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.     

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.     

Reasoning strategies used by students to solve stoichiometry problems and its relationship to alternative conceptions,prior knowledge,and cognitive variables

Achievement in science depends on a series of factors that characterize the cognitive abilities of the students and the complex interactions between these factors and the environment that intervenes in the formation of students' background. The objective of this study is to: a) investigate reasoning strategies students use in solving stoichiometric problems; b) explore the relation between these strategies and alternative conceptions, prior knowledge and cognitive variables; and c) interpret the results within an epistemological framework. Results obtained show how stoichiometric relations produce conflicting situations for students, leading to conceptual misunderstanding of concepts, such as mass, atoms and moles. The wide variety of strategies used by students attest to the presence of competing and conflicting frameworks (progressive transitions, cf. Lakatos, 1970), leading to greater conceptual understanding. It is concluded that the methodology developed in this study (based on a series of closely related probing questions, generally requiring no calculations, that elicit student conceptual understanding to varying degrees within an intact classroom context) was influential in improving student performance. This improvement in performance, however, does not necessarily affect students' hard core of beliefs.     

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.     

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.     

Case analysis of children's reasoning in problem-solving process

Recognising critical reasoning and problem-solving as one of the key skills for twenty-first century citizenship, various types of problem contexts have been practiced in science classrooms to enhance students’ understandings and use of evidence-based thinking and justification. Good problems need to allow students to adapt and evaluate the effectiveness of their knowledge, reasoning and problem-solving strategies. When students are engaged in complex and open-ended problem tasks, it is assumed their reasoning and problem-solving paths become complex with creativity and evidence in order to justify their conclusion and solutions. This study investigated the levels of reasoning evident in student discourse when engaging in different types of problem-solving tasks and the role of teacher interactions on students’ reasoning. Fifteen students and a classroom teacher in a Grade 5–6 classroom participated in this study. Through case analyses, the study findings suggest that (a) there was no clear co-relation between certain structures of problem tasks and the level of reasoning in students’ problem-solving discourse, (b) students exhibited more data-based reasoning than evidence-based and rule-based justification in experiment-based problem-solving tasks, and (c) teacher intervention supported higher levels of student reasoning. Pedagogical reflections on the difficulties of constructing effective problem-solving tasks and the need for developing teacher scaffolding strategies are discussed.     

Zwischen Schule und Universität: Argumentation in der Mathematik

Several studies show that university students in Germany still have problems in reasoning mathematically although this already should be fostered at high school since the implementation of standards for school mathematics. Mathematical argumentation is a core competence and highly important, especially in academic mathematics. To foster mathematical argumentation at the beginning of university studies, competence models are needed which give more detailed insights in the skills that are necessary for reasoning. As mathematical argumentation is a complex process, especially at the higher secondary level or at university, many little steps are needed to complete a competence model for argumentation at the secondary–tertiary transition gradually. A possible step can be to initially identify several aspects of mathematical argumentation competence that influence the reasoning quality. The empirical basis for identifying those aspects is a cross-sectional study with 439 engineering students who participate in a transition course in mathematics. We address the following questions: (1) how is the quality of student’s reasoning? (2) Which kind of arguments do students use? (3) What resources do students who reasoned correctly use for solving the problems? (4) Does the content of the tasks play an important role? The results show a great influence of the content on the reasoning quality, especially if the content is abstract or concrete. Argumentation quality of students decreases with an increasing level of abstraction of the content. Furthermore, the results reveal that students often use routines for solving the problems. That indicates that procedural approaches still play an important role in school mathematics. If procedures could be used for solving the tasks, students are more successful. Competence models for mathematical argumentation at the beginning of the tertiary level should, therefore, include these factors.     

The role of epistemic emotions in mathematics problem solving

The purpose of this research was to examine the antecedents and consequences of epistemic and activity emotions in the context of complex mathematics problem solving. Seventy-nine elementary students from the fifth grade participated. Students self-reported their perceptions of control and value specific to mathematics problem solving, and were given a complex mathematics problem to solve over a period of several days. At specific time intervals during problem solving, students reported their epistemic and activity emotions. To capture self-regulatory processes, students thought out loud as they solved the problem. Path analyses revealed that both perceived control and value served as important antecedents to the epistemic and activity emotions students experienced during problem solving. Epistemic and activity emotions also predicted the types of processing strategies students used across three phases of self-regulated learning during problem solving. Finally, shallow and deep processing cognitive and metacognitive strategies positively predicted problem-solving performance. Theoretical and educational implications are discussed.     

