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Descriptors:
Teaching Methods; Grade 6; Grade 7; Algebra; Mathematical Concepts; Mathematics; Cognitive Structures; Mathematics Achievement; Middle School Students

Abstract:
Previous research has demonstrated the effectiveness of particular instructional practices that support students' constructions of the partitive unit fraction scheme and measurement concepts for fractions. Another body of research has demonstrated the power of a particular mental operation--the splitting operation--in supporting students' development of advanced fractional knowledge and algebraic reasoning. Steffe (2010) has hypothesized that students construct splitting through the unification of partitioning and iterating operations contained within the partitive unit fraction scheme. We used written assessments of 49 students, across sixth and seventh grades, to test this hypothesis. Our results show that students who have constructed a partitive unit fraction scheme go on to construct splitting within a relatively short period of time. Conversely, students who have not constructed a partitive unit fraction scheme generally do not construct splitting. We discuss these results and their implications for designing instruction and curricula that support students' development of algebraic reasoning. (Contains 10 figures, 5 tables and 1 footnote.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Inferences; Novelty (Stimulus Dimension); Preschool Children; Language Acquisition; Context Effect; Cognitive Structures; Language Processing; Language Research

Abstract:
Does making an inference lead to better learning than being instructed directly? Two experiments evaluated preschoolers' ability to learn new words, comparing their memory for words learned via inference or instruction. On Inference trials, one familiar and one novel object was presented and children were asked to "Point at the [object name (i.e., pizer)]." These trials required the child to infer that the novel label referred to the novel object and not to the familiar object. On Instruction trials, a novel object label directly referred to a novel object (e.g., "This is a glark") and no familiar distracter object was shown. We found that although children looked longer at the novel target on Instruction trials, they showed poorer retention of the newly learned label compared to words learned on Inference trials. Hence, we found that inferential learning was superior to instruction. Relevance for optimal learning contexts and education are discussed. (Contains 4 figures.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Computer Assisted Testing; Computer Software Evaluation; College Students; Comparative Analysis; Concept Formation; Program Effectiveness; Feedback (Response); Novices; Expertise; Formative Evaluation; Cognitive Science; Cognitive Measurement; Problem Solving; Mathematics Instruction; Models; Internet; Computer Assisted Instruction; College Instruction; College Faculty; Cognitive Structures

Abstract:
Cognitive scientists investigate mental models (how humans organize and structure knowledge in their minds) so as to understand human understanding of and interactions with the world. Cognitive and mental model research is concerned with internal conceptual systems that are not easily or directly observable. The goal of this research was to investigate the use of Evaluation of Mental Models (EMM) to assess the mental models of individuals and groups in solving complex problems and to compare novices and experts models as bases for providing feedback to learners. This study tested a qualified web-based assessment tool kit, Highly Interactive Model-based Assessment Tools and Technologies (HIMATT), in an as yet untested domain--mathematics. In this study, university students and their mathematics instructors used two tools in HIMATT, Dynamic Evaluation of Enhanced Problem Solving (DEEP) and Text-Model Inspection Trace of Concepts and Relations (T-MITOCAR). The research questions include: Do novice participants exhibit common patterns of thoughts when they conceptualize complex mathematical problems? Do novices conceptualize complex mathematical problems differently from experts? What differences in DEEP and T-MITOCAR patterns and responses exist according to the measures of HIMATT? Findings suggest that EMM and HIMATT could effectively support formative assessment in a complex mathematical domain. Finally, this study confirms a common assumption of cognitive scientists that the tool being used could affect the tool user's understanding of the problem being solved. In this case, while DEEP and T-MITOCAR led to somewhat different expert models, both tools prove useful in support of formative assessment. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Navigation (Information Systems); Online Searching; Hypermedia; Predictor Variables; Program Effectiveness; Information Retrieval; Cognitive Style; Feedback (Response); Cognitive Structures; Metacognition; Search Strategies; Search Engines; High School Students; Educational Experiments; Computer Software Evaluation; Educational Technology; Computer Software; Use Studies; Comparative Analysis; Visual Aids

