RESEARCH REPORT

The purpose of this study was to examine the relationship between student understanding of the nature of science and their problem-solving strategies. Six hundred and twenty Year 8 students in Taiwan twice completed two conceptual problem-solving tests and a questionnaire on the nature of science. Four of these students were selected for follow-up interviews. The result of stepwise multiple regression indicated that the subscale on the nature of the scientific method consistently appeared as the best predictor for student problem-solving ability, explaining about 22% of the variance. It was also found that problem-solving strategies were more conceptually based for students that were high scorers on the nature of science survey.     

Effect of explicit problem solving instruction on high school students' problem-solving performance and conceptual understanding of physics

In this study a two-sample, pre/posttest, quasi-experimental design was used to investigate the effect of explicit problem-solving instruction on high school students' conceptual understanding of physics. Eight physics classes, with a total of 145 students, were randomly assigned to either a treatment or comparison group. The four treatment classes were taught how to use an explicit problem-solving strategy, while the four comparison classes were taught how to use a textbook problem-solving strategy. Students' problem-solving performance and conceptual understanding were assessed both before and after instruction. The results indicated that the explicit strategy improved the quality and completeness of students' physics representations more than the textbook strategy, but there was no difference between the two strategies on match of equations with representations, organization, or mathematical execution. In terms of conceptual understanding, there was no overall difference between the two groups; however, there was a significant interaction between the sex of the students and group. The explicit strategy appeared to benefit female students, while the textbook strategy appeared to benefit male students. The implications of these results for physics instruction are discussed. © 1997 John Wiley & Sons, Inc. J Res Sci Teach 34: 551–570, 1997.     

早期留守经历会影响农村大学生的问题解决能力吗 ——基于全国本科生能力测评的实证分析

基于全国本科生能力测评数据,探讨了早期留守经历对农村大学生问题解决能力的影响及其变化。研究发现,早期留守经历对大一新生问题解决能力的影响是负向的,且对女生的负向影响大于男生,对独生子女的负向影响大于非独生子女。在高等教育期间,实习经历、社团经历、学习主动性对有早期留守经历的大四毕业生的问题解决能力具有更明显的正向影响,其可能是使有无早期留守经历的大四毕业生问题解决能力差异不再明显的重要因素。     

Redesigning problem-based learning in the knowledge creation paradigm for school science learning

The introduction of problem-based learning into K-12 science classrooms faces the challenge of achieving the dual goal of learning science content and developing problem-solving skills. To overcome this content-process tension in science classrooms, we employed the knowledge-creation approach as a boundary object between the two seemingly contradicting activities: learning of science content and developing problem-solving skills. As part of a design research, we studied a group of Grade 9 students who were solving a problem related to the Law of Conservation of Energy. Through the lens of the activity theory, we found that students’ understanding of the intended science knowledge deepened as they made sense of the disciplinary-content knowledge in the context of the problem and concurrently, the students successfully developed solutions for the problem. This study shows that developing problem-solving competencies and content learning need not be disparate activities. On the contrary, we can harness the interdependency of these two activities to achieve dual goals in learning.     

论中小学数学课程中的情境及其作用

作为一种数学学习资源,情境在数学教学中发挥着多种作用:激发兴趣,促进学生参与数学学习;揭示知识的产生背景,促进学生对数学的理解;启迪思维,引导学生探寻解决问题的策略;提供运用数学的机会,培养学生解决问题的能力;等等。深刻理解情境多方面的作用,有助于促进学生有意义的数学学习。     

The Development,Implementation, and Evaluation of a Problem Solving Heuristic

Problem-solving is one of the main goals in science teaching and is something many students find difficult. This research reports on the development, implementation and evaluation of a problem-solving heuristic. This heuristic intends to help students to understand the steps involved in problem solving (metacognitive tool), and to provide them with an organized approach to tackling problems in a systematic way. This approach guides students by means of logical reasoning to make a qualitative representation of the solution of a problem before undertaking calculations, using a backwards strategy, which thus comprises a cognitive tool. The findings of the study suggest that students found the heuristic useful in setting up and solving quantitative chemical problems, and helped them to understand the phases of the problem solving process. Possible applications of the heuristic in the classroom include its use in formative assessment, to identify and to overcome student alternative conceptions, problem-solving in a cooperative environment, and to reduce the gender gap in science.     

Complex problem solving in L1 education: Senior high school students' knowledge of the language problem-solving process

The solving of reasoning problems in first language (L1) education can produce an understanding of language, and student autonomy in language problem solving, both of which are contemporary goals in senior high school education. The purpose of this study was to obtain a better understanding of senior high school students' knowledge of the language problem-solving process. Fifty-three 11th-grade high school students solved standard, comprehension, and linguistic reasoning problems. Before solving the problems, the participants had filled in open-ended questions inquiring about their knowledge regarding the effectiveness of a chosen problem-solving strategy. Content analysis of the responses indicated four categories and nine subcategories. The implications of the relatively few responses in the category of explicit knowledge of the language problem-solving process are discussed in the light of the changing needs of L1 students.     

