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Michael Mitchelmore - One of the best experts on this subject based on the ideXlab platform.
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promoting early Mathematical structural Development through an integrated assessment and pedagogical program
2018Co-Authors: Joanne Mulligan, Michael MitchelmoreAbstract:Early Development of Mathematical patterns and structures has been the focus of a suite of studies with four- to eight-year olds comprising the Australian Pattern and Structure Project over the past decade. Awareness of Mathematical Pattern and Structure (AMPS) has been identified and measured, and found to be indicative of general Mathematical achievement. A revised interview-based assessment, the Pattern and Structure Assessment (PASA) is represented in three forms, validated in a recent study with children in the first two years of formal schooling. The Pattern and Structure Mathematics Awareness Program (PASMAP) is described as two phases of Learning Pathways according to five structural groupings: sequences, structured counting, shape and alignment, equal spacing and partitioning. These groupings were found to be critical to developing coherent Mathematical concepts and relationships. Implications for research in early Mathematical Development are outlined.
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awareness of pattern and structure in early Mathematical Development
Mathematics Education Research Journal, 2009Co-Authors: Joanne Mulligan, Michael MitchelmoreAbstract:Recent educational research has turned increasing attention to the structural Development of young students’ Mathematical thinking. Early algebra, multiplicative reasoning, and spatial structuring are three areas central to this research. There is increasing evidence that an awareness of Mathematical structure is crucial to Mathematical competence among young children. The purpose of this paper is to propose a new construct, Awareness of Mathematical Pattern and Structure (AMPS), which generalises across Mathematical concepts, can be reliably measured, and is correlated with general Mathematical understanding. We provide supporting evidence drawn from a study of 103 Grade 1 students.
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awareness of pattern and structure in early Mathematical Development
Mathematics Education Research Journal, 2009Co-Authors: Joanne Mulligan, Michael MitchelmoreAbstract:Recent educational research has turned increasing attention to the structural Development of young students’ Mathematical thinking. Early algebra, multiplicative reasoning, and spatial structuring are three areas central to this research. There is increasing evidence that an awareness of Mathematical structure is crucial to Mathematical competence among young children. The purpose of this paper is to propose a new construct, Awareness of Mathematical Pattern and Structure (AMPS), which generalises across Mathematical concepts, can be reliably measured, and is correlated with general Mathematical understanding. We provide supporting evidence drawn from a study of 103 Grade 1 students.
Joanne Mulligan - One of the best experts on this subject based on the ideXlab platform.
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supporting early Mathematical Development through a pattern and structure intervention program
Journal on Mathematics Education, 2020Co-Authors: Joanne Mulligan, Gabrielle Oslington, Lyndall EnglishAbstract:An Australian longitudinal study of 319 Kindergartners developed, implemented and evaluated an intervention, the Pattern and Structure Mathematics Awareness Program (PASMAP). It comprised of repetitions and growing patterns, structured counting and grouping, grids and shapes, partitioning, additive and multiplicative structures, measurement and data, and transformations. Each component was implemented, evaluated and refined as a cyclic process in collaboration with co-operating teachers, replacing and extending the regular mathematics program. An innovative pedagogical approach was effective in engaging students in modelling and representing, visualising and generalising, and sustaining their learning. On an interview-based measure of mathematics achievement pre- and post-intervention, there were significant differences found between the intervention and comparison groups at the end of the intervention year (p < 0.026) and highly significant differences found at the follow-up assessment (p < 0.002) ten months later. A descriptive analysis showed students’ progress through five levels of structural Development where most students advanced through one or more levels as they progressed through the program. The upper third of students demonstrated emergent generalisations at the structural and advanced structural level which supported early algebraic thinking. Less-able students also showed impressive growth—half of these students moved from pre-structural to at least emergent level over the duration of the program. Students’ growth in structural Development is exemplified at five points during the intervention through fine-grained analyses of Mathematical representations and explanations. The study demonstrates that Kindergartners are capable of developing Mathematical patterns and structural relationships well beyond curriculum expectations.
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promoting early Mathematical structural Development through an integrated assessment and pedagogical program
2018Co-Authors: Joanne Mulligan, Michael MitchelmoreAbstract:Early Development of Mathematical patterns and structures has been the focus of a suite of studies with four- to eight-year olds comprising the Australian Pattern and Structure Project over the past decade. Awareness of Mathematical Pattern and Structure (AMPS) has been identified and measured, and found to be indicative of general Mathematical achievement. A revised interview-based assessment, the Pattern and Structure Assessment (PASA) is represented in three forms, validated in a recent study with children in the first two years of formal schooling. The Pattern and Structure Mathematics Awareness Program (PASMAP) is described as two phases of Learning Pathways according to five structural groupings: sequences, structured counting, shape and alignment, equal spacing and partitioning. These groupings were found to be critical to developing coherent Mathematical concepts and relationships. Implications for research in early Mathematical Development are outlined.
