.0–7.4 L m-2 day-1. Assessment of groundwater nutrient concentrations was not feasible due to the volume of the chamber (16 L) and the deployment period required to determine infiltration rates. Littoral groundwater infiltration likely constitutes a significant proportion of the inflow to these lakes, and rates appear to be volumetrically proportional to the linear distance to the catchment boundary from the point of sampling, and to variance in catchment rainfall. Littoral infiltration rates responded quickly (<24 hours) to total precipitation preceding sampling; however, this may be partially due to the higher-than-average rainfall and soil saturation during the 2023 survey period. 

Sediment nutrient release rates were determined using benthic incubation chambers deployed at or near the deepest point of each lake during the spring of 2023. Four dark chambers were deployed in each lake for between 32–68 hours, water samples were pumped from each chamber and analysed for dissolved nutrients. Lakes Kawaupaku, Ōkaihau, Te Kanae and Whatihua were strongly stratified with anoxic bottom waters and sediment nutrient release rates could not be determined. Bottom water samples taken at the time of chamber deployment in these lakes found ammonium and nitrate concentrations were high (>0.2 mg N L-1) but dissolved reactive phosphorus (DRP) concentrations were near or below detection limits (<0.004 mg P L-1); indicating that internal lake phosphorus loading was likely limited in comparison to nitrogen loading.  

The shallow, polymictic nature of the Tomarata, Spectacle and Slipper lakes provided more suitable conditions for determination of in situ sediment nutrient fluxes, although a second deployment in Lake Tomarata was conducted in August 2024. The measured nutrient flux rates, maximum nutrient flux rates and half saturation constants for ammonium and dissolved reactive phosphorus are presented in the table below. The low phosphorus release rates may be due to low external phosphorus loading, associated with episodic sediment loading from the mostly ephemeral surface inflows to the lakes. These findings align with previous work carried out in Lake Tomarata demonstrating the sedimental total phosphorus (TP) pool to have a low redox sensitive phosphorus fraction despite sediment iron content being reasonably high (Waters, 2022). 

Prolonged stratification of lakes Kawaupaku, Ōkaihau, Te Kanae and Whatihua provided limited opportunity to directly assess internal nutrient loading. However, external phosphorus loading to these lakes is likely to be constrained as they are primarily groundwater fed with small, ephemeral surface inflows. In addition, hypolimnetic DRP concentrations and sediment phosphorus release rates determined for lakes Tomarata, Slipper and Spectacle indicate that internal phosphorus loading is low compared to other New Zealand lakes. External nitrogen loading is likely to be more substantial than phosphorus loading, but internal loading also appears to be lower than average. These findings underscore the distinct processes driving nitrogen and phosphorus loading, and consequently nutrient concentrations in the lakes studied. They also provide data critical for the parameterisation of subsequent water quality models, which might be used to inform land use practices through comprehensive scenario testing of various management options.

text: Benthic nutrient release from Auckland dune lakes New Zealand’s freshwater lakes are under pressure from land use intensification, discharge of nutrient contaminants and over-allocation of groundwater resources. Dune lakes are comparatively rare ecosystems formed by wind-blown sand which creates depressions or water impoundments. Often isolated and diversity depauperate, their geomorphological features can make them particularly vulnerable to anthropogenic eutrophication. Ecological models provide a tool for assessing potential strategies for remediation of lake eutrophication. However, they require an understanding of the drivers of water quality decline, including external and internal nutrient loading. The University of Waikato was contracted by Auckland Council to assess lake littoral groundwater infiltration rates and sediment nutrient release rates in seven dune lakes to support the development of ecological models for the lakes.  

Littoral groundwater infiltration was measured using custom moulded clear acrylic domes fitted with valves which allowed water passage into an attached collection bag. The chambers were deployed in the winter and of late spring of 2023. Depending on lake size and site suitability, between one and four chambers were deployed in the littoral zone (generally ~0.5m depth) of each lake and left in place for 24 hours. Net groundwater efflux was not detected by any of the chambers, while groundwater infiltration rates ranged from 1.0–7.4 L m-2 day-1. Assessment of groundwater nutrient concentrations was not feasible due to the volume of the chamber (16 L) and the deployment period required to determine infiltration rates. Littoral groundwater infiltration likely constitutes a significant proportion of the inflow to these lakes, and rates appear to be volumetrically proportional to the linear distance to the catchment boundary from the point of sampling, and to variance in catchment rainfall. Littoral infiltration rates responded quickly (<24 hours) to total precipitation preceding sampling; however, this may be partially due to the higher-than-average rainfall and soil saturation during the 2023 survey period. 

