A schematic–Theoretic view of problem solving and development of algebraic thinking

This study explored the problem-solving schemas developed by 7th-grade pre-algebra students as they participated in a teaching experiment that was designed to help students develop effective schemas for solving algebraic problem situations involving contexts of (1) growth and change and (2) size and shape. This article describes the qualities and types of schemas that students developed through examples of problems used to develop schemas, examples of students' reasoning and writing, and excerpts from student interviews. Findings from the study indicated that there is a link between the type of generalizations students construct and the schemas they are forming. By using these schemas students recognize, extend, and generalize patterns and quantitative relationships both verbally and symbolically. This revised version was published online in July 2006 with corrections to the Cover Date.     

A research method using microcomputers to assess conceptual understanding and problem solving

Important goals in science education include the elucidation of how students develop a world view, reason about new information, and solve problems. This paper focuses on a research strategy using microcomputers that is directed towards elucidating conceptual understanding and problem solving strategies used by subjects interacting with an open-ended genetics simulation. The field method employed in this study is termed “structured observations”. The use of this method facilitated the generation of data during problem solving sessions by subjects in a think aloud protocol. Three sets of synchronized information of subjects’ interactions with the software were obtained: a video image which provided the sequence and duration of computer screen displays, a video image of subjects, and an audio track of verbal commentaries. The verbal protocol data, complemented by synchronized visual data, were analyzed using software tools for qualitative analysis. The use of these kinds of software programs aided researchers in the analysis of complex, qualitative data. The data were subjected to codings as text files, searches for patterns, and retrievals of patterns among coded variables. Frequency tables of the codes and patterns were generated for further interpretation. By these means, patterns of operations can be identified and inferences made about problem solvers’ conceptual understanding. Specializations: computer-based problem solving secondary teacher education. Specializations: computer-based problem solving, software design and development.     

Mathematics knowledge for understanding and problem solving

Two important aspects of transfer in mathematics learning are the application of mathematical knowledge to problem solving and the acquisition of more advanced concepts, both in mathematics and in other domains. This paper discusses general assumptions and themes of current cognitive research on mathematics learning, focusing on issues of the understanding thought to facilitate transfer of mathematical knowledge. Two studies illustrating these themes are presented, one concerning students' understanding of numerical relationships involved in basic addition and subtraction combinations, the other dealing with students' understanding of algebraic expressions and transformations. Implications of these cognitive perspectives for instruction are discussed.     

基于问题解决指向学科理解——高中化学教学转型的探寻

在阐释问题解决教学和化学学科理解基本内涵的基础上,提出丰厚学科知识,增进教师学科理解;开展深度教学,构建结构化的认知;彰显教育启蒙,回归科学探究本义;在实践应用中,提升学生学科理解;以创新为导向,倡导真实多元评价等高中化学教学转型的思考与探寻.     

Technology in the curriculum: A vehicle for the development of children's understanding of science concepts through problem solving

This research was carried out over a period of ten months with children in Grades 2 and 3 (aged 7 and 8) who were participating in a sequence of technology activities. Since the introduction into Victorian primary schools ofThe Technology Studies Framework P-10 (Crawford, 1988), more teachers are including technology studies in their classrooms and by so doing may assist children's understanding of science concepts. Children are being exposed to science phenomena related to the technology activities and Technology Studies may be a way of providing children with science experiences. ‘Technology Studies’ in this context refers to children carrying out practical problem solving tasks which can be completed without any particular scientific knowledge. Participation in the technology activities may encourage children to become actively involved, thereby facilitating an exploration of the related science concepts. The project identified the importance of challenge in relation to the children's involvement in the technology activities and the conference paper (available from the first author) discusses particular topics in terms of the balance between cognitive/metacognitive and affective influences (Baird et al., 1990) Specializations: science and technology education, interest and attitudinal change. Specialization: technology in the primary school.     

Understanding individual problem-solving style: A key to learning and applying creative problem solving

More than five decades of research and development have focused on making the Creative Problem Solving process and tools accessible across a wide range of ages and contexts. Recent evidence indicates that when individuals, in both school and corporate settings, understand their own style of problem solving, they are able to learn and apply process tools more effectively, and when teams appreciate the styles of their individual members, their problem solving efforts are enhanced. We summarize recent studies and report new data supporting the conclusion that individual style differences provide an important key to understanding the interaction of person, process, product, and press when managing change.     

Contribution of teacher ratings of behavioral characteristics to the prediction of divergent thinking and problem solving

Divergent thinking and problem-solving performance of 382 fourth, fifth, and sixth graders from two suburban, middle-class elementary schools was predicted from teachers' ratings of students' affective/behavioral characteristics and from standard intelligence and achievement test scores. Median Rs were. 61 and. 38, for full-model (ratings plus cognitive measures) and reduced-model (only ratings) predictions, respectively. Results across schools and sexes were similar, with teachers' ratings of sensitivity to beauty, risk taking, awareness of impulses and openness to the irrational, and sense of humor the most frequent significant predictors in addition to the standardized measures. The usefulness of affective/behavioral plus cognitive measures in creative thinking identification procedures is discussed.     