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awareness of pattern and structure in early Mathematical Development
Mathematics Education Research Journal, 2009Co-Authors: Joanne Mulligan, Michael MitchelmoreAbstract:Recent educational research has turned increasing attention to the structural Development of young students’ Mathematical thinking. Early algebra, multiplicative reasoning, and spatial structuring are three areas central to this research. There is increasing evidence that an awareness of Mathematical structure is crucial to Mathematical competence among young children. The purpose of this paper is to propose a new construct, Awareness of Mathematical Pattern and Structure (AMPS), which generalises across Mathematical concepts, can be reliably measured, and is correlated with general Mathematical understanding. We provide supporting evidence drawn from a study of 103 Grade 1 students.
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awareness of pattern and structure in early Mathematical Development
Mathematics Education Research Journal, 2009Co-Authors: Joanne Mulligan, Michael MitchelmoreAbstract:Recent educational research has turned increasing attention to the structural Development of young students’ Mathematical thinking. Early algebra, multiplicative reasoning, and spatial structuring are three areas central to this research. There is increasing evidence that an awareness of Mathematical structure is crucial to Mathematical competence among young children. The purpose of this paper is to propose a new construct, Awareness of Mathematical Pattern and Structure (AMPS), which generalises across Mathematical concepts, can be reliably measured, and is correlated with general Mathematical understanding. We provide supporting evidence drawn from a study of 103 Grade 1 students.
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the role of structure in children s Development of multiplicative reasoning
2002Co-Authors: Joanne MulliganAbstract:Key features of developing multiplicative structure were analysed from case studies of twenty four students representing extremes in Mathematical ability. Data drawn from a longitudinal study from Years 2 through 5 of schooling indicated that low ability students represented multiplicative situations without structure and Development progressed from the use of pictorial to ikonic representations. Absence of any underlying structures persisted through to the end of Year 5 for half of these students. From the outset in Year 2, high ability students used notational representations with well-developed structures, and dynamic imagery featured strongly in their responses. Multiplicative reasoning is essential in the Development of concepts and processes such as ratio and proportion, area and volume, probability and data analysis. It is clear that failure to develop multiplicative structures in the early years impedes the general Mathematical Development of students into the secondary school, for example, in using algebra, functions and graphs. It appears that difficulties faced by older students can be attributed, at least in part, to the lack of Development of an equal-grouping structure in early concept formation (Mulligan & Mitchelmore, 1997). Often young students' own representations lack any recognisable cohesive structure and they are unable to use their representations flexibly. Using structure is also important in the organization and interpretation of multiplicative situations shown as models, diagrams, tables and graphs. It is still unclear how the Development of underlying structures, whether they are essentially Mathematical or related to spatial organisation, influences Mathematical Development. This paper reports one aspect of a 4-year longitudinal study on children's number concepts. It describes the Development of a theoretical framework for analysing the role of structure in multiplicative reasoning supported by data from twenty-four case studies of students followed from Years 2 through 5 of schooling.
Semail Eric - One of the best experts on this subject based on the ideXlab platform.
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Virtual current vector‐based method for inverter open‐switch and open‐phase fault diagnosis in multiphase permanent magnet synchronous motor drives
HAL CCSD, 2021Co-Authors: Trabelsi Mohamed, Semail EricAbstract:International audienceMultiphase permanent magnet synchronous motor (PMSM) drives. First defined are adequate variables called virtual current vectors. The projection of the zero‐sequence current component on these variables was used to define two simple fault indices. High sensitivity to fault is thus induced but with a good robustness to transient states and variation of machine parameters. The Mathematical Development of the proposed method is provided and supported by experimental tests conducted on two prototypes of multiphase machines in the laboratory: sinusoidal and bi‐harmonic PMSMs. The experimental results confirm the effectiveness and the robustness of the proposed method and its capability to detect the single and multiple open‐switches and open‐phase faults in the electric drive
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Virtual current vector‐based method for inverter open‐switch and open‐phase fault diagnosis in multiphase permanent magnet synchronous motor drives
'Institution of Engineering and Technology (IET)', 2021Co-Authors: Trabelsi Mohamed, Semail EricAbstract:Multiphase permanent magnet synchronous motor (PMSM) drives. First defined are adequate variables called virtual current vectors. The projection of the zero‐sequence current component on these variables was used to define two simple fault indices. High sensitivity to fault is thus induced but with a good robustness to transient states and variation of machine parameters. The Mathematical Development of the proposed method is provided and supported by experimental tests conducted on two prototypes of multiphase machines in the laboratory: sinusoidal and bi‐harmonic PMSMs. The experimental results confirm the effectiveness and the robustness of the proposed method and its capability to detect the single and multiple open‐switches and open‐phase faults in the electric drive.European Regional Development Fund (ERDF); French State; French Region of Hauts-de-Franc
Trabelsi Mohamed - One of the best experts on this subject based on the ideXlab platform.
