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.     

Neo-piagetian predictors of achievement in physical science

This article examines the predictive value of the cognitive variables of developmental level, mental capacity, cognitive style, short-term storage space, and numerical inductive reasoning for student achievement in college science. Achievement was analyzed for each of the categories of pure recall, computational, complex items, and total score of a midterm exam as well as for the composite score on a final exam. The sample for this study consisted of a class of 32 nonscience majors enrolled in Physical Science I at the University of Southern Mississippi. The results showed that developmental level was the single best predictor of achievement. Short-term storage space and mental capacity were significant predictors of achievement for computational and complex items, but, as expected from theoretical considerations, not for pure recall items. The degree of field dependence did not well predict performance on pure recall or computational items. The results also indicate that mental capacity and field dependence do not contribute significantly to the variance if developmental level is held constant. The pattern of the predictive power of numerical inductive reasoning parallels, in magnitude, that of mental capacity. The results of this study and its implications indicate that the construct of short-term storage space has great potential to guide classroom practice and the development of instructional materials. A strategy is outlined that would guide curriculum planners and classroom teachers in the development of materials which would allow students to develop complex problem-solving behaviors.     

Correlates of formal operational reasoning: A neo-piagetian analysis

Most Piagetian formal operational reasoning tasks show horizontal decalage; that is, subjects pass certain tasks and fail others that have the same logical structure. The study reported here analyzes the importance of individual difference variables, as postulated by the neo-Piagetian theory of Pascual-Leone, in explaining subject performance in formal reasoning. A sample of 72 freshman students were administered a test of formal reasoning having 20 items of different types of reasoning, and the tests of the individual difference variables. Results obtained from multiple regression analyses show that Pascual-Leone's structural M-capacity (M_s) is the most consistent predictor of success in the different formal reasoning tasks, followed by Witkin's cognitive style, and to a much lesser degree Raven's progressive matrices, and Pascual-Leone's functional M-capacity (M_f). It was found that in the total score on the 20 items of formal reasoning, M_s accounted for 23.3% of the variance (R = 0.483, F = 6.39, p = 0.014) and Witkin's Group Embedded Figures Test, increased the multiple R significantly (F = 7.77, p = 0.007) and accounted for 7.6% of the variance. M_f and the Raven test did not make a significant contribution to the regression equation. Correlation coefficients among most of the items having the same reasoning pattern but different content are generally low but statistically significant (p < 0.01). Intercorrelations among items having the same formal reasoning pattern and content are fairly high (p < 0.001). These results emphasize the importance of individual difference variables: information-processing capacity (Pascual-Leone) and oversensitivity to potentially misleading information (Witkin). It is suggested that in order to understand student performance in formal reasoning tasks, we should expect horizontal decalages as a rule and not the exception, as Piaget had postulated. Educational implications are drawn.     

Facilitating successful prediction problem solving in biology through application of skill theory

The purpose of this study was to identify cognitive factors associated with differences in prediction problem-solving success among high school biology students, and to determine whether guided practice facilitated successful prediction. The Group Assessment of Logical Thinking was used to evaluate subjects' cognitive operational level, written prediction worksheets and think-aloud interviews were used to measure predictive success and identify problem-solving tendencies. Treatment group subjects received 8 hr of directed prediction practice using interactive computer simulations, whereas the control group practiced prediction without focusing on specific skills, after which all subjects were retested. Predictive reasoning success showed a significant correlation (p < .01) to both formal operational development and five specific cognitive skills: (a) identifying relevant knowledge in long-term memory, (b) using a systematic problem-solving strategy, (c) applying cause-effect reasoning, (d) reviewing solutions for logical inconsistency, and (e) evaluating alternative solutions. Analysis of covariance indicated significantly increased prediction success for treatment group subjects following practice in the five identified skills (p < .01). © 1996 John Wiley & Sons, Inc.     

The development of reasoning on the balance beam

The study described in this article examined the factors in the development of reasoning on the balance beam. The results of this and other investigations by the author led to the development of a model of problem solving and of the transition between levels of performance, that is, from novice to expert behaviors in a specific problem domain. The sample for this study consisted of 34 nonscience majors enrolled in Physical Science I at the University of Southern Mississippi. The results of this study showed (a) significant correlations between the predictor variables of numerical inductive reasoning ability and ratio span and the dependent measure of amount of practice until mastery of balance beam problems, (b) that there existed significant differences on the predictors between subjects who used the ratio scheme versus those who used the product-moment rule to do balance beam problems, (c) that the sequence of behaviors until mastery of the balance beam was not invariant, and (d) that there existed significant negative correlations between individuals' tendencies to avoid unsuccessful algorithms and the frequency of incidences of monitoring the learning process on one side and the amount of practice and the construct of short-term storage space on the other side. The results of this and other studies by the author are used to develop a model of problem solving and of the development of problem-solving behaviors. This model also includes recent findings in short-term memory and problem-solving research. The implications of this model for instruction are discussed.     

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.     

The Influence of Different Representations on Solving Concentration Problems at Elementary School

This study investigated the students’ learning process of the concept of concentration at the elementary school level in Taiwan. The influence of different representational types on the process of proportional reasoning was also explored. The participants included nineteen third-grade and eighteen fifth-grade students. Eye-tracking technology was used in conducting the experiment. The materials were adapted from Noelting’s (1980a) “orange juice test” experiment. All problems on concentration included three stages (the intuitive, the concrete operational, and the formal operational), and each problem was displayed in iconic and symbolic representations. The data were collected through eye-tracking technology and post-test interviews. The results showed that the representational types influenced students’ solving of concentration problems. Furthermore, the data on eye movement indicated that students used different strategies or rules to solve concentration problems at the different stages of the problems with different representational types. This study is intended to contribute to the understanding of elementary school students’ problem-solving strategies and the usability of eye-tracking technology in related studies.     

