title: Embedding problem-solving in a primary mathematics programme

authors: Bailey, Judy

abstract: New Zealand curriculum documents have long referred to mathematics as a problem-solving endeavour. Although this has been an intended focus for more than 25 years, problem-solving has often been an aspect of mathematics teaching that has been overlooked (Holton, 2009). This research explores the experiences of one teacher who is committed to enhancing children’s learning by embedding a problem-solving approach within her mathematics programme. The teacher reports that while students respond positively to mathematics as problem-solving, a number of constraints have been encountered. The teacher’s ongoing efforts responding to these are shared.

text: Embedding problem-solving in a primary mathematics programme New Zealand curriculum documents have long referred to mathematics as a problem-solving endeavour. Although this has been an intended focus for more than 25 years, problem-solving has often been an aspect of mathematics teaching that has been overlooked (Holton, 2009). This research explores the experiences of one teacher who is committed to enhancing children’s learning by embedding a problem-solving approach within her mathematics programme. The teacher reports that while students respond positively to mathematics as problem-solving, a number of constraints have been encountered. The teacher’s ongoing efforts responding to these are shared.

year: 2017

title: An analysis of the surface water resources of the upper Taieri River, Otago

authors: Simmers, I.

abstract: To plan a water resource survey data collection programme, it is vital to first establish the purpose for which the gathered data are to be used, and the degree of precision of the information at a particular confidence level that will be adequate. Purpose will determine the required data precision. Precision requirements will in turn dictate minimum record lengths of each variable necessary to estimate population parameters at a point, and the network density needed for parameter estimation over an area. 
This study is concerned with the data requirements and analyses for the planning of an irrigation scheme in the Maniototo Plains and Styx Basin, Central Otago. The 95 percent confidence level is adopted for required data precision. Allowable standard errors of population parameter estimates are stated to be 10 percent for streamflow and precipitation and five percent for temperature. 
Measured monthly, seasonal, and annual parameter values of these variables are summarised and discussed. Although the data collection networks are shown to be theoretically acceptable for most purposes, the measured data do not allow estimation of all the needed total - and sub-catchment population parameters at the required precision level. Record synthesis is necessary in order to increase the amount of information contained at this stage in the precipitation and streamflow data series. 
Techniques chosen for time series extension and spatial extrapolation are linear7 curvilinear and multiple regression analyses, water balance, conceptual and stochastic models. Each model is described, and limitations or advantages outlined. Also discussed are the theoretical aspects which concern precision of population parameter estimates from blended data, standard errors of prediction for synthetic records, and the relative simulation and prediction abilities of the models chosen. Split-record techniques are used to evaluate within and between model efficiencies. 
Addition of synthesised records to the precipitation and streamflow data series still does not permit estimates of all required population parameters at the levels of precision stated as needed. In some instances, record extension results in a decrease in statistical information. For design of any irrigation scheme to proceed now, therefore, the chosen error criteria must be judged too stringent for the Upper Taieri data. If the calculated standard errors cannot be accepted, all precipitation and streamflow records from the study area will require extension by additional observations.
 The study is also used as an opportunity to check the validity of commonly. accepted concepts of 'regional hydrology', at least within the East Otago Region. It is concluded that for low flows, hydrological homogeneity cannot be assumed to equate with uniformity of basin characteristics. Regions are better defined in terms of allowable areal variation for stated hydrological parameters. The study area is not hydrologically homogeneous by the defined criteria. Further, the boundaries of hydrologically similar regions vary dependent on which streamflow parameter is considered. 
Results are presented in British units throughout this study, since these are the units in which the basic data were measured and analysed.

