title: The number of (0,1) - Matrices with fixed row and column sums

authors: Pule, Solomone Tahamano

abstract: Let R and S be non-negative and non-increasing vectors of order m and n respectively. We consider the set A(R, S) of all m x n matrices with entries restricted to {0, 1}. We give an alternative proof of the Gale-Ryser theorem, which determines when A(R, S) is non-empty. We show conditions for R and S so that ∣A(R, S) ∣ ∈ {1, n!}. We also examine the case where ∣A(R, S) ∣ = 2 and describe the structure of those matrices. We show that for each positive integer k, there is a possible choice of R and S so that ∣A(R, S) ∣ = k. Furthermore, we explore gm,n(x; y), the generating function for the cardinality ∣A(R, S) ∣ of all possible combinations of R and S.

text: The number of (0,1) - Matrices with fixed row and column sums Let R and S be non-negative and non-increasing vectors of order m and n respectively. We consider the set A(R, S) of all m x n matrices with entries restricted to {0, 1}. We give an alternative proof of the Gale-Ryser theorem, which determines when A(R, S) is non-empty. We show conditions for R and S so that ∣A(R, S) ∣ ∈ {1, n!}. We also examine the case where ∣A(R, S) ∣ = 2 and describe the structure of those matrices. We show that for each positive integer k, there is a possible choice of R and S so that ∣A(R, S) ∣ = k. Furthermore, we explore gm,n(x; y), the generating function for the cardinality ∣A(R, S) ∣ of all possible combinations of R and S.

year: 2013

title: Introducing WebQuests in mathematics: A study of Qatari students’ reactions and emotions

authors: Murphy, Carol

subjects: collaborative inquiry

abstract: There is a need to investigate didactic strategies that can enhance engagement in science and mathematics education. This paper reports on the introduction of WebQuests, as part of collaborative inquiry, to enhance students’ engagement in their mathematics lessons in Qatar. We present interview data gathered from eight student focus groups (grades 5 to 9) before and after the introduction of WebQuest lessons. Constant comparative analysis was used to examine students’ reactions to using WebQuests in developing student-directed learning and collaboration in relation to support for learning. The analysis identified prospective reactions that were often confirmed retrospectively following the WebQuest lessons. These reactions were further analysed as external expressions of affect encoded by trait-like emotions that were similar to Goldin et al.’s (2011) notion of engagement structures. We suggest that the confirmation of reactions and emotions was influenced by students’ levels of tolerance for ambiguity as a common element across engagement structures.

text: Introducing WebQuests in mathematics: A study of Qatari students’ reactions and emotions There is a need to investigate didactic strategies that can enhance engagement in science and mathematics education. This paper reports on the introduction of WebQuests, as part of collaborative inquiry, to enhance students’ engagement in their mathematics lessons in Qatar. We present interview data gathered from eight student focus groups (grades 5 to 9) before and after the introduction of WebQuest lessons. Constant comparative analysis was used to examine students’ reactions to using WebQuests in developing student-directed learning and collaboration in relation to support for learning. The analysis identified prospective reactions that were often confirmed retrospectively following the WebQuest lessons. These reactions were further analysed as external expressions of affect encoded by trait-like emotions that were similar to Goldin et al.’s (2011) notion of engagement structures. We suggest that the confirmation of reactions and emotions was influenced by students’ levels of tolerance for ambiguity as a common element across engagement structures.

year: 2020

title: E kore koe e ngaro e tōku reo rangatira

authors: Puke, Te Manawanui

subjects: Reo Māori

abstract: Ka whakapeto ngoi ahau ki te wānanga i ngā tini āhuatanga e kōhuru nei, he patu kino nei, e panoni haere nei, e whakamate nei i tōku reo rangatira! E kaha tōmina nei kia kore rawa ai ia e ngaro. Nā reira, ka tīkina te matū o tēnei kaupapa, ka takitaki haere ai mei kore noa e tūpono ka hīnātore mai he māramatanga, he ihumaneatanga i ēnei kōrero āku.

text: E kore koe e ngaro e tōku reo rangatira Ka whakapeto ngoi ahau ki te wānanga i ngā tini āhuatanga e kōhuru nei, he patu kino nei, e panoni haere nei, e whakamate nei i tōku reo rangatira! E kaha tōmina nei kia kore rawa ai ia e ngaro. Nā reira, ka tīkina te matū o tēnei kaupapa, ka takitaki haere ai mei kore noa e tūpono ka hīnātore mai he māramatanga, he ihumaneatanga i ēnei kōrero āku.

year: 2016