106 research outputs found
Developing young children's understanding of place-value using multiplication and quotitive division
No full textThis paper focuses on selected findings from a study that explored the use of multiplication and division with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. The focus of instructional tasks was on working with groups of ten to support the understanding of place value. Findings from relevant assessment tasks and children’s work highlighted the importance of encouraging young children to move from unitary (counting by ones) to tens-structured thinking
Supporting the development of number fact knowledge in five- and six-year-olds
No full textThis paper focuses on children’s number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children’s knowledge of number facts, including single digit addition, subtraction, and doubles had improved. However, they did not always apply this knowledge to relevant problem-solving situations. The magnitude of the numbers did not necessarily determine the difficulty level for achieving automaticity of number fact knowledge
Fiji and New Zealand Pasifika students' perceptions of mathematics and their attitudes towards mathematics learning
No full textAbstract
This thesis explores the perceptions and attitudes towards mathematics learning of 36 students from Fiji and 12 Pasifika students living in New Zealand. The students were in Years 7 and 8, included a range of abilities in maths as assessed by their teachers. The New Zealand (NZ) students attended a school that had participated in the Numeracy Development Project (NDP) several years prior to the study. Data was collected using semi-structured and clinical interviews. Seven key questions were the main focus of this study. The students were asked about their views on: working collectively or individually, the importance of knowing and sharing solution strategies with others, the nature of mathematics, people who supported their maths learning, their attitudes towards mathematics, and how good they thought they were at maths. They solved problems involving subtraction, division and proportional problems.
The findings revealed that nearly all of the Fiji students but just over half of the NZ students supported group work. On their views about the value of knowing others' strategies, nearly seven tenths of the Fiji students and just under a half of the NZ students thought that it was important. However, all the children were unanimous in their view that explaining their solution strategies to others was important. The findings also revealed that nearly all the students from both countries thought that mathematics was about numbers and operations. Most of the Fiji children commented that it was also about problem solving, whereas the NZ students mentioned having alternative strategies as what they thought mathematics all about.
The students' views about a teacher's role in helping them learn mathematics greatly differed between the two countries. Slightly more than half of the Fiji students thought that the teacher's role was to show them strategies. The Fiji students also described their teachers as someone who gave them notes to copy and provided exercises from the textbook. In contrast the NZ students mentioned their teacher as someone who helped their mathematics learning by sharing clues, giving tasks that challenged them and grouped them by ability before helping them. The responses of all the students revealed that there was great support from friends, parents and relatives towards their mathematics learning. The students also rated their feelings towards mathematics on a three-point rating scale with happy, neutral and sad faces. Half of the students from both countries chose the happy face with the other half choosing the neutral face. None of them chose the sad face as matching how they felt about maths most of the time.
The students also assessed themselves on how good they were at maths. The majority of the students from both countries rated themselves as good and none of them chose the box showing very poor . The students were asked to do some tasks on subtraction, division and proportional problems. There was a major contrast between the two countries on how they worked out their answers. The Fiji students' responses showed their fluency with standard written algorithms and a high level of procedural knowledge. The NZ students on the other hand hardly used algorithms. Instead their responses showed the use of mental strategies for solving tasks ranging from stage 2, (counting from one on materials) to stage 7, (advanced multiplicative part-whole) on the NDP Number Framework
Exploring the transition into Year 3 of Year 2 students who use counting on to solve mathematics problems
No full textThis research project examined how five Year 2 students, at stage 4 on the Number Framework (counting on), experienced mathematics as they transitioned into a Year 3 and 4 classroom. It investigated the support structures put in place to shift students from counting on to part-whole thinking, as part of the Numeracy Development Projects (NDP) approach to teaching mathematics. An additional transition of two teachers into Year 3 and 4 (one up from Year 2 and one down from Year 5 and 6) provided evidence of teacher transition experiences when shifting teaching levels. The setting, role of the teacher, and external influences were examined.
This research was a qualitative investigation framed within a case study approach. The main source of data was classroom observations and semi-structured interviews. The teachers’ interviews focused on their approach to teaching and learning, attitude, student ability, assessment, and knowledge of the mathematics curriculum from Level 1 to Level 2. The combination of classroom observation and student interviews demonstrated the current level students were operating at and any signs of shift in their knowledge, as well as attitude towards mathematical learning.
The thesis illustrates how classroom practices and teaching approaches encouraged students to count on instead of shifting into part-whole thinking. The findings highlight possible barriers, student experience, the importance of teacher knowledge and understanding, and the impact of teaching practices that support and undermine the shift. The findings also show that teachers are still following the NDP material very closely, without a full understanding of the pedagogy of number knowledge which can bridge Level 1 to Level 2 of the New Zealand Curriculum.
The findings also indicate that the NDP teaching model is not being fully incorporated into classroom teaching, with a decrease of manipulatives used over the transition, a limited use of visualisation through diagrams and pictures, and students experiencing abstract representations without a full understanding of their meaning. The findings also show that the current reform in mathematics is only operating at a surface level. Teacher practices reflected an instrumental, procedurally-based approach to the teaching and learning of mathematics.
The evidence contained within this thesis points to the link between knowledge and strategy not being made explicit, with limited experiences of exploring relationships between numbers and quantity. It considers a critical aspect of student understanding is to develop a full understanding of number relationships through the concept of subitising, part-whole relationships, and more-and-less relationships. Continuing Professional Learning and Development is needed for teachers to develop a deeper understanding of these relationships and how they support student shift from ‘counting on’ to part-whole thinking
Students' perspectives on the nature of mathematics
No full textThis paper reports on one small component of a much larger study that explored the perspectives of students towards mathematics learning. Students were asked “What do you think maths is all about?” Some students responded in terms of mathematical content. Others commented on learning in general, or on problem-solving in particular. Some students talked about the usefulness of mathematics for everyday life. An overwhelming number of students answered the question by talking about the importance of mathematics for the future
The mathematical content knowledge and attitudes of New Zealand pre-service primary teachers
No full textThis paper presents data on the mathematical content knowledge and attitudes of pre-service primary teacher education students. The assessment consisted of nine tasks, including 2-digit computations and proportional reasoning. Students rated their liking for mathematics at three time points: primary, secondary, .and when assessed. Fewer than half the students liked mathematics, currently. Those with positive attitudes tended to perform well on mathematics tasks, but some low scorers were positive and some high' scorers were negative about mathematics. Most students used algorithmic procedures to solve problems and several consistent misconceptions were identified. Performance was noticeably poor on adding common fractions and converting fractions to percentages using knowledge of common factors. The implications of these findings for Initial Teacher Education (ITE) providers are presented
Atlantic Guardian, vol. 05, no. 03 (June 1948)
No full textThe challenge of education / Fred R. Emerson -- Something new has been added / Jessie B. Mifflin -- Newspapers of Newfoundland : The Twillingate Sun / John C. Loveridge -- Newfoundland Teachers' Association / S. J. Hefferton -- "A savings account for every child" / James Murdock -- He helped build a fleet / Richard A. White -- Document found in a bottle / Joel Nichols -- The Gosling Memorial Library -- Calling all motorists! -- Guardian angles -- Regional libraries -- Nfld. clubs abroad -- Stamps of Nfld.A popular magazine covering Newfoundland news and human interest stories with features such as Newfoundlanders Abroad, the Baby of the Month and community profiles, as well as poetry and short stories. Heavily illustrated with photographs. -- "Atlantic Guardian's platform: to make Newfoundland better known at home and abroad; to promote trade and travel in the Island; to encourage development of the Island's natural resources; to foster good relations between Newfoundland and her neighbors" (on all title pages after vol. 1, no. 4).Published monthly 1945-57, thereafter absorbed by the Atlantic Advocate (1952-92); suspended publication: October 1952-May 1953. Missing issues: vol. 14, nos. 7-8. -- An index to vols. 1-10 by author and/or article type is in vol. 11, no. 1 (January-February 1954), p. 33-48
A Critique of Topos Logic in Measurement-Based Quantum Computation
No full textTopos theory and quantum mechanics are both known for having a logic that is different from ordinary logic. With this in mind, much work has been done on unifying these two fields. Loveridge, Dridi and Raussendorf apply this unification to measurement-based quantum computation [14], revealing links between computation, contextuality and the failure of the law of excluded middle in the topoi associated with each computation. We review their work, fill in gaps, follow their research suggestion and have some criticism. Our main original finding is a formula, in the formal language of the topos associated with a computation, that expresses that the computation is deterministic.Applied Mathematic
Observed cloud morphology and inferred microphysics over the South Pacific from MISR and MODIS measurements of shortwave reflectivity
No full textA rapid study of boundary layer clouds over the Southern Ocean compared to their Northern Hemisphere counterparts reveals statistical differences in the probability of glaciation at the same cloud-top temperature, and in the respective plane parallel albedo biases. The preliminary study indicates that a more comprehensive study of these features is merited, with a view to improving the cloud parameterizations currently used in climate models.VoR - Version of Recor
Embedding the Multinational: Bridging Internal and External Networks in Transitional Institutional Contexts
No full textThe social embeddedness of the guest multinational enterprise (MNE) is presented as a multi-layered series of interfaces between expatriate managers and agencies and actors within the host state. In contrast to the unilinear and intentional development of strategic relations between the parties described in much of the literature on international business, the author seeks to demonstrate that relations are segmented by a diversity of micro- and macro-social and political considerations. Not least among these are differences of life chances among ethnic groups in the host country and by careers within the guest MNE. The study that provides the basis for these observations is presented as a ‘high-context’ deep description of roles and actors within the head offices of 20 European MNEs and within their affiliates located in Brunei Darassalam, Singapore, Malaysia and Thailand
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