title: A conjecture of De Koninck regarding particular square values of the sum of divisors function

authors: Broughan, Kevin A.

subjects: Science & Technology

abstract: We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. If the prime dividing a solution n is congruent to 3 modulo 8 then it must be greater than 41, and every solution is divisible by at least the fourth power of an odd prime. Moreover at least 2/5 of the exponents a of the primes dividing any solution have the property that a + 1 is a prime power. Lastly we prove that the number of solutions up to x > 1 is at most x¹/⁶⁺є, for any є > 0 and all x > xє.

text: A conjecture of De Koninck regarding particular square values of the sum of divisors function We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. If the prime dividing a solution n is congruent to 3 modulo 8 then it must be greater than 41, and every solution is divisible by at least the fourth power of an odd prime. Moreover at least 2/5 of the exponents a of the primes dividing any solution have the property that a + 1 is a prime power. Lastly we prove that the number of solutions up to x > 1 is at most x¹/⁶⁺є, for any є > 0 and all x > xє.

year: 2014

title: Automating vocabulary tests and enriching online courses for language learners

authors: König, Jemma Lynette

subjects: Computer science

abstract: The past decade has seen a massive growth in online academic courses, most of which are offered in the English language. However, although more people speak English as their second language than as their first, online course providers do not offer language assistance. Providing online learners with language resources would allow them to both learn about a subject through a foreign language and learn the foreign language through the subject. This is referred to as “content-based language learning”. 

Supporting content-based language learning using online courses raises several challenges, three of which are addressed in this thesis. First, courses teach subjects in particular domains, but supporting domain-specific language requires knowledge of specialised vocabulary. This thesis develops an automated approach to generating domain-specific corpora and wordlists, extracting domain-specific vocabulary in a way that can be applied to any online course. 

Second, acquiring and measuring language come hand-in-hand. Tools that help learners acquire new language should also include methods for testing. This thesis takes an existing vocabulary test and automates it. This has two main advantages: it requires no assumed knowledge of the language, allowing automatic generation of vocabulary tests; and the tests reflect the wordlists used to create them, allowing them to be targeted toward a particular domain.

Finally, for content-based language learning to be used successfully, the language components must be smoothly integrated into courses without disturbing the original content. Furthermore, vocabulary support should include multi-word lexical items as well as single words. The thesis describes a tool that enhances online course content, via a browser extension. It is completely automated, though would also lend itself to selective teacher intervention. It is illustrated here with reference to courses offered by the FutureLearn MOOC consortium.

text: Automating vocabulary tests and enriching online courses for language learners The past decade has seen a massive growth in online academic courses, most of which are offered in the English language. However, although more people speak English as their second language than as their first, online course providers do not offer language assistance. Providing online learners with language resources would allow them to both learn about a subject through a foreign language and learn the foreign language through the subject. This is referred to as “content-based language learning”. 

Supporting content-based language learning using online courses raises several challenges, three of which are addressed in this thesis. First, courses teach subjects in particular domains, but supporting domain-specific language requires knowledge of specialised vocabulary. This thesis develops an automated approach to generating domain-specific corpora and wordlists, extracting domain-specific vocabulary in a way that can be applied to any online course. 

Second, acquiring and measuring language come hand-in-hand. Tools that help learners acquire new language should also include methods for testing. This thesis takes an existing vocabulary test and automates it. This has two main advantages: it requires no assumed knowledge of the language, allowing automatic generation of vocabulary tests; and the tests reflect the wordlists used to create them, allowing them to be targeted toward a particular domain.

Finally, for content-based language learning to be used successfully, the language components must be smoothly integrated into courses without disturbing the original content. Furthermore, vocabulary support should include multi-word lexical items as well as single words. The thesis describes a tool that enhances online course content, via a browser extension. It is completely automated, though would also lend itself to selective teacher intervention. It is illustrated here with reference to courses offered by the FutureLearn MOOC consortium.

year: 2019

title: The Effects of a Shared Reading Intervention on the English Reading Skills of Year One Students in a Level Two Māori-medium Educational Context

