title: Forming conjectures within a spreadsheet environment

authors: Calder, Nigel Stuart

subjects: education

abstract: This paper is concerned with the use of spreadsheets within mathematical investigational tasks. Considering the learning of both children and pre-service teaching students, it examines how mathematical phenomena can be seen as a function of the pedagogical media through which they are encountered. In particular, it shows how pedagogical apparatus influence patterns of social interaction, and how this interaction shapes the mathematical ideas that are engaged with. Notions of conjecture, along with the particular faculty of the spreadsheet setting, are considered with regard to the facilitation of mathematical thinking. Employing an interpretive perspective, a key focus is on how alternative pedagogical media and associated discursive networks influence the way that students form and test informal conjectures.

text: Forming conjectures within a spreadsheet environment This paper is concerned with the use of spreadsheets within mathematical investigational tasks. Considering the learning of both children and pre-service teaching students, it examines how mathematical phenomena can be seen as a function of the pedagogical media through which they are encountered. In particular, it shows how pedagogical apparatus influence patterns of social interaction, and how this interaction shapes the mathematical ideas that are engaged with. Notions of conjecture, along with the particular faculty of the spreadsheet setting, are considered with regard to the facilitation of mathematical thinking. Employing an interpretive perspective, a key focus is on how alternative pedagogical media and associated discursive networks influence the way that students form and test informal conjectures.

year: 2006

title: Numerical investigation of cold-formed steel channels with edge-stiffened and unstiffened elongated web holes under shear

authors: Chandramohan, Dinesh Lakshmanan

subjects: elongated web holes

abstract: Over the past decade, cold-formed steel (CFS) channel sections having edge-stiffened circular web holes have been developed in New Zealand. Such edge-stiffened holes increase the strength of the CFS channel sections, compared to an equivalent section having unstiffened web holes, while still allowing full building service integration. In the case of shear, previous research has found that the use of edge-stiffened web holes significantly improves the shear strength of such channel sections. However, no studies are available in the literature investigating the shear strength of CFS channel sections with edge-stiffened elongated web holes. The issue is addressed herein. Non-linear finite element (FE) analyses are used to investigate the shear strength of CFS channel sections with a shear span aspect ratio of 2.0. The FE models were validated against the experimental test results of sections having unstiffened elongated web holes and edge-stiffened circular web holes; good agreement in terms of the load-displacement curves and failure behaviour was shown. Using the validated FE models, a parametric study was conducted, comprising 2124 finite element analyses (FEA) results. The parametric results were then compared to the design predictions of the American Iron and Steel Institute (AISI 2016), and Australia/New Zealand Standards (AS/NZS 2018) and Wanniarchchi et al. (2017) for unstiffened elongated web holes, showing that the design predictions are unconservative in comparison results. Moreover, the direct strength method (DSM) approach of Pham et al. (2020a and 2023) provides conservative results for channels with unstiffened elongated web holes. It was also found that the design equations proposed by Chen et al. (2022) for edge-stiffened circular web holes were unconservative in predicting the shear strength of channels having edge-stiffened elongated web holes. Therefore, design equations in the form of a shear reduction factor and a modified DSM approach for CFS channel sections having unstiffened and edge-stiffened elongated web holes were proposed. Finally, a reliability analysis was carried out to ensure that the proposed equations are reliable to predict the shear strength of CFS channel sections with edge-stiffened and unstiffened web holes.

text: Numerical investigation of cold-formed steel channels with edge-stiffened and unstiffened elongated web holes under shear Over the past decade, cold-formed steel (CFS) channel sections having edge-stiffened circular web holes have been developed in New Zealand. Such edge-stiffened holes increase the strength of the CFS channel sections, compared to an equivalent section having unstiffened web holes, while still allowing full building service integration. In the case of shear, previous research has found that the use of edge-stiffened web holes significantly improves the shear strength of such channel sections. However, no studies are available in the literature investigating the shear strength of CFS channel sections with edge-stiffened elongated web holes. The issue is addressed herein. Non-linear finite element (FE) analyses are used to investigate the shear strength of CFS channel sections with a shear span aspect ratio of 2.0. The FE models were validated against the experimental test results of sections having unstiffened elongated web holes and edge-stiffened circular web holes; good agreement in terms of the load-displacement curves and failure behaviour was shown. Using the validated FE models, a parametric study was conducted, comprising 2124 finite element analyses (FEA) results. The parametric results were then compared to the design predictions of the American Iron and Steel Institute (AISI 2016), and Australia/New Zealand Standards (AS/NZS 2018) and Wanniarchchi et al. (2017) for unstiffened elongated web holes, showing that the design predictions are unconservative in comparison results. Moreover, the direct strength method (DSM) approach of Pham et al. (2020a and 2023) provides conservative results for channels with unstiffened elongated web holes. It was also found that the design equations proposed by Chen et al. (2022) for edge-stiffened circular web holes were unconservative in predicting the shear strength of channels having edge-stiffened elongated web holes. Therefore, design equations in the form of a shear reduction factor and a modified DSM approach for CFS channel sections having unstiffened and edge-stiffened elongated web holes were proposed. Finally, a reliability analysis was carried out to ensure that the proposed equations are reliable to predict the shear strength of CFS channel sections with edge-stiffened and unstiffened web holes.

year: 2024

title: Imagining our own approaches

authors: Smith, Linda Tuhiwai

abstract: I spent some formative years of my life either in the back of museums or their basements helping my father, a scholar of Māori Studies, and keeping myself out of trouble. In the late 1960s I had one small job in the library basement of the Peabody Museum in Salem, Massachusetts, typing new labels for the captains’ log books of ships that were sailing during the American Revolution. I read most of those journals that consisted of pages and pages of wind directions with the rare glimpse of an encounter with another ship or a list of supplies. Why were we there in Salem when we came from Aotearoa, New Zealand? We were there because Salem was the home base for ships that sailed into the Pacific and returned home with collections of materials from the various Pacific Islands countries they visited. My father was studying elaborately carved items from the Marquesa Islands that looked very much like Māori designs.

text: Imagining our own approaches I spent some formative years of my life either in the back of museums or their basements helping my father, a scholar of Māori Studies, and keeping myself out of trouble. In the late 1960s I had one small job in the library basement of the Peabody Museum in Salem, Massachusetts, typing new labels for the captains’ log books of ships that were sailing during the American Revolution. I read most of those journals that consisted of pages and pages of wind directions with the rare glimpse of an encounter with another ship or a list of supplies. Why were we there in Salem when we came from Aotearoa, New Zealand? We were there because Salem was the home base for ships that sailed into the Pacific and returned home with collections of materials from the various Pacific Islands countries they visited. My father was studying elaborately carved items from the Marquesa Islands that looked very much like Māori designs.

year: 2015