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Nikol Rummel - One of the best experts on this subject based on the ideXlab platform.
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Preparatory effects of problem solving versus studying examples prior to Instruction
Instructional Science, 2021Co-Authors: Christian Hartmann, Tamara Gog, Nikol RummelAbstract:The Productive Failure (PF) approach prompts students to attempt to solve a problem prior to Instruction – at which point they typically fail. Yet, research on PF shows that students who are involved in problem solving prior to Instruction gain more conceptual knowledge from the Subsequent Instruction compared to students who receive the Instruction first. So far, there is no conclusive evidence, however, that the beneficial effects of PF are explained by the attempt to generate one’s own solutions prior to Instruction. The literature on example-based learning suggests that observing someone else engaging in problem-solving attempts may be an equally effective means to prepare students for Instruction. In an experimental study, we compared a PF condition, in which students were actively engaged in problem solving prior to Instruction, to two example conditions, in which students either observed the complete problem-solving-and-failing process of another student engaging in PF or looked at the outcome of this process (i.e., another student’s failed solution attempts). Rather than worked examples of the correct solution procedure, the students observed examples of failed solution attempts. We found that students’ own problem solving was not superior to the two example conditions. In fact, students who observed the complete PF process even outperformed students who engaged in PF themselves. Additional analyses revealed that the students’ prior knowledge moderated this effect: While students who observed the complete PF process were able to take advantage of their prior knowledge to gain more conceptual knowledge from the Subsequent Instruction, prior knowledge did not affect students’ post-test performance in the PF condition.
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When failure fails to be productive: probing the effectiveness of productive failure for learning beyond STEM domains
Instructional Science, 2020Co-Authors: Valentina Nachtigall, Katja Serova, Nikol RummelAbstract:The current work builds on research demonstrating the effectiveness of Productive Failure (PF) for learning. While the effectiveness of PF has been demonstrated for STEM learning, it has not yet been investigated whether PF is also beneficial for learning in non-STEM domains. Given this need to test PF for learning in domains other than mathematics or science, and the assumption that features embodied in a PF design are domain-independent, we investigated the effect of PF on learning social science research methods. We conducted two quasi-experimental studies with 212 and 152 10th graders. Following the paradigm of typical PF studies, we implemented two conditions: PF, in which students try to solve a complex problem prior to Instruction, and Direct Instruction (DI), in which students first receive Instruction followed by problem solving. In PF, students usually learn from their failure. Failing to solve a complex problem is assumed to prepare students for deeper learning from Subsequent Instruction. In DI, students usually learn through practice. Practicing and applying a given problem-solving procedure is assumed to help students to learn from previous Instruction. In contrast to several studies demonstrating beneficial effects of PF on learning mathematics and science, in the present two studies, PF students did not outperform DI students on learning social science research methods. Thus, the findings did not replicate the PF effect on learning in a non-STEM domain. The results are discussed in light of mechanisms assumed to underlie the benefits of PF.
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The effect of contrasting cases during problem solving prior to and after Instruction
Instructional Science, 2020Co-Authors: Katharina Loibl, Nikol Rummel, Marcel Tillema, Tamara GogAbstract:Research on productive failure suggests that attempting to solve a problem prior to Instruction facilitates conceptual understanding compared to receiving Instruction prior to problem solving. The assumptions are that during the problem-solving phase, students activate their prior knowledge, become aware of their knowledge gaps, and discover deep features of the target content, which prepares them to better process the Subsequent Instruction. Unclear is whether this effect results from merely changing the order of the learning phases (i.e., Instruction or problem solving first) or from additional features, such as presenting problem-solving material in the form of cases that differ in one feature at a time. Contrasting such cases may highlight the deep features and provide grounded feedback to students’ problem-solving attempts. In addition, the effect of the order of Instruction and problem solving on procedural fluency is still unclear. The present experiment ( N = 181, mean age = 14.53) investigated in a 2 × 2 design the effects of order (Instruction or problem solving first) and of contrasting cases in the problem-solving material (yes/no) on conceptual understanding and procedural fluency. Additionally, the quality and quantity of students’ solution attempts from the problem-solving phase were coded. Regarding the learning outcomes, the ANOVA results suggest that for procedural fluency Instruction prior to problem solving was more beneficial than problem solving prior to Instruction. Merely delaying Instruction did not increase conceptual understanding. The contrasting cases did not affect the quality of solution attempts, nor the posttest results. As expected, students who received Instruction first generated fewer, but higher-quality solution attempts.