Identifying Multiple Levels of Discussion-Based Teaching Strategies for Constructing Scientific Models

This study sought to identify specific types of discussion-based strategies that two successful high school physics teachers using a model-based approach utilized in attempting to foster students' construction of explanatory models for scientific concepts. We found evidence that, in addition to previously documented dialogical strategies that teachers utilize to engage students in effectively communicating their scientific ideas in class, there is a second level of more cognitively focused model-construction-supporting strategies that these teachers utilized in attempting to foster students' learning. A further distinction between macro and micro strategy levels within the set of cognitive strategies is proposed. The relationships between the resulting three levels of strategies are portrayed in a diagramming system that tracks discussions over time. The study attempts to contribute to a clearer understanding of how discussion-leading strategies may be used to scaffold the development of conceptual understanding.     

Themes and Interplay of Beliefs in Mathematical Reasoning

Upper secondary students’ task solving reasoning was analysed with a focus on arguments for strategy choices and conclusions. Passages in their arguments for reasoning that indicated the students’ beliefs were identified and, by using a thematic analysis, categorized. The results stress three themes of beliefs used as arguments for central decisions: safety, expectations and motivation. Arguments such as ‘I don’t trust my own reasoning’, ‘mathematical tasks should be solved in a specific way’ and ‘using this specific algorithm is the only way for me to solve this problem’ exemplify these three themes. These themes of beliefs seem to interplay with each other, for instance in students’ strategy choices when solving mathematical tasks.     

Factors in the development of proportional reasoning strategies by concrete operational college students

This study was designed as a test for two neo-Piagetian theories. More specifically, this research examined the relationships between the development of proportional reasoning strategies and three cognitive variables from Pascual-Leone's and Case's neo-Piagetian theories. A priori hypotheses linked the number of problems students worked until they induced a proportional reasoning strategy to the variables of M-space, degree of field dependence, and short-term storage space. The subjects consisted of students enrolled in Physical Science I, a science course for nonscience majors at the University of Southern Mississippi. Of the 34 subjects in the study, 23 were classified as concrete operational on the basis of eight ratio tasks. Problems corresponding to five developmental levels of proportional reasoning (according to Piagetian and neo-Piagetian theory), were presented by a microcomputer to the 23 subjects who had been classified as concrete operational. After a maximum of 6 hours of treatment, 17 of the 23 subjects had induced ratio schemata at the upper formal level (IIIB), while the remaining subjects used lower formal level (IIIA) schemata. The data analyses showed that neither M-space and degree of field-dependence, either alone or in combination, nor short-term storage predicted the number of problems students need to do until they induce an appropriate problem-solving strategy. However, there were significant differences in the short-term storage space of those subjects who mastered ratio problems at the highest level and those who did not. Also, the subjects' degree of field-dependence was not a predictor of either the ability to transfer problem-solving strategies to a new setting or the reuse of inappropriate strategies. The results of this study also suggest that short-term storage space is a variable with high correlations to a number of aspects of learning such as transfer and choice of strategy after feedback.     

Mathematical development: the role of broad cognitive processes

This study investigated the role of broad cognitive processes in the development of mathematics skills among children and adolescents. Four hundred and forty-seven students (age mean [M] = 10.23 years, 73% boys and 27% girls) from an elementary school district in the US southwest participated. Structural equation modelling tests indicated that calculation complexity was predicted by long-term retrieval and working memory; calculation fluency was predicted by perceptual processing speed, phonetic coding, and visual processing; problem solving was predicted by fluid reasoning, crystallised knowledge, working memory, and perceptual processing speed. Younger students’ problem solving skills were more strongly associated with fluid reasoning skills, relative to older students. Conversely, older students’ problem solving skills were more strongly associated with crystallised knowledge skills, relative to younger students. Findings are consistent with the theoretical suggestion that broad cognitive processes play specific roles in the development of mathematical skills among children and adolescents. Implications for educational psychologists are discussed.     

An investigation of undergraduates' transformational problem solving strategies: cognitive/metacognitive processes as predictors of holistic/analytic strategies

Recent years have seen increasing interest in the role of metacognition in mathematical problem solving. The study described in this paper explored problem solving strategies used by undergraduates. Furthermore, cognitive/metacognitive processes are predicted each of holistic and analytic strategies. Educational sciences students (n=178) were asked to talk/think aloud while solving two constructed response transformational problems. The protocols were transcribed and analysed, revealing that the cohort used nine strategies. The results showed that a holistic strategy was predicted by five cognitive/metacognitive processes, two of which were suppressors; whilst an analytic strategy was predicted by four cognitive/metacognitive processes, three of which were suppressors.     

Effect of computer interfaces on chemistry problem solving among various ethnic groups: A comparison of Pen-Point and Powerbook computers

This study investigated the effect of Pen-Point and Powerbook computers on solving a multiple step chemistry (molaritý) problem among White, Afro-American and Hispanic students (N=60) at the high school level. The screens on both computers were partitioned into a work field and a reasoning field. Both computers were programmed to record the time spent in each field, the number of entries made, and a copy of the entries made. Statistical analysis of data showed that more of the White and Afro-American Pen-Point computer users solved the problem correctly than did students using the Powerbook computer. All three ethnic groups made fewer entries, and took less time using the Pen-Point computer than the Powerbook. Attitude survey results of all ethnic groups showed that more Pen-Point computer users felt comfortable working with computers. Over all, the results suggest that the Pen-Point computer has a more positive effect on the problem solving performance and attitude of students towards computers than the Powerbook computer.     

课堂教学策略对中学生科学创造力的影响

以广东省两所普通高中的学生为调查对象,采用《青少年科学创造力测验》和《中学课堂教学策略感知量表》,测量中学生的科学创造力水平、教师的课堂教学策略实效以及课堂教学策略对中学生科学创造力的影响情况,研究发现,中学课堂教学策略中的教学动机策略维度和教学方法策略维度能够正向预测学生的科学创造力水平。为了优化课堂教学策略,促进学生科学创造力的发展,教师可以通过教学动机策略维持学生认知与情感的开放性、制造学生情感与认知的冲突;通过教学方法策略引导学生从多个角度发现和解决问题、训练学生复杂的思维过程和想象力、提升学生解决真实问题的能力。     

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.     

An investigation into the capacity of student motivation and emotion regulation strategies to predict engagement and resilience in the middle school classroom

Although most of the initial research on self-regulated learning focused on cognitive and meta-cognitive aspects, there has been a growing interest in the emotion and motivation domains of self-regulation. This article reports on research undertaken to investigate specific motivation and emotion regulation strategies used by middle school students and the relationship between the use of such strategies and student engagement and resilience. The research targeted one type of motivation regulation??goal-oriented strategies??and two types of emotion regulation: antecedent and stress release strategies, together with avoidance strategies. Students who used goal-oriented motivation regulation strategies were more likely than others to be resilient. Contrasting results were obtained when investigating the ability of each emotion regulation strategy type to predict engagement and resilience. As expected, students who used avoidant strategies were less likely than others to develop resilience. This article discusses the implications of the research for the classroom, including the teaching of particular motivation and emotion regulation strategies to students and providing the right classroom environment for strategy development.     

Rule-Learning Events in the Acquisition of a Complex Skill: An Evaluation of Cascade

Acquiring a complex cognitive skill often involves learning principles of the task domain in the midst of solving problems or studying examples. Cascade is a model of such learning. It includes both rule-based reasoning and several kinds of analogical, case-based reasoning. Task domain principles are represented as rules, and Cascade learns new rules at rule-learning events, which are initiated by an impasse and utilize multiple kinds of reasoning. In this article, I evaluate Cascade's model of rule-learning events by analyzing ones gleaned from protocols of physics students solving problems and studying examples. As expected, Cascade's model is overly simple, but it appears feasible to extend it to cover all the observed learning events. The data themselves were surprising in that there are few learning events relative to the number that could have occurred, and those that did occur often involved forms of reasoning that are considerably shallower than expected. The data suggest ways that instruction can be improved to increase both the quantity and depth of learning events.     

How Swedish pupils,aged 12‐15 years,understand light and its properties‡

The reasoning patterns used by a sample of Western Australian secondary school students aged 13‐16 were investigated with regard to the following reasoning modes: proportional reasoning, controlling variables, probabilistic reasoning, correlational reasoning, and combinatorial reasoning.

There was a wide range in students’ reasoning abilities at all year levels. Large percentages of students did not use formal operational reasoning patterns when they attempted to solve problems assessing their ability to use each of the five reasoning modes. Commonly used, but incorrect reasoning patterns were identified for each reasoning mode.

The students’ ability to use formal reasoning patterns was found to be an important factor in determining student achievement in lower secondary science, in their selection of year 11 science subjects, and their achievement in these subjects.

The results of the study indicate that it is important for teachers to be aware of the reasoning patterns of their students and the cognitive demands of course content, so that they can optimally match the content and their teaching strategies with the abilities of their students. Further research is needed to establish the nature of instruction which might best facilitate cognitive growth.