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Descriptors:
Secondary School Mathematics; Geometry; Secondary School Students; Interaction; Problem Solving; Virtual Classrooms; Teamwork; Protocol Analysis; Sequential Learning; Sequential Approach; Pattern Recognition; Object Manipulation; Construction (Process); Reflection; Visual Aids

Abstract:
We analyze the interaction of 3 students working on mathematics problems over several days in a virtual math team. Our analysis traces out how successful collaboration in a later session is contingent upon the work of prior sessions and shows how the development of representational practices is an important aspect of these participants' problem solving. We trace the formation, transformation, and refinement of 2 problem-solving practices (i.e., problem decomposition and inscribe first solve second) and 2 representational practices (i.e., modulate perspective and visualize decomposition). The analysis shows how inscriptions become representations for the group through a historical trajectory of negotiation: Learners appropriate inscriptional resources over time as they develop their representational competencies. We show how analysis of the contingently relevant situation may reach into temporally prior episodes in which interaction relevant resources and practices are constructed. (Contains 4 tables and 9 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:
Animation; Computer Assisted Instruction; Prior Learning; Learner Controlled Instruction; Novices; Chinese; Short Term Memory; Pacing; Science Instruction; Cognitive Processes; Difficulty Level; Learning Strategies; Self Management; Educational Experiments; Retention (Psychology); Educational Technology; Instructional Design; Instructional Effectiveness; Comparative Analysis; Pretests Posttests; Sequential Learning; Ideography

Abstract:
Learning with instructional animations may overstretch limited working memory resources due to intense processing demands associated with transient information. The authors investigated whether explicit instructional advice coupled with a task-specific learner control mechanism (such as a timeline scrollbar) could facilitate the successful self-management of transient information. The effectiveness of a timeline scrollbar that allowed self-pacing and self-sequencing of animations was compared with computer-controlled animations. Experiment 1 demonstrated that a timeline scrollbar (with instructional advice on its strategic use) enhanced the retention of stroke sequences in writing Chinese characters. In Experiment 2, a timeline scrollbar was used in an integrated set of narrated animations dealing with complex scientific information. Retention and comprehension post-tests indicated that although a scrollbar accompanied by instructional advice in its use assisted novice learners, no such effect was found with participants who possessed higher levels of prior knowledge. The findings have implications for the formulation of criteria for the effective incorporation of learner control into the design of instructional animations. 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:
Performance; College Students; Short Term Memory; Sequential Learning; Role; Task Analysis

Abstract:
When learning highly organized sequential patterns of information, humans and nonhuman animals learn rules regarding the hierarchical structures of these sequences. In three experiments, we explored the role of working memory in college students' sequential pattern learning and performance in a computerized task involving a sequential multiple-choice paradigm. In Experiment 1, we explored whether working memory was necessary to abstract the structure of sequential patterns both with and without violations of pattern structure. In Experiment 2, we investigated whether working memory was necessary for accurate pattern performance after patterns with and without violations to pattern structure were learned well. Results indicated working memory was necessary for abstracting the rule describing overall pattern structure for patterns both with and without a violation of pattern structure. Further, once the pattern was well learned, working memory was required only for accurate performance of patterns containing a violation of pattern structure. In Experiment 3, we evaluated whether occupying working memory impaired participants' ability to track their location within a sequence while performing the sequence or impaired their ability to abstract the rule governing the sequence. Results suggested that occupying working memory impaired participants' ability to learn the rule describing the sequence. (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:
Chemistry; Foreign Countries; Secondary School Science; High Schools; Visualization; Scientific Concepts; Teaching Methods; Conventional Instruction; Sequential Learning; Science Achievement; Gender Differences; Correlation; Concept Formation; Hypothesis Testing

Abstract:
Five Canadian high school Chemistry classes in one school, taught by three different teachers, studied the concepts of dynamic chemical equilibria and Le Chatelier's Principle. Some students received traditional teacher-led explanations of the concept first and used an interactive scientific visualisation second, while others worked with the visualisation first and received the teacher-led explanation second. Students completed a test of their conceptual understanding of the relevant concepts prior to instruction, after the first instructional session and at the end of instruction. Data on students' academic achievement (highest, middle or lowest third of the class on the mid-term exam) and gender were also collected to explore the relationship between these factors, conceptual development and instructional sequencing. Results show, within this context at least, that teaching sequence is not important in terms of students' conceptual learning gains. (Contains 1 figure and 6 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:
Academic Achievement; Student Behavior; Task Analysis; Mathematics Instruction; Word Problems (Mathematics); Instructional Materials; Academic Standards; Alignment (Education); Middle School Students; Middle School Teachers; Moderate Mental Retardation; Secondary School Mathematics; Activity Units; Teaching Methods; Achievement Gains; Mathematics Skills; Skill Development; Academic Accommodations (Disabilities); Sequential Learning

Abstract:
The purpose of this study was to examine the effects of grade-aligned math instruction on math skill acquisition of four middle schools with moderate intellectual disability. Teachers were trained to follow a task analysis to teach grade-aligned math to middle school students using adapted math problem stories and graphic organizers. The teacher implemented four math units representing four of the five National Council of Teachers of Mathematics recommended math standards (i.e., algebra, geometry, measurement, and data analysis/probability; NCTM, 2002). A multiple probe across unit design was used to examine the effects of the math instruction on the number of steps completed on each math standard task analysis. Results indicated a functional relationship between math instruction and student behavior with an overall increase in independent correct responses. Implications for practice and future research are discussed. Limitations and suggestions for future research and practice are discussed. (Contains 6 figures and 3 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:
Mathematics Education; Grade 2; Geometry; Sequential Learning; Elementary School Mathematics; Teaching Methods

Abstract:
In mathematics education, there is a continuing debate about the nature of mathematics, which some claim to be an objective science, whereas others note its socially and individually constructed nature. From a strict cultural-historical perspective, the objective and subjective sides of mathematics are but manifestations of a higher-order phenomenon that may be summarized by the aphorism that mind is in society to the extent that society is in the mind. In this study, we show, drawing on exemplifying materials from a second-grade unit on three-dimensional geometry, how mathematics manifests itself both as objective science all the while being subjectively produced. A particular three-turn interactional sequence comes to play a central role. We conclude by re-assigning a positive role to a much-maligned sequentially ordered conversational routine. 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:
Information Seeking; Sampling; Prediction; Influences; Student Motivation; Sequential Learning; Cognitive Processes; Learner Engagement; Investigations; Models; Bias

Abstract:
People must often engage in sequential sampling in order to make predictions about the relative quantities of two options. We investigated how directional motives influence sampling selections and resulting predictions in such cases. We used a paradigm in which participants had limited time to sample items and make predictions about which side of the screen contained more of a critical item. Sampling selections were biased by monetary desirability manipulations, and participants exhibited a desirability bias for both dichotomous and continuous predictions. (Contains 1 figure.) Note:The following two links are not-applicable for text-based browsers or screen-reading software. Show Hide Full Abstract

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Grade 3; Investigations; Preschool Education; Task Analysis; Spatial Ability; Cognitive Mapping; Sequential Learning; Cognitive Development; Age Differences; Children; Cognitive Processes; Mathematics Education

Abstract:
The representation of numerical and non-numerical ordered sequences was investigated in children from preschool to grade 3. The child's conception of how sequence items map onto a spatial scale was tested using the Number-to-Position task (Siegler & Opfer, 2003) and new variants of the task designed to probe the representation of the alphabet (i.e., letter sequence) and the calendar year (i.e., month sequence). The representation of non-numerical order showed the same developmental pattern previously observed for numerical representation, with a logarithmic mapping in the youngest children and a shift to linear mapping in older children. Although the individual ability to position non-numerical items was related to the child's knowledge of the sequence, a significant amount of unique variance was explained by her type of number-line representation. These results suggest that the child's conception of numerical order is generalized to non-numerical sequences and that the concept of linearity is acquired in the numerical domain first and progressively extended to all ordinal sequences. (Contains 3 figures 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:
Skill Development; Sequential Learning; Age Differences; Reaction Time; Probability; Accuracy; Early Adolescents; Learning Processes

Abstract:
Implicit skill learning underlies obtaining not only motor, but also cognitive and social skills through the life of an individual. Yet, the ontogenetic changes in humans' implicit learning abilities have not yet been characterized, and, thus, their role in acquiring new knowledge efficiently during development is unknown. We investigated such learning across the lifespan, between 4 and 85 years of age with an implicit probabilistic sequence learning task, and we found that the difference in implicitly learning high- vs. low-probability events--measured by raw reaction time (RT)--exhibited a rapid decrement around age of 12. Accuracy and z-transformed data showed partially different developmental curves, suggesting a re-evaluation of analysis methods in developmental research. The decrement in raw RT differences supports an extension of the traditional two-stage lifespan skill acquisition model: in addition to a decline above the age 60 reported in earlier studies, sensitivity to raw probabilities and, therefore, acquiring new skills is significantly more effective until early adolescence than later in life. These results suggest that due to developmental changes in early adolescence, implicit skill learning processes undergo a marked shift in weighting raw probabilities vs. more complex interpretations of events, which, with appropriate timing, prove to be an optimal strategy for human skill learning. 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:
Video Technology; Electronic Learning; Technology Uses in Education; Interactive Video; Eye Movements; Cognitive Style; Integrated Learning Systems; Visual Learning; Sequential Learning; Multimedia Materials; Adults; Graduate Students; Foreign Countries

Abstract:
More and more videos are now being used in e-learning context. For improving learning effect, to understand how students view the online video is important. In this research, we investigate how students deploy their attention when they learn through interactive slide video in the aim of better understanding observers' learning style. Felder and Silverman's learning style scale was applied to identify learner's learning preference. Participants' eye movement was recorded in an eye-tracking lab. "Eye-mind" assumption is supported by a mild correlation between posttest score and viewing ratio. Different viewing behavior of different learners with strong and intermediate visual learning preference is investigated. Some eye movement metrics like fixation time, speed and direction related to global and sequential learning style are investigated. The result showed a high consistence with corresponding learning style characteristics, which provides another way to verify the validity of learning style. Possible applications such as incorporating with adaptive learning management system are discussed. (Contains 3 figures and 8 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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