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The array representation and primary children’s understanding and reasoning in multiplication 总被引：1，自引：0，他引：1
Patrick Barmby Tony Harries Steve Higgins Jennifer Suggate 《Educational Studies in Mathematics》2009,70(3):217-241
We examine whether the array representation can support children’s understanding and reasoning in multiplication. To begin,
we define what we mean by understanding and reasoning. We adopt a ‘representational-reasoning’ model of understanding, where
understanding is seen as connections being made between mental representations of concepts, with reasoning linking together
the different parts of the understanding. We examine in detail the implications of this model, drawing upon the wider literature
on assessing understanding, multiple representations, self explanations and key developmental understandings. Having also
established theoretically why the array representation might support children’s understanding and reasoning, we describe the
results of a study which looked at children using the array for multiplication calculations. Children worked in pairs on laptop
computers, using Flash Macromedia programs with the array representation to carry out multiplication calculations. In using
this approach, we were able to record all the actions carried out by children on the computer, using a recording program called
Camtasia. The analysis of the obtained audiovisual data identified ways in which the array representation helped children,
and also problems that children had with using the array. Based on these results, implications for using the array in the
classroom are considered. 相似文献
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Louise Starkey 《Teachers and Teaching》2013,19(2):233-244
Beginning teachers are entering the profession with increasing confidence in their ability to use digital technologies which has the potential to change the way teachers of the future make pedagogical decisions. This paper explores how pedagogical reasoning and action might occur in the digital age, comparing Schulman’s 1987 model with the reality for a small sample of digitally able beginning teachers as part of the emerging generation of teachers. The latter were examined through a multiple case study during their first year of teaching as they made decisions about using digital technologies within their teaching practice which gave an insight into pedagogical reasoning and action through the use of open‐ended interviews and observation. The conclusion drawn is that while the pedagogical reasoning and action model remains relevant, it was based on an assumption that teaching involves knowledge being passed from a teacher to their students, which was found to restrict innovation by digitally able teachers. A broader interpretation of knowledge and teaching within this model building on emerging learning theory could help reform practice once again, providing a framework for teachers in the digital age. 相似文献
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Mustafa Sami Topcu 《欧洲师范教育杂志》2011,34(1):99-125
The purpose of the present study was to explore the relationships among Turkish elementary student teachers’ epistemological beliefs and moral reasoning, and to determine which types of epistemological beliefs elementary student teachers exhibit. The findings of the present study demonstrated that epistemological beliefs did not make a unique contribution to moral reasoning and student teachers’ epistemological beliefs developed as more or less independent beliefs. The factor analyses results suggest that multidimensional theory is more appropriate than unidimensional theory in explaining student teachers’ epistemological beliefs. 相似文献
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Bracha Kramarski 《Metacognition and Learning》2008,3(2):83-99
This study investigates algebraic reasoning and self-regulation skills among elementary school teachers who participated in
a professional development program either with IMPROVE metacognitive questioning (PD + Meta) or with no metacognitive guidance (PD). Sixty-four Israeli teachers participated in a 3-year program designed to enhance
mathematical knowledge. Results indicated that the PD + Meta teachers outperformed the PD teachers on various algebraic procedural
and real-life tasks regarding conceptual mathematical explanations. In addition, the PD + Meta group outperformed the PD group
in using self-monitoring and evaluation strategies in algebraic problem solving. We discuss educational and practical implications. 相似文献
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The tensions between environmental protection and economic growth are critical to future well-being, and it is therefore important to understand how young people conceptualize these tensions. The aim of the present study is to explore students’ solutions to the dilemma of economic development and mitigating climate change, with regard to societal responses to the challenge of climate change. The study was conducted in China’s Green Schools. Green School is an international long-term programme with the aim of increasing students’ knowledge of environmental issues, and transferring this knowledge into positive actions to affect the wider community. The data were obtained through semi-structured pre- and post-interviews with 15–16-year-old students in three groups (12 students) from Green Schools in the Beijing area. The results show that students’ discussions focused exclusively on economic growth and social welfare. Students seem to believe that environmental problems are inevitable, nature is a ‘box’ of resources, and economic development is necessary in order to sustain and even improve nature. Therefore, there is no dilemma between economic development and environmental protection. The paper ends with a discussion on research and implications for teaching climate change. 相似文献
