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Descriptors:
Bilingual Education; Comparative Analysis; Bilingualism; Language of Instruction; Bilingual Education Programs; Mathematics Education; High School Students; German; French; Problem Solving; Cognitive Ability; Code Switching (Language); Second Language Learning

Abstract:
Bilingual education programs implicitly assume that the acquired knowledge is represented in a language-independent way. This assumption, however, stands in strong contrast to research findings showing that information may be represented in a way closely tied to the specific language of instruction and learning. The present study aims to examine whether and to which extent cognitive costs appear during arithmetic learning when language of instruction and language of retrieving differ. Thirty-nine high school students participating in a bilingual education program underwent a four-day training on multiplication and subtraction problems in one language (German or French), followed by a test session in which they had to solve trained as well as untrained problems in both languages. We found that cognitive costs related to language switching appeared for both arithmetic operations. Implications of our findings are discussed with respect to bilingual education as well as to cognitive mechanisms underlying different arithmetic operations. (Contains 4 figures and 1 table.) 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:
Physical Education; Teaching Methods; Articulation (Education); Preservice Teacher Education; Physical Education Teachers; Grounded Theory; Problem Solving; Constructivism (Learning); Teacher Educators; Preservice Teachers; Pedagogical Content Knowledge; Decision Making; Focus Groups; Interviews; Graduate Students

Abstract:
Examining how teacher education influences preservice teachers' (PSTs) application of content knowledge, decision making when planning for teaching, creation of innovative teaching practices and design of aligned instruction, has significant implications for understanding learning to teach. The purpose of this study was to explore the extent to which the constructivist pedagogies (e.g., interactive community discussions, problem solving, group challenges) employed by teacher educators through the implementation of a rich task (Macdonald, Hunter, & Tinning, 2007) assisted PSTs in their understanding and construction of knowledge about instructional alignment. Data collection employed rich tasks and focus-group interviews with a sample of 31 physical education teacher education (PETE) PSTs enrolled on a one-year Graduate Diploma Physical Education program. Data were analysed inductively (Patton, 1990) using the constant comparative method (Rubin & Rubin, 1995). Results revealed that PSTs varied in their articulation of the various elements of instructional alignment that were captured in the rich task. Through the use of such constructivist strategies as problem solving, group discussions, and critical friends, PSTs understood and valued the process of instructional alignment as they moved from feelings of fear and apprehension to being confident in their own development. Areas of strength and deficiency that were noted in the PSTs' attempts to design instructionally aligned lessons will guide the teacher educators in revising program components and their own practice. (Contains 1 figure and 5 tables.) 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:
Prior Learning; Individual Differences; Novices; Organic Chemistry; Scientific Concepts; Misconceptions; Expertise; STEM Education; Introductory Courses; Visualization; Visual Aids; Adoption (Ideas); Science Instruction; Educational Experiments; Instructional Effectiveness; Teaching Methods; Problem Solving; Learning Processes; Eye Movements

Abstract:
Students are frequently presented with novel visualizations introducing scientific concepts and processes normally unobservable to the naked eye. Despite being unfamiliar, students are expected to understand and employ the visualizations to solve problems. Domain experts exhibit more competency than novices when using complex visualizations, but less is known about how and when learners develop representational fluency. This project examined students' moment-by-moment adoption patterns for scientific visualizations. In a laboratory experiment, introductory-level organic chemistry students viewed familiar ball-and-stick and novel electrostatic potential map representations while solving chemistry problems. Eye movement patterns, verbal explanations, and individual difference analyses showed that students initially relied on familiar representations, particularly for difficult questions. However, as the task unfolded, students with more prior knowledge began relying upon the novel visualizations. These results indicate adoption and fluent use of visualizations is not given; rather, it is a function of prior knowledge and unfolding experience with presented content. (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:
Disabilities; Mathematics Curriculum; Calculators; Mathematics Instruction; Problem Solving; Comparative Analysis; Mathematics Achievement; Grade 6; Grade 7; Standardized Tests; Learning Strategies; Educational Technology

Abstract:
This study assessed if students with and without disabilities used calculators (fourfunction, scientific, or graphing) to solve mathematics assessment problems and whether using calculators improved their performance. Participants were sixth and seventh-grade students educated with either National Science Foundation (NSF)-funded or traditional mathematics curriculum materials. Students solved multiple choice and open-ended problems based on items from the State's released previous assessments. A linear mixed model was conducted for each grade to analyze the factors impacting students' self-reported calculator use. Chi Square tests were also performed on both grade's data to determine the relationship between using a calculator and correctly solving problems. Results suggested only time as a main factor impacting calculator use and students who self-reported using a calculator were more likely to answer questions correctly. The results have implications for practice given the controversy over calculator use by students both with and without disabilities. 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:
College Mathematics; College Students; Cooperative Learning; Problem Solving; Video Technology; Mathematics Education; Teaching Methods; Validity; Mathematical Logic; Symbols (Mathematics); Mathematical Concepts; Learning Strategies

