Comparing Learning From Productive Failure and Vicarious Failure

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students generated solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students evaluated the solutions generated by PF students before receiving the same instruction. Student-generated solutions were either suboptimal or incorrect, and in this sense can be conceived as failed problem-solving attempts. Although there was no difference on self-reported engagement, PF students reported significantly greater mental effort and interest in knowing the canonical solution to the problem than VF students. When preexisting differences in general ability, math ability, and prior knowledge were controlled, PF students outperformed VF students on conceptual understanding and transfer without compromising procedural fluency. These results suggest that when learning a new math concept, people learn better from their own failed solutions than those of others provided appropriate instruction on the targeted concept is given after the generation or evaluation activity.     

Designs for learning about climate change as a complex system

This paper reports on a study in which students used agent-based computer models to learn about complex systems ideas of relevance to understanding climate change. The experimental condition used a Productive Failure (PF) learning design in which ninth grade students initially worked with agent-based computer models to solve challenge problems followed by teacher instruction about targeted climate and complexity ideas. In contrast, the comparison condition employed a Direct Instruction (DI) learning design in which the teacher instruction was provided initially, followed by the students working on the same computer models and challenge problems as the experimental group. The students in the PF group scored significantly higher on the post-test on measures of climate and complex systems explanatory knowledge and near and far knowledge transfer. Theoretical and practical implications of these findings are considered.     

谈不定积分方法的灵活运用

求不定积分是一元函数微分学难点之一，虽然教材上给出了四种基本方法，但在解题时，初学仍不能灵活运用，为了丰富初学的解题经验，本从一道基本题，进行多方位剖析。     

Changes in Handedness Associated with Onset or Disappearance of Stuttering

The relationships between scores on the Sixteen Personality Factor Questionnaire (16 PF), the Brown Personal Beliefs and Teaching Practices Inventories, and the Rokeach Dogmatism Scale for 191 female, beginning teacher education students were investigated using canonical and simple correlation analyses. A significant canonical correlation of .51 was established between these measures, with factors M (Practical vs. Imaginative), and Q1 (Conservative vs. Experimenting) of the 16 PF and total scores on the Brown inventories accounting for the multivariate correlation. Teacher education students who indicate high agreement with Dewey’s philosophy on the Brown instruments appear to also score high on the imagination and experimentation factors of the 16 PF. An additional finding of importance was the absence of significant relationships between the 16 PF and the Rokeach Dogmatism Scale.     

Knowing what you don't know makes failure productive

To progress from intuitive ideas to deep conceptual understanding, students need to become aware of gaps in their ideas. Attempting to solve problems prior to instruction may lead to a global awareness of knowledge gaps (i.e., awareness without being able to identify which specific component is lacking). These gaps may subsequently be specified by comparing students' solutions to the canonical solution. In our first experiment, the teacher highlighted specific gaps by comparing typical student solutions to the canonical solution before or after problem solving. The second experiment varied the factors form of instruction (with or without student solutions) and timing of instruction (problem-solving prior to or after instruction). Problem-solving prior to instruction triggered a global awareness of knowledge gaps. While this was beneficial for learning when combined with instruction with student solutions, our results indicate that comparing student solutions during instruction to specify the gaps is the most relevant factor.     

Bits of Experience in the Oral Practice of Teaching Grammar

English learners may have such experience that most of them can‘t be able to speak English apropriately and fluently even if they have gained a lot of grammar knowledge.The approach of teaching grammar discussed in this paper focuses on training students‘ communicative ability.And it is benefical to stimulating the activeness and interest of students and fostering the ability to solve the problems independently.     

Related factors of the MTAI and the 16PF

The Minnesota Teacher Attitude Inventory (MTAI) and the Sixteen Personality Factors Questionnaire (16PF) were administered to 395 undergraduate teachers-in-training. The MTAI and the 16PF were compared using canonical analysis. They contained three related factors accounting for 41% of their total variance. It was concluded that teachers' attitudes toward their pupils are determined in large part by measurable personality traits.     

Designing a Bridging Discourse: Re-Mediation of a Mathematical Learning Disability

Students with disabilities present a unique instructional design challenge. These students often have qualitatively different ways of processing information, meaning that standard instructional approaches may not be effective. In this study I present a case study of a student with a mathematical learning disability for whom standard instruction on fractions had been ineffective. With regard to theory, I draw on Lev Vygotsky’s framing of disability and then use Anna Sfard’s conceptualization of mathematics as a discourse to design a fraction re-mediation that provided a bridge from the student’s discourse to the canonical mathematics discourse. This bridging discourse was used in 5 videotaped re-mediation sessions with the case study student. A fine-grained analysis of the re-mediation sessions traced the ways in which the student’s discourse shifted over time, which enabled her to solve problems she had previously been unable to solve. This study provides a proof of concept for reconceptualizing remediation and illustrates the potential utility of a bridging discourse to help students who have a history of failure gain access to the canonical mathematics discourse and content.     