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《Journal of moral education》2012,41(2):201-224
The purpose of this study was to examine how moral reasoning develops for 236 students enrolled in either a diversity course or a management course. These courses were compared based on the level of diversity inclusion and type of pedagogy employed in the classroom. We used causal modelling to compare the two types of courses, controlling for the effects of demographic (i.e., race, gender), curricular (i.e., previous course-related diversity learning) and pedagogical (i.e., active learning) covariates. Results showed that students enrolled in the diversity course demonstrated higher levels of moral reasoning than students enrolled in the management course. In addition, results show that previous diversity courses as well as current enrolment in a diversity course contributed to moral reasoning gains. Implications are discussed. 相似文献
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In this paper, we focus on Finnish pre-service elementary teachers’ (N?=?269) and upper secondary students’ (N?=?1,434) understanding of division. In the questionnaire, we used the following non-standard division problem: “We know that 498:6?=?83. How could you conclude from this relationship (without using long-division algorithm) what 491:6?=?? is?” This problem especially measures conceptual understanding, adaptive reasoning, and procedural fluency. Based on the results, we can conclude that division seems not to be fully understood: 45% of the pre-service teachers and 37% of upper secondary students were able to produce complete or mainly correct solutions. The reasoning strategies used by these two groups did not differ very much. We identified four main reasons for problems in understanding this task: (1) staying on the integer level, (2) an inability to handle the remainder, (3) difficulties in understanding the relationships between different operations, and (4) insufficient reasoning strategies. It seems that learners’ reasoning strategies in particular play a central role when teachers try to improve learners’ proficiency. 相似文献
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《Contemporary educational psychology》2002,27(4):499-528
This inquiry uses a Cognitive Developmental Domain theory framework to examine how male and female teachers balance different moral and non-moral components when reasoning about hypothetical school fights. The potential impact of teachers’ attributions towards the gender of the intervening teacher and fighting students, and the location of the fight were examined. This investigation found that male middle school teachers expressed more conflict than female middle school teachers when reasoning about whether the gender of the intervening teacher or the fighting student impacted a teacher’s response. When asked to reason about a hypothetical fight, female middle school teachers were more conflicted than female elementary school teachers, particularly when the location of the fight was manipulated. Theoretical implications are discussed. 相似文献
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In this paper we investigate whether computer programming has an impact on high school student’s reasoning skills, problem solving and self-efficacy in Mathematics. The quasi-experimental design was adopted to implement the study. The sample of the research comprised 66 high school students separated into two groups, the experimental and the control group according to their educational orientation. The research findings indicate that there is a significant difference in the reasoning skills of students that participated in the “programming course” compared to students that did not. Moreover, the self-efficacy indicator of students that participated in the experimental group showed a significant difference from students in the control group. The results however, failed to support the hypothesis that computer programming significantly enhances student’s problem solving skills. 相似文献
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Educational technology research and development - Despite the last 40 years of research showing that computer-aided diagramming tools improve student learning, very little research reveals... 相似文献
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Muammer Çalık Alipaşa Ayas Jazlin V. Ebenezer 《Research in Science & Technological Education》2013,31(3):283-308
The study aims to demonstrate evidence of (a) students’ conceptual change on solution rates; (b) students’ sub‐microscopic explanations of dissolution; and (c) retention of the concepts of solution rates. The sample consists of 44 Grade 9 students (18 boys and 26 girls) drawn purposively from two different classes (22 each) in the city of Trabzon, Turkey. The current study incorporates multiple methods of data collection: items from a solution concept test, clinical interviews and examination of students’ self‐assessment tasks. The results reveal that there is a statistically significant difference between scores in pre‐test and post‐test and between pre‐test and delayed test (p < 0.05). This research indicates that the intervention has improved students’ understanding of the conceptual relationship between solution rates and the sub‐microscopic explanation of dissolution. It has also helped in overcoming students’ alternative conceptions to some extent. However, alternative conceptions have not been eliminated completely. In the light of the results, this current study suggests that a simple model such as the four‐step constructivist teaching (4E) is efficient. 相似文献