text: An analysis of the surface water resources of the upper Taieri River, Otago To plan a water resource survey data collection programme, it is vital to first establish the purpose for which the gathered data are to be used, and the degree of precision of the information at a particular confidence level that will be adequate. Purpose will determine the required data precision. Precision requirements will in turn dictate minimum record lengths of each variable necessary to estimate population parameters at a point, and the network density needed for parameter estimation over an area. 
This study is concerned with the data requirements and analyses for the planning of an irrigation scheme in the Maniototo Plains and Styx Basin, Central Otago. The 95 percent confidence level is adopted for required data precision. Allowable standard errors of population parameter estimates are stated to be 10 percent for streamflow and precipitation and five percent for temperature. 
Measured monthly, seasonal, and annual parameter values of these variables are summarised and discussed. Although the data collection networks are shown to be theoretically acceptable for most purposes, the measured data do not allow estimation of all the needed total - and sub-catchment population parameters at the required precision level. Record synthesis is necessary in order to increase the amount of information contained at this stage in the precipitation and streamflow data series. 
Techniques chosen for time series extension and spatial extrapolation are linear7 curvilinear and multiple regression analyses, water balance, conceptual and stochastic models. Each model is described, and limitations or advantages outlined. Also discussed are the theoretical aspects which concern precision of population parameter estimates from blended data, standard errors of prediction for synthetic records, and the relative simulation and prediction abilities of the models chosen. Split-record techniques are used to evaluate within and between model efficiencies. 
Addition of synthesised records to the precipitation and streamflow data series still does not permit estimates of all required population parameters at the levels of precision stated as needed. In some instances, record extension results in a decrease in statistical information. For design of any irrigation scheme to proceed now, therefore, the chosen error criteria must be judged too stringent for the Upper Taieri data. If the calculated standard errors cannot be accepted, all precipitation and streamflow records from the study area will require extension by additional observations.
 The study is also used as an opportunity to check the validity of commonly. accepted concepts of 'regional hydrology', at least within the East Otago Region. It is concluded that for low flows, hydrological homogeneity cannot be assumed to equate with uniformity of basin characteristics. Regions are better defined in terms of allowable areal variation for stated hydrological parameters. The study area is not hydrologically homogeneous by the defined criteria. Further, the boundaries of hydrologically similar regions vary dependent on which streamflow parameter is considered. 
Results are presented in British units throughout this study, since these are the units in which the basic data were measured and analysed.

year: 1975

title: He whakaemi kōrero mō Ngā Ruahine

authors: Manuirirangi, Hōri

abstract: Ko te whāinga o tēnei tuhingaroa, hei whakaemi kōrero mō Ngā Ruahine. I whāia e au te āhua o te tipu o te rākau hei hanga i aku kōhinga kōrero mō Ngā Ruahine. Ko te ūpoko tuatahi, ko ngā pakiaka, arā te tīmatatanga o Ngā Ruahine. I konei ka tirohia ngā kōrero mō ngā waka tawhito mete whakapapa hoki o ngā tūpuna tāngatawhenua o Ngā Ruahine. Whai muri i tēnā, he wāhanga e pā ana ki te haeretanga mai o Aotea waka, ā, ka tirohia hoki tētehi kōrero tawhito mō te wehenga o ngā iwi o Aotea.
Mai i ngā pakiaka ka piki ake ki te tinana o te rākau. Koinei te wāhanga e pā ana ki ngā korero whenua o Ngā Ruahine. Kei te ūpoko tuarua nei, ka āta tirohia ngā kōrero mō ngā tongi o te rohe o Ngā Ruahine, me ngā take kōrero e whakawhanaunga ana i te tangata ki te whenua. Kei te ūpoko tuarua anō hoki ētehi whakaaturanga whenua mō te rohe o Ngā Ruahine, hei āwhina i te kaipānui.  
Mai i te tinana, ka aro atu ki ngā peka o te rākau i raro i te ūpoko tuatoru. Koinei te wāhanga nui o tēnei tuhingaroa, nā te tokomaha o ngā toronga o ngā peka nei. I roto i te ūpoko tuatoru, ka tirohia ētehi kōrero mō ia hapū o Ngā Ruahine. Mai i ngā kōrero mō ngā rohe whenua o ia hapū, ki ngā kōrero mō ngā marae me ngā pā tawhito o ērā hapū, ā, tae atu hoki ki ngā tūpuna rongonui me ā rātou mahi whakaari.  
Hei te mutunga, ka herea katoatia ngā kōrero o te tuhinga nei i raro i te ūpoko tuawhā, kia kite ai , he aha ngā hua e pūawai ai i tēnei tuhinga. Koinei te whakamutunga o ngā kōrero, arā ko te whakakapīnga o ngā kōrero.  
Ko tēnei tuhingaroa, he whakaemi kōrero mai i ngā kaumātua o Ngā Ruahine, ā, he mea tango mai hoki ētehi kōrero i ngā pukapuka, ko ēnei kōrero kua whakatakotoria i roto i tēnei tuhingaroa hei whakawhāriki iho ki te aroaro o te tini. Ko te tūmanako, he tuhinga rangahau tēnei hei āwhina i ngā rangatahi o Ngā Ruahine, kia rongo ai rātou i ngā kōrero kāore i te tino rangona i ēnei rā, kia mau hoki ngā kōrero a ngā kaumātua o Ngā Ruahine, kei ngaro. Erangi, he whakamōhio tēnei, he tīmatanga anahe tēnei tuhingaroa mō te kaupapa nei. Ko te tūmanako, he hua anō ka puta i tēnei rangahau, hei whāngai i ngā manu hiakai o Ngā Ruahine.

