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     

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.     

Cognitive restructuring as an early stage in problem solving

This article examines the hypothesis that there are preliminary stages in problem solving which most chemists neglect when trying to teach their students how to solve problems in introductory chemistry courses. It is during these early stages that relevant information is disembedded from the question and the problem is restructured. Unless students can successfully complete these cognitive restructuring stages, they cannot proceed on to the more analytic stages in problem solving that have received more attention from chemists. Preliminary evidence for this hypothesis consists of linear correlations between student ability to handle disembedding and cognitive restructuring tasks in the spatial domain and their ability to solve chemistry problems.     

初中生在几何解题中所出现错误的调查研究

学生几何解题中的错误可分为以下5类：“阅读理解(包括对图形的理解)”错误；“转换”错误；“加工技能”错误；“策略选择”错误；“编码”错误．其中“加工技能”的错误率最高，其次是“策略选择”．而导致错误的主要原因是过强的动机、不正确的观念和认知图式存在缺陷。     

A study of two measures of spatial ability as predictors of success in different levels of general chemistry

Preliminary data (Bodner and McMillen, 1986) suggested a correlation between spatial ability and performance in a general chemistry course for science and engineering majors. This correlation was seen not only on highly spatial tasks such as predicting the structures of ionic solids (r = 0.29), but also on tasks such as multiple-choice stoichiometry questions (r = 0.32) that might not be expected to involve spatial skills. To further investigate the relationship between spatial ability and performance in introductory chemistry courses, two spatial tests were given to 1648 students in a course for science and engineering majors (Carter, 1984) and 850 students in a course for students from nursing and agriculture (La-Russa, 1985) at Purdue. Scores on the spatial tests consistently contributed a small but significant amount to success on measures of performance in chemistry. Correlations were largest, however, for subscores that grouped questions that tested problem solving skills rather than rote memory or the application of simple algorithms, and correlations were also large for verbally complex questions thaty required the students to disembed and restructure relevant information.     

Development and Assessment of A Diagnostic Tool to Identify Organic Chemistry Students’ Alternative Conceptions Related to Acid Strength

The central goal of this study was to create a new diagnostic tool to identify organic chemistry students’ alternative conceptions related to acid strength. Twenty years of research on secondary and college students’ conceptions about acids and bases has shown that these important concepts are difficult for students to apply to qualitative problem solving. Yet, few published studies document how students’ prior knowledge of acids influences their understanding of acid strength in organic chemistry contexts. We developed a nine-item multiple-tier, multiple-choice concept inventory to identify alternative conceptions that organic chemistry students hold about acid strength, to determine the prevalence of these conceptions, and to determine how strongly these conceptions bias student reasoning. We identified two significant alternative conceptions that organic chemistry students hold about acid strength. Students who answered items incorrectly were more confident about their answers than peers who answered items correctly, suggesting that after one semester of organic chemistry, students do not know what they do not know. Implications for the teaching of acid strength are discussed.     

Visual‐Spatial Representation,Mathematical Problem Solving,and Students of Varying Abilities

The purpose of this study was to investigate students' use of visual imagery while solving mathematical problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N= 66) participated in this study. Students were assessed on measures of mathematical problem solving and visual‐spatial representation. Visual‐spatial representations were coded as either primarily schematic representations that encode the spatial relations described in the problem or primarily pictorial representations that encode persons, places, or things described in the problem. Results indicated that gifted students used significantly more visual‐spatial representations than the other two groups. Students with LD used significantly more pictorial representations than their peers. Successful mathematical problem solving was positively correlated with use of schematic representations; conversely, it was negatively correlated with use of pictorial representations.     

Finding and using patterns in linear generalising problems

Linear generalising problems are questions which require students to observe and use a linear pattern of the formf(n)=an+b withb0. This study reports responses of students aged between 9 and 13 to these questions, documenting the mathematical models that they select, the strategies used in implementing them and the explanations they give. Substantial inconsistency of choice of model is observed; students who began a question correctly frequently adopted a simpler but incorrect model for more difficult parts of the question. Students who had undertaken a course in problem solving implicitly used a linear model more frequently and consistently and their explanations more often related the spatial patterns and the number patterns. They seemed to understand the relationship between the data and the generalising rule more completely.     

Spatial visualization, visual imagery, and mathematical problem solving of students with varying abilities

The purpose of this study was to investigate students' use of visual imagery and its relationship to spatial visualization ability while solving mathematical word problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N = 66) participated in this study. Students were assessed on measures of mathematical problem solving, visual imagery representation, and spatial visualization ability. The results indicated that gifted students performed better on both spatial visualization measures than students with LD and average-achieving students. Use of visual images was positively correlated with higher mathematical word-problem-solving performance. Furthermore, the use of schematic imagery was significantly and positively correlated with higher performance on each spatial visualization measure; conversely, it was negatively correlated with the use of pictorial images.     

化学教学中提高学生提问能力的对策

在化学课堂教学中,很少有学生主动向老师提出问题,这样很难提高学生的创新思维能力和解决问题的能力。本文主要对这种现象进行分析并提出提高学生提问能力的对策。     

Conceptual Versus Algorithmic Problem-solving: Focusing on Problems Dealing with Conservation of Matter in Chemistry

The students?? performance in various types of problems dealing with the conservation of matter during chemical reactions has been investigated at different levels of schooling. The participants were 499 ninth grade (ages 14, 15 years) and 624 eleventh grade (ages 16, 17 years) Greek students. Data was collected using a written questionnaire concerning basic chemical concepts. Results of statistical factor and correlation analysis confirmed the classification of the problems used in three types: ??algorithmic-type??, ??particulate-type??, and ??conceptual-type??. All the students had a far better performance in ??particulate-type?? problems than in the others. Although students?? ability in solving ??algorithmic-type?? problem increases as their school experience in chemistry progresses, their ability in solving ??conceptual-type?? problems decreases. Students?? achievement in chemistry was measured by a Chemical Concepts Test (CCT) containing 57 questions of various forms. High-achievement students scored higher both on ??algorithmic-type?? and ??particulate-type?? problems than low achievers with the greatest difference observed in solving ??algorithmic-type?? problems. It is concluded that competence in ??particulate-type?? and ??algorithmic-type?? problem solving may be independent of competence in solving ??conceptual-type?? ones. Furthermore, it was found that students?? misconceptions concerning chemical reactions and equivalence between mass and energy are impediments to their problem solving abilities. Finally, based on the findings, few suggestions concerning teaching practices are discussed.     

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.     

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.     

Cognitive strategies used by chemistry students to solve volumetric analysis problems

The study investigated the strategies used by 47 high school students to solve volumetric analysis problems in chemistry. Using the talking-aloud technique, the students were required to calculate the concentration of hydrochloric acid used in a titration with NaOH after having performed the titration themselves. Students were met individually and their verbalization audiotaped. After making this calculation, each student was asked to use the same data to predict the concentration of acid in three situations involving different mole ratios. It was found that two main strategies, Formula Approach and Proportional Approach with their variants, were employed by the students during the problem solving process. The Formula Approach was found to be used mainly by the students in the high ability group while students in the low ability group used the Proportional Approach. It was also found that problems involving 2:1 stoichiometric ratios presented a number of conceptual problems to the students. These conceptual problems were found to be related to their inability to write balanced equations or write correct formulas, focusing on only the strength of acid, inability to use the mole ratios in the calulations and deriving the mole ratios from the formulas of reactants.     

PROBING THE RELATIONSHIP BETWEEN PROCESS OF SPATIAL PROBLEMS SOLVING AND SCIENCE LEARNING: AN EYE TRACKING APPROACH

There were two purposes in the study. One was to explore the cognitive activities during spatial problem solving and the other to probe the relationship between spatial ability and science concept learning. Twenty university students participated in the study. The Purdue Visualization of Rotations Test (PVRT) was used to assess the spatial ability, whose items were divided into different types of problems with respect to the rotation angles and levels of plane invisibility. The eye tracking technology and the interview technique were employed to analyze subjects’ the online cognitive processes and problem solving strategies. Students’ concept gains were examined by content analysis after reading a science report. The result shows that, first, the interview analysis shows that students of different PVRT performances employed different problem solving strategies. Second, rotation angles as well as levels of plane invisibility inserted significant effects on the online processes and performances of the spatial problem solving. Third, the accuracy performance of PVRT was correlated with eye movement patterns. At last, it was found that concept performance was not correlated with PVRT performance but associated with spatial memory and problem solving strategies.     

