化学教学中问题解决法初探

问题解决是思维的最一般形式,是人类适应环境、解决生存与发展中各种问题的基本方式。实际的教学中则是通过创设问题情境,在教学内容与学生的求知心理之间建立一种不平衡状态,把学生引入到与问题有关的情境之中。利用此模式的教学是改变以被动接受为主的教学模式,实行探究学习与合作学习的重要途径。     

Problem solving strategies and mathematical resources: A longitudinal view on problem solving in a function based approach to algebra

This study is an attempt to analyze students' construction of function based problem solving methods in introductory algebra. It claims that for functions to be a main concept for learning school algebra, a complex process that has to be developed during a long period of learning must take place. The article describes a longitudinal observation of a pair of students that studied algebra for 3 years using a function approach, including intensive use of graphing technology. Such a long observation is difficult to carry out and even more difficult to report. We watched for three years classrooms using the ‘Visual-Math’ sequence, and sampled students that exhibited various levels of mathematics achievement. The analysis method presented here is a non-standard case study of a pair of lower achievers students and their work is often juxtaposed to the work of other pairs participating in the study. The students' attempts to solve a linear break-even problem is analyzed along three interviews which present the development of the use of mathematical resources and the patterns of problem solving at different learning phases. Beyond describing solving attempts, the article offers terms for describing and explaining what and how do learners appreciate and make out of solving introductory school algebra problems over a three years course. This revised version was published online in July 2006 with corrections to the Cover Date.     

Imitative problem solving: Why transfer of learning often fails to occur

The paper presents empirical evidence for imitativeproblem solving and the Interpretation Theorydescribed in Robertson and Kahney (1996). According tothe theory beginners use imitation as their primary problem solving method when learning about an unfamiliar domain. Imitative problem solving can explain much of the evidence that analogical transfereven within a domain is often hard to find. The paperpresents an analysis of algebra word problems topredict in detail exactly where solvers will havedifficulty in using a worked out example to solveeither a close or distant variant of the problem type.In a 2 × between-groups design, secondary schoolstudents were given an explanation of an algebra wordproblem taken from Reed et al. (1985)or an explanation of the problem that also includedinformation about how the solution could be adapted tosolve a distant variant. They were then given eithera close or distant variant to solve. Results were inline with the predictions derived from theInterpretation Theory analysis.     

Teachers' approaches towards word problem solving: Elaborating or restricting the problem context

This contribution reports about a seven-month long video-based study in two regular Flemish sixth-grade mathematics classrooms. The focus is on teachers' approaches towards problem solving. In our analysis we distinguished between a paradigmatic-oriented (focus on the mathematical structure) and a narrative-oriented (focus on the contextual aspects of a problem) perspective on the problem-solving process. The findings have highlighted that the word problem-solving lessons were more dominated by a paradigmatic than a narrative approach and that interventions in which the relation between the mathematics structure and the realistic constraints of the problem context is addressed, were rare.     

Examining the unique contributions and developmental stability of individual forms of relational reasoning to mathematical problem solving

Relational reasoning, a higher-order cognitive ability that identifies meaningful patterns among information streams, has been suggested to underlie STEM development. This study attempted to explore the potentially unique contributions of four forms of relational reasoning (i.e., analogy, anomaly, antinomy, and antithesis) to mathematical problem solving. Two separate samples, fifth graders (n = 254) and ninth graders (n = 198), were assessed on their mathematical problem solving ability and the different forms of relational reasoning ability. Linear regression analysis was conducted, with participants’ age, working memory, and spatial skills as covariates. The results showed that analogical and antithetical reasoning abilities uniquely predicted mathematical problem solving. This pattern demonstrated developmental stability across a four-year time frame. The findings clarify the unique significance of individual forms of relational reasoning to mathematical problem solving and call for a shift of research direction to reasoning abilities when exploring dissimilarity-based relations (opposites in particular).     

