title: Number sense in a secondary school context

authors: McChesney, Jane

abstract: Current mathematics education research in New Zealand is directed at primary school or senior secondary school, in the areas of numeracy, technology innovations, student achievement and teacher professional development. This study investigated junior secondary mathematics lessons as contexts for distributed mathematical activity. Two Year 9 classes and one Year 10 class from the same school constituted case studies; two case studies were lower band and one was middle band. All three teachers continued with their normal mathematics programmes. Using an interpretivist methodology, participant observation was the main method used to collect data of sequential mathematics lessons over five weeks. The data was organised around three domains of classroom activity: classroom social norms, mathematical tools, and interaction. The data analysis focussed on aspects of these domains that afforded and constrained the negotiation of mathematical meaning. 
In each classroom context, social norms associated with lesson events were found to afford student participation. Student participation was afforded by interactional spaces; that is, regular opportunities for students to volunteer mathematical contributions and to adopt different roles in joint activity. Interactional spaces provided students with greater access to more diverse mathematical resources. Students activated interactional spaces in different ways with questions, suggestions, explanations, errors and, in one classroom, a discourse of primary school mathematics. 
Using a sociocultural perspective, school mathematical artefacts were conceptualised as cognitive mathematical tools. Cognitive tools were identified as representations, thinking devices and analogous models. Tools that were both representations and thinking devices afforded further resources for students, such as mathematical information, cues and other signifiers. The only technological tool in the case study classrooms was the scientific calculator. The roles of the calculator were as a recording device, calculating machine and exploratory object. In these roles, the calculator afforded further resources for students. 
The findings in the interaction domain challenge the assumption that traditional classroom mathematics programmes have limited discursive opportunities. Students initiated more focussed negotiations in both whole class and localised situations. In each case study, students and the teacher actively contributed mathematical resources. For these lower and middle ability students, access to mathematical resources was a significant affordance for further mathematical activity. In each classroom context, activity was found to be distributed over social norms, tools and interaction. Number sense activity was distributed according to the adapted 'environment' metaphor (Greeno, 1991 ). Students negotiated mathematical meanings by activating and using cognitive tools and discursive resources in the number sense 'environment'.

text: Number sense in a secondary school context Current mathematics education research in New Zealand is directed at primary school or senior secondary school, in the areas of numeracy, technology innovations, student achievement and teacher professional development. This study investigated junior secondary mathematics lessons as contexts for distributed mathematical activity. Two Year 9 classes and one Year 10 class from the same school constituted case studies; two case studies were lower band and one was middle band. All three teachers continued with their normal mathematics programmes. Using an interpretivist methodology, participant observation was the main method used to collect data of sequential mathematics lessons over five weeks. The data was organised around three domains of classroom activity: classroom social norms, mathematical tools, and interaction. The data analysis focussed on aspects of these domains that afforded and constrained the negotiation of mathematical meaning. 
In each classroom context, social norms associated with lesson events were found to afford student participation. Student participation was afforded by interactional spaces; that is, regular opportunities for students to volunteer mathematical contributions and to adopt different roles in joint activity. Interactional spaces provided students with greater access to more diverse mathematical resources. Students activated interactional spaces in different ways with questions, suggestions, explanations, errors and, in one classroom, a discourse of primary school mathematics. 
Using a sociocultural perspective, school mathematical artefacts were conceptualised as cognitive mathematical tools. Cognitive tools were identified as representations, thinking devices and analogous models. Tools that were both representations and thinking devices afforded further resources for students, such as mathematical information, cues and other signifiers. The only technological tool in the case study classrooms was the scientific calculator. The roles of the calculator were as a recording device, calculating machine and exploratory object. In these roles, the calculator afforded further resources for students. 
The findings in the interaction domain challenge the assumption that traditional classroom mathematics programmes have limited discursive opportunities. Students initiated more focussed negotiations in both whole class and localised situations. In each case study, students and the teacher actively contributed mathematical resources. For these lower and middle ability students, access to mathematical resources was a significant affordance for further mathematical activity. In each classroom context, activity was found to be distributed over social norms, tools and interaction. Number sense activity was distributed according to the adapted 'environment' metaphor (Greeno, 1991 ). Students negotiated mathematical meanings by activating and using cognitive tools and discursive resources in the number sense 'environment'.

