Deaf children's use of cognitive strategies in simple arithmetic problems

Research shows that deaf children have inferior achievement in simple arithmetic compared to their hearing agemates. The reported study investigates whether the reasons for deaf children's poor achievement can be sought in their strategy development. As this is a central issue, the strategies used by deaf children when solving symbolic addition and subtraction problems are identified, classified and compared to findings from earlier research, involving both deaf and hearing children. The effect of Sign Language in strategy invention and use is the main concern in this study. One result from the present study is that structural aspects of Sign Language counting may influence deaf children's thinking in a way that does not lead to a developed conceptual knowledge base, but instead to refined procedural competence. This is a development in simple arithmetic that is compatible with that of less able hearing children. The counting procedures used by the deaf children involve both oral counting and Sign Language counting. Due to the small sample size, and the shortcomings of the research design, the results are more suggestive than conclusive. Thus, further studies are needed in this area.This revised version was published online in September 2005 with corrections to the Cover Date.     

Cognitive and metacognitive aspects in conceptual change by analogy

This study is a qualitative investigation on the teaching-learning by analogy of complex curriculum concepts in natural and relevant environments, such as classrooms, to improve the ecological validity of the research itself. It aimed at exploring whether students' successful use of analogy in learning science was related a) to the level of their understanding of a specific analogy and b) to their metacognitive awareness of how the analogy was to be used and of the changes produced in their own conceptual structures. During the implementation of a biological curriculum unit, sixty 5th graders were engaged in understanding the ways in which the new concepts (concerning the human circulatory system) were similar to a familiar source (the mail delivery system) by detecting all the relations between the two systems and mapping the relevant information from the source to the target. Learners' preexisting mental models have been taken into account in order to examine their conceptual growth and change via the analogy. Qualitative data are presented for the analysis of elicited and spontaneous analogical inferences, based on structural and semantic similarities, as well as of the identification of where the analogy breaks down. Moreover, qualitative data also concern children's metacognitive awareness of the meaning and the purpose of the analogy, and their personal use of the analogy in changing initial conceptions. As hypothesized, results showed a high correlation between level of conceptual understanding of the new science topic, level of understanding of the analogy itself, and the effective use of the analogy in integrating the new information into the pre-existing conceptual structures. Some implications on the use of analogy for conceptual change are considered from an educational standpoint.     

什么是“儿童心理理论”?——评儿童心理理论发展研究中的“概念混淆”

本文围绕什么是“儿童心理理论”的本质,对儿童心理理论发展研究中的一些关键概念进行了剖析,特别是致力于澄清当前研究中普遍存在的“概念混淆”问题。论文表明,明确儿童心理理论发展研究的概念基础,是推进和深化这一研究的方法论前提。     

Representation and Reasoning in Early Numerical Development: Counting, Conservation, and Comparisons between Sets

The first experiment examined the developmental relation between counting and number conservation in the 3–6-year-old age range. Results indicated extended developments in both children's counting and their conservation reasoning, and a close relation between the 2. Only the oldest children gave evidence of conserving, and they also differentiated appropriately between conservation and control problems in their use of counting. The second and third experiments extended the finding that children below 6 years of age do not conserve to conditions in which counting was precluded. These results provide evidence of protracted developments in young children's understanding of relational aspects of number.     

试论儿童的既有认知与理科学习

以对理科学习的不同见解分析为基础,以影响儿童认知学习的内在要因"儿童的既有认知"为视角,深入探讨了对儿童既有认知的认识,以及儿童既有认知对理科学习的影响机制和儿童既有认知对理科学习的启示。     

Fragile knowledge of angle in turtle geometry

This paper describes an investigation into how the use of Logo affects children's basic knowledge of angle. It shows that teachers should not assume that unstructured use of Logo with a minimum of teacher intervention will have a beneficial effect on children's knowledge of angle and how it is measured. It appears to be the case that children make erroneous adjustments to their conceptual knowledge of angle in order to accommodate the results of an acquired procedural interaction with the computer.     

