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11.
Marilena Chrysostomou Demetra Pitta-Pantazi Chara Tsingi Eleni Cleanthous Constantinos Christou 《Educational Studies in Mathematics》2013,83(2):205-223
Recently, a new cognitive style approach was introduced, which refers to two types of visualizers. This approach is based on neuropsychological evidence and neuroimaging results, which suggest the existence of two distinct imagery subsystems, the object and the spatial imagery subsystems. The goal of the study was twofold: first to examine a possible relationship between this new cognitive style approach and achievement in number sense and algebraic reasoning tasks, and second to explore a possible relationship between the strategies used in solving the aforementioned tasks and cognitive styles. A mathematical test on number sense and algebraic reasoning and the self-report Object–Spatial Imagery and Verbal cognitive style questionnaire were administrated to 83 prospective school teachers (PSTs). The results indicated that spatial imagery, in contrast to the object imagery and verbal cognitive styles, is related to achievement in number sense and algebraic reasoning. In addition to this, the results revealed that the higher the PSTs’ tendency towards spatial imagery cognitive style, the more conceptual and flexible strategies they employ in algebraic reasoning and number sense tasks. 相似文献
12.
Demetra?Pitta-PantaziEmail author Constantinos?Christou 《Journal of Mathematics Teacher Education》2011,14(2):149-169
Lamon (Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teachers,
2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005) claimed that the development of proportional reasoning relies on various kinds of understanding and thinking processes. The
critical components suggested were individuals’ understanding of the rational number subconstructs, unitizing, quantities
and covariance, relative thinking, measurement and “reasoning up and down”. In this study, we empirically tested a theoretical
model based on the one suggested by Lamon (Teaching fractions and ratios for understanding. Essential content knowledge and
instructional strategies for teachers, 2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005), as well as an extended model which included an additional component of solving missing value proportional problems. Data
were collected from 238 prospective kindergarten teachers. To a great extent, the data provided support for the extended model.
These findings allow us to make some first speculations regarding the knowledge that prospective kindergarten teachers possess
in regard to proportional reasoning and the types of processes that might be emphasized during their education. 相似文献
13.
Eddie Gray Marcia Pinto Demetra Pitta David Tall 《Educational Studies in Mathematics》1999,38(1-3):111-133
This paper begins by considering the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum. We base our theoretical development on fundamental cognitive activities, namely, perception of the world, action upon it and reflection on both perception and action. We see an emphasis on one or more of these activities leading not only to different kinds of mathematics, but also to a spectrum of success and failure depending on the nature of the focus in the individual activity. For instance, geometry builds from the fundamental perception of figures and their shape, supported by action and reflection to move from practical measurement to theoretical deduction and euclidean proof. Arithmetic, on the other hand, initially focuses on the action of counting and later changes focus to the use of symbols for both the process of counting and the concept of number. The evidence that we draw together from a number of studies on children's arithmetic shows a divergence in performance. The less successful seem to focus more on perceptions of their physical activities than on the flexible use of symbol as process and concept appropriate for a conceptual development in arithmetic and algebra. Advanced mathematical thinking introduces a new feature in which concept definitions are formulated and formal concepts are constructed by deduction. We show how students cope with the transition to advanced mathematical thinking in different ways leading once more to a diverging spectrum of success.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
14.
Charalambos Y. Charalambous Demetra Pitta-Pantazi 《Educational Studies in Mathematics》2007,64(3):293-316
Teaching and learning fractions has traditionally been one of the most problematic areas in primary school mathematics. Several
studies have suggested that one of the main factors contributing to this complexity is that fractions comprise a multifaceted
notion encompassing five interrelated subconstructs (i.e., part-whole, ratio, operator, quotient, and measure). Kieren was
the first to establish that the concept of fractions is not a single construct, but consists of several interrelated subconstructs.
Later on, in the early 1980s, Behr et al. built on Kieren’s conceptualization and suggested a theoretical model linking the
five subconstructs of fractions to the operations of fractions, fraction equivalence, and problem solving. In the present
study we used this theoretical model as a reference point to investigate students’ constructions of the different subconstructs
of fractions. In particular, using structural equation modeling techniques to analyze data of 646 fifth and sixth graders’
performance on fractions, we examined the associations among the different subconstructs of fractions as well as the extent
to which these subconstructs explain students’ performance on fraction operations and fraction equivalence. To a great extent,
the data provided support to the associations included in the model, although, they also suggested some additional associations
between the notions of the model. We discuss these findings taking into consideration the context in which the study was conducted
and we provide implications for the teaching of fractions and suggestions for further research. 相似文献
15.
The development of two observational tools for assessing metacognition and self-regulated learning in young children 总被引：1，自引：1，他引：0
David Whitebread Penny Coltman Deborah Pino Pasternak Claire Sangster Valeska Grau Sue Bingham Qais Almeqdad Demetra Demetriou 《Metacognition and Learning》2009,4(1):63-85
This paper reports on observational approaches developed within a UK study to the identification and assessment of metacognition
and self-regulation in young children in the 3–5 year age range. It is argued that the development of observational tools,
although containing methodological difficulties, allows us to make more valid assessments of children’s metacognitive and
self-regulatory abilities in this age group. The analysis of 582 metacognitive or self-regulatory videotaped ‘events’ is described,
including the development of a coding framework identifying verbal and non-verbal indicators. The construction of an observational
instrument, the Children’s Independent Learning Development (CHILD 3–5) checklist, is also reported together with evidence
of the reliability with which it can be used by classroom teachers and early indications of its external validity as a measure
of metacognition and self-regulation in young children. Given the educational significance of children’s development of metacognitive
and self-regulatory skills, it is argued that the development of such an instrument is potentially highly beneficial. The
establishment of the metacognitive and self-regulatory capabilities of young children by means of the kinds of observational
tools developed within this study also has clear and significant implications for models and theories of metacognition and
self-regulation. The paper concludes with a discussion of these implications.
相似文献
| David WhitebreadEmail: |
16.
There is a growing consensus that algebra is an important aspect of mathematics teaching and learning and several abilities are required in order students to have successful performance in algebra. The present study uses insights from the domain of psychology to enrich what is currently known in the domain of mathematics education about the relationship of algebraic thinking with abilities involved in fundamental cognitive processes. In total, 190 students between the ages of 13–17 years old were tested through two tests. The first test addressed four types of cognitive systems which are responsible for the representation and processing of different types of relations in the environment: the spatial-imaginal, the causal-experimental, the qualitative-analytic and the verbal-propositional. The second test addressed algebraic thinking. The results support the key role of the four types of cognitive processes in students’ algebraic thinking. The results also suggest that abilities involved in the four types of cognitive processes predict algebraic thinking abilities, irrespective of the age of the students. 相似文献