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This study explores interactions with diagrams that are involved in geometrical reasoning; more specifically, how students publicly make and justify conjectures through multimodal representations of diagrams. We describe how students interact with diagrams using both gestural and verbal modalities, and examine how such multimodal interactions with diagrams reveal their reasoning. We argue that when limited information is given in a diagram, students make use of gestural and verbal expressions to compensate for those limitations as they engage in making and proving conjectures. The constraints of a diagram, gestures and linguistic systems are semiotic resources that students may use to engage in geometrical reasoning. 相似文献
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Minsu Ha Xin Wei Jian Wang Dan Hou Ross H. Nehm 《International Journal of Science Education》2019,41(5):628-651
The goal of our study was to examine a large (>400), cross-sectional sample of Chinese pre-service biology teachers (PBTs) in order to document their evolution acceptance levels, evolution knowledge, and evolutionary reasoning patterns. This approach was taken in order to better understand the degree to which particular evolutionary reasoning difficulties exist independent of religious worldviews. The sample included (1) 160 PBTs tasked with completing four items from the ACORNS instrument, (2) 320 PBTs who completed the CINS and MATE instruments, and (3) 32 teachers who completed semi-structured clinical interviews using four ACORNS items. Findings from these samples revealed that Chinese PBTs’ knowledge (CINS) and acceptance (MATE) were equivalent with teachers’ scores from other countries, whereas performance on explanation tasks was lower. Scores from the CINS, MATE, and ACORNS did not reveal any significant improvements through the four-year teacher education programme. Although a large body of work has shown the important roles that religious affiliation and religiosity can play in evolutionary understanding and acceptance, our findings demonstrate that many evolutionary reasoning difficulties extend beyond religious factors, and add to a growing body of work showing that religiosity does not adequately account for PBTs’ moderate evolution acceptance. 相似文献
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This study examined 307 elementary school children’s judgements and reasoning about bullying and other repeated transgressions when school rules regulating these transgressions have been removed in hypothetical school situations. As expected, children judged bullying (repeated moral transgressions) as wrong independently of rules and as more wrong than all the other repeated transgressions. They justified their judgement in terms of harm that the actions caused. Moreover, whereas children tended to judge repeated structuring transgressions as wrong independently of rules (but to a lesser degree than when they evaluated bullying) and justified their judgements in terms of the disruptive, obstructive or disturbing effects that the actions caused, they tended to accept repeated etiquette transgressions by arguing that the acts had no negative effects or simply that the rule had been removed. The findings confirm as well as extend previous social-cognitive domain research on children’s socio-moral reasoning. 相似文献
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Valentina Gizzonio Maria Chiara Bazzini Cosima Marsella Pamela Papangelo Giacomo Rizzolatti Maddalena Fabbri-Destro 《Child development》2022,93(1):134-149
Cognitive abilities are essential to children's overall growth; thus, the implementation of early and effective training interventions is a major challenge for developmental psychologists and teachers. This study explores whether an intervention simultaneously operating on fluid reasoning (FR), visuospatial, narrative, and motor abilities could boost these competencies in a group of Italian preschoolers (N = 108, 54 males 54 females, Agemean = 4.04). FR and visuospatial abilities showed training-related increases at the end of the training and 1-year follow-up (moderate effect size). Interestingly, positive correlations with working memory and mathematical abilities were found. Beyond their scientific relevance, the short- and long-term effects provide fundamental indications for designing and implementing educational programs dedicated to preschoolers. 相似文献
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A proof is a connected sequence of assertions that includes a set of accepted statements, forms of reasoning and modes of representing arguments. Assuming reasoning to be central to proving and aiming to develop knowledge about how teacher actions may promote students’ mathematical reasoning, we conduct design research where whole-class mathematical discussions triggered by exploratory tasks play a key role. We take mathematical reasoning as making justified inferences and we consider generalizing and justifying central reasoning processes. Regarding teacher actions, we consider inviting, informing/suggesting, supporting/guiding and challenging actions can be identified in whole-class discussions. This paper presents design principles for an intervention geared to tackle such reasoning processes and focuses on a whole-class discussion on a grade 7 lesson about linear equations and functions. Data analysis concerns teacher actions in relation to design principles and to the sought mathematical reasoning processes. The conclusions highlight teacher actions that lead students to generalize and justify. Generalizations may arise from a central challenging action or from several guiding actions. Regarding justifications, a main challenging action seems to be essential, while follow-up guiding actions may promote a further development of this reasoning process. Thus, this paper provides a set of design principles and a characterization of teacher actions which enhance students’ mathematical reasoning processes such as generalization and justification. 相似文献