Cognitive play and mathematical learning in computer microworlds

Based on the constructivist principle of active learning, we focus on children's transformation of their cognitive play activity into what we regard as independent mathematical activity. We analyze how, in the process of this transformation, children modify their cognitive play activities. For such a modification to occur, we argue that the cognitive play activity has to involve operations of intelligence which yield situations of mathematical schemes.We present two distinctly different cases. If the first case, the medium of the cognitive play activity was a discrete computer microworld. we illustrate how two children transformed the playful activity of making pluralities into situations of their counting schemes. In the second case, the medium was a continuous microworld. We illustrate two children's transformation of the playful activity of making line segments (sticks) into situations of their counting schemes. We explain one child's transformation as a generalizing assimilation because it was immediate and powerful. The transformation made by the other child was more protracted, and social interaction played a prominent role. We specify several types of accommodations induced by this social interaction, accommodations we see as critical for understanding active mathematics learning. Finally, we illustrate how a playful orientation of independent mathematical activity can be inherited from cognitive play.     

A framework for designing interactive multimedia to scaffold young children's understanding of historical chronology

Young children's understanding of thehistorical past is often characterised by alack of temporal differentiation and a sense oftotal discontinuity with the present. Researchhas suggested that this situation may be causedin part by their formation of inappropriaterepresentations when solving problems ofchronology. To help children construct moreappropriate external representations forparticular tasks and reason more effectivelywith them about chronological concepts, weinvestigated the role that interactivemultimedia might play in scaffoldingteacher-led activities in the classroom. Inthis paper we report on our conceptual designand pedagogical approach to developingeffective dynamic, interactive representationsand activities at the computer interface, aimedat bridging the conceptual gap between concreteexperience and abstract concepts. Evaluationsof the software built using this frameworkshowed that the program was well received bychildren and teachers alike, and that it wasable to facilitate children's understanding of,and ability to reason about, chronology.     

Individual differences in children's developing theory of mind and implications for metacognition

For readers interested in metacognition broadly, this review article introduces some of the recent research and theory concerning children's developing understanding of mental states, focusing particularly on attempts to understand individual differences in development. We contend that the conceptual developments investigated by “theory of mind” researchers constitute a foundation for later metacognition. We examine studies that have focused on individual differences in children's developing understanding of mental states, particularly those investigating its antecedents in early social interactions. Implications from theory-of-mind research for an understanding of metacognition are articulated.     

Beyond rote learning in organic chemistry: the infusion and impact of argumentation in tertiary education

ABSTRACT

There exists bias among students that learning organic chemistry topics requires rote learning. In this paper, we address such bias through an organic chemistry activity designed to promote argumentation. We investigated how pre-service science teachers engage in an argumentation about conformational analysis. Analysis of the outcomes concentrated on (a) pre-service teachers’ understanding of conformations of alkanes (b) the nature of the pre-service teachers’ discourse; (c) the quality of pre-service teachers’ argumentation; and (d) pre-service teachers’ spatial ability. Various measures were used to trace (a) conceptual understanding through the answers in the writing frames, (b) the nature of the pre-service teachers’ discourse using two different codes, (c) the quality of pre-service teachers’ argumentation by counting the number of episodes with higher-level argumentation, and (d) spatial ability by Spatial Ability Test. The results showed that high performing groups had multiple rebuttals in their argumentation and low performing groups had problems in evaluating the credibility of evidence. Furthermore, we observed that spatial abilities play an important role in pre-service teachers’ engagement in argumentation. The findings help understanding of how to further enhance pre-service teachers’ conceptual understanding and engagement in argumentation regarding organic chemistry concepts.     