Analysing student written solutions to investigate if problem-solving processes are evident throughout

An interdisciplinary science course has been implemented at a university with the intention of providing students the opportunity to develop a range of key skills in relation to: real-world connections of science, problem-solving, information and communications technology use and team while linking subject knowledge in each of the science disciplines. One of the problems used in this interdisciplinary course has been selected to evaluate if it affords students the opportunity to explicitly display problem-solving processes. While the benefits of implementing problem-based learning have been well reported, far less research has been devoted to methods of assessing student problem-solving solutions. A problem-solving theoretical framework was used as a tool to assess student written solutions to indicate if problem-solving processes were present. In two academic years, student problem-solving processes were satisfactory for exploring and understanding, representing and formulating, and planning and executing, indicating that student collaboration on problems is a good initiator of developing these processes. In both academic years, students displayed poor monitoring and reflecting (MR) processes at the intermediate level. A key impact of evaluating student work in this way is that it facilitated meaningful feedback about the students’ problem-solving process rather than solely assessing the correctness of problem solutions.     

The impact of guidance during problem-solving prior to instruction on students’ inventions and learning outcomes

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.     

Mathematical enculturation from the students’ perspective: shifts in problem-solving beliefs and behaviour during the bachelor programme

This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as experienced bachelor students, they again fill in the questionnaire. As an educational exercise in academic reflection, they have to explain their individual shifts in beliefs, if any. Significant shifts for the group as a whole are reported, such as the growth of attention to metacognitive aspects in problem-solving or the growth of the belief that problem-solving is not only routine but has many productive aspects. On the one hand, the changes in beliefs and behaviour are mostly towards their teachers’ beliefs and behaviour, which were measured using the same questionnaire. On the other hand, students show aspects of the development of an individual problem-solving style. The students explain the shifts mainly by the specific nature of the mathematics problems encountered at university compared to secondary school mathematics problems. This study was carried out in the theoretical framework of learning as enculturation. Apparently, secondary mathematics education does not quite succeed in showing an authentic image of the culture of mathematics concerning problem-solving. This aspect partly explains the low number of students choosing to study mathematics.

Elaborating the structures of a science discipline to improve problem-solving instruction: An account of Classical Genetics' theory structure,function, and development

Situating the conceptual knowledge of a science discipline in the context of its use in the solving of problems allows students the opportunity to develop: a highly structured and functional understanding of the conceptual structure of the discipline; general and discipline-specific problem-solving strategies and heuristics; and insight into the nature of science as an intellectual activity. In order realize these potential learning outcomes, the reconstructions of scientific theories used in problem solving must provide a detailed account of (1) realistic scientific problems and their solutions; (2) problem-solving strategies and patterns of reasoning of disciplinary experts; (3) the various ways that theories function for both disciplinary experts and students; and (4) the way theories, as solutions to realistic scientific problems, develop over time. The purpose of this paper, therefore, is to provide further specificity regarding a philosophical reconstruction of the structure of Classical Genetics Theory that can facilitate problem-solving instruction. We analyze syntactic, semantic and problem-based accounts of theory structure with respect to the above criteria and develop a reconstruction that incorporates elements from the latter two. We then describe how that reconstruction can facilitate realistic problem solving on the part of students.     

“PBL教学法”在《助产技术》教学中的尝试

目的探讨以问题为中心的教学法（PBL）在《助产技术》教学中的应用及效果。方法对95名2009级助产生实施分组教学,其中实验组48人采用PBL教学法,对照组47人采用传统教学法;课程结束后评价教学效果。结果实验组学生考核成绩（83.12±6.16）分,显著高于对照组班（72.36±7.35）分,差异有显著性意义（P〈0.01）。实验组学生自主学习的动力、理论知识的系统化理解、分析问题和解决问题的能力及角色适应能力显著高于对照组（P〈0.05或P〈0.01）。结论在《助产技术》教学中运用PBL教学法能激发学生自主学习的动力,增强学生自信心,提高综合素质,同时也提高了教学质量,有效地提高学生的学习成绩。     

促进深度学习的教学推理:实践逻辑与策略选择

学生的深度学习是以学生的知识理解与运用为价值取向,以培养学生的高阶思维能力和问题解决能力为目标的一种学习。但知识论证不充足、知识点状分布、绝对真理知识观等表层知识教学已偏离了学习的本质及价值,产生了知识教学阻滞深度学习的困局。教学推理是教师根据已知教学条件及个体情境认知,确定问题并生成教学策略的连续性思维活动。它克服了以往僵化的教学方式,为促进深度学习提供可能逻辑。其中,学科知识逻辑能促进学习触及知识的意义世界,学生经验逻辑能促进学习进入学生的心灵世界,实践自为逻辑能促进学习关联自我的生活世界。最后,促进深度学习的教学推理策略应着力于以"批判与交融"为取向的教学理解,形成以"联结与转化"为纽带的教学逻辑,开展以"假设与证据"为核心的课堂论证教学,创设以"推断与评估"为特质的教学情境。     