year: 2004

title: The potential for inferring trophic state of Lake Wairarapa using zooplankton community composition

authors: Duggan, Ian C.

abstract: The use of biotic responses to infer lake trophic state (i.e., the bioindicator approach) is commonly neglected in favour of chemical and physical methods. Duggan et al. (2001a, 2001b, 2002) found that trophic state was the main determinant of rotifer distribution among North Island, New Zealand, lakes. Based on these responses developed a quantitative bioindicator index, using rotifer community composition, to infer Trophic Lake Index (TLI) values (sensu Burns et al. 1999). This approach was recently used successfully to infer trophic state changs in lakes of the Auckland region (Duggan & Barnes 2006). In this report I evaluate whether Lake Wairarapa would be a suitable candidate for monitoring trophic state using zooplankton during Wellington Regional Council's regular quarterly sampling, and what the number of net samples would be required during monitoring (i.e.., to collect greater than 300 individual zooplankton).

text: The potential for inferring trophic state of Lake Wairarapa using zooplankton community composition The use of biotic responses to infer lake trophic state (i.e., the bioindicator approach) is commonly neglected in favour of chemical and physical methods. Duggan et al. (2001a, 2001b, 2002) found that trophic state was the main determinant of rotifer distribution among North Island, New Zealand, lakes. Based on these responses developed a quantitative bioindicator index, using rotifer community composition, to infer Trophic Lake Index (TLI) values (sensu Burns et al. 1999). This approach was recently used successfully to infer trophic state changs in lakes of the Auckland region (Duggan & Barnes 2006). In this report I evaluate whether Lake Wairarapa would be a suitable candidate for monitoring trophic state using zooplankton during Wellington Regional Council's regular quarterly sampling, and what the number of net samples would be required during monitoring (i.e.., to collect greater than 300 individual zooplankton).

year: 2006-08

title: Sweet as – the [ADJ + as] intensifier construction in Māori English/ Aotearoa English.

authors: Calude, Andreea S.

abstract: We introduce the Waikato Māori English Conversation (MEC) corpus, which consists of 43 dyadic conversations between 49 young adults who self-recorded informal conversations with close friends, in their own homes, with no topic of conversation specified (83 hours of dialogue; nearly 800,000 words). The resulting materials are colloquial and unstructured, capturing a wider range of pragmatic and stylistic modes than is possible in a standard sociolinguistic interview. Here, we report on one such feature, the [ADJ + as] construction, for example: ‘sorry some of the questions are like awkward as’ and ‘that caused a big as drama eh’. This intensifier construction has been identified as a distinctive New Zealand English (NZE) innovation, yet little has been written about this it. However, the Waikato MEC corpus presents the opportunity to analyse the construction in a more systematic manner and to fill existing gaps in analyses of Māori English grammar.

text: Sweet as – the [ADJ + as] intensifier construction in Māori English/ Aotearoa English. We introduce the Waikato Māori English Conversation (MEC) corpus, which consists of 43 dyadic conversations between 49 young adults who self-recorded informal conversations with close friends, in their own homes, with no topic of conversation specified (83 hours of dialogue; nearly 800,000 words). The resulting materials are colloquial and unstructured, capturing a wider range of pragmatic and stylistic modes than is possible in a standard sociolinguistic interview. Here, we report on one such feature, the [ADJ + as] construction, for example: ‘sorry some of the questions are like awkward as’ and ‘that caused a big as drama eh’. This intensifier construction has been identified as a distinctive New Zealand English (NZE) innovation, yet little has been written about this it. However, the Waikato MEC corpus presents the opportunity to analyse the construction in a more systematic manner and to fill existing gaps in analyses of Māori English grammar.

year: 2025