Sediment nutrient release rates were determined using benthic incubation chambers deployed at or near the deepest point of each lake during the spring of 2023. Four dark chambers were deployed in each lake for between 32–68 hours, water samples were pumped from each chamber and analysed for dissolved nutrients. Lakes Kawaupaku, Ōkaihau, Te Kanae and Whatihua were strongly stratified with anoxic bottom waters and sediment nutrient release rates could not be determined. Bottom water samples taken at the time of chamber deployment in these lakes found ammonium and nitrate concentrations were high (>0.2 mg N L-1) but dissolved reactive phosphorus (DRP) concentrations were near or below detection limits (<0.004 mg P L-1); indicating that internal lake phosphorus loading was likely limited in comparison to nitrogen loading.  

The shallow, polymictic nature of the Tomarata, Spectacle and Slipper lakes provided more suitable conditions for determination of in situ sediment nutrient fluxes, although a second deployment in Lake Tomarata was conducted in August 2024. The measured nutrient flux rates, maximum nutrient flux rates and half saturation constants for ammonium and dissolved reactive phosphorus are presented in the table below. The low phosphorus release rates may be due to low external phosphorus loading, associated with episodic sediment loading from the mostly ephemeral surface inflows to the lakes. These findings align with previous work carried out in Lake Tomarata demonstrating the sedimental total phosphorus (TP) pool to have a low redox sensitive phosphorus fraction despite sediment iron content being reasonably high (Waters, 2022). 

Prolonged stratification of lakes Kawaupaku, Ōkaihau, Te Kanae and Whatihua provided limited opportunity to directly assess internal nutrient loading. However, external phosphorus loading to these lakes is likely to be constrained as they are primarily groundwater fed with small, ephemeral surface inflows. In addition, hypolimnetic DRP concentrations and sediment phosphorus release rates determined for lakes Tomarata, Slipper and Spectacle indicate that internal phosphorus loading is low compared to other New Zealand lakes. External nitrogen loading is likely to be more substantial than phosphorus loading, but internal loading also appears to be lower than average. These findings underscore the distinct processes driving nitrogen and phosphorus loading, and consequently nutrient concentrations in the lakes studied. They also provide data critical for the parameterisation of subsequent water quality models, which might be used to inform land use practices through comprehensive scenario testing of various management options.

year: 2025

title: Understanding cultural relationships: Whānau, whanaungatanga and Māori student attainment of university entrance in a mainstream secondary school in Aotearoa, New Zealand

authors: McGill, Kristin

subjects: Cultural relationships

abstract: This study seeks to understand the importance of cultural relationships in supporting Māori student achievement of University Entrance.  This research is based on the stories of five female ākonga Māori, all of whom completed five years of secondary education, and their whānau.  It looks deeply into their relational experiences of whanaungatanga and whānautanga with their school, and the impact this had on their academic achievement of NCEA Level 3 and University Entrance. 

The results highlight the importance of culturally grounded transformative praxis and the risk of attempting to incorporate culturally located principles such as whānau and whanaungatanga into a schooling context, while still operating within historical hegemonic frameworks.

text: Understanding cultural relationships: Whānau, whanaungatanga and Māori student attainment of university entrance in a mainstream secondary school in Aotearoa, New Zealand This study seeks to understand the importance of cultural relationships in supporting Māori student achievement of University Entrance.  This research is based on the stories of five female ākonga Māori, all of whom completed five years of secondary education, and their whānau.  It looks deeply into their relational experiences of whanaungatanga and whānautanga with their school, and the impact this had on their academic achievement of NCEA Level 3 and University Entrance. 

The results highlight the importance of culturally grounded transformative praxis and the risk of attempting to incorporate culturally located principles such as whānau and whanaungatanga into a schooling context, while still operating within historical hegemonic frameworks.

year: 2023