The CLIA-model: A framework for designing powerful learning environments for thinking and problem solving

A major challenge for education and educational research is to build on our present understanding of learning for designing environments for education that are conducive to fostering in students self-regulatory and cooperative learning skills, transferable knowledge, and a disposition toward competent thinking and problem solving. Taking into account inquiry-based knowledge on learning and recent instructional research, this article presents the CLIA-model (Competence, Learning, Intervention, Assessment) as a framework for the design of learning environments aimed to be powerful in eliciting in students learning processes that facilitate the acquisition of productive knowledge and competent learning and thinking skills. Next, two intervention studies are described that embody major components of this framework, one focussing on mathematical problem solving in primary school, and a second one relating to self-regulatory skills in university freshmen. Both studies were carried out in parallel with the development of the framework, and were instrumental in identifying and specifying the different components of the model. They yielded both promising initial support for the model by showing that CLIA-based learning environments are indeed powerful in facilitating in students the acquisition of high-literacy learning results, especially the acquisition and transfer of self-regulation skills for learning and problem solving.     

A computational model of student cognitive processes while solving a critical thinking problem in science

Critical thinking when engaged in science problem solving around even simple tasks such as the Piagetian volume conservation task is a complex endeavor. Tasks such as the conservation task often require the interaction of multiple cognitive systems. Parity judgment, retrieval, and lateral thinking are three examples of such systems interacting with critical thinking during a student’s attempt to solve the Piagetian task. The purpose of this computational ablation study is to establish the role of critical thinking as a necessary component of a system of cognition used for the completion of the Piagetian volume conservation task. This ablation study consists of three phases. The confidence interval between the ablation model and the elementary students do not overlap, indicating they are not statistically significantly different. This provides evidence that the model successfully emulates aspects of human cognition and the model can provide a robust picture of science student cognitive processes.     

看似合理 其实不然——一道习题引发的思考

本文对一道电磁感应题目中提供的已知数据进行了计算,论述证明了其不合理性.旨在研究在物理问题中如何给出合理的已知数据.本文主要计算了当物体受到与速度有关的变力作用时,物体的速度、加速度和位移公式,证明过程用到了简单的高等数学的知识.     

Cognitive development and problem solving of Afro-American students in chemistry

The aims of this study were to investigate the level of cognitive development of Afro-American students enrolled in general chemistry courses at the college level and to determine the strategies used by both successful and unsuccessful Afro-American students in solving specific types of stoichiometric problems. It was found that the choice of a strategy is not significantly related to cognitive development of the student in specific types of stoichiometric problems. However, the following trend was noted: Students who are formal-operational in thought are more likely to be successful when solving mole-volume problems and complex mole-mole problems than are their concrete-operational counterparts. Additionally, a systematic strategy proved to be successful for the students, regardless of the cognitive development, when balancing simple and complex chemical equations. Also, algorithmic/reasoning strategies were needed to solve the mole-volume problem. A higher level of cognitive development and reasoning may be crucial factors in solving the more sophisticated types of problems in stoichiometry.     

把数学思想渗透到解题方法之中

从数学教育的目的出发 ,阐述了数学思想和解题方法以及它们之间的关系。指出了当前在数学思想和解题方法教学上的一些不足之处 ,并结合实例提出了在解题教学中如何运用数学思想和解题方法的一些观点和做法。     

再探讨数学“问题解决”

本回眸数学问题解决的历史，对一些关键性的论题作了探讨，并提出的展望，期待为我国数学创新教育提供参考。     

Radiation: The key to understanding the universe

The only source of information about the universe is the radiation that we receive from various astronomical sources. This article describes some of the methods used by astronomers to analyze this radiation to unveil the mysteries of the universe.     

Cognitive development,genetics problem solving,and genetics instruction: A critical review

Recent studies have analyzed the cognitive demands of solving problems in genetics, focusing primarily on the Piagetian schemas of combinations, proportions, and probability. Based on data from these primarily correlational studies, some authors have argued for the elimination of classical genetics from the high school curriculum. The critical review of the literature presented in this article reaffirms that formal-operational thought is conducive to successful genetics problem solving. The weight of the evidence to date, however, does not support the position that formal operational thought is strictly required for solving typical genetics problems. Arguments are therefore presented in support of the inclusion of genetics and genetics problem solving in high school biology. Implications of this analysis for the selection of appropriate content, problems, and instructional techniques for genetics instruction for nonformal students are presented.