title: ‘Summative’ and ‘Formative’: Confused by the assessment terms?

authors: Ussher, William (Bill) Grant

subjects: education

abstract: The terms ‘formative’ and ‘summative’ when linked to assessment can cause confusion. Should these terms be dropped? Should we move on from them? This paper argues that it is the common shortening of the full and meaningful terms, ‘assessment for formative purposes’ and ‘assessment for summative purposes’ that contributes to a confusion over assessments, information and methods, particularly for pre-service teachers and those with less teaching experience. By being well-informed about both purpose and assessment activity, teachers will have greater clarity in understanding, communication and practice regarding these important and useful concepts.

text: ‘Summative’ and ‘Formative’: Confused by the assessment terms? The terms ‘formative’ and ‘summative’ when linked to assessment can cause confusion. Should these terms be dropped? Should we move on from them? This paper argues that it is the common shortening of the full and meaningful terms, ‘assessment for formative purposes’ and ‘assessment for summative purposes’ that contributes to a confusion over assessments, information and methods, particularly for pre-service teachers and those with less teaching experience. By being well-informed about both purpose and assessment activity, teachers will have greater clarity in understanding, communication and practice regarding these important and useful concepts.

year: 2010

title: Critical sets of full Latin squares

authors: Raass, Petelo Vaipuna

abstract: This thesis explores the properties of critical sets of the full n-Latin square and related combinatorial structures including full designs, (m,n,2)-balanced Latin rectangles and n-Latin cubes.

In Chapter 3 we study known results on designs and the analogies between critical sets of the full n-Latin square and minimal defining sets of the full designs.

Next in Chapter 4 we fully classify the critical sets of the full (m,n,2)-balanced Latin square, by describing the precise structures of these critical sets from the smallest to the largest.

Properties of different types of critical sets of the full n-Latin square are investigated in Chapter 5. We fully classify the structure of any saturated critical set of the full n-Latin square. We show in Theorem 5.8 that such a critical set has size exactly equal to n³ - 2n² - n. In Section 5.2 we give a construction which provides an upper bound for the size of the smallest critical set of the full n-Latin square. Similarly in Section 5.4, another construction gives a lower bound for the size of the largest non-saturated critical set. We conjecture that these bounds are best possible.

Using the results from Chapter 5, we obtain spectrum results on critical sets of the full n-Latin square in Chapter 6. In particular, we show that a critical set of each size between (n - 1)³ + 1 and n(n - 1)² + n - 2 exists.

In Chapter 7, we turn our focus to the completability of partial k-Latin squares. The relationship between partial k-Latin squares and semi-k-Latin squares is used to show that any partial k-Latin square of order n with at most (n - 1) non-empty cells is completable.

As Latin cubes generalize Latin squares, we attempt to generalize some of the results we have established on k-Latin squares so that they apply to k-Latin cubes. These results are presented in Chapter 8.

text: Critical sets of full Latin squares This thesis explores the properties of critical sets of the full n-Latin square and related combinatorial structures including full designs, (m,n,2)-balanced Latin rectangles and n-Latin cubes.

In Chapter 3 we study known results on designs and the analogies between critical sets of the full n-Latin square and minimal defining sets of the full designs.

Next in Chapter 4 we fully classify the critical sets of the full (m,n,2)-balanced Latin square, by describing the precise structures of these critical sets from the smallest to the largest.

Properties of different types of critical sets of the full n-Latin square are investigated in Chapter 5. We fully classify the structure of any saturated critical set of the full n-Latin square. We show in Theorem 5.8 that such a critical set has size exactly equal to n³ - 2n² - n. In Section 5.2 we give a construction which provides an upper bound for the size of the smallest critical set of the full n-Latin square. Similarly in Section 5.4, another construction gives a lower bound for the size of the largest non-saturated critical set. We conjecture that these bounds are best possible.

Using the results from Chapter 5, we obtain spectrum results on critical sets of the full n-Latin square in Chapter 6. In particular, we show that a critical set of each size between (n - 1)³ + 1 and n(n - 1)² + n - 2 exists.

In Chapter 7, we turn our focus to the completability of partial k-Latin squares. The relationship between partial k-Latin squares and semi-k-Latin squares is used to show that any partial k-Latin square of order n with at most (n - 1) non-empty cells is completable.

As Latin cubes generalize Latin squares, we attempt to generalize some of the results we have established on k-Latin squares so that they apply to k-Latin cubes. These results are presented in Chapter 8.

year: 2016

title: Ka hao te rangatahi: Exploring school and work pathways for rangatahi Māori / Youth  growing up within gang space in Aotearoa

authors: Maihi, Bonnie

subjects: Rangatahi

abstract: This thesis explores the experiences of rangatahi Māori growing up in gang environments in Aotearoa, focusing on their educational and employment journeys. The research aims to elevate the rangatahi narratives without reducing them to mere statistics or stereotypes, highlighting their resilience and insights in contexts often characterized by stigma and judgement. Employing principles of Kaupapa Māori, Critical Pedagogy, and a Waka navigation framework, this study challenges deficit-based perspectives that typically dominate discussions about gangs. 

On a practical level, it advocates for trust-based partnerships with gang whānau, emphasizing the importance of honesty and respect to foster collaboration. Existing Whānau -led initiatives illustrate the possibilities of merging cultural knowledge with everyday survival, showcasing resilience as a lived reality. Theoretically, the research offers an insider perspective, positioning myself as researcher to honor lived experiences and mitigate traditional negative framings of gang spaces, instead framing them as complex sites of identity and resilience. 

Ultimately, this thesis posits that rangatahi Māori in gang settings are not merely problems to be solved but are agents of hope and strength, rooted in their heritage. Their futures should be shaped by their identities rather than deficits, affirming their tino rangatiratanga and capacities for meaningful contributions within their communities.

text: Ka hao te rangatahi: Exploring school and work pathways for rangatahi Māori / Youth  growing up within gang space in Aotearoa This thesis explores the experiences of rangatahi Māori growing up in gang environments in Aotearoa, focusing on their educational and employment journeys. The research aims to elevate the rangatahi narratives without reducing them to mere statistics or stereotypes, highlighting their resilience and insights in contexts often characterized by stigma and judgement. Employing principles of Kaupapa Māori, Critical Pedagogy, and a Waka navigation framework, this study challenges deficit-based perspectives that typically dominate discussions about gangs. 

On a practical level, it advocates for trust-based partnerships with gang whānau, emphasizing the importance of honesty and respect to foster collaboration. Existing Whānau -led initiatives illustrate the possibilities of merging cultural knowledge with everyday survival, showcasing resilience as a lived reality. Theoretically, the research offers an insider perspective, positioning myself as researcher to honor lived experiences and mitigate traditional negative framings of gang spaces, instead framing them as complex sites of identity and resilience. 

Ultimately, this thesis posits that rangatahi Māori in gang settings are not merely problems to be solved but are agents of hope and strength, rooted in their heritage. Their futures should be shaped by their identities rather than deficits, affirming their tino rangatiratanga and capacities for meaningful contributions within their communities.

year: 2025