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Productive Failure as strategy against the double curse of incompetence
Learning: Research and Practice, 2015Co-Authors: Katharina Loibl, Nikol RummelAbstract:Learners who lack knowledge often also lack the ability to assess their limited competence correctly. Due to the incorrect self-assessment, they are unlikely to apply strategies that would help them to acquire relevant knowledge. This effect is known as the double curse of incompetence. When students solve problems prior to being taught the canonical solution in a so-called Productive Failure setting (PF), they usually come up with solution ideas that are erroneous or incomplete. Due to this struggle with the problem at hand, they may become aware of the limitations of their knowledge. Demonstrating how typical student solutions fail to solve the problem during Subsequent Instruction may further help students to assess their competence correctly. Improved awareness of limited competence, in turn, may foster fruitful learning strategies when learning the canonical solution. Indeed, our empirical study showed that students in PF conditions have a more realistic perception of their own knowledge than student...
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The impact of guidance during problem-solving prior to Instruction on students’ inventions and learning outcomes
Instructional Science, 2014Co-Authors: Katharina Loibl, Nikol RummelAbstract:Multiple studies have shown benefits of problem-solving prior to Instruction (cf. Productive Failure, Invention) in comparison to direct Instruction. However, students’ solutions prior to Instruction are usually erroneous or incomplete. In analogy to guided discovery learning, it might therefore be fruitful to lead students towards the discovery of the canonical solution. In two quasi-experimental studies with 104 students and 175 students, respectively, we compared three conditions: problem-solving prior to Instruction, guided problem-solving prior to Instruction in which students were led towards the discovery of relevant solution components, and direct Instruction. We replicated the beneficial effects of problem-solving prior to Instruction in comparison to direct Instruction on posttest items testing for conceptual knowledge. Our process analysis further revealed that guidance helped students to invent better solutions. However, the solution quality did not correlate with the posttest results in the guided condition, indicating that leading students towards the solution does not additionally promote learning. This interpretation is supported by the finding that the two conditions with problem-solving prior to Instruction did not differ significantly at posttest. The second study replicated these findings with a greater sample size. The results indicate that different mechanisms underlie guided discovery learning and problem-solving prior to Instruction: In guided discovery learning, the discovery of an underlying model is inherent to the method. In contrast, the effectiveness of problem-solving prior to Instruction does not depend on students’ discovery of the canonical solution, but on the cognitive processes related to problem-solving, which prepare students for a deeper understanding during Subsequent Instruction.
Katharina Loibl - One of the best experts on this subject based on the ideXlab platform.
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The effect of contrasting cases during problem solving prior to and after Instruction
Instructional Science, 2020Co-Authors: Katharina Loibl, Nikol Rummel, Marcel Tillema, Tamara GogAbstract:Research on productive failure suggests that attempting to solve a problem prior to Instruction facilitates conceptual understanding compared to receiving Instruction prior to problem solving. The assumptions are that during the problem-solving phase, students activate their prior knowledge, become aware of their knowledge gaps, and discover deep features of the target content, which prepares them to better process the Subsequent Instruction. Unclear is whether this effect results from merely changing the order of the learning phases (i.e., Instruction or problem solving first) or from additional features, such as presenting problem-solving material in the form of cases that differ in one feature at a time. Contrasting such cases may highlight the deep features and provide grounded feedback to students’ problem-solving attempts. In addition, the effect of the order of Instruction and problem solving on procedural fluency is still unclear. The present experiment ( N = 181, mean age = 14.53) investigated in a 2 × 2 design the effects of order (Instruction or problem solving first) and of contrasting cases in the problem-solving material (yes/no) on conceptual understanding and procedural fluency. Additionally, the quality and quantity of students’ solution attempts from the problem-solving phase were coded. Regarding the learning outcomes, the ANOVA results suggest that for procedural fluency Instruction prior to problem solving was more beneficial than problem solving prior to Instruction. Merely delaying Instruction did not increase conceptual understanding. The contrasting cases did not affect the quality of solution attempts, nor the posttest results. As expected, students who received Instruction first generated fewer, but higher-quality solution attempts.
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How to make failure productive: Fostering learning from errors through elaboration prompts
Learning and Instruction, 2019Co-Authors: Katharina Loibl, Timo LeudersAbstract:Abstract Research on conceptual change, learning from errors, and ‘productive failure’ suggests that elaborating on errors during Instruction is crucial for learning in settings which put problem solving before Instruction. To reveal the role of elaboration and comparison of errors, we investigated the effect of prompting students to engage in such cognitive processes: Students in all conditions first worked on an identical problem-solving activity (targeting the comparison of fractions) without prior Instruction about the targeted concepts and procedures. In the Subsequent Instruction phase, students in the different conditions received 1) only correct solutions, 2) correct and erroneous examples, or 3) additional comparison prompts. Students who were prompted to compare erroneous solution attempts to correct solutions significantly outperformed their peers at posttest. Elaborating on errors seemed to mediate this effect. In accordance with the theoretical assumptions, the difference between conditions was only significant for students whose initial solution resembled the erroneous examples.
