title: A calculator for supporting derivation in constructive type-theory: PICTCalc

authors: Reeves, Steve

subjects: proof assistant

abstract: PICTCalc is an interactive program written in LPA Prolog which has encoded within it the rules of Martin-Löf's constructive type theory (CTT), a formal system based on the constructive or intuitionistic mathematics of Brouwer, Heyting and others. It allows us to specify and express any total, computable function, so from a computer science point of view we can write both specifications and programs, along with the derivations which lead from one to the other, in a single language. PICTCalc is a more recent version of MacPICT which is itself a reconstruction of PICT [Ham92] and is intended as a test-bed for providing formal support for work within CTT. Many of the developments and improvements were suggested by students since they used the system to work on substantial courseworks. As we shall see, PICTCalc can be used to assist in the development of derivations in CTT and so it is called a derivation assistant (DA). In this paper I show how PICTCalc can be used for supporting derivations in CTT and consider what current experience suggests for future improvement. The examples in this paper will not require any knowledge of CTT since the meaning will either be clear to anyone with experience of logic and programming notations in general or will be explained as necessary.

text: A calculator for supporting derivation in constructive type-theory: PICTCalc PICTCalc is an interactive program written in LPA Prolog which has encoded within it the rules of Martin-Löf's constructive type theory (CTT), a formal system based on the constructive or intuitionistic mathematics of Brouwer, Heyting and others. It allows us to specify and express any total, computable function, so from a computer science point of view we can write both specifications and programs, along with the derivations which lead from one to the other, in a single language. PICTCalc is a more recent version of MacPICT which is itself a reconstruction of PICT [Ham92] and is intended as a test-bed for providing formal support for work within CTT. Many of the developments and improvements were suggested by students since they used the system to work on substantial courseworks. As we shall see, PICTCalc can be used to assist in the development of derivations in CTT and so it is called a derivation assistant (DA). In this paper I show how PICTCalc can be used for supporting derivations in CTT and consider what current experience suggests for future improvement. The examples in this paper will not require any knowledge of CTT since the meaning will either be clear to anyone with experience of logic and programming notations in general or will be explained as necessary.

year: 1994-06

title: Quality assessment by science teachers: Five focus areas

authors: Edwards, Frances

subjects: assessment capability

abstract: In order to teach science well, science teachers need to know what to focus on in order to ensure their assessment of student learning is meaningful and useful for the students’ on going learning and development. The diversity and range of content and skills within the subject of science mean that the assessment capabilities required by science teachers are wide ranging and complex, requiring specialist knowledge and skills in the assessment of science learning as part of the teachers’ pedagogical content knowledge (PCK). Based on a review of the literature this paper proposes a framework for quality assessment in science which focuses on five areas: teaching, students, evidence of learning, future decision-making and impact. This paper advocates a concurrent consideration of all five areas of the framework to provide a substantial, rich, broad, rigorous quality assessment approach on which teachers and students can base teaching and learning.

text: Quality assessment by science teachers: Five focus areas In order to teach science well, science teachers need to know what to focus on in order to ensure their assessment of student learning is meaningful and useful for the students’ on going learning and development. The diversity and range of content and skills within the subject of science mean that the assessment capabilities required by science teachers are wide ranging and complex, requiring specialist knowledge and skills in the assessment of science learning as part of the teachers’ pedagogical content knowledge (PCK). Based on a review of the literature this paper proposes a framework for quality assessment in science which focuses on five areas: teaching, students, evidence of learning, future decision-making and impact. This paper advocates a concurrent consideration of all five areas of the framework to provide a substantial, rich, broad, rigorous quality assessment approach on which teachers and students can base teaching and learning.

year: 2013

title: Countering gentrification in Tāmaki Makarau: Towards a framework for urban environmental justice

authors: Terruhn, Jessica

abstract: This policy brief argues for urban policies that actively aim to end gentrification.

Gentrification is intimately tied to state-led processes of urban renewal. Though historically understood as the displacement of low-income households as an unfortunate byproduct of socioeconomic and demographic neighbourhood change, contemporary gentrification is constituted by profit-driven investment decisions that erase undervalued neighbourhoods and their communities in the name of urban renewal (variously referred to as redevelopment, regeneration, renaissance, or revitalisation).

These processes of gentrification fundamentally contribute to environmental injustice. At the same time as creating ‘zones of abundance’, neighbourhood regeneration projects simultaneously (re-)create ‘zones of neglect and sacrifice’, which are burdened with environmental risks. As low-income and ethnic minority households are more likely to either reside in or to be displaced into these neighbourhoods, they are disproportionately exposed to environmental risk factors.

Moreover, gentrification enables and legitimises the exclusion of marginalised communities in multiple ways: 1) it devalues existing places and their residents in favour of regeneration, 2) it displaces longtime residents from regenerated neighbourhoods because of increasing property values, and/or 3) it alienates longtime residents as neighbourhood aesthetics, amenities and services change and become unaffordable and/or irrelevant.

As gentrification contributes to low-income households’ experiences of precarity and severs community ties and place attachments, it generates significant costs to personal and community health and wellbeing as well as social cohesion. The recommendations articulated in this brief emphasise the importance of transformative policy solutions that actively counter gentrification.
These include:
• Equitable investment in urban infrastructure
• Prioritising affordable housing
• Ensuring accessible transportation
• Empowering local communities
• Implementing a Te Tiriti o Waitangi approach to policy development

text: Countering gentrification in Tāmaki Makarau: Towards a framework for urban environmental justice This policy brief argues for urban policies that actively aim to end gentrification.

Gentrification is intimately tied to state-led processes of urban renewal. Though historically understood as the displacement of low-income households as an unfortunate byproduct of socioeconomic and demographic neighbourhood change, contemporary gentrification is constituted by profit-driven investment decisions that erase undervalued neighbourhoods and their communities in the name of urban renewal (variously referred to as redevelopment, regeneration, renaissance, or revitalisation).

These processes of gentrification fundamentally contribute to environmental injustice. At the same time as creating ‘zones of abundance’, neighbourhood regeneration projects simultaneously (re-)create ‘zones of neglect and sacrifice’, which are burdened with environmental risks. As low-income and ethnic minority households are more likely to either reside in or to be displaced into these neighbourhoods, they are disproportionately exposed to environmental risk factors.

Moreover, gentrification enables and legitimises the exclusion of marginalised communities in multiple ways: 1) it devalues existing places and their residents in favour of regeneration, 2) it displaces longtime residents from regenerated neighbourhoods because of increasing property values, and/or 3) it alienates longtime residents as neighbourhood aesthetics, amenities and services change and become unaffordable and/or irrelevant.

As gentrification contributes to low-income households’ experiences of precarity and severs community ties and place attachments, it generates significant costs to personal and community health and wellbeing as well as social cohesion. The recommendations articulated in this brief emphasise the importance of transformative policy solutions that actively counter gentrification.
These include:
• Equitable investment in urban infrastructure
• Prioritising affordable housing
• Ensuring accessible transportation
• Empowering local communities
• Implementing a Te Tiriti o Waitangi approach to policy development

year: 2025