Abstract:
We report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulation. We suggest and illustrate four aspects of situations in which example generation seems to play a positive role in proving. These aspects integrate qualities of students and of problems: "experience of utility of examples in proving," "personal example spaces and technical tools," "formulation of the problem," and "relational necessity." Our analysis led to integrating two theoretical ideas: the alignment of "conceptual insight" and "technical handle" when trying to prove; and "manipulating," "getting-a-sense-of," and "articulating" as phases of work associated with example construction. 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:
Foreign Countries; Mathematics Instruction; Grade 1; Mathematics Teachers; Thinking Skills; Mathematical Logic; Grade 2; Academic Achievement; Mathematics; Interviews; Problem Solving

Abstract:
This paper examines the perceptions and understandings of ten grades 1 and 2 Singapore mathematics teachers as they learned to use clinical interviews (Ginsburg, "Human Development" 52:109-128, 2009) to understand students' mathematical thinking. This study challenged teachers' pedagogical assumptions about what it means to teach for student understanding. Clinical task-based interviews opened a window into students' knowledge, problem-solving and reasoning, and helped teachers reflect on their teaching and assessment of student learning. Teachers also learnt about what it means to establish a culture of thoughtful questioning in the classroom and developed an emerging awareness that this requires a readiness to hear students' ideas and connect informal or invented strategies with classroom mathematics. 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:
Linguistic Theory; Personal Narratives; Rhetoric; Humanities; Educational Philosophy; Educational Theories; Problem Solving

Abstract:
Over the last few decades there has been a strong narrative "turn" within the humanities and social sciences in general and educational studies in particular. Especially Jerome Bruner's theory of narrative as a specific "mode of knowing" was very important for this growing body of work. To understand how the narrative mode works Bruner proposes to study narratives "at their far reach"--as an art form--and on several occasions he refers to the "dramatistic pentad" as an important method for "unpacking" narratives. The pentad proposed by Bruner to study narratives was developed by the American philosopher and rhetorician Kenneth Burke and is embedded in his general linguistic theory of "dramatism". From an educational perspective Bruner's reference to the work of Burke has not been elaborated upon thus far. In this paper we aim to take Bruner's suggestion at hand and explore how his educational theory of narrative as a mode of knowing can indeed be enriched by Kenneth Burke's theory and method of dramatism. We claim that specifically the rhetorical framework that is developed by dramatism offers an important "perspective about perspectives" for education in a context that is increasingly confronted with a plurality of interpretive frameworks. 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 Software; Computer Assisted Instruction; Multimedia Instruction; Content Analysis; Discourse Analysis; Cooperative Learning; Geometry; Problem Solving; Interpersonal Communication; Group Activities; Research Methodology; Coordination

Abstract:
In CSCL research, collaborative activity is conceptualized along various yet intertwined dimensions. When functioning within these multiple dimensions, participants make use of several resources, which can be social or content-related (and sometimes temporal) in nature. It is the effective coordination of these resources that appears to characterize successful collaborative activity. This study proposes a methodological approach for studying coordination of resources when solving geometry problems with dynamic geometry software. The aim is to suggest a methodological lens to capture both the content-related and social discourse within the context of geometry problem solving using dynamic geometry software. As an example, the paper also provides an analysis of a dyad's face-to-face interaction using the suggested framework. 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:
Middle School Students; Interaction; Problem Solving; Mathematics Instruction; Synchronous Communication; Visual Aids; Computer Mediated Communication; Discussion; Computer Assisted Instruction; Multimedia Instruction; Multimedia Materials; Content Analysis; Discourse Analysis; Cooperative Learning; Instructional Effectiveness; Learning Processes

Abstract:
In this paper we examine how two groups of middle school students arrive at shared understandings of and solutions to mathematical problems. Our data consists of logs of student participation in the Virtual Math Teams (VMT) system as they work on math problems. The project supports interaction both through chat and through a virtual whiteboard. We have examined in detail, the sequential work these students do to constitute and specify "the problem" on which they are working in the ways they produce whiteboard objects and text postings. Solutions emerge as students come to understand the problem on which they are working. This understanding is achieved through gradual respecification of the math problem on which they are working. 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:
Factor Analysis; Cognitive Processes; Foreign Countries; Novelty (Stimulus Dimension); Creativity; Young Children; Preschool Teachers; Teacher Attitudes; Problem Solving; Teacher Characteristics; Teacher Education Programs; Preschool Education

Abstract:
The study aimed to uncover the conceptions of creativity among early childhood teachers in Hong Kong. The sample comprised 563 early childhood teachers. Factor analysis supported the multidimensional hypothesis of teachers' conceptions of creativity. Five dimensions were found: novelty, product, problem solving, cognitive processes and personal attributes. Early childhood teachers in Hong Kong ascribed high importance to these dimensions as defining characteristics of creativity, with a person's cognitive processes and personal attributes being ascribed relatively more important while product as relatively less importance. In particular, imagination, multiple perspectives and curiosity were perceived as very important concepts of creativity. Teachers with different teaching backgrounds shared very similar conceptions of creativity. Significant results were found with regard to product only. The findings have implications for early childhood teacher education programmes and professional development in Hong Kong. (Contains 3 tables and 2 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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