1,720,996 research outputs found
Teachers enhancing numeracy
No full textThe authors present findings on a project that focused on identifying elements in the learning environment that promote numeracy outcomes. The project included both quantitative and qualitative components. Teacher-academic collaborations impacted positively on almost all the project teachers in terms of teacher mathematics knowledge, mathematics teaching knowledge and classroom engagement. These factors, in turn enhanced teachers' classroom practices and student numeracy outcome
Year 6 students' cognitive structures and mechanisms for processing tenths and hundredths
No full textThis study explored the cognitive functioning of Year 6 students in the domain of decimal-number numeration, particularly with the intention of: (a) comparing the knowledge structure of proficient and semiproficient students with respect to tenths and hundredths knowledge; (b) constructing frameworks and models which explain the structural knowledge differences of proficient and semiproficient students with respect to tenths and hundredths; and (c) drawing implications for instruction. Forty- five students (12 high proficient, 12 semiproficient, 8 medium proficient, 8 medium semiproficient, 5 low proficient) were identified for semistructured individual interviews (Burns, 1994). The interview was informed by the numeration model and, as a consequence, incorporated tasks relating to position and order, to multiplicativity, and to the unitisation and reunitisation of decimal fractions. The interview results revealed that: (a) knowledge of position and order differentiated between high- performing (high proficient, high semiproficient, medium proficient) and low-performing (medium semiproficient, low proficient) students; and (b) availability and accessibility of multiplicativity tasks were the major factors which differentiated performance amongst the high-performing students. As a result of analyses of students' interview responses and the knowledge subcomponents of the decimal-number taxonomy, structural models that represented the cognitions and connections held by the composite performance categories for position/order, multiplicativity, and unitisation/reunitisation were constructed. From a comparison of the structural models, cumulative models that combined findings for each performance category across position/ order, multiplicativity, and unitisation/reunitisation were constructed. The cumulative models represented the two domains involved in decimal-number numeration understanding, namely, whole numbers and fractions, with multiplicativity represented as the structural knowledge that unifies and integrates the structural knowledge of position/order and unitisation/reunitisation. The models were used to draw implications for instruction in decimal numbers and mathematics generally
Getting to know probability: A descriptive study of the cognitive processes employed by Year 12 students engaged on probability tasks
No full textPresented to the School of Mathematics, Science and Technology Education, Queensland University of Technology. Thesis (M. Ed.-Maths)--Queensland University of Technology, Brisbane, 1992
Spreadsheets and upper primary mathematics
No full textOne area of research into how students come to understand some aspects of mathematics has focused on the construction of different knowledge types and their connections. Structural knowledge (that is, connected schema) should be the endpoint of formal instruction. This paper provides some spreadsheet activities designed to promote the various types of knowledge
Developing mathematics understanding through cognitive diagnostic assessment tasks
No full textAssessment is undertaken for a variety of reasons but none so important as when it is undertaken to inform the teaching-learning process with respect to determining the extent of individual student knowledge and the effectiveness of teaching. This book contains Cognitive Diagnostic Assessment Tasks (CDAT) to elicit students' understanding of the important mathematical concepts and processes that are required for processing whole numbers, fractions and probability effectively
Place value, multiplicativity, reunitizing and\ud effective classroom teaching of decimal numeration\ud
No full textStudent understanding of decimal number is poor (e.g., Baturo, 1998; Behr, Harel, Post & Lesh, 1992). This paper reports on a study which set out to determine the cognitive complexities inherent in decimal-number numeration and what teaching experiences need to be provided in order to facilitate an understanding of decimal-number numeration. The study gave rise to a theoretical model which incorporated three levels of knowledge. Interview tasks were developed from the model to probe 45 students’ understanding of these levels, and intervention episodes undertaken to help students construct the baseline knowledge of position and order (Level 1 knowledge) and an understanding of multiplicative structure (Level 3 knowledge). This paper describes the two interventions and reports on the results which suggest that helping students construct appropriate mental models is an efficient and effective teaching strategy
Construction of a numeration model: A theoretical analysis
No full textThis paper analyses the major concepts and processes within decimal-number numeration in terms of the cognitions inherent in their structure to determine how they are related to each other, how they are different and, if possible, to determine which are more difficult conceptually. It synthesises this analysis into a cognitive model that provides a framework for decimal-number knowledge
Integrating Computers into the Classroom Through Virtual Mathematics
No full textIn Australia, most school classrooms have Microsoft Office software and a few computers but there is often little integration of these computers and the software into classroom teaching. The author has developed a way in which teachers can use the PowerPoint component of Office to introduce mathematics ideas by constructing teacher-made activities in which students can use mouse movements to manipulate virtual copies of physical materials that are commonly used in Australian classrooms to introduce those ideas.\ud
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Virtual mathematics activities are very similar to the activities with the physical materials that they replicate. As a consequence, technophobic teachers (teachers who are afraid to use computers in their classrooms) are willing to risk computers to use the virtual materials with their students. Virtual materials are more abstract than concrete matterials but less abstract than pictorial representations and therefore are able to help bridge the gap from concrete to pictorial representations and, then, to abstraction (the gap between action and expression that Noss, Healy & Hoyles, 1997, argue is difficult to bridge). Therefore virtual mathematics activities should be generally effective with students making the experience with the computers positive and encouraging teachers to try other uses of computers.\ud
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This presentation will describe the virtual mathematics approach and discuss its effectiveness in Queensland classrooms (particularly low socio-economic classrooms). In Queensland, student manipulation of virtual materials is a very different use of computers in mathematics education than that commonly seen in schools. Initial findings from trials in classrooms are indicating that virtual materials do provide a bridge from the acquisition of computer skills to the implementation of classroom activities, and that teachers do find virtual activities easy to develop and effective in promoting positive learning outcomes (Baturo & Cooper, 2001). It also appears that the comforting similarities between virtual and physical materials enables teachers to recognise opportunities for translating their traditional teaching activities to computer activities. Teachers have been impressed by the excitement, prolonged engagement, and natural collaboration provoked by virtual activities.\ud
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Virtual mathematics activities can be "debugged, reconstructed, transformed, separated and combined together" (Healey & Hoyles, 1999, p. 59) and saved for later reuse for the same or other students. They enable students' manipulations to be saved and stored for later assessment, providing teachers with unique knowledge of all students' proficiency with all components of the manipulations. They are multi-representational (providing visuals, language and symbols) and dynamic (showing transformations and changes as well as relationships). They use the visual, symbolic and operational power of technology and provide another pedagogical and didactical tool for teachers' use of technology
Construction of multiplicative abstract schema for decimal-number numeration
No full textThis paper reports on an intervention study planned to help Year 6 students construct the multiplicative structure underlying decimal-number numeration. Three types of intervention were designed from a numeration model developed from a large study of 173 Year 6 students’ decimal-number knowledge. The study found that students could acquire multiplicative structure as an abstract schema if instruction took account of prior knowledge as informed by the model
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