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Virtual current vector‐based method for inverter open‐switch and open‐phase fault diagnosis in multiphase permanent magnet synchronous motor drives
HAL CCSD, 2021Co-Authors: Trabelsi Mohamed, Semail EricAbstract:International audienceMultiphase permanent magnet synchronous motor (PMSM) drives. First defined are adequate variables called virtual current vectors. The projection of the zero‐sequence current component on these variables was used to define two simple fault indices. High sensitivity to fault is thus induced but with a good robustness to transient states and variation of machine parameters. The Mathematical Development of the proposed method is provided and supported by experimental tests conducted on two prototypes of multiphase machines in the laboratory: sinusoidal and bi‐harmonic PMSMs. The experimental results confirm the effectiveness and the robustness of the proposed method and its capability to detect the single and multiple open‐switches and open‐phase faults in the electric drive
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Virtual current vector‐based method for inverter open‐switch and open‐phase fault diagnosis in multiphase permanent magnet synchronous motor drives
'Institution of Engineering and Technology (IET)', 2021Co-Authors: Trabelsi Mohamed, Semail EricAbstract:Multiphase permanent magnet synchronous motor (PMSM) drives. First defined are adequate variables called virtual current vectors. The projection of the zero‐sequence current component on these variables was used to define two simple fault indices. High sensitivity to fault is thus induced but with a good robustness to transient states and variation of machine parameters. The Mathematical Development of the proposed method is provided and supported by experimental tests conducted on two prototypes of multiphase machines in the laboratory: sinusoidal and bi‐harmonic PMSMs. The experimental results confirm the effectiveness and the robustness of the proposed method and its capability to detect the single and multiple open‐switches and open‐phase faults in the electric drive.European Regional Development Fund (ERDF); French State; French Region of Hauts-de-Franc
Nonie K Lesaux - One of the best experts on this subject based on the ideXlab platform.
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the language of mathematics investigating the ways language counts for children s Mathematical Development
Journal of Experimental Child Psychology, 2013Co-Authors: Rose K Vukovic, Nonie K LesauxAbstract:Abstract This longitudinal study examined how language ability relates to Mathematical Development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling (SEM) framework was used to evaluate the relation between children’s language ability and gains in different domains of Mathematical cognition (i.e., arithmetic, data analysis/probability, algebra, and geometry). The results showed that language ability predicts gains in data analysis/probability and geometry, but not in arithmetic or algebra, after controlling for visual–spatial working memory, reading ability, and sex. The effect of language on gains in Mathematical cognition did not differ between language minority learners and native English speakers. These findings suggest that language influences how children make meaning of mathematics but is not involved in complex arithmetical procedures whether presented with Arabic symbols as in arithmetic or with abstract symbols as in algebraic reasoning. The findings further indicate that early language experiences are important for later Mathematical Development regardless of language background, denoting the need for intensive and targeted language opportunities for language minority and native English learners to develop Mathematical concepts and representations.
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the relationship between linguistic skills and arithmetic knowledge
Learning and Individual Differences, 2013Co-Authors: Rose K Vukovic, Nonie K LesauxAbstract:article i nfo Although language is implicated in children's Mathematical Development, few studies have focused specifically on how different linguistic skills relate to children's Mathematical performance. Building on the model proposed by LeFevre et al. (2010), this study examined how general verbal ability and phonological skills were differentially related to children's arithmetic knowledge. Third grade children (N=287) were assessed on verbal analogies, phonological decoding, symbolic number skill, procedural arithmetic, and arithmetic word problems. Using mediation analyses, the results indicated that verbal analogies were indirectly related to arithmetic knowledge through symbolic number skill, whereas phonological decoding had a direct relationship with arithmetic perfor- mance. These results suggest that general verbal ability influences how children understand and reason with numbers, whereas phonological skills are involved in executing conventional arithmetic problems.
