Exploring the Development of Conceptual Understanding through Structured Problem‐solving in Physics

A study on the effect of a structured problem‐solving strategy on problem‐solving skills and conceptual understanding of physics was undertaken with 189 students in 16 disadvantaged South African schools. This paper focuses on the development of conceptual understanding. New instruments, namely a solutions map and a conceptual index, are introduced to assess conceptual understanding demonstrated in students’ written solutions to examination problems. The process of the development of conceptual understanding is then explored within the framework of Greeno’s model of scientific problem‐solving and reasoning. It was found that students who had been exposed to the structured problem‐solving strategy demonstrated better conceptual understanding of physics and tended to adopt a conceptual approach to problem‐solving.     

Balancing Plan-Driven and Agile Methods in Software Engineering Project Courses

Abstraction is a major concept in computer science and serves as a powerful tool in software development. Pattern-oriented instruction (POI) is a pedagogical approach that incorporates patterns in an introductory computer science course in order to structure the learning of algorithmic problem solving. This paper examines abstraction processes in the course of solving an algorithmic problem and highlights three distinct, although interrelated, facets of abstraction: pattern recognition, black-boxing, and structure identification. A study that examined the influence of the POI approach on students' abstraction skills is described; students who learned according to the POI approach were compared with students who learned in a traditional manner with regard to analogical reasoning and problem decomposition and solution, as well as verbal expression. The three facets of abstraction were used to analyze students' abstraction skills and their competency in algorithmic problem solving.     

美国数学课程标准中“问题解决”的变化及启示

全美数学教师理事会(NCTM)在2000年出版发行了《学校数学教育的原则和标准》,与之前相比,此文件中“问题解决”这一过程标准,在坚持以前的一些基本观点的同时,进一步明确“问题解决不仅是学习数学的一个目标,也是学习数学的一种主要方式”;而且增加了新的目标——“使学生能够检验和反思数学问题解决的过程”。由此可见,“课程标准”的制定必然有一个继承和不断改进的过程。自我国的数学课程标准将“解决问题”作为课程目标提出以来,在课程设计和教学实践中出现了一些变化和问题。在借鉴他国经验的同时,应根据我国的国情,继承和发展我国在“解决问题”方面的各种理论和实践成果,研究出培养学生解决问题能力的课程设计方案。     

谈高校大学生学习过程的信息化

信息技术的快速发展逐渐改变着高校大学生的学习过程,学生的学习资源和解决问题的方式越来越多样化。但大学生利用网络学习的效率较低,自控能力较弱,学习信息化程度不高。因此,高校要加强学习过程信息化的硬件环境和软件环境的建设以及教师信息素养的培养,通过构建学习过程信息化模型提高学生信息化学习效率。     

Computer simulations in the high school: Students' cognitive stages,science process skills and academic achievement in microbiology

Computer-assisted learning, including simulated experiments, has great potential to address the problem solving process which is a complex activity. It requires a highly structured approach in order to understand the use of simulations as an instructional device. This study is based on a computer simulation program, 'The Growth Curve of Microorganisms', which required tenth grade biology students to use problem solving skills whilst simultaneously manipulating three independent variables in one simulated experiment. The aims were to investigate the computer simulation's impact on students' academic achievement and on their mastery of science process skills in relation to their cognitive stages. The results indicate that the concrete and transition operational students in the experimental group achieved significantly higher academic achievement than their counterparts in the control group. The higher the cognitive operational stage, the higher students' achievement was, except in the control group where students in the concrete and transition operational stages did not differ. Girls achieved equally with the boys in the experimental group. Students' academic achievement may indicate the potential impact a computer simulation program can have, enabling students with low reasoning abilities to cope successfully with learning concepts and principles in science which require high cognitive skills.     

Josephus问题的动态图形演示

本大讨论了用动态图形方式演示求解Ｊｏｓｅｐｈｕｓ问题的原理和方法，该方法对如何在教学中使用ＣＡＩ技术提出了一个实例、本文同时给出了用Ｃ语言编制的Ｊｏｓｅｐｈｕｓ问题求解过程的动态图形演示ＣＡＩ软件。     

The Effect of Hints and Model Answers in a Student-Controlled Problem-Solving Program for Secondary Physics Education

Many students experience difficulties in solving applied physics problems. Most programs that want students to improve problem-solving skills are concerned with the development of content knowledge. Physhint is an example of a student-controlled computer program that supports students in developing their strategic knowledge in combination with support at the level of content knowledge. The program allows students to ask for hints related to the episodes involved in solving a problem. The main question to be answered in this article is whether the program succeeds in improving strategic knowledge by allowing for more effective practice time for the student (practice effect) and/or by focusing on the systematic use of the available help (systematic hint-use effect). Analysis of qualitative data from an experimental study conducted previously show that both the expected effectiveness of practice and the systematic use of episode-related hints account for the enhanced problem-solving skills of students.     

Empowering educationally disadvantaged mathematics students through a strategies-based problem solving approach

A major impediment to problem solving in mathematics in the great majority of South African schools is that disadvantaged students from seriously impoverished learning environments are lacking in the necessary informal mathematical knowledge to develop their own strategies for solving non-routine problems. A randomized pretest–posttest control group design was used to empirically investigate the effectiveness of a strategies-based problem solving approach on the problem solving performance of 9th grade disadvantaged students. In this approach students receive explicit instruction on a wide repertoire of problem solving strategies. The results reported in this study show a significant improvement in problem solving performance when a strategies-based approach to problem solving was being implemented. Quantitative and qualitative analyses of the responses to the items showed how the treatment group students had internalized as part of their problem solving repertoire the strategies on which they had been explicitly instructed on. The findings of this study make a case for the adoption of this approach so that the gap between the student’s existing problem solving competence, and the cognitive demands of a problem solving task can be bridged.     

The effects of a problem solving strategy on the achievement of earth science students

A review of the stated goals for education reveals a consistent emphasis on problem solving. Problem solving is compatible with the investigative nature of science and with higher order thinking. Consequently, a problem solving strategy was developed to improve the achievement of eighth grade students enrolled in earth science. The sample consisted of 287 eighth grade students randomly assigned to fourteen sections taught by four teachers. This resulted in seven control sections and seven experimental sections. The students in the treatment groups received approximately six weeks of instruction with the experimental groups receiving a variety of problem solving activities. A forty item posttest consisting of four subtests was administered to all students. The results indicate that the problem solving approach was useful in improving the overall achievement of students. It was particular effective in facilitating application of earth science subject matter. This problem solving approach appears to be a feasible strategy to use in most secondary science classrooms.     

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.     

Teaching and learning logic programming in virtual worlds using interactive microworld representations

Logic Programming (LP) follows the declarative programming paradigm, which novice students often find hard to grasp. The limited availability of visual teaching aids for LP can lead to low motivation for learning. In this paper, we present a platform for teaching and learning Prolog in Virtual Worlds, which enables the visual interpretation and verification of program results in a straightforward fashion and requires students to adopt a collaborative problem‐solving approach. The results of the pilot application and student‐centered evaluation of the platform are encouraging regarding group learning performance and user experience. The paper contributes to current practice of teaching and learning LP by proposing a metaphor and a system that can empower the educational process with toy world examples visualized in a shared 3D environment.     

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.     

Managing Uncertainty During Collaborative Problem Solving in Elementary School Teams: The Role of Peer Influence in Robotics Engineering Activity

This study investigated how interaction with peers influenced the ways students managed uncertainty during collaborative problem solving in a 5th-grade class. The analysis focused on peer responses to individuals’ attempts to manage uncertainty they experienced while engaged in collaborative efforts to design, build, and program robots and achieve assignment objectives. Patterns of peer response were established through discourse analysis of work sessions for 5 teams engaged in 2 collaborative projects. Three socially supportive peer responses and 2 unsupportive peer responses were identified. Peer interaction was influential because students relied on supportive social response to enact most of their uncertainty management strategies. This study provides a useful theoretical contribution to understanding the roles of peer interaction in collaborative problem solving. Conceptualizing collaborative problem solving as a process of negotiating uncertainties can help instructional designers shape tasks and relational contexts to facilitate learning.     