text: He whakaemi kōrero mō Ngā Ruahine Ko te whāinga o tēnei tuhingaroa, hei whakaemi kōrero mō Ngā Ruahine. I whāia e au te āhua o te tipu o te rākau hei hanga i aku kōhinga kōrero mō Ngā Ruahine. Ko te ūpoko tuatahi, ko ngā pakiaka, arā te tīmatatanga o Ngā Ruahine. I konei ka tirohia ngā kōrero mō ngā waka tawhito mete whakapapa hoki o ngā tūpuna tāngatawhenua o Ngā Ruahine. Whai muri i tēnā, he wāhanga e pā ana ki te haeretanga mai o Aotea waka, ā, ka tirohia hoki tētehi kōrero tawhito mō te wehenga o ngā iwi o Aotea.
Mai i ngā pakiaka ka piki ake ki te tinana o te rākau. Koinei te wāhanga e pā ana ki ngā korero whenua o Ngā Ruahine. Kei te ūpoko tuarua nei, ka āta tirohia ngā kōrero mō ngā tongi o te rohe o Ngā Ruahine, me ngā take kōrero e whakawhanaunga ana i te tangata ki te whenua. Kei te ūpoko tuarua anō hoki ētehi whakaaturanga whenua mō te rohe o Ngā Ruahine, hei āwhina i te kaipānui.  
Mai i te tinana, ka aro atu ki ngā peka o te rākau i raro i te ūpoko tuatoru. Koinei te wāhanga nui o tēnei tuhingaroa, nā te tokomaha o ngā toronga o ngā peka nei. I roto i te ūpoko tuatoru, ka tirohia ētehi kōrero mō ia hapū o Ngā Ruahine. Mai i ngā kōrero mō ngā rohe whenua o ia hapū, ki ngā kōrero mō ngā marae me ngā pā tawhito o ērā hapū, ā, tae atu hoki ki ngā tūpuna rongonui me ā rātou mahi whakaari.  
Hei te mutunga, ka herea katoatia ngā kōrero o te tuhinga nei i raro i te ūpoko tuawhā, kia kite ai , he aha ngā hua e pūawai ai i tēnei tuhinga. Koinei te whakamutunga o ngā kōrero, arā ko te whakakapīnga o ngā kōrero.  
Ko tēnei tuhingaroa, he whakaemi kōrero mai i ngā kaumātua o Ngā Ruahine, ā, he mea tango mai hoki ētehi kōrero i ngā pukapuka, ko ēnei kōrero kua whakatakotoria i roto i tēnei tuhingaroa hei whakawhāriki iho ki te aroaro o te tini. Ko te tūmanako, he tuhinga rangahau tēnei hei āwhina i ngā rangatahi o Ngā Ruahine, kia rongo ai rātou i ngā kōrero kāore i te tino rangona i ēnei rā, kia mau hoki ngā kōrero a ngā kaumātua o Ngā Ruahine, kei ngaro. Erangi, he whakamōhio tēnei, he tīmatanga anahe tēnei tuhingaroa mō te kaupapa nei. Ko te tūmanako, he hua anō ka puta i tēnei rangahau, hei whāngai i ngā manu hiakai o Ngā Ruahine.

year: 1998