Abstract:
It is critical that students learn how to retrieve useful information in hypermedia environments, a task that is often especially difficult when it comes to image retrieval, as little text feedback is given that allows them to reformulate keywords they need to use. This situation may make students feel disorientated while attempting image searching. This study thus designed an image navigation tool, location-based hierarchical navigation support (LHINS), which can dynamically construct a compact WordNet-based hierarchy augmented by location. Using this tool, learners can assimilate new information based on their existing knowledge structure, thus avoiding cognitive overload so as to scaffold their metacognitive skills. Sixty-four high school students were invited to take part in an experiment to test the efficacy of the proposed tool compared to a normal keyword-based search (NKBS) system. The experiment evaluated not only the students' task completion time in the NKBS and LHINS groups, but also their keyword reformulation process, in order to determine the differences in their metacognitive skills. The results revealed that the LHINS group tended to complete the tasks faster and develop better metacognitive skills related to keyword reformulation as compared to the NKBS group. This finding suggests that an image search engine, enhanced by a compact hierarchical navigation tool, can help learners develop better search strategies. When examining how learners with different cognitive styles used the tool, the results showed that learner performance depends on cognitive style, as well as the image retrieval system used, and thus a more detailed investigation of the interaction between the tool and cognitive styles was conducted. Based on these results, several suggestions are derived for designing a more powerful image navigation tool. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Higher Education; Schools of Education; Foundations of Education; Social Environment; Social Cognition; Social Influences; Role; Ideology; Criticism; Reflection; Critical Theory; Social Sciences; Scholarship; Cognitive Structures; Futures (of Society); Teacher Education

Abstract:
This article addresses the unique role performed by social foundations programs in colleges of education and in addressing broader issues facing education today, which fundamentally include the development of interpretive, normative, and critical perspectives in academia. All three perspectives serve to create a scholarly framework within which students and academicians interpret and normatively reflect upon existing educational, political, historical, religious, economic, and social institutions critically. In other words, although many departments in colleges of education tend to fulfill the functional, professional, and institutional requirements essential in preparing future teachers to enter public and private schools, social foundations programs utilize interdisciplinary expertise, primarily from the social sciences and humanities, to explicate extrainstitutional critiques, interpretations, and normative analyses of existing social structures, including schools. Although social foundations programs perform a variety of academic functions, it is this unique reflexive and normatively critical capacity--what critical theorists refer to as ideology critique--that augments social foundations programs and informs present and future scholars in the field. (Contains 3 notes.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Professional Education; Cognitive Structures; Faculty Development; Professional Occupations; Allied Health Occupations; Health Occupations; Cognitive Processes

Abstract:
When appraising the performance of others, assessors must acquire relevant information and process it in a meaningful way in order to translate it effectively into ratings, comments, or judgments about how well the performance meets appropriate standards. Rater-based assessment strategies in health professional education, including scale and faculty development strategies aimed at improving them have generally been implemented with limited consideration of human cognitive and perceptual limitations. However, the extent to which the task assigned to raters aligns with their cognitive and perceptual capacities will determine the extent to which reliance on human judgment threatens assessment quality. It is well recognized in medical decision making that, as the amount of information to be processed increases, judges may engage mental shortcuts through the application of schemas, heuristics, or the adoption of solutions that satisfy rather than optimize the judge's needs. Further, these shortcuts may fundamentally limit/bias the information perceived or processed. Thinking of the challenges inherent in rater-based assessments in an analogous way may yield novel insights regarding the limits of rater-based assessment and may point to greater understanding of ways in which raters can be supported to facilitate sound judgment. This paper presents an initial exploration of various cognitive and perceptual limitations associated with rater-based assessment tasks. We hope to highlight how the inherent cognitive architecture of raters might beneficially be taken into account when designing rater-based assessment protocols. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Electronics; Comprehension; Cognitive Structures; Elementary School Students; Grade 3; Small Group Instruction; Science Instruction; Measurement

