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.     

Teaching algorithmic problem solving or conceptual understanding: Role of developmental level,mental capacity,and cognitive style

It has been shown previously that many students solve chemistry problems using only algorithmic strategies and do not understand the chemical concepts on which the problems are based. It is plausible to suggest that if the information is presented in differing formats, the cognitive demand of a problem changes. The main objective of this study is to investigate the degree to which cognitive variables, such as developmental level, mental capacity, and disembedding ability explain student performance on problems which: (1) could be addressed by algorithms or (2) require conceptual understanding. All conceptual problems used in this study were based on a figurative format. The results obtained show that in all four problems requiring algorithmic strategies, developmental level of the students is the best predictor of success. This could be attributed to the fact that these are basically computational problems, requiring mathematical transformations. Although all three problems requiring conceptual understanding had an important aspect in common (the figurative format), in all three the best predictor of success is a different cognitive variable. It was concluded that: (1) the ability to solve computational problems (based on algorithms) is not the major factor in predicting success in solving problems that require conceptual understanding; (2) solving problems based on algorithmic strategies requires formal operational reasoning to a certain degree; and (3) student difficulty in solving problems that require conceptual understanding could be attributed to different cognitive variables.     

Reasoning strategies of students in solving chemistry problems as a function of developmental level,functional M‐capacity and disembedding ability

Achievement in science depends among other factors on hypothetico‐deductive reasoning ability, that is, developmental level of the students. Recent research indicates that the developmental level of students should be studied along with individual difference variables, such as Pascual‐Leone's M‐capacity (information processing) and Witkin's Cognitive Style (disembedding ability). The purpose of this study is to investigate reasoning strategies of students in solving chemistry problems as a function of developmental level, functional M‐capacity and disembedding ability. A sample of 109 freshman students were administered tests of formal operational reasoning, functional M‐capacity, disembedding ability and chemistry problems (limiting reagent, mole, gas laws). Results obtained show that students who scored higher on cognitive predictor variables not only have a better chance of solving chemistry problems, but also demonstrated greater understanding and used reasoning strategies indicative of explicit problem‐solving procedures based on the hypothetico‐deductive method, manipulation of essential information and sensitivity to misleading information. It was also observed that students who score higher on cognitive predictor variables tend to anticipate important aspects of the problem situation by constructing general figurative and operative models, leading to a greater understanding. Students scoring low on cognitive predictor variables tended to circumvent cognitively more demanding strategies and adopt others that helped them to overcome the constraints of formal reasoning, information processing and disembedding ability.     

Team-based complex problem solving: a collective cognition perspective

Today, much problem solving is performed by teams, rather than individuals. The complexity of these problems has exceeded the cognitive capacity of any individual and requires a team of members to solve them. The success of solving these complex problems not only relies on individual team members who possess different but complementary expertise, but more importantly, their collective problem solving ability. To better conceptualize large scale complex problem solving, an understanding of collective cognitive components and processes during team-based complex problem solving is necessary. This paper offers a conceptual discussion about complex problem solving from a collective cognition perspective. The types of cognitive processing and cognitive components of team-based problem solving (TBPS) as well as the cognitive states of collective emergent cognitive states and the interactive mechanisms will be discussed. Also, implications from the model for assessing TBPS performance and suggestions for future research will be offered.     

Multidimensional analysis system for quantitative chemistry problems: Symbol,macro, micro,and process aspects

There is a consensus regarding the fact that students encounter difficulties in understanding scientific concepts, such as the particulate nature of matter, the mole, and the interpretation of chemical symbols. Researchers and practitioners have been looking for teaching methods to improve students' understanding of quantitative chemistry and their ability to solve related problems. This study describes the Multidimensional Analysis System (MAS), an approach to constructing, classifying, and analyzing quantitative chemistry problems. MAS enables classification based on complexity and transformation levels of a quantitative problem. We define three transformation levels: symbol ? macro, symbol ? micro, and symbol ? process. Applying this framework to teaching and research, we investigated the relationships between MAS‐classified chemistry problems and student achievement in solving these problems. The research population, 241 high school chemistry students, studied problem solving according to MAS for 9 weeks; the control group studied the same topic for the same duration in the traditional way. Student achievement was sorted by mathematics level and gender. We found that the success rate of the entire student population in solving these problems decreased as the problem difficulty increased. Experimental group students scored significantly higher than their control group peers. The improvement in student achievement was significantly dependent on the pretest score and the mathematics level, and independent of gender. Students who studied mathematics in the basic level benefited significantly more from MAS‐based teaching than their peers, whose mathematics level was advanced. Based on the research findings, we recommend applying the multidimensional analysis approach while teaching quantitative problems in chemistry. © 2003 Wiley Periodicals, Inc. J Res Sci Teach 40: 278–302, 2003     