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Productive Failure as strategy against the double curse of incompetence
Learning: Research and Practice, 2015Co-Authors: Katharina Loibl, Nikol RummelAbstract:Learners who lack knowledge often also lack the ability to assess their limited competence correctly. Due to the incorrect self-assessment, they are unlikely to apply strategies that would help them to acquire relevant knowledge. This effect is known as the double curse of incompetence. When students solve problems prior to being taught the canonical solution in a so-called Productive Failure setting (PF), they usually come up with solution ideas that are erroneous or incomplete. Due to this struggle with the problem at hand, they may become aware of the limitations of their knowledge. Demonstrating how typical student solutions fail to solve the problem during Subsequent Instruction may further help students to assess their competence correctly. Improved awareness of limited competence, in turn, may foster fruitful learning strategies when learning the canonical solution. Indeed, our empirical study showed that students in PF conditions have a more realistic perception of their own knowledge than student...
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The impact of guidance during problem-solving prior to Instruction on students’ inventions and learning outcomes
Instructional Science, 2014Co-Authors: Katharina Loibl, Nikol RummelAbstract:Multiple studies have shown benefits of problem-solving prior to Instruction (cf. Productive Failure, Invention) in comparison to direct Instruction. However, students’ solutions prior to Instruction are usually erroneous or incomplete. In analogy to guided discovery learning, it might therefore be fruitful to lead students towards the discovery of the canonical solution. In two quasi-experimental studies with 104 students and 175 students, respectively, we compared three conditions: problem-solving prior to Instruction, guided problem-solving prior to Instruction in which students were led towards the discovery of relevant solution components, and direct Instruction. We replicated the beneficial effects of problem-solving prior to Instruction in comparison to direct Instruction on posttest items testing for conceptual knowledge. Our process analysis further revealed that guidance helped students to invent better solutions. However, the solution quality did not correlate with the posttest results in the guided condition, indicating that leading students towards the solution does not additionally promote learning. This interpretation is supported by the finding that the two conditions with problem-solving prior to Instruction did not differ significantly at posttest. The second study replicated these findings with a greater sample size. The results indicate that different mechanisms underlie guided discovery learning and problem-solving prior to Instruction: In guided discovery learning, the discovery of an underlying model is inherent to the method. In contrast, the effectiveness of problem-solving prior to Instruction does not depend on students’ discovery of the canonical solution, but on the cognitive processes related to problem-solving, which prepare students for a deeper understanding during Subsequent Instruction.
Manu Kapur - One of the best experts on this subject based on the ideXlab platform.
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Is having more prerequisite knowledge better for learning from productive failure?
Instructional Science, 2017Co-Authors: Pee Li Leslie Toh, Manu KapurAbstract:A critical assumption made in Kapur’s (Instr Sci 40:651–672, 2012 ) productive failure design is that students have the necessary prerequisite knowledge resources to generate and explore solutions to problems before learning the targeted concept. Through two quasi-experimental studies, we interrogated this assumption in the context of learning a multilevel biological concept of monohybrid inheritance. In the first study, students were either provided or not provided with prerequisite micro-level knowledge prior to the generation phase. Findings suggested that students do not necessarily have adequate prior knowledge resources, especially those at the micro-level, to generate representations and solution methods for a multilevel concept such as monohybrid inheritance. The second study examined how this prerequisite knowledge provision influenced how much students learned from the Subsequent Instruction. Although the prerequisite knowledge provision helped students generate and explore the biological phenomenon at the micro- and macro-levels, the provision seemingly did not confer further learning advantage to these students. Instead, they had learning gains similar to those without the provision, and further reported lower lesson engagement and greater mental effort during the Subsequent Instruction.
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The preparatory effects of problem solving versus problem posing on learning from Instruction
Learning and Instruction, 2015Co-Authors: Manu KapurAbstract:Abstract Two randomized-controlled studies compare the preparatory effects of problem-solving versus problem-posing on learning from Subsequent Instruction. Students engaged in either problem-solving (where they generated solutions to a novel problem) or problem-posing (where they generated problems, and where possible, the associated solutions) prior to learning a novel math concept. Study 1 found that problem-posing prior to Instruction resulted in significantly better transfer to novel problems than problem-solving, without any significant difference in procedural knowledge and conceptual understanding. Study 2 further showed that when problem-posing was designed to focus only on the generation of problems without the solutions, problem-solving prior to Instruction resulted in better conceptual understanding than problem-posing. However, the transfer effect remained in favor of problem-posing, albeit weaker than in Study 1. These findings suggest that although solution generation prior to Instruction plays a critical role in the development of conceptual understanding and transfer, generating problems can further enhance transfer.