Assessment of expert-novice chemistry problem solving using HyperCard: Early findings

Results of a HyperCard method for assessing the performance of expert and novice high school chemistry students solving stoichiometric chemistry problems (balancing chemical equations) have been reported. The assessment involved the use of a HyperCard instrument (Hyperequation) developed on a Macintosh platform to administer a set of five chemistry problems, register student responses, and collect data related to student performance. The chemistry problems have been previously tested and validated in traditional (pen-paper) assessment settings by other researchers. MANOVA results indicate a significant difference between the performance of expert and novice students solving the five stoichiometric chemistry problems using the Hyperequation. The study shows promise in that a HyperCard assessment method could differentiate between the performance of experts and novices in problem solving. The implication is that HyperCard might be a suitable technology for developing performance assessment methods not only in chemistry but also in other science disciplines.     

Non‐mathematical problem solving in organic chemistry

Differences in problem‐solving ability among organic chemistry graduate students and faculty were studied within the domain of problems that involved the determination of the structure of a molecule from the molecular formula of the compound and a combination of IR and ¹H NMR spectra. The participants' performance on these tasks was compared across variables that included amount of research experience, year of graduate study, and level of problem‐solving confidence. Thirteen of the 15 participants could be classified as either “more successful” or “less successful.” The participants in this study who were “more successful” adopted consistent approaches to solving the problems; were more likely to draw molecular fragments obtained during intermediate stages in the problem‐solving process; were better at mining the spectral data; and were more likely to check their final answer against the spectra upon which the answer was based. Experience from research, teaching, and course work were found to be important factors influencing the level of participants' success. © 2009 Wiley Periodicals, Inc. J Res Sci Teach 47:643–660, 2010     

Strategic transfer: A tool for academic problem solving

Within the context of classroom learning, strategic transfer can be viewed as a tool for academic problem solving. Strategic transfer is defined as the spontaneous access and retrieval (remembering) of previously learned formal procedures for the successful solution of a problem. The transfer-appropriate processing encoding model (Morris, Bransford, and Franks, 1977), and the transfer-appropriate procedures retrieval model (Roediger, Weldon, and Challis, 1989) are reviewed. An integration of the two models is proposed through the development of a training-for-transfer paradigm (Phye, 1990). By integrating encoding and retrieval processing in a single transfer paradigm the issue of accessing prior knowledge (Bransford, 1990) that is also referred to as the inert knowledge problem (Whitehead, 1929) can directly be addressed.     

The consistency effect in word problem solving is effectively reduced through verbal instruction

In mathematical word problem solving, a relatively well-established finding is that more errors are made on word problems in which the relational keyword is inconsistent instead of consistent with the required arithmetic operation. This study aimed at reducing this consistency effect. Children solved a set of compare word problems before and after receiving a verbal instruction focusing on the consistency effect (or a control verbal instruction). Additionally, we explored potential transfer of the verbal instruction to word problems containing other relational keywords (e.g., larger/smaller than) than those in the verbal instruction (e.g., more/less than). Results showed a significant pretest-to posttest reduction of the consistency effect (but also an unexpected decrement on marked consistent problems) after the experimental verbal instruction but not after the control verbal instruction. No significant effects were found regarding transfer. It is concluded that our verbal instruction was useful for reducing the consistency effect, but future research should address how this benefit can be maintained without hampering performance on marked consistent problems.     

Manipulatives and number sentences in computer aided arithmetic word problem solving

In this study we investigated the relative contribution of two main components often used in the instruction of arithmetic word problem solving to first-grade children and children with learning problems, external representation with manipulatives and formal mathematical representation with number sentences. Four computer aided treatments were developed along these dimensions. Furthermore, an assessment control group was formed.It was shown that performance improved significantly after treatment in comparison to the performance of the assessment control group. Comparison of the different training conditions showed that a number sentence treatment was the most effective training component. However, this effect was only present with the relatively high competent children and not with the relatively low performing children.     

The effects of knowledge,strategies, and the interaction between the two in verbal analogy problem solving

An experiment was conducted to assess how accessibility to relevant knowledge would affect performance on verbal analogy problems as well as the efficacy, perception, and continuation of use of a componential strategy for solving these problems. Participants were either taught to use a componential strategy for solving verbal analogy problems or just given practice opportunities while the accessibility of relevant knowledge was manipulated and the performance and perception of the strategy was assessed. We also investigated whether variations in accessibility to relevant knowledge affected the continuance of strategy use. Results showed that knowledge accessibility affected both performance and the way in which the strategy was perceived. Participants rated the strategy as more useful, easier to use, and less effortful when their initial strategy experience involved solving analogy problems based on familiar vocabulary and relationships. Also, participants who had experience with easily accessible vocabulary and relationships were significantly more likely to choose to continue to use of the strategy on a subsequent task. It is also argued that accessibility to knowledge and strategy use play independent, as opposed to interactive, roles in determining performance.     

Epistemic profiles and self-regulated learning: Examining relations in the context of mathematics problem solving

Relations were examined between epistemic profiles, regulation of cognition, and mathematics problem solving. Two hundred sixty-eight students were sampled from undergraduate mathematics and statistics courses. Students completed inventories reflecting their epistemic profiles and learning strategies, and were profiled as rational, empirical, or both. Based on their profiles, 24 students participated in two problem-solving sessions. Episodes were coded for planning, monitoring, control, use of empirical and rational argumentation, and justification for solutions. For both self-reported metacognitive self-regulation and regulation of cognition during problem solving, students profiled as rational had the highest self-reported mean and actual frequency of regulation of cognition compared to students profiled as predominantly empirical. Moreover, students profiled as predominantly rational correctly solved more problems than the other two groups. Finally, students’ approaches to problem solving were consistent with their epistemic profiles. Relations are discussed in the context of various theoretical frameworks.     

Linking complex problem solving to opportunity identification competence within the context of entrepreneurship

Today’s working life is increasingly characterized by entrepreneurial challenges. Entrepreneurial challenges start at an individual level with the identification of entrepreneurial opportunities, which is acknowledged as one of the key competencies for lifelong learning. Since the identification of entrepreneurial opportunities relies heavily on the opportunity identification competence (OIC) of individuals, understanding the meaning of OIC is relevant. Until now, OIC has been explored in the young entrepreneurship research field. However, entrepreneurship researchers until now have not fully explored OIC. According to several authors, the research on complex problem solving (CPS) in the cognitive research field might contribute to understanding OIC. In this paper, we review the link between OIC and CPS by comparing the cognitive and entrepreneurship research fields. We argue that those who excel in identifying opportunities share core characteristics with high-level complex problem-solvers. We propose to conduct empirical research in the future to investigate the relation between OIC and CPS within a work context in order to gain more insight into OIC. We believe that the cognitive research field contributes to the entrepreneurship research field and provides a deeper understanding of the initial steps of the entrepreneurial process.     

Tutor-student interaction in undergraduate chemistry: a case of learning to make relevant distinctions of molecular structures for determining oxidation states of atoms

ABSTRACT

In this study, we explore the issues and challenges involved in supporting students’ learning to discern relevant and critical aspects of determining oxidation states of atoms in complex molecules. We present a detailed case of an interaction between three students and a tutor during a problem-solving class, using the analytical tool of practical epistemology analysis (PEA). The results show that the ability to make relevant distinctions between the different parts of a molecule for solving the problem, even with the guidance of the tutor, seemed to be challenging for students. These shifts were connected to both purposes that were specific for solving the problem at hand, and additional purposes for general learning of the subject matter, in this case how to assign oxidation states in molecules. The students sometimes could not follow the additional purposes introduced by the tutor, which made the related distinctions more confusing. Our results indicate that in order to provide adequate support and guidance for students the tutor needs to consider how to sequence, move between, and productively connect the different purposes introduced in a tutor-student interaction. One way of doing that is by first pursuing the purposes for solving the problem and then successively introduce additional, more general purposes for developing students’ learning of the subject matter studied. Further recommendations drawn from this study are discussed as well.     