The Role of Study Habits in Foreign Language Courses

The purpose of this study was to determine which study habits distinguish successful from unsuccessful foreign language learners. Participants were 219 college students from a variety of disciplinary backgrounds, enrolled in either Spanish, French, German or Japanese classes. A canonical discriminant analysis (F [6, 117], p < 0.0001; canonical R = 0.92) revealed that, compared to their high-performing counterparts, students with the lowest levels of foreign language performance tended to report that: (a) they frequently include a lot of irrelevant or unimportant information in their notes; (b) when they have difficulty with their assignments, they do not seek help from their instructor; (c) they put their lecture notes away after taking the test and never consult them again; (d) they have to be in the mood before attempting to study; (e) they have a tendency to doodle or to daydream when they are trying to study; and (f) they do not look up in a dictionary the meanings of words that they do not understand. Implications are discussed.     

先行组织者模式在中小学英语音标教学中的应用

奥苏伯尔的先行组织者模式强调在学习者接受新观念时 ,要重视学习者的认知基础。在进行教学时 ,如果没有上位观念可以同化新观念 ,教师就应该在引入新观念时先介绍先行组织者 ,然后用其同化新观念。本文分析了目前英语音标教学方面的不足 ,并试图运用先行组织者模式来解决这些问题 ,以使学习者能够在今后的英语学习中更深刻地理解和运用音标     

Concept mapping as a follow-up strategy to learning from texts: what characterizes good and poor mappers?

Concept maps consist of nodes that represent concepts and links that represent relationships between concepts. Various studies have shown that concept mapping fosters meaningful learning. However, little is known about the specific cognitive processes that are responsible for such mapping effects. In a thinking-aloud study, we analyzed the relations between cognitive processes during concept mapping as well as the characteristics of the concept maps that the learners produced and learning outcomes (38 university students). To test whether differences in learning outcome are due to differences in general abilities, verbal and spatial abilities were also assessed. In a cluster-analysis two types of ineffective learners were identified: ‘non-labeling mappers’ and ‘non-planning mappers’. Effective learners, in contrast, showed much effort in planning their mapping process and constructing a coherent concept map. These strategies were more evident in students with prior concept-mapping experience (‘advanced beginners’) than in those who had not used this learning strategy before (‘successful beginners’). Based on the present findings, suggestions for a direct training approach (i.e., strategy training with worked-out examples) and an indirect training approach (i.e., supporting the learners with strategy prompts) were developed.     

How handwriting behaviors during problem solving are related to problem-solving success in an engineering course

If we carefully observe the spatial and temporal organization of students' pen strokes as they solve an engineering problem, can we predict their ability to achieve the correct answer? To address this question, 122 college students were asked to solve exam problems in an engineering course using a smartpen that recorded their writing as digitized timestamped pen strokes. The pen stroke data was used to compute a collection of 10 metrics characterizing various elements of problem-solving fluency including the tendency to progress down the page without revisions, the amount of time with no activity, and the frequency of constructing and using equations. The primary finding is that, on average across 13 different exam problems, these elements of problem-solving process explained 40% of the variance in scores of the correctness of the problem solution. In short, success on generating correct solutions was related to the fluency of the student's problem-solving process (i.e., working sequentially from the top to the bottom of the page, working without detours or long pauses, and working by constructing equations). This work is consistent with the idea that expertise in solving common engineering problems involves being able to treat them like routine rather than non-routine problems.     

Diagnosing Portuguese Students' Misconceptions about the Mineral Concept

Educational researchers and teachers are well aware that misconceptions—erroneous ideas that differ from the scientifically accepted ones—are very common amongst students. Daily experiences, creative and perceptive thinking and science textbooks give rise to students' misconceptions which lead them to draw erroneous conclusions that become strongly attached to their views and somehow affect subsequent learning. The main scope of this study was to understand what students consider a mineral to be and why. Therefore, the goals were (1) to identify eleventh-grade students' misconceptions about the mineral concept; (2) to understand which variables (gender, parents' education level and attitude towards science) influenced students' conceptions; and (3) to create teaching tools for the prevention of misconceptions. In order to achieve these goals, a diagnostic instrument (DI), constituted of a two-tier diagnostic test and a Science Attitude Questionnaire, was developed to be used with a sample of 89 twelfth-grade students from five schools located in central Portugal. As far as we know, this is the first DI developed for the analysis of misconceptions about the mineral concept. Data analysis allows us to conclude that students had serious difficulties in understanding the mineral concept, having easily formed misconceptions. The variables gender and parents' education level influence certain students' conceptions. This study provides a valuable basis for reflection on teaching and learning strategies, especially on this particular theme.     

数学教学中如何进行学习方法指导

在数学教学中必须重视学习方法指导,一是加强概念教学,引导学生探究概念形成过程,灵活运用概念解题;二是指导学生改进学习方法,注重课前预习,上课积极思考,课后注重整理归纳.     

Using concept maps to elicit and study student teachers’ perceptions about inclusive education: a Tanzanian experience

In this study, concept map activities were used to trigger group discussions about inclusive education, with a focus on learners with disabilities. The participants were 226 Tanzanian student teachers. This article reports and discusses how the maps were analysed and what they indicate about the students’ thinking about certain aspects of inclusive education. The results also indicate that concept mapping as an activity in teacher education may be useful and engaging for students. It may help them to organise knowledge and make them aware of their own and others’ understanding of inclusive education practices. An analysis of concept maps constructed by student teachers may also help lecturers to identify views, misconceptions, knowledge gaps and insights about inclusion in education settings.     