问题解决情境下认知工具的设计研究——以数学应用题为例

运用有效认知工具支持学生的问题解决过程逐渐成为当前研究的热点和趋势。针对目前问题解决过程中缺乏有效认知工具支持的现状,文章首先梳理了国内外对认知工具的相关研究,然后以数学应用题为例,总结了影响解题的一般因素,并针对影响因素提出可以辅助教师教学设计和学生学习的认知工具,旨在提高学生的问题解决能力。在此基础上,从问题解决的角度提出了相应认知工具的设计原则和系统模型。     

Spatial ability and its role in organic chemistry: A study of four organic courses

The relationship between spatial ability and performance in organic chemistry was studied in four organic chemistry courses designed for students with a variety of majors including agriculture, biology, health sciences, pre-med, pre-vet, pharmacy, medicinal chemistry, chemistry, and chemical engineering. Students with high spatial scores did significantly better on questions which required problem solving skills, such as completing a reaction or outlining a multi-step synthesis, and questions which required students to mentally manipulate two-dimensional representations of a molecule. Spatial ability was not significant, however, for questions which could be answered by rote memory or by the application of simple algorithms. Students who drew preliminary figures or extra figures when answering questions were more likely to get the correct answer. High spatial ability students were more likely to draw preliminary figures, even for questions that did not explicitly require these drawings. When questions required preliminary or extra figures, low spatial ability students were more likely to draw figures that were incorrect. Low spatial ability students were also more likely to draw structures that were lopsided, ill-proportioned, and nonsymmetric. The results of this study are interpreted in terms of a model which argues that high spatial ability students are better at the early stages of problem solving described as “understanding” the problem. A model is also discussed which explains why students who draw preliminary or extra figures for questions are more likely to get correct answers.     

Structured Collaboration versus Individual Learning in Solving Physics Problems

The research issue in this study is how to structure collaborative learning so that it improves solving physics problems more than individual learning. Structured collaborative learning has been compared with individual learning environments with Schoenfeld’s problem‐solving episodes. Students took a pre‐test and a post‐test and had the opportunity to solve six physics problems. Ninety‐nine students from a secondary school in Shanghai participated in the study. Students who learnt to solve problems in collaboration and students who learnt to solve problems individually with hints improved their problem‐solving skills compared with those who learnt to solve the problems individually without hints. However, it was hard to discern an extra effect for students working collaboratively with hints—although we observed these students working in a more structured way than those in the other groups. We discuss ways to further investigate effective collaborative processes for solving physics problems.     

Effects of multimedia on cognitive load, self-efficacy, and multiple rule-based problem solving

This study investigates effects of multimedia on cognitive load, self-efficacy and learners' ability to solve multiple rule-based problems. Two hundred twenty-two college students were randomly assigned to interactive and non-interactive multimedia groups. Based on Engelkamp's multimodal theory, the present study investigates the role of multimedia in multiple rule-based problem solving. The findings indicate that providing learners with manipulative function in multimedia would facilitate their problem solving through reduced cognitive load and improved self-efficacy. The study identifies a significant mediator effect for self-efficacy that mediates between multimedia and learners' problem solving. Discussion focuses on the effects of multimedia and self-efficacy on learners' performance in multiple rule-based problem solving. Suggestions are made with regard to the design of problem solving in future studies.     

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     

初中化学物质鉴别题的解答探究

在初中化学学习中,物质鉴别类的题目是考试中的热点与难点。提高学生解决这类题目的能力,对学生化学素养的培养有重要作用。文章从物质鉴别例题出发,为学生提出一些解题思路和技巧,以提升学生的解题速度,培养学生良好的化学推理思维。     

Varying effects of subgoal labeled expository text in programming,chemistry, and statistics

Originally intended as a replication study, this study discusses differences in problem solving performance among different domains caused by the same instructional intervention. The learning sciences acknowledges similarities in the learners’ cognitive architecture that allow interventions to apply across domains, but it also argues that each domain has characteristics that might affect how interventions impact learning. The present study uses an instructional design technique that had previously improved learners’ problem solving performance in programming: subgoal labeled expository text and subgoal labeled worked examples. It intended to replicate this effect for solving problems in statistics and chemistry. However, each of the experiments in the three domains had a different pattern of results for problem solving performance. While the subgoal labeled worked example consistently improved performance, the subgoal labeled expository text, which interacted with subgoal labeled worked examples in programming, had an additive effect with subgoal labeled worked examples in chemistry and no effect in statistics. Differences in patterns of results are believed to be due to complexity of the content to be learned, especially in terms of mapping problem solving procedures to solving problems, and the familiarity of tools used to solve problems in the domain. Subgoal labeled expository text was effective only when students learned more complex content and used unfamiliar problem solving tools.     

Small-group composition and peer effects

This paper reviews research on grouping of students within classes and its effects on learning. Primary consideration is given to grouping and mixing students by ability, though consideration is also given to grouping and mixing students by ethnicity and gender as well as to research on the effects of group size. Results of meta-analyses of grouping show a small but meaningful advantage of forming students into groups for instruction as compared to using whole-class instruction. In teacher-led, homogeneous ability groups, peer effects result from the normative environment to the extent that peers contribute to norms for behavior, constructed through cycles of reciprocal teacher–student interaction. In peer-led, heterogeneous ability groups, peer effects stem directly from group interactions and discourse among students that lead to cognitive restructuring, cognitive rehearsal, problem solving, and other forms of higher-level thinking. Similarly, in groups of different ethnic and gender composition, peer effects stem from interactions among students according to their perceived status and relative influence within the groups. We argue that these peer influences interact with instructional processes to mediate the effects of group composition on students’ learning.     

Problem-solving skills of high school chemistry students

What strategies do high school students use when solving chemistry problems? The purpose for conducting this study was to determine the general problem-solving skills that students use in solving problems involving moles, stoichiometry, the gas laws, and molarity. The strategies were examined for success in problem solving for 266 students of varying proportional reasoning ability, using interviews incorporating the think-aloud technique. Data were coded using a scheme based on Polya's heuristics. Results indicated that successful students and those with high proportional reasoning ability tended to use algorithmic reasoning strategies more frequently than nonsuccessful and low proportional reasoning students. However, the majority of all students solved the chemistry problems using only algorithmic methods, and did not understand the chemical concepts on which the problems were based.     

Relationship between inductive arithmetic argumentation and deductive algebraic proof

In this paper, we present a cognitive analysis of the relationship between the argumentation process leading to the construction of a conjecture and its algebraic proof in solving Calendar Algebra problems. To solve this kind of problem, students encounter two sources of potential difficulties: the shift from using arithmetic in the argumentation to using algebra in the proof and the shift from an inductive argument towards a deductive proof. Thus, the aims of this article are to describe these cognitive difficulties and to show how students overcome them. Methodologically, we compare students’ problem solving process corresponding to three problems presented in the first four lessons of a teaching experiment. The analysis and comparison between these three resolution processes is performed using Toulmin’s model.     

动力学中有关参考系的选择

采用不同的参考系解动力学问题,以培养学生的发散思维,使学生具备灵活解决动力学问题的能力.     

Some Consequences of Prompting Novice Physics Students to Construct Force Diagrams

We conducted a series of experiments to investigate the extent to which prompting the construction of a force diagram affects student solutions to simple mechanics problems. A total of 891 university introductory physics students were given typical force and motion problems under one of the two conditions: when a force diagram was or was not prompted as part of the solution. Results indicated that students who were prompted to draw the force diagram were less likely to obtain a correct solution than those who were not prompted to solve the problem in any particular way. Analysis of the solution methods revealed that those students prompted to use a diagram tended to use the formally taught problem‐solving method, and those students not prompted to draw a force diagram tended to use more intuitive methods. Students who were prompted to draw diagrams were also more likely to depict incorrect forces. These results may be explained by two factors. First, novice students may simply be more effective using intuitive, situational reasoning than using new formal methods. Second, prompting the construction of a force diagram may be misinterpreted by the student as a separate task, unrelated to solving the problem. For instruction, the results of this study imply that ignoring students’ prior abilities to solve problems and their necessary developmental stages in learning formal problem‐solving techniques may lead to serious mismatches in what is taught and what is intended to be learned.     

Does a transformation approach improve students’ ability in constructing auxiliary lines for solving geometric problems? An intervention-based study with two Chinese classrooms

We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students’ ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were 130 eighth-grade students in two classes with a comparable background that were taught by the same teacher. A two-week intervention was implemented in the experimental class aiming to help students learn how to use geometric transformations to draw auxiliary lines in solving geometric problems. The data were collected from a teacher interview, video-recordings of the intervention, and pre- and post-tests. The results revealed that there was a positive impact of using geometric transformations on the experimental students’ ability in solving high-level cognitive problems by adding auxiliary lines, though the impact on the students’ ability in solving general geometric problems as measured using the overall average scores was not statistically significant. Recommendations for future research are provided at the end of the article.     

Elementary school teachers' knowledge and beliefs regarding non-routine problems

This study focuses on the knowledge exhibited by 30 elementary school in-service and pre-service teachers in solving non-routine mathematical problems and on their beliefs regarding these kinds of problems. Interviews were used to reveal teachers' knowledge and beliefs. The findings indicated that these teachers had difficulty in solving non-routine problems and that their ability to solve these problems was influenced by their professional backgrounds. Most of the teachers, although failing to solve the given problems, expressed their willingness to give such problems to their students in class, explaining that such problems are important for students to learn how to solve as they help develop mathematical thinking and the skill of solving problems in everyday life. However, the teachers were unwilling to include such problems in examinations.