Numerical competence in young children and in children with mathematics learning disabilities

A longitudinal study was conducted on 82 children to investigate, firstly the numerical competence of young children and the predictive value of (pre)-numerical tests in kindergarten, and, secondly, whether children's knowledge of the numerical system and representation of the number size is related to their computation and logical knowledge and to their counting skills. In an additional cross-sectional study on 30 children with a clinical diagnosis of mathematical learning disability (MLD) of 8,5 years, age- and ability-matched with 2 × 30 children the same parameters of numerical competence were assessed. The longitudinal data showed individual differences in numerosity, as well as the relationship between a delay in arithmetics in grade l and problems on numerosity in kindergarten. In the cross-sectional results some evidence was found for the independence of numerical abilities in MLD-children. About 13% of them had still severe pre-numerical processing deficits (in number sequence production, cardinality skills and logical knowledge) in grade 3. About 67% had severe difficulties in executing calculation procedures and a lack of conceptual knowledge. A feature of 87% of the MLD-children was severe translation deficits, with a significantly worse knowledge of number words compared with the knowledge of Arab numerals. Finally a severe deficit in subitizing was found to be present in 33% of the MLD children. On a group level the processing deficits were linked to understanding numerosity, since the ability-matched younger children and the MLD-children had the same pre-numerical and numerical profile. Implications for the assessment of mathematical disabilities and the value of TEDI-MATH® as an instrument in this process are discussed.     

Une introduction non classique aux algorithmes d'addition et de soustraction

The aim of our study was to analyze a didactical sequence for the teaching of addition and subtraction procedures and algorithms. In the conception of that sequence, we have taken into account diagnostic and repair models for procedural bugs in addition and subtraction algorithms, as well as learning and teaching methods for multi digit additions and subtractions. The didactical sequence included situations involving many of the characteristics associated with procedural bugs; however, when the children encountered those situations they had many conceptual tools to detect their mistakes and correct them, giving that way a meaning to the actions made in addition and subtraction procedures and algorithms. Our teaching activities were submitted to second grade school children (7–8 years old). The didactical interactions and the procedures used by children in problem solving activities were analyzed in order to get a better understanding of the interaction between numbers, numeration and operations knowledge which are involved in the construction of addition and subtraction procedures and algorithms and to relate children's knowledge acquisition to the didactical situations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Elementary School Students’ Mental Computation Proficiencies

Mental computation helps children understand how numbers work, how to make decisions about procedures, and how to create different strategies to solve math problems. Although researchers agree on the importance of mental computation skills, they debate how to help students develop these skills. The present study explored the existing literature in order to identify key points that are related to students’ use of different mental calculation strategies in a variety of settings and their conceptual understanding of those strategies.     

Improving pre-laboratory preparation of first year university chemistry students

This study uses an action research approach to investigate how different modes of pre-laboratory preparation contribute towards a fruitful laboratory experience for first year students on an access programme. We considered the experience to be fruitful if the students successfully acquired procedural understanding, communicative competence and were able to apply the conceptual understanding to make the purpose of the labs meaningful. A group of students was observed by participant observers during 1996. Data was gathered during laboratory sessions and from written pre-laboratory work. These data were analysed and changes were instituted in the running and conceptualization of the laboratory in the subsequent year. A group of students was again observed and data collected. Two important factors emerged from the analysis of the data. One finding was the importance of adequate student preparation for the laboratories, regardless of the mode of preparation employed. Another was that the ability to prepare depended on the conceptual and procedural understanding of the laboratory as a whole. Preparedness is also important if conceptual benefit is to be obtained from the practical experience.     

Revealing conceptual understanding of international business

This study aims to identify an adequate approach for revealing conceptual understanding in higher professional education. Revealing students’ conceptual understanding is an important step towards developing effective curricula, assessment and aligned teaching strategies to enhance conceptual understanding in higher education. Essays and concept maps were used to determine how students’ conceptual understanding of international business can be revealed adequately. To this end, 132 international business students in higher professional education were randomly assigned to four conditions to write essays and to construct concept maps about an international business research topic. The conditions were: essay alone, essay after concept map, concept map alone, and concept map after essay. An assessment rubric was used to assess the breadth and depth of students’ conceptual understanding. Results show essays are the most adequate approach for revealing conceptual understanding of international business. In particular, concept maps revealed fewer facts and less reasoning than essays. Essays written after concept maps were less effective than essays, possibly since students perceived these essays as redundant. Further research is suggested on how educators can foster conceptual understanding.     