Embellishing Problem-Solving Examples with Deep Structure Information Facilitates Transfer

Appreciation of problem structure is critical to successful learning. Two experiments investigated effective ways of communicating problem structure in a computer-based learning environment and tested whether verbal instruction is necessary to specify solution steps, when deep structure is already embellished by instructional examples. Participants learned to solve algebra-like problems and then solved transfer problems that required adjustment of learned procedures. Experiment 1 demonstrated that verbal instruction helped learning by reducing learners' floundering, but its positive effect disappeared in the transfer. More importantly, students transferred better when they studied with examples that emphasized problem structure rather than solution procedure. Experiment 2 showed that verbal instruction was not necessarily more effective than nonverbal scaffolding to convey problem structure. Final understanding was determined by transparency of problem structure regardless of presence of verbal instruction. However, verbal instruction had a positive impact on learners by having them persist through the task, and optimal instructional choices were likely to differ depending on populations of learners.     

Using educational data mining methods to assess field-dependent and field-independent learners’ complex problem solving

The present study investigated the problem-solving performance of 101 university students and their interactions with a computer modeling tool in order to solve a complex problem. Based on their performance on the hidden figures test, students were assigned to three groups of field-dependent (FD), field-mixed (FM), and field-independent (FI) learners, and were instructed to use integrated-format materials and Model-It^® in order to solve a problem about immigration policy. The results showed that there were significant differences among the three groups of learners in terms of their problem-solving performance. Consequently, the study employed educational data mining (EDM) methods in order to examine how FD and FI learners actually interacted with Model-It^® in order to solve the problem. The EDM methods provided rich analytical information and details about learners’ interactions with the computer tool. Implications for designing effective joint cognitive systems are discussed.     

从FonF看整体听写中对语言形式的关注方式

通过实验证明,在学习者自主的小组互动中,学习者能在有意义的交流中自发地通过提问等各种方式关注语言形式,并依靠自身或他人资源积极寻求解决问题的途径。与重意义的小组交流相比,在整体听写中,学习者会更多地运用纠错、元语言讨论的方式对语言形式进行关注,而由于整体听写的活动设计所限,学习者真正的意义协商较少,活动还需改进。     

The Emergence of 3D Geometry From Children's (Teacher-Guided) Classification Tasks

In this article, we describe the design principles undergirding productive failure (PF; M. Kapur, 2008 Kapur, M. 2008. Productive failure. Cognition and Instruction, 26: 379–424. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). We then report findings from an ongoing program of research on PF in mathematical problem solving in 3 Singapore public schools with significantly different mathematical ability profiles, ranging from average to lower ability. In the 1st study, 7th-grade mathematics students from intact classes experienced 1 of 2 conditions: (a) PF, in which students collaboratively solved complex problems on average speed without any instructional support or scaffolds up until a teacher-led consolidation; or (b) direct instruction (DI), in which the teacher provided strong instructional support, scaffolding, and feedback. Findings suggested that although PF students generated a diversity of linked representations and methods for solving the complex problems, they were ultimately unsuccessful in their problem-solving efforts. Yet despite seemingly failing in their problem-solving efforts, PF students significantly outperformed DI students on the well-structured and complex problems on the posttest. They also demonstrated greater representation flexibility in solving average speed problems involving graphical representations, a representation that was not targeted during instruction. The 2nd and 3rd studies, conducted in schools with students of significantly lower mathematical ability, largely replicated the findings of the 1st study. Findings and implications of PF for theory, design of learning, and future research are discussed.     

Agreed discoveries: students’ negotiations in a virtual laboratory experiment

This paper presents an analysis of the scientific reasoning of a dyad of secondary school students about the phenomenon of dissolution of gases in water as they work on this in a simulated laboratory experiment. A web-based virtual laboratory was developed to provide learners with the opportunity to examine the influence of physical factors on gas solubility in water. An evaluation process involving 180 students revealed that the concepts connected to the dissolution of gas in water caused problems for the students even after having experimented with the virtual laboratory. To investigate the nature of learners’ reasoning about the visualised events, 13 video-recorded groups of learners were analysed. This study follows the reasoning of one group that displayed a possibly productive way of solving the problem. The results address the students’ general difficulty of discovering something that they are conceptually unprepared for within the virtual laboratory. The analysis shows how the students eventually found a way out of their dilemma by making an analogy with other dissolving processes. In effect, the analysis elucidates some of the analytical work that had to be done by the participants when collaboratively negotiating a shared meaning of a scientific concept in concord with a given task and set of instructional materials. Implications for design might be to provide the learning material with explicit hints that enable students to connect to specific phenomena related to the one investigated concept. The findings show the usefulness of video analytic research, informed by CA and ethnomethodology. This analytical framework can support design processes and provide useful information, which might identify hurdles to learning a scientific concept by simulated events and pathways to overcome these hurdles.