Development and validation of a scientific (formal) reasoning test for college students

We present a multiple-choice test, the Montana State University Formal Reasoning Test (FORT), to assess college students' scientific reasoning ability. The test defines scientific reasoning to be equivalent to formal operational reasoning. It contains 20 questions divided evenly among five types of problems: control of variables, hypothesis testing, correlational reasoning, proportional reasoning, and probability. The test development process included the drafting and psychometric analysis of 23 instruments related to formal operational reasoning. These instruments were administered to almost 10,000 students enrolled in introductory science courses at American universities. Questions with high discrimination were identified and assembled into an instrument that was intended to measure the reasoning ability of students across the entire spectrum of abilities in college science courses. We present four types of validity evidence for the FORT. (a) The test has a one-dimensional psychometric structure consistent with its design. (b) Test scores in an introductory biology course had an empirical reliability of 0.82. (c) Student interviews confirmed responses to the FORT were accurate indications of student thinking. (d) A regression analysis of student learning in an introductory biology course showed that scores on the FORT predicted how well students learned one of the most challenging concepts in biology, natural selection.     

Problem-solving analysis: A piagetian study

Fifty-nine second-year medical students were asked to solve 12 Piagetian formal operational tasks. The purpose was to describe the formal logical characteristics of this medical student sample (59 of a total 65 possible) in terms of their abilities to solve problems in four formal logical schemata-combinatorial logic, probabilistic reasoning, propositional logic, and proportional reasoning. These tasks were presented as videotape demonstrations or in written form, depending on whether or not equipment manipulation was required, and were scored using conventional, prespecified scoring criteria. The results of this study show approximately 96% of the sample function at the transitional (Piaget's 3A level) stage of formal operations on all tasks and approximately 4% function at the full formal (Piaget's 3B level) stage of formal operations on all tasks. This sample demonstrates formal level thinking to a much greater degree than other samples reported in the literature to date and suggests these students are adequately prepared and developed to meet the challenge of their training (i.e., medical problem solving).     

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.     

The rate of acquisition of formal operational schemata in adolescence: A secondary analysis

A theoretical model of cognitive development is applied to the study of the acquisition of formal operational schemata by adolescents. The model predicts that the proportion of adolescents who have not yet acquired the ability to perform a a specific Piagetian-like task is an exponentially decreasing function of age. The model has been used to analyze the data of two large-scale studies performed in the United States and in Israel. The functional dependence upon age was found to be the same in both countries for tasks which are used to assess the following formal operations: proportional reasoning, probabilistic reasoning, correlations, and combinatorial analysis. Different functional dependence was found for tasks assessing conservation, control of variables, and prepositional logic. These results give support to the “unity” hypothesis of cognitive development, that is, the hypothesis that the various schemata of formal thought appear simultaneously.     

Problem-Solving Strategies

This article reviews recent research on problem-solving strategies and their relationship to leaning and problem-solving processes. A distinction is made between schema-driven and search-based problem-solving strategies, and expert-novice differences in the use of these strategies are discussed. General strategies that facilitate the learning of problem schemata associated with expertise are contrasted with strategies that hinder schema learning. Constraints on the use of problem-solving strategies and the consequent implications for education are discussed. Suggestions for future research are made, which include the study of search-based strategies in experts and the effects of training on strategy use.     

Formal operations as predictor of university academic achievement

Abstract

In view of the postulated relationship between Piaget's theory of formal operations and academic achievement, this article investigates the extent to which university students in possession of proportional and combinatorial reasoning would perform in an educational psychology graduate course at the University of Transkei. The findings show that those who had the concepts of proportional and combinatorial reasoning significantly outperformed those who had not attained formal operations. This is a clear demonstration that pursuit of academic studies at university subsumes the acquisition of formal operations.     

A review of research on formal reasoning and science teaching

A central purpose of education is to improve students' reasoning abilities. The present review examines research in developmental psychology and science education that has attempted to assess the validity of Piaget's theory of formal thought and its relation to educational practice. Should a central objective of schools be to help students become formal thinkers? To answer this question research has focused on the following subordinate questions: (1) What role does biological maturation play in the development of formal reasoning? (2) Are Piaget's formal tasks reliable and valid? (3) Does formal reasoning constitute a unified and general mode of intellectual functioning? (4) How does the presence or absence of formal reasoning affect school achievement? (5) Can formal reasoning be taught? (6) What is the structural or functional nature of advanced reasoning? The general conclusion drawn is that although Piaget's work and that which has sprung from it leaves a number of unresolved theoretical and methodological problems, it provides an important background from which to make substantial progress toward a most significant educational objective. All our dignity lies in thought. By thought we must elevate ourselves, not by space and time which we can not fill. Let us endeavor then to think well; therein lies the principle of morality. Blaise Pascal 1623-1662.     

Trends in the development of student level of reasoning in pattern generalization tasks across grade level

This paper explored (1) the developmental trend of student level of reasoning across grade level in pattern generalization; (2) the mediatory role of task variables in the developmental trend of student level of reasoning within and across tasks; and (3) developmental trend of student level of reasoning associated with strategy use across grade level. A test designed to measure student level of reasoning was given to a sample of 1232 students from grades 4 to 11 from 5 schools in Lebanon. The Structure of the Learned Outcomes or Responses (SOLO) was used as a theoretical model. Results show that student level of reasoning exhibited an increasing trend across clusters of grade levels and that there were several SOLO levels in each cluster of grade levels. Type of task (immediