title: The Mātauranga Māori in Mathematics Directive: Exploring the place of mātauranga Māori in Mathematics teaching and learning

authors: Williams, Jessica Elizabeth

subjects: mathematics education

abstract: This thesis explores issues concerning mātauranga Māori in mathematics teaching and learning here in Aotearoa. The Ministry of Education has directed that mana ōrite mō te mātauranga Māori be embedded in teaching, learning, and assessment. Thus, this research primarily aims to understand the development leading to the directive of including mātauranga Māori in education policies. For the English-medium secondary education settings, the second and third aims of this research are to explore what mātauranga Māori means to teachers of mathematics and to consider the connections between mātauranga Māori and mathematics teaching and learning. To investigate these aims, a semi-structured group discussion with four secondary mathematics teachers from an English-medium setting was conducted. The results of this thesis highlight the confusion and challenges secondary mathematics educators have toward defining, and subsequently, implementing mātauranga Māori in their classrooms. This thesis also found that there is enthusiasm and interest around learning how to ensure indigenous and marginalised learners reach their mathematics potential. Believing that indigenous worldviews have the potential to shift education outcomes for minority learners, this thesis adds to literature related to indigenous education, secondary mathematics education, and English-medium education of Māori learners.

text: The Mātauranga Māori in Mathematics Directive: Exploring the place of mātauranga Māori in Mathematics teaching and learning This thesis explores issues concerning mātauranga Māori in mathematics teaching and learning here in Aotearoa. The Ministry of Education has directed that mana ōrite mō te mātauranga Māori be embedded in teaching, learning, and assessment. Thus, this research primarily aims to understand the development leading to the directive of including mātauranga Māori in education policies. For the English-medium secondary education settings, the second and third aims of this research are to explore what mātauranga Māori means to teachers of mathematics and to consider the connections between mātauranga Māori and mathematics teaching and learning. To investigate these aims, a semi-structured group discussion with four secondary mathematics teachers from an English-medium setting was conducted. The results of this thesis highlight the confusion and challenges secondary mathematics educators have toward defining, and subsequently, implementing mātauranga Māori in their classrooms. This thesis also found that there is enthusiasm and interest around learning how to ensure indigenous and marginalised learners reach their mathematics potential. Believing that indigenous worldviews have the potential to shift education outcomes for minority learners, this thesis adds to literature related to indigenous education, secondary mathematics education, and English-medium education of Māori learners.

year: 2023

title: E kui Rāwinia

authors: Maxwell, Te Kahautu

subjects: Waiata tangi

abstract: He waiata tangi tēnei mō Rāwinia Te Kani he uri nō Te Whakatōhea.  I whānau mai a Rāwinia ki roto o Ngāti Rua he hapū nō Te Whakatōhea, i pakeke mai ia ki roto o Ngāti Rua ki Ōmarumutu, ā, i kuraina ia ki reira.  He wahine rongonui a Rāwinia ki roto o Tūranga i moe ia i a Tokorua Te Kani he ariki nō roto o Tūranga.  Hoi anō he wahine haka a Rāwinia he kuia tāngia ki te moko kauae me te tautoko i ngā mokopū wānanga puta i te motu.  He waiata tangi tēnei mōna nā tana iwi a Te Whakatōhea.

text: E kui Rāwinia He waiata tangi tēnei mō Rāwinia Te Kani he uri nō Te Whakatōhea.  I whānau mai a Rāwinia ki roto o Ngāti Rua he hapū nō Te Whakatōhea, i pakeke mai ia ki roto o Ngāti Rua ki Ōmarumutu, ā, i kuraina ia ki reira.  He wahine rongonui a Rāwinia ki roto o Tūranga i moe ia i a Tokorua Te Kani he ariki nō roto o Tūranga.  Hoi anō he wahine haka a Rāwinia he kuia tāngia ki te moko kauae me te tautoko i ngā mokopū wānanga puta i te motu.  He waiata tangi tēnei mōna nā tana iwi a Te Whakatōhea.

year: 2016

title: Structure from randomness in halfspace learning with the zero-one loss

authors: Kabán, Ata

abstract: We prove risk bounds for halfspace learning when the data dimensionality is allowed to be larger than the sample size, using a notion of compressibility by random projection. In particular, we give upper bounds for the empirical risk minimizer learned efficiently from randomly projected data, as well as uniform upper bounds in the full high-dimensional space. Our main findings are the following: i) In both settings, the obtained bounds are able to discover and take advantage of benign geometric structure, which turns out to depend on the cosine similarities between the classifier and points of the input space, and provide a new interpretation of margin distribution type arguments. ii) Furthermore our bounds allow us to draw new connections between several existing successful classification algorithms, and we also demonstrate that our theory is predictive of empirically observed performance in numerical simulations and experiments. iii) Taken together, these results suggest that the study of compressive learning can improve our understanding of which benign structural traits – if they are possessed by the data generator – make it easier to learn an effective classifier from a sample.

text: Structure from randomness in halfspace learning with the zero-one loss We prove risk bounds for halfspace learning when the data dimensionality is allowed to be larger than the sample size, using a notion of compressibility by random projection. In particular, we give upper bounds for the empirical risk minimizer learned efficiently from randomly projected data, as well as uniform upper bounds in the full high-dimensional space. Our main findings are the following: i) In both settings, the obtained bounds are able to discover and take advantage of benign geometric structure, which turns out to depend on the cosine similarities between the classifier and points of the input space, and provide a new interpretation of margin distribution type arguments. ii) Furthermore our bounds allow us to draw new connections between several existing successful classification algorithms, and we also demonstrate that our theory is predictive of empirically observed performance in numerical simulations and experiments. iii) Taken together, these results suggest that the study of compressive learning can improve our understanding of which benign structural traits – if they are possessed by the data generator – make it easier to learn an effective classifier from a sample.

year: 2020