Connected Chemistry—Incorporating Interactive Simulations into the Chemistry Classroom

The aim of this paper is to describe a novel modeling and simulation package, connected chemistry, and assess its impact on students' understanding of chemistry. Connected chemistry was implemented inside the NetLogo modeling environment. Its design goal is to present a variety of chemistry concepts from the perspective of emergent phenomena—that is, how macro-level patterns in chemistry result from the interactions of many molecules on a submicro-level. The connected chemistry modeling environment provides students with the opportunity to observe and explore these interactions in a simulated environment that enables them to develop a deeper understanding of chemistry concepts and processes in both the classroom and laboratory. Here, we present the conceptual foundations of instruction using connected chemistry and the results of a small study that explored its potential benefits. A three-part, 90-min interview was administered to six undergraduate science majors regarding the concept of chemical equilibrium. Several commonly reported misconceptions about chemical equilibrium arose during the interview. Prior to their interaction with connected chemistry, students relied on memorized facts to explain chemical equilibrium and rigid procedures to solve chemical equilibrium problems. Using connected chemistry students employed problem-solving techniques characterized by stronger attempts at conceptual understanding and logical reasoning.     

KNOWLEDGE USE IN THE CONSTRUCTION OF GEOMETRY PROOF BY SRI LANKAN STUDENTS

Within the domain of geometry, proof and proof development continues to be a problematic area for students. Battista (2007) suggested that the investigation of knowledge components that students bring to understanding and constructing geometry proofs could provide important insights into the above issue. This issue also features prominently in the deliberations of the 2009 International Commission on Mathematics Instruction Study on the learning and teaching of proofs in mathematics, in general, and geometry, in particular. In the study reported here, we consider knowledge use by a cohort of 166 Sri Lankan students during the construction of geometry proofs. Three knowledge components were hypothesised to influence the students’ attempts at proof development: geometry content knowledge, general problem-solving skills and geometry reasoning skills. Regression analyses supported our conjecture that all 3 knowledge components played important functions in developing proofs. We suggest that whilst students have to acquire a robust body of geometric content knowledge, the activation and the utilisation of this knowledge during the construction of proof need to be guided by general problem-solving and reasoning skills.     

Visual spatial representation in mathematical problem solving by deaf and hearing students

This research examined the use of visual-spatial representation by deaf and hearing students while solving mathematical problems. The connection between spatial skills and success in mathematics performance has long been established in the literature. This study examined the distinction between visual-spatial "schematic" representations that encode the spatial relations described in a problem versus visual-spatial "pictorial" representations that encode only the visual appearance of the objects described in a problem. A total of 305 hearing (n = 156) and deaf (n = 149) participants from middle school, high school, and college participated in this study. At all educational levels, the hearing students performed significantly better in solving the mathematical problems compared to their deaf peers. Although the deaf baccalaureate students exhibited the highest performance of all the deaf participants, they only performed as well as the hearing middle school students who were the lowest scoring hearing group. Deaf students remained flat in their performance on the mathematical problem-solving task from middle school through the college associate degree level. The analysis of the students' problem representations showed that the hearing participants utilized visual-spatial schematic representation to a greater extent than did the deaf participants. However, the use of visual-spatial schematic representations was a stronger positive predictor of mathematical problem-solving performance for the deaf students. When deaf students' problem representation focused simply on the visual-spatial pictorial or iconic aspects of the mathematical problems, there was a negative predictive relationship with their problem-solving performance. On two measures of visual-spatial abilities, the hearing students in high school and college performed significantly better than their deaf peers.     

A comparison of strategic development for multiplication problem solving in low-, average-, and high-achieving students

The present study investigated the differences of strategy use between low-, average-, and high-achieving students when solving different multiplication problems. Nineteen high-, 48 average-, and 17 low-achieving students participated in this study. All participants were asked to complete three different multiplication tests and to explain how they solved these problems. Results suggested that low achievers used incorrect operation strategies more frequently, indicating a lack of conceptual understanding of multiplication. High-achieving students demonstrated greater flexibility in problem-solving and were more accurate in performing direct retrieval or math algorithm strategies. Results were discussed about improving low achievers’ use of advanced strategies, enhancing their flexibility in choosing strategies and improving students’ accuracy in using direct retrieval or math algorithms.     

Promoting skilled problem-solving behavior among beginning physics students

Beginning physics students were constrained to analyze mechanics problems according to a hierarchical scheme that integrated concepts, principles, and procedures. After five 1-hour sessions students increased their reliance on the use of principles in categorizing problems according to similarity of solution and in writing qualitative explanations of physical situations. In contrast, no consistent shift toward these expert-like competencies was observed using control treatments in which subjects spent the same amount of time solving problems using traditional approaches. In addition, when successful at performing the qualitative analyses, novices showed significant improvements in problem-solving performance in comparison to novices who directed their own problem-solving activities. The implications of this research are discussed in terms of instructional strategies aimed at promoting a deeper understanding of physics.