Measuring School Readiness: Conceptual and Practical Considerations

Recent interest and investment in early childhood education as a means of promoting children's school readiness has prompted the need for clear definitions of school readiness. Traditionally school readiness has been viewed within a maturationist frame, based on a chronological set-point, which led to the emergence of readiness testing. Following a brief review of this literature, this article provides an overview of the conceptual and practical considerations that must be given to such a definition. Among conceptual concerns are the lack of agreement about the key components of school readiness and theoretical models to connect them. Also of concern is the need to consider multiple purposes of assessment, and the appropriate use of assessments. Practical considerations include the need to incorporate multiple stakeholders' views in a definition, the availability of adequate measurement tools and how resultant data can be used. The article closes with a discussion of possible future directions by laying out a series of assumptions about the nature of school readiness.     

Making meaning from data on school-related gender-based violence by examining discourse and practice: insights from a mixed methodology study in Ghana and Mozambique

Efforts to address school-related gender-based violence (SRGBV) globally are hampered by conceptual and methodological difficulties in capturing meaningful data needed to inform policy and practice. Whilst the emphases of influential studies tend to be on measuring practice of violence, the authors investigate whether they can develop a more meaningful analysis that incorporates attention to both discourse and practice. They do this by examining data collected through a five-year mixed-methods study assessing change in SRGBV in Ghana and Mozambique. The analysis reveals how in the two quite different contexts there were different discursive emphases and in turn practices which were invisible in the SRGBV disclosure data. They identify how both quantitative and qualitative data contribute to understanding changing gender violence in ways that can be illuminating. It is by understanding the interplay between discourse and practice that can really help us understand ‘what works’ to address SRGBV.     

Social and cognitive correlates of children's lying behavior

The relation between children's lie-telling and their social and cognitive development was examined. Children (3–8 years) were told not to peek at a toy. Most children peeked and later lied about peeking. Children's subsequent verbal statements were not always consistent with their initial denial and leaked critical information revealing their deceit. Children's conceptual moral understanding of lies, executive functioning, and theory-of-mind understanding were also assessed. Children's initial false denials were related to their first-order belief understanding and their inhibitory control. Children's ability to maintain their lies was related to their second-order belief understanding. Children's lying was related to their moral evaluations. These findings suggest that social and cognitive factors may play an important role in children's lie-telling abilities.     

Thinking Like a Scientist: Using Vee-Maps to Understand Process and Concepts in Science

It is considered important for students to participate in scientific practices to develop a deeper understanding of scientific ideas. Supporting students, however, in knowing and understanding the natural world in connection with generating and evaluating scientific evidence and explanations is not easy. In addition, writing in science can help students to understand such connections as they communicate what they know and how they know it. Although tools such as vee-maps can scaffold students?? efforts to design investigations, we know less about how these tools support students in connecting scientific ideas with the evidence they are generating, how these connections develop over time, or how writing can be used to encourage such connections. In this study, we explored students?? developing ability to reason scientifically by examining the relationship between students?? understanding of scientific phenomena and their understanding of how to generate and evaluate evidence for their ideas in writing. Three high school classes completed three investigations. One class used vee-mapping each time, one used vee-mapping once, and one did not use vee-mapping. Students?? maps and written reports were rated for understanding of relevant science procedural and conceptual ideas. Comparisons between groups and over time indicate a positive relationship between improved procedural and conceptual understanding. Findings also indicate that improved procedural understanding preceded improved conceptual understanding, and thus, multiple experiences were needed for students to connect evidence and explanation for science phenomena.