title: Making multiplication meaningful: Teaching for conceptual understanding

authors: Mills, Judith Patricia

subjects: Conceptual understanding

abstract: The term numeracy is used widely in schools today and brings with it the expectation that students will be taught both how to do the mathematics, alongside an understanding of the concepts associated with the procedural application. One issue, which has arisen with the terminology ‘numeracy classroom’, is how to best support teachers to enhance their teaching of mathematics to allow this understanding to occur. This article stems from a larger research study that analysed the professional knowledge of teachers when teaching numeracy, and the impact their mathematics knowledge and procedural application had on children’s learning. This article presents observations of three teachers teaching a multiplication lesson (the first in a series of lessons over a six-week period) as they developed their students’ understanding of the mathematical concepts associated with the interpretation of the multiplication symbol. An analysis of the findings shows when the teachers used manipulatives, related word problems to the children’s lives, and promoted discussion in groups, a greater understanding of multiplication was apparent.

text: Making multiplication meaningful: Teaching for conceptual understanding The term numeracy is used widely in schools today and brings with it the expectation that students will be taught both how to do the mathematics, alongside an understanding of the concepts associated with the procedural application. One issue, which has arisen with the terminology ‘numeracy classroom’, is how to best support teachers to enhance their teaching of mathematics to allow this understanding to occur. This article stems from a larger research study that analysed the professional knowledge of teachers when teaching numeracy, and the impact their mathematics knowledge and procedural application had on children’s learning. This article presents observations of three teachers teaching a multiplication lesson (the first in a series of lessons over a six-week period) as they developed their students’ understanding of the mathematical concepts associated with the interpretation of the multiplication symbol. An analysis of the findings shows when the teachers used manipulatives, related word problems to the children’s lives, and promoted discussion in groups, a greater understanding of multiplication was apparent.

year: 2019

title: Soils and hydrology of Seabee Hook, Cape Hallett, Antarctica

authors: Hofstee, Erica H.

abstract: The soils and hydrology of Seabee Hook, Cape Hallett, Antarctica were investigated during the 2003-04 and 2004-05 summer periods. Seabee Hook is a low lying spit that has been built up by the deposition of material, from nearby cliffs, by strong tidal currents. Seabee Hook is also the location of a large Adelie penguin (Pygoscelis adeliae) colony and was the location of a USNNZ research base, occupied from 1957-73.

A soil map is presented of the Seabee Hook area. A soil association was identified between penguin mounds and intermound areas. Penguins build nests of stones on elevated sites, which at Cape Hallett are relict beach ridges. The penguins have exaggerated the topography of the beach ridges, primarily by adding 3-10 cm size stones ("penguin-stones") and guano, to form penguin mounds. Soils on penguin mounds contain guano in the upper 50 cm of the gravelly and sandy profile, and the guano layer overlies sub-rounded beachdeposited gravel and sand. Soils between beach ridges contain a thin veneer ( <3cm) of guano overlying the same basaltic gravelly sand found in the lower parts of the mound soils. The soils formed on the mounds have been classified usingUSDA Soil Taxonomy as Typic Haplorthels, and the soils formed between mounds have been classified as Typic Haplorthels/Typic Aquorthels depending on their soil moisture contents. 
The soil of the penguin mounds was enriched in many elements including nitrogen, organic carbon, phosphorus, cadmium, zinc, copper and it had increased electrical conductivity in soil horizons influenced by penguin guano compared to guano free horizons, soils from intermound areas, and soils away from the penguin colony. 
Radiocarbon dates from five penguin bones buried at the bottom of soil profiles indicate that Seabee Hook has been colonized by penguins for at least1000 years. That the colonization of Seabee Hook may have been rapid is evidenced by the consistent thickness of "penguin stones" and guano on top of the beach ridges throughout the area.
 Groundwater was situated perched above the ice cement as a shallow (<1-30 cm thickness of groundwater) unconfined aquifer. Groundwater within the penguin colony was sourced from melting snow drifts and ground ice. The occurrence of groundwater within the penguin colony at Seabee Hook showed considerable spatial and temporal variations over the 2003-04 and 2004-05summers, with ice cement levels decreasing from November and groundwater beginning to accumulate in early-December. Groundwater velocity through the permeable gravel and sand (porosity 23-33%) was up to 7.8 m day⁻¹, with hydraulic conductivities of 5 x 10⁻⁴ m s⁻¹ to 5 x 10⁻⁹ m s⁻¹.  Groundwater abundance varied on an annual basis depending on the amount of snowmelt occurring during summer. The 2003-04 summer had a higher water table within the penguin colony than the 2004-05 summer. During 2003-04, surface water commonly occurred as ephemeral and intermittent streams and ponds. During2004-05, water was mostly confined to groundwater within the penguin colony, where it occurred in topographic lows. Surface water was present in only a few ponds within the colony during 2004-05, and was more common in the high meltwater zones away from the penguin colony. 
The penguins and close proximity to the ocean have affected the groundwater chemistry, with groundwater in the penguin colony elevated in salt (14 times more sodium, 41 times more potassium), nitrogen (7 times more nitrate,416 times more ammonia), and phosphorus (33 time more total phosphorus)compared to groundwater sourced away from the penguin colony on Seabee Hookand also compared to other terrestrial waters in Antarctica.

text: Soils and hydrology of Seabee Hook, Cape Hallett, Antarctica The soils and hydrology of Seabee Hook, Cape Hallett, Antarctica were investigated during the 2003-04 and 2004-05 summer periods. Seabee Hook is a low lying spit that has been built up by the deposition of material, from nearby cliffs, by strong tidal currents. Seabee Hook is also the location of a large Adelie penguin (Pygoscelis adeliae) colony and was the location of a USNNZ research base, occupied from 1957-73.