Todd G. Ruskell - One of the best experts on this subject based on the ideXlab platform.
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Using InkSurvey with Pen-Enabled Mobile Devices for Real-Time Formative Assessment II. Indications of Effectiveness in Diverse Educational Environments
Human–Computer Interaction Series, 2015Co-Authors: Frank V. Kowalski, Susan E. Kowalski, Thomas J. Colling, J. V. Gutierrez Cuba, Tracy Q. Gardner, Gus Greivel, Enrique Palou, Todd G. RuskellAbstract:InkSurvey is free, web-based software designed to facilitate the collection of real-time formative assessment. Using this tool, the instructor can embed formative assessment in the Instruction process by posing an open-format question. Students equipped with pen-enabled mobile devices are then actively engaged in their learning as they use digital ink to draw, sketch, or graph their responses. When the instructor receives these responses instantaneously, it provides insights into student thinking and what the students do and do not know. Subsequent Instruction can then repair and refine student understanding in a very timely manner.
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Using InkSurvey with Pen-Enabled Mobile Devices for Real-Time Formative Assessment: I Applications in Diverse Educational Environments
Human–Computer Interaction Series, 2015Co-Authors: Frank V. Kowalski, Susan E. Kowalski, Thomas J. Colling, J. V. Gutierrez Cuba, Tracy Q. Gardner, Gus Greivel, Enrique Palou, Todd G. RuskellAbstract:InkSurvey is a free, web-based software designed to facilitate the collection of real-time formative assessment. Using this tool, the instructor can embed formative assessment in the Instruction process by posing an open-format question. Students equipped with pen-enabled mobile devices (tablet PCs, iPads, Android devices including some smartphones) are then actively engaged in their learning as they use digital ink to draw, sketch, or graph their responses. When the instructor receives these responses instantaneously, it provides insights into student thinking and what the students do and do not know. Subsequent Instruction can then repair and refine student understanding in a very timely manner.
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Using Inksurvey with Pen-enabled Movile Devices for Real-time Formative Assessment II: Indications of Effectiveness in Diverse Educational Environments
arXiv: Physics Education, 2013Co-Authors: Frank V. Kowalski, Tracy Q. Gardner, Gus Greivel, Enrique Palou, Todd G. Ruskell, T. J. Collin, J. V. Gutierrez, Susan E. KowalskiAbstract:InkSurvey is free, web-based software designed to facilitate the collection of real-time formative assessment. Using this tool, the instructor can embed formative assessment in the Instruction process by posing an open-format question. Students equipped with pen-enabled mobile devices are then actively engaged in their learning as they use digital ink to draw, sketch, or graph their responses. When the instructor receives these responses instantaneously, it provides insights into student thinking and what the students do and do not know. Subsequent Instruction can then repair and refine student understanding in a very timely manner. In a companion paper, we illustrate the wide applicability of this use of technology by reporting a series of seven vignettes featuring instructors of diverse subjects (physics, mathematics, chemical engineering, food science, and biology), with students using diverse pen-enabled mobile devices (tablet PCs, iPads, and Android 4.0 tablets/smartphones), in diverse educational environments (K-12, community college, publicly-funded engineering university, private university, and graduate school), in two countries (United States and Mexico). In this paper, each instructor shares some data, insights, and/or conclusions from their experiences that indicate the effectiveness of this pedagogical model in diverse educational environments.