Abstract:
Pupils' qualitative understanding of DC-circuit phenomena is reported to be weak. In numerous research reports lists of problems in understanding the functioning of simple DC-circuits have been presented. So-called mental model surveys have uncovered difficulties in different age groups, and in different phases of instruction. In this study, the concept of qualitative understanding, and the content or position of reported mental models of DC-circuit phenomena are discussed. On the grounds of this review, new tools for investigating qualitative understanding and analysing external representations of DC-circuit phenomena are presented. According to this approach, the external representations of DC-circuit phenomena that describe pupils' expressed conceptions of the topic should include both empirical-based models and theoretical explanations. In the empirical part of this study, third-graders (9-year-olds) learning DC-circuit phenomena in a comprehensive school in a small group were scrutinised. The focus of the study is the external representations manifested in the talk of the small group. The study challenges earlier studies, which claim that children exhibit a wide range of qualitative difficulties when learning DC-circuit phenomena. In this study it will be shown that even in the case of abstract subject matter like DC-circuit phenomena, small groups that highlight empirical-based modelling and activate talk can be a fruitful learning environment, where pupils' qualitative understanding really develops. Thus, the study proposes taking a closer look at pupils' external representations concerning DC-circuit phenomena. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Evaluation Methods; Cognitive Structures; Geometry; Associative Learning; Networks; Statistical Analysis; Concept Formation; Teaching Methods; Learning Processes

Abstract:
The present research approached a problem which has a twofold aspect: the concept of angle and the techniques needed to represent how pupils construct that concept in their cognitive structure during their years in school. In order to access the knowledge of the concept of angle, we used the pathfinder associative networks. This technique provided us with the data of the 458 networks of the participating students, using 11 concepts related to the general concept of angle. We used quantitative indicators on the network characteristics: coherence, complexity, and similarity with others. Results showed how the pupil's cognitive structure evolutioned during instruction and what were the most relevant concepts for them. On the basis of the results, we have proposed what we call the "Theory of Nuclear Concepts" which offers a new focus to understanding how the processes of teaching and learning occur. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Cognitive Mapping; Cognitive Structures; Knowledge Base for Teaching; Preservice Teachers; Data Analysis; Statistics; Mathematics Education; Preservice Teacher Education

Abstract:
This report describes a model for mapping cognitive structures related to content knowledge for teaching. The model consists of knowledge elements pertinent to teaching a content domain, the nature of the connections among them, and a means for representing the elements and connections visually. The model is illustrated through empirical data generated as prospective teachers were in the process of developing knowledge for teaching nominal categorical data analysis. During a course focused on the development of statistical knowledge for teaching, the prospective teachers analyzed statistical problems, descriptions of children's statistical thinking, and related classroom scenarios. Their analyses suggested various types of knowledge structures in development. In some cases, they constructed all knowledge elements targeted in the course. In many cases, however, their knowledge structures had missing, incompatible, and/or disconnected elements preventing them from carrying out recommendations for teaching elementary nominal categorical data analysis in an optimal manner. The report contributes to teacher education by drawing attention to prospective teachers' learning needs, and it contributes to research on teachers' cognition by providing a method for modeling their cognitive structures. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Descriptors:
Concept Formation; Interviews; Earth Science; Children; Cognitive Structures; Academic Discourse; Social Influences

Abstract:
Tao, Oliver, and Venville's paper addresses a debate between two hypotheses of children's development of conceptual understandings of the Earth. The authors aim to investigate whether culture influences students' conceptions of the Earth. However, one questionable assumption shared among conception and conceptual change studies is that researchers can identify children's mental models, through their discourse, to explain their conceptions of scientific phenomena. In this commentary, I challenge this assumption by looking closely at various interview data and examining different dimensions of interview discourse about the Earth. Based on my findings, I suggest that instead of seeing science talk as representations of mental models, we look at children's science talk as discursive practices mediated by the immediate social situation and the broader social milieu. Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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