Chemistry problem solving instruction: a comparison of three computer-based formats for learning from hierarchical network problem representations

Within the cognitive load theory framework, we designed and compared three alternative instructional solution formats that can be derived from a common static hierarchical network representation depicting problem structure. The interactive-solution format permitted students to search in self-controlled manner for solution steps, static-solution format displayed all solutions steps, and no-solution format did not have solution steps. When we matched instructional time across the formats, in relation to the complex molarity problems rather than the dilution problems, differential transfer performance existed between the static-solution or no-solution formats and the interactive-solution format, but not between the static-solution format and no-solution format. The manner in which learners interact with the static-solution and no-solution formats depends on their level of expertise in the chemistry domain. With considerable learner expertise, provision of solution steps may be redundant incurring extraneous cognitive load. Absence of the solution steps may not have left sufficient cognitive capacity for germane cognitive load as some beginning learners lacked the prior knowledge to deduce the solution steps. Searching for solution steps presumably incurred extraneous cognitive load which interfered with learning and hence, in the interactive-solution format, it outweighed the benefit of engaging in self-regulated interaction with the content. Hence, cognitive load theory is a promising tool to predict the mental load associated with learning from the three alternative computer-based instructional formats.     

Volunteer motivation,social problem solving,self-efficacy,and mental health: a structural equation model approach

The study aimed to investigate the direct effect of volunteer motivation on social problem-solving ability, self-efficacy, and mental health and examine the mediating effects on volunteer motivation and mental health by testing social problem-solving ability and self-efficacy. We examined a hypothetical model that integrates the concepts of Self-Determination Theory, the Social Problem Solving Model, and the Self-Efficacy Belief Model. Results demonstrated that volunteer motivation was significantly associated with social problem-solving ability and self-efficacy amongst 1530 undergraduate students. Three subscales of social problem-solving ability (positive problem orientation, negative problem orientation, and avoidance style) and self-efficacy served are significant mediators. Model statistics for SEM demonstrated an adequate fit with the data. Volunteer motivation provides a way to enhance social problem-solving ability and self-efficacy. It also leads to better mental health by enhancing positive problem orientation and self-efficacy and by reducing negative problem orientation and avoidance style.     

Individual differences in memory updating in relation to arithmetic problem solving

The study investigates the relationship between memory updating and arithmetic word problem solving. Two groups of 35 fourth graders with high and low memory-updating abilities were selected from a sample of 89 children on the basis of an updating task used by Palladino et al. [Memory & Cognition 29 (2002) 344]. The two groups were required to solve a set of arithmetic word problems and to recall relevant information from another set of problems. Several span tasks, a computation test, and the PMA verbal subtest were also administered. The group with a high memory-updating ability performed better in problem solving, recalling text problems, and in the computation test. The two groups did not differ in the PMA verbal subtest or in the digit and word spans. Results were interpreted as supporting the importance of updating ability in problem solving and of the substantial independence between memory updating and problem solving on one hand and verbal intelligence on the other.     

Junior high school physics: Using a qualitative strategy for successful problem solving

Students at the junior high school (JHS) level often cannot use their knowledge of physics for explaining and predicting phenomena. We claim that this difficulty stems from the fact that explanations are multi‐step reasoning tasks, and students often lack the qualitative problem‐solving strategies needed to guide them. This article describes a new instructional approach for teaching mechanics at the JHS level that explicitly teaches such a strategy. The strategy involves easy to use visual representations and leads from characterizing the system in terms of interactions to the design of free‐body force diagrams. These diagrams are used for explaining and predicting phenomena based on Newton's laws. The findings show that 9th grade students who studied by the approach advanced significantly from pretests to post‐tests on items of the Force Concept Inventory—FCI and on other items examining specific basic and complex understanding performances. These items focused on the major learning goals of the program. In the post‐tests the JHS students performed on the FCI items better than advanced high‐school and college students. In addition, interviews conducted before, during, and after instruction indicated that the students had an improved ability to explain and predict phenomena using physics ideas and that they showed retention after 6 months. © 2010 Wiley Periodicals, Inc. J Res Sci Teach 47: 1094–1115, 2010     

The contribution of external representations in pre-school mathematical problem solving

Could problem solving be the object of teaching in early education? Could appropriate teaching interventions develop to scaffold children's efforts to solve problems? These were the central questions of this article. The sample consisted of 18 children attending public pre-school in Cyprus. The problem they were asked to solve was to find all solutions of the pentomino. The children's problem solving was supported by graphically representing their solutions on squared paper. The findings show that children responded positively to the problem and were successful in finding all solutions for the specific problem. The graphical representation of the solutions and the forms of teacher–children and children–children interactions played an important role in the positive outcome of the activity.