Enhancing Student Learning in Food Engineering Using Computational Fluid Dynamics Simulations

Abstract: The current generation of students coming into food science and engineering programs is very visually oriented from their early experiences. To increase their interest in learning, new and visually appealing teaching materials need to be developed. Two diverse groups of students may be identified based on their math skills. Food science students tend to find it difficult to use mathematics as a problem‐solving tool for food engineering problems. Food engineering students, on the other hand, should be challenged to use emerging mathematical tools to develop their problem‐solving skills. Therefore, the approach of this project involved the development of a curriculum to train undergraduate food engineers in the effective use of computational fluid dynamics (CFD) software to solve food engineering problems by engaging them in the creation of food engineering teaching tools. These CFD outputs were then used as innovative teaching tools for the food science students. In this paper, this concept will be illustrated by unsteady‐state heat transfer and fluid flow problems. To evaluate the efficiency of the teaching materials developed, a student focus group was asked to answer the same quiz following a conventional and CFD output aided teaching session. The assessment result showed an improved understanding of the subject after the CFD teaching session. These visual aids were excellent tools to illustrate the validity of the formulas presented in class. In addition, the new visual materials enabled a better understanding of the relationships among different process parameters. In general, this helped the food science students better appreciate the food engineering concepts that govern food processing operations.     

Development of an Online Orientation for an Instructional Technology Masters Program

Four graduate students were tasked with creating a real-world solution to a problem faced by the instructional technology masters program in which they were participating. While taking an online course in multimedia instructional product development, part of East Carolina University??s Masters of Science in Instructional Technology degree program, a team of students faced the challenges of being physically separated, lacking some software and hardware tools, and the relatively brief development period of a semester??s time, to produce supplemental instructional content for students new to the masters program. Working from locations scattered throughout North Carolina, the production team found the time and resources, and relied on the strengths of individual team members, to produce an online orientation for students new to the instructional technology masters program.     

Problem-Solving Preferences of Mathematics Teachers: Focusing on Symmetry

The aim of the study presented in this paper was to explore factors that influence teachers' problem-solving preferences in the process of (a) solving a problem, (b) explaining it to a peer, (c) liking it, and (d) teaching it. About 170 mathematics teachers took part in the different stages of the study. A special mathematical activity was designed to examine factors that influence teachers' problem-solving preferences and to develop teachers' preferences concerning whether to use symmetry when solving the problems. It was implemented and explored in an in-service program for professional development of high-school mathematics teachers. As a result, three interrelated factors that influence teachers' problem-solving preferences were identified: (i) Two patterns in teachers' problem-solving behavior, i.e., teachers' tendency to apply a stereotypical solution to a problem and teachers' tendency to act according to problem-solving beliefs, (ii) the way in which teachers characterize a problem-solving strategy, (iii) teachers' familiarity with a particular problem-solving strategy and a mathematical topic to which the problem belongs. Findings were related to teachers' developing thinking in solving problems and using them with their students. The activity examined in this paper may serve as a model for professional development of mathematic teachers and be useful for different professional development programs.     

问题解决理论视角下师生冲突的处理

问题解决作为心理学一个重要的理论概念,对于处理师生冲突有重要的启发意义。将师生冲突看作是问题来解决,其影响因素有专家与新手的区别、知识表征方式、定势、功能固着、教师处理冲突的动机、教师的情绪、师生之间的关系等七个方面,师生冲突的处理过程可以借助问题解决的步骤来进行,同时问题解决过程中所运用的策略也有助于师生冲突的处理。     

Revitalizing Algebra: the effect of the use of a cognitive tutor in a remedial course

This study investigated the effect of instruction with a cognitive tutoring software system in a remedial algebra course. The performance on algebra tasks of students who attended the experimental (cognitive tutor) and a control class was compared. The results indicated that the two groups of students were equally proficient with respect to algebraic manipulation skills. However, students who attended the experimental algebra section performed significantly better in problem solving than students in the control section. This finding suggested that the use of the cognitive tutor (a) improved students' problem‐solving abilities; (b) fostered student development of richer concepts of variable and function; and (c) improved students' procedural abilities in approaching and carrying through mathematical analyses of relatively complex situations.