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Using Inksurvey with Pen-enabled Mobile Devices for Real-time Formative Assessment I: Applications in Diverse Educational Enviroments
arXiv: Physics Education, 2013Co-Authors: Frank V. Kowalski, Thomas J. Colling, Tracy Q. Gardner, Gus Greivel, Enrique Palou, Todd G. Ruskell, J. V. Gutierrez, Susan E. KowalskiAbstract:InkSurvey is free, web-based software designed to facilitate the collection of real-time formative assessment. Using this tool, the instructor can embed formative assessment in the Instruction process by posing an open-format question. Students equipped with pen-enabled mobile devices (tablet PCs, iPads, Android devices including some smartphones) are then actively engaged in their learning as they use digital ink to draw, sketch, or graph their responses. When the instructor receives these responses instantaneously, it provides insights into student thinking and what the students do and do not know. Subsequent Instruction can then repair and refine student understanding in a very timely manner. Although this pedagogical tool is appealing because of its broad theoretical foundations, the cost of pen-enabled mobile technology was until recently a significant barrier to widely implementing this teaching model. However, less expensive tablets, iPads, and Android devices are now filling the market (and student backpacks) and greatly lowering that barrier. To illustrate the wide applicability of this use of technology, we report a series of seven vignettes featuring instructors of diverse subjects (mathematics, food chemistry, physics, biology, and chemical engineering), with students using diverse pen-enabled mobile devices (tablet PCs, iPads, and Android 4.0 tablets), in diverse educational environments (K-12, community college, publicly-funded engineering university, private university, graduate school), in two countries (United States and Mexico). In a companion paper, each instructor also shares some data, insights, and/or conclusions from their experiences regarding the effectiveness of this tool.
Nagarajan Ranganathan - One of the best experts on this subject based on the ideXlab platform.
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Redundancy Mining for Soft Error Detection in Multicore Processors
IEEE Transactions on Computers, 2011Co-Authors: Ransford Hyman, Koustav Bhattacharya, Nagarajan RanganathanAbstract:The trends in technology scaling and the reduction in supply voltages have significantly improved the performance and energy consumption in modern microprocessors. Microprocessors are being built with higher degrees of spatial parallelism and deeper pipelines to improve performance, which, however, makes them more susceptible to transient faults. Radiation causes "transient faults” or "single-event transients” in logic, which, once propagated and latched, become full cycle errors or soft errors. If radiation hits memory elements, this is usually called an "single-event upset” or "soft error” as it can further propagate as a full cycle error. The problem of soft errors is further exacerbated in large multiprocessors employed in servers in which reliability is a key concern. In the past, the technique of lockstep execution of the original and the duplicate Instructions has been used for error detection in multiprocessors. However, the execution of redundant threads in the on-chip multiprocessor (CMP) provides error detection at lower overheads, since the branch outcomes of the leading thread can be exploited during the execution of the trailing thread, and also because the interprocessor communication latency is a key concern for lockstepping. In this paper, we show that by mining various redundancies inherent within a single core, the interprocessor communication can be brought down to a minimum. Toward this, we propose techniques based on 1) temporal redundancy, 2) data value redundancy, and 3) information redundancy for error detection in multicore designs. We exploit temporal redundancy by using the "latency slack cycles” (LSC) of an Instruction, which we define as the number of cycles before the computed result from the Instruction becomes the source operand of a Subsequent Instruction. The value-based detection technique is explored by exploiting the width of the operands with small data values and information redundancy is exploited by the generation of residue code check bits for the source operands. We show that with a clustered core multiprocessor, the interprocessor communication overhead can be significantly reduced. In our proposed multicore design, when a soft error is detected, error correction is achieved by rolling back the execution to a previous checkpoint state and re-executing the Instructions. The proposed techniques have been implemented on the RSIM simulation framework and validated using the SPLASH benchmarks. Experimental results indicate that the soft error detection schemes proposed in this work, can be implemented, on the average, with less than 10 percent increase in CPI on modern multicore designs.
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ISCAS - A strategy for soft error reduction in multi core designs
2009 IEEE International Symposium on Circuits and Systems, 2009Co-Authors: Ransford Hyman, Koustav Bhattacharya, Nagarajan RanganathanAbstract:With the continous decrease in the minimum feature size and increase in the chip density, modern processors are being increasingly susceptible to soft errors. In the past, the technique of lockstep execution with redundant threads on duplicated pipelines have been used for soft error rate reduction which can achieve high error coverage but at the cost of large overheads in terms of area and performance. In this paper, we propose techniques for protection against soft errors in multi-core designs using (i) the properties of spatial and temporal redundancy and (ii) value based detection. We utilize temporal redundancy by using the “latency use slack” (LSC) of an Instruction, which we de£ne as the number of cycles before the computed result from the Instruction becomes the source operand of a Subsequent Instruction, while spatial redundancy is exploited by duplicating the Instruction to a nearby idle processor core. Further, the value based detection technique is explored by exploiting the width of the operands with small data values and the generation of residue code check bits for the source operands. When a soft error is detected, error correction is achieved by rolling back the execution to a previous checkpoint state and re-executing the Instructions. The proposed techniques have been implemented on the RSIM simulation framework and validated using the SPLASH benchmarks. Our results indicate that the soft error detection schemes proposed in this work, can be implemented, on average, with less than 10% increase in CPI on modern multi-core designs.