Performance on Middle School Geometry Problems With Geometry Clues Matched to Three Different Cognitive Styles

ABSTRACT— This study investigated the relationship between 3 ability‐based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems provided clues compatible with their cognitive style. Students were identified as having a particular cognitive style when they scored equal to or above the median on the measure assessing this ability. A geometry test was developed in which each problem could be solved on the basis of verbal reasoning clues (matching verbal deductive cognitive style), mental rotation clues (matching spatial imagery cognitive style), or shape memory clues (matching object imagery cognitive style). Straightforward cognitive style–clue‐compatibility relationships were not supported. Instead, for the geometry problems with either mental rotation or shape memory clues, students with a combination of both verbal and spatial cognitive styles tended to do the best. For the problems with verbal reasoning clues, students with either a verbal or a spatial cognitive style did well, with each cognitive style contributing separately to success. Thus, both spatial imagery and verbal deductive cognitive styles were important for solving geometry problems, whereas object imagery was not. For girls, a spatial imagery cognitive style was advantageous for geometry problem solving, regardless of type of clues provided.     

Beyond ball-and-stick: Students' processing of novel STEM visualizations

Students are frequently presented with novel visualizations introducing scientific concepts and processes normally unobservable to the naked eye. Despite being unfamiliar, students are expected to understand and employ the visualizations to solve problems. Domain experts exhibit more competency than novices when using complex visualizations, but less is known about how and when learners develop representational fluency. This project examined students' moment-by-moment adoption patterns for scientific visualizations. In a laboratory experiment, introductory-level organic chemistry students viewed familiar ball-and-stick and novel electrostatic potential map representations while solving chemistry problems. Eye movement patterns, verbal explanations, and individual difference analyses showed that students initially relied on familiar representations, particularly for difficult questions. However, as the task unfolded, students with more prior knowledge began relying upon the novel visualizations. These results indicate adoption and fluent use of visualizations is not given; rather, it is a function of prior knowledge and unfolding experience with presented content.     

Flowing Toward Correct Contributions During Group Problem Solving: A Statistical Discourse Analysis

Groups that created more correct ideas (correct contributions or CCs) might be more likely to solve a problem, and students' recent actions (micro-time context) might aid CC creation. 80 high school students worked in groups of 4 on an algebra problem. Groups with higher mathematics grades or more CCs were more likely to solve the problem. Dynamic multilevel analysis statistically identified watersheds (breakpoints) that divided each group's conversation into distinct time periods with many CCs versus few CCs, and modeled the groups' 2,951 conversation turns. Wrong contributions, correct evaluations of one another's ideas, justifications, and polite disagreements increased the likelihood of a CC. In contrast, questions, rude disagreements, and agreements reduced it. Justifications had the largest effects, whereas the effects of correct evaluations lasted 3 speaker turns. Some effects differed across groups or time periods. In groups that solved the problem, justifications were more likely to yield CCs, and questions were more likely to elicit explanations. Meanwhile, the effects of agreements and correct evaluations on CCs differed across time periods. Applied to practice, teachers can encourage students to evaluate others' ideas carefully and politely, express and justify their own ideas, and explain their answers to group members' questions.     

Students' cognitive focus during a chemistry laboratory exercise: Effects of a computer‐simulated prelab

To enhance the learning outcomes achieved by students, learners undertook a computer‐simulated activity based on an acid–base titration prior to a university‐level chemistry laboratory activity. Students were categorized with respect to their attitudes toward learning. During the laboratory exercise, questions that students asked their assistant teachers were used as indicators of cognitive focus. During the interviews, students' frequency and level of “spontaneous” use of chemical knowledge served as an indicator of knowledge usability. Results suggest that the simulation influenced students toward posing more theoretical questions during their laboratory work and, regardless of attitudes, exhibiting a more complex, correct use of chemistry knowledge in their interviews. A more relativistic student attitude toward learning was positively correlated with interview performance in both the control and treatment groups. © 2007 Wiley Periodicals, Inc. J Res Sci Teach 44: 1108–1133, 2007