authors: Te Arihi, Kylie

subjects: English Reading Skills

abstract: One of the biggest challenges confronting literacy education in Aotearoa  New Zealand is accommodating the differences in English reading-related variables at school entry to produce equitable outcomes in later reading achievement (Wilkinson, Freebody, & Elkins, 2000).  English-medium schools in Aotearoa struggle to negotiate effective literacy practices that validate and cater for the cognitive, cultural, and linguistic differences children bring to the process of learning to read in English.  Whereas, the role of English reading instruction in Māori-medium schools has been an under-researched and controversial issue.  How to accommodate for these differences to achieve equitable English reading outcomes in a year 1 level 2 Māori-medium context is the theme that this research seeks to explore.
	This Masters thesis reports on a shared reading intervention that explicitly teaches phonological awareness and alphabet knowledge to examine its effects on the English reading skills of year 1 students in a level 2 Māori-medium setting.  The research implemented a Kaupapa Māori framework and used interviews, surveys, reliable literacy measures, and research-based literacy instruction to explore reading acquisition for this particular cohort.  Thus, the purposes of the study were (a) to glean an in-depth understanding of the literacy and language practices that potentially shaped the participants English reading–related variables, (b) to examine the range of English reading-related skills for this cohort, and (c) to determine the effects of the intervention on their English reading skills.
	Eight students were divided and matched with a pair according to their reported pre-test phonemic awareness and alphabet knowledge scores, and then randomly assigned to either an intervention (n = 4) or treatment control (n = 4) group.  The intervention programme was carried out over a six week period and comprised 12, 30 minute lessons that integrated phonological and alphabetic based decoding skills within the shared reading approach.  The duration of the treatment control programme was also carried out over a six week period and comprised 12, 30 minutes lessons that integrated semantic, syntactic, and visual graphophonic sources of information to recognise words.  The results indicated the breadth and depth of English reading skills in year 1 level 2 Māori-medium contexts are diverse and the children had a positive attitude and sense of efficacy towards reading.  A comparison of the test results between the intervention and treatment control group demonstrated that a shared reading intervention that focused explicitly on phonological awareness and alphabet knowledge is effective in raising letter-naming knowledge, pseudoword decoding, phonemic awareness, and invented spelling.  The results are discussed in light of theoretical assumptions about reading acquisition that underlie word-base and text-base approaches to word recognition.
	Overall, this study supports the development and reform of training and professional development opportunities in phonological awareness and alphabet knowledge to better support, inform, and educate Aotearoa reading teachers.  This study contributes to the knowledge of English reading acquisition that validate the depth and breadth of early cognitive and linguistic differences to increase equitable English reading outcomes in level 2 Māori-medium contexts.

text: The Effects of a Shared Reading Intervention on the English Reading Skills of Year One Students in a Level Two Māori-medium Educational Context One of the biggest challenges confronting literacy education in Aotearoa  New Zealand is accommodating the differences in English reading-related variables at school entry to produce equitable outcomes in later reading achievement (Wilkinson, Freebody, & Elkins, 2000).  English-medium schools in Aotearoa struggle to negotiate effective literacy practices that validate and cater for the cognitive, cultural, and linguistic differences children bring to the process of learning to read in English.  Whereas, the role of English reading instruction in Māori-medium schools has been an under-researched and controversial issue.  How to accommodate for these differences to achieve equitable English reading outcomes in a year 1 level 2 Māori-medium context is the theme that this research seeks to explore.
	This Masters thesis reports on a shared reading intervention that explicitly teaches phonological awareness and alphabet knowledge to examine its effects on the English reading skills of year 1 students in a level 2 Māori-medium setting.  The research implemented a Kaupapa Māori framework and used interviews, surveys, reliable literacy measures, and research-based literacy instruction to explore reading acquisition for this particular cohort.  Thus, the purposes of the study were (a) to glean an in-depth understanding of the literacy and language practices that potentially shaped the participants English reading–related variables, (b) to examine the range of English reading-related skills for this cohort, and (c) to determine the effects of the intervention on their English reading skills.
	Eight students were divided and matched with a pair according to their reported pre-test phonemic awareness and alphabet knowledge scores, and then randomly assigned to either an intervention (n = 4) or treatment control (n = 4) group.  The intervention programme was carried out over a six week period and comprised 12, 30 minute lessons that integrated phonological and alphabetic based decoding skills within the shared reading approach.  The duration of the treatment control programme was also carried out over a six week period and comprised 12, 30 minutes lessons that integrated semantic, syntactic, and visual graphophonic sources of information to recognise words.  The results indicated the breadth and depth of English reading skills in year 1 level 2 Māori-medium contexts are diverse and the children had a positive attitude and sense of efficacy towards reading.  A comparison of the test results between the intervention and treatment control group demonstrated that a shared reading intervention that focused explicitly on phonological awareness and alphabet knowledge is effective in raising letter-naming knowledge, pseudoword decoding, phonemic awareness, and invented spelling.  The results are discussed in light of theoretical assumptions about reading acquisition that underlie word-base and text-base approaches to word recognition.
	Overall, this study supports the development and reform of training and professional development opportunities in phonological awareness and alphabet knowledge to better support, inform, and educate Aotearoa reading teachers.  This study contributes to the knowledge of English reading acquisition that validate the depth and breadth of early cognitive and linguistic differences to increase equitable English reading outcomes in level 2 Māori-medium contexts.

year: 2014