A soil map is presented of the Seabee Hook area. A soil association was identified between penguin mounds and intermound areas. Penguins build nests of stones on elevated sites, which at Cape Hallett are relict beach ridges. The penguins have exaggerated the topography of the beach ridges, primarily by adding 3-10 cm size stones ("penguin-stones") and guano, to form penguin mounds. Soils on penguin mounds contain guano in the upper 50 cm of the gravelly and sandy profile, and the guano layer overlies sub-rounded beachdeposited gravel and sand. Soils between beach ridges contain a thin veneer ( <3cm) of guano overlying the same basaltic gravelly sand found in the lower parts of the mound soils. The soils formed on the mounds have been classified usingUSDA Soil Taxonomy as Typic Haplorthels, and the soils formed between mounds have been classified as Typic Haplorthels/Typic Aquorthels depending on their soil moisture contents. 
The soil of the penguin mounds was enriched in many elements including nitrogen, organic carbon, phosphorus, cadmium, zinc, copper and it had increased electrical conductivity in soil horizons influenced by penguin guano compared to guano free horizons, soils from intermound areas, and soils away from the penguin colony. 
Radiocarbon dates from five penguin bones buried at the bottom of soil profiles indicate that Seabee Hook has been colonized by penguins for at least1000 years. That the colonization of Seabee Hook may have been rapid is evidenced by the consistent thickness of "penguin stones" and guano on top of the beach ridges throughout the area.
 Groundwater was situated perched above the ice cement as a shallow (<1-30 cm thickness of groundwater) unconfined aquifer. Groundwater within the penguin colony was sourced from melting snow drifts and ground ice. The occurrence of groundwater within the penguin colony at Seabee Hook showed considerable spatial and temporal variations over the 2003-04 and 2004-05summers, with ice cement levels decreasing from November and groundwater beginning to accumulate in early-December. Groundwater velocity through the permeable gravel and sand (porosity 23-33%) was up to 7.8 m day⁻¹, with hydraulic conductivities of 5 x 10⁻⁴ m s⁻¹ to 5 x 10⁻⁹ m s⁻¹.  Groundwater abundance varied on an annual basis depending on the amount of snowmelt occurring during summer. The 2003-04 summer had a higher water table within the penguin colony than the 2004-05 summer. During 2003-04, surface water commonly occurred as ephemeral and intermittent streams and ponds. During2004-05, water was mostly confined to groundwater within the penguin colony, where it occurred in topographic lows. Surface water was present in only a few ponds within the colony during 2004-05, and was more common in the high meltwater zones away from the penguin colony. 
The penguins and close proximity to the ocean have affected the groundwater chemistry, with groundwater in the penguin colony elevated in salt (14 times more sodium, 41 times more potassium), nitrogen (7 times more nitrate,416 times more ammonia), and phosphorus (33 time more total phosphorus)compared to groundwater sourced away from the penguin colony on Seabee Hookand also compared to other terrestrial waters in Antarctica.

year: 2006

title: The processes involved in formulating a marae-based Māori language regeneration plan for Whakamārama marae: Outline, analysis and evaluation

authors: Lewis, Roger

subjects: New Zealand

abstract: We provide here a criterion referenced evaluation of the processes involved in the creation of a Māori language regeneration strategy for Whakamārama marae. Working voluntarily and often under difficult circumstances, core group members demonstrated that they possessed the essential characteristics of commitment, motivation and determination. In addition, they demonstrated the willingness and ability to use existing skills and knowledge effectively and to develop further skills and knowledge as the project proceeded. Perhaps most important, they developed a caring and effective working culture. However, the weaknesses of the project included a lack of preparation and planning prior to the commencement of the project which led to delays in producing outcomes and some loss of momentum. This also led, indirectly, to the views of two or three members of the core group being overrepresented in the language planning goals. We believe that the information and analysis provided here are likely to be of interest to any language community involved in micro-level language regeneration activities of a similar type.

text: The processes involved in formulating a marae-based Māori language regeneration plan for Whakamārama marae: Outline, analysis and evaluation We provide here a criterion referenced evaluation of the processes involved in the creation of a Māori language regeneration strategy for Whakamārama marae. Working voluntarily and often under difficult circumstances, core group members demonstrated that they possessed the essential characteristics of commitment, motivation and determination. In addition, they demonstrated the willingness and ability to use existing skills and knowledge effectively and to develop further skills and knowledge as the project proceeded. Perhaps most important, they developed a caring and effective working culture. However, the weaknesses of the project included a lack of preparation and planning prior to the commencement of the project which led to delays in producing outcomes and some loss of momentum. This also led, indirectly, to the views of two or three members of the core group being overrepresented in the language planning goals. We believe that the information and analysis provided here are likely to be of interest to any language community involved in micro-level language regeneration activities of a similar type.

year: 2008