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Learning edge momentum: A new account of outcomes
 in cs1. Computer Science Education, 2010. In
"... Compared to other subjects the typical introductory programming (CS1) course has higher than usual rates of both failing and high grades, creating a characteristic bimodal grade distribution. In this paper I explore two possible explanations. The conventional explanation has been that learners natur ..."
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Compared to other subjects the typical introductory programming (CS1) course has higher than usual rates of both failing and high grades, creating a characteristic bimodal grade distribution. In this paper I explore two possible explanations. The conventional explanation has been that learners naturally fall into populations of programmers and nonprogrammers. A review of decades of research, however, finds little or no evidence to support this account. I propose an alternative explanation, the learning edge momentum (LEM) effect. This hypothesis is introduced by way of a simulated model of grade distributions, then grounded in the psychological and educational literature. LEM operates such that success in acquiring one concept makes learning other closely linked concepts easier (whereas failure makes it harder). This interaction between the way that people learn and the tightly integrated nature of the concepts comprising a programming language creates an inherent structural bias in CS1 which drives students towards extreme outcomes.
Effects of Multiple Learning Mechanisms in a Cognitive Architecture
"... Human learning involves multiple sources of information. Their ability to adapt to changes in the environment depends on having such multiple learning modes. In this paper, we extend an existing cognitive architecture to have three distinct learning modes, in an effort to test the hypothesis that mu ..."
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Human learning involves multiple sources of information. Their ability to adapt to changes in the environment depends on having such multiple learning modes. In this paper, we extend an existing cognitive architecture to have three distinct learning modes, in an effort to test the hypothesis that multiple learning capabilities bring synergistic effect in the overall performance. We show experimental results in a simplified route generation domain.
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"... edisc l to dem y, re ty to and tens s, bo Instructional analogies provide opportunities for teachers to amon eptions en & tner, L alogies math, but t xampl emon and resist overextensions of potential analogies. For instance in the above example, one cannot extrapolate from the ability to add pe ..."
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edisc l to dem y, re ty to and tens s, bo Instructional analogies provide opportunities for teachers to amon eptions en & tner, L alogies math, but t xampl emon and resist overextensions of potential analogies. For instance in the above example, one cannot extrapolate from the ability to add percentages (10 % + 5 % = 15%) to adding ratios (3:5 + 3:5 = 6:10). Accordingly, students must be able to identify and differentiate the conceptual structure of mathematical representations in order to identify relationships with previously While essential, learners often show difficulties in noticing a surface level independent of mathematical structure. Thus, problems that are mathematically similar may appear different (e.g., two word problems appear different if one is about pizza and the other about dividing work hours, even if they are mathematically equivalent), and problems that are mathematically different may appear similar (e.g., two word problems about trains that are mathematically dissimilar). This distinction has proven useful in understanding the challenges for mathematics students. When contexts are less well understood, novices tend to map correspondences based on sur
Reducing Cognitive Load in Learning by Analogy
"... The ability to draw connections between concepts, problems, or representations is crucial to mathematical proficiency, though teachers face challenges in capitalizing on classroom opportunities to develop such connected thinking. An experiment with fifthgrade students tests theoretically grounded c ..."
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The ability to draw connections between concepts, problems, or representations is crucial to mathematical proficiency, though teachers face challenges in capitalizing on classroom opportunities to develop such connected thinking. An experiment with fifthgrade students tests theoretically grounded cuing strategies for supporting learning from instructional analogies. Posttest results indicate that an analogy between division of natural numbers and rational numbers improved students ' proficiency in dividing fractions regardless of the addition of analogical cuing strategies, but that the additional cuing led to more conceptual, flexible problem solving. These cuing strategies may be effective ways to enhance students ' ability to draw connections across
Analogy and Classroom Mathematics Learning
"... A young child sits down with blocks to solve a new problem the teacher has given her as a followup to earlier instruction on addition. The child exclaims: "Oh, I can do this one, this is sort of like that problem we did before." This child's simple statement reflects a sophisticated ..."
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A young child sits down with blocks to solve a new problem the teacher has given her as a followup to earlier instruction on addition. The child exclaims: "Oh, I can do this one, this is sort of like that problem we did before." This child's simple statement reflects a sophisticated recognition of analogical similarity between the mathematical structure of two instances, separated by time and context. Supporting the flexible, generative understanding reflected in this child's analogy lies at the heart of high quality mathematics instruction. The domain structure of mathematics creates an epistemology of necessary classroom mathematical knowledge that is quite different from retention of verbatim details, as might be privileged in other academic domains such as geography or spelling. In fact, information taught in mathematics classrooms is rarely instructed with the intention that children retain the verbatim details (e.g., the context or numbers used in problem 4). Rather, mathematical proficiency is more directly related to learners ' ability to draw inferences from prior knowledge and instruction to represent and solve previously unseen
Concept Maps: Theory, Methodology, Technology
"... Abstract. There has been significant interest among researchers in the instructional use of concept maps and collaboration scripts. Some studies focus on students ' collaboration on concept mapping tasks; others focus on scripts to structure learning tasks and guide interactions. Little is know ..."
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Abstract. There has been significant interest among researchers in the instructional use of concept maps and collaboration scripts. Some studies focus on students ' collaboration on concept mapping tasks; others focus on scripts to structure learning tasks and guide interactions. Little is known about scripted collaborative concept mapping. This article reports a study in which we examine the effects on meaningful learning of scripting students ' argumentative interactions during collaborative "enriched skeleton concept mapping". Each concept in the enriched skeleton concept map (ESCoM) contains "annotated factual multimedia information " and an embedded micro collaboration script. The study was performed in a Biomolecules course of the Bachelor of Applied Science program. Firstyear students were randomly assigned to an experimental group of 44 students and a control group of 49 students. In the experimental group, students worked together in pairs on an ESCoM guided by embedded collaboration scripts. The control group received the regular course. The results show that students were able to handle and appreciate the enriched skeleton concept mapping products and processes. Moreover, concept maps appeared to be scored reliable and validly. Finally, the regular course exam showed that the experimental group outperformed the control group. Enriched skeleton concept mapping resulted in a better understanding of the conceptual structure of the domain, the concepts and their relations. 1
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"... elve he he ip. and instruction. We structure the article around two interrelated Author's personal copy take (as in algebra problems), but sometimes have vague goals or ambiguity about what solution methods are possible. The latter are called illstructured problems and are considered much mo ..."
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elve he he ip. and instruction. We structure the article around two interrelated Author's personal copy take (as in algebra problems), but sometimes have vague goals or ambiguity about what solution methods are possible. The latter are called illstructured problems and are considered much more difficult than wellstructured problems. Developing expertise in problem solving is critical to the success of a wide range of human activities, including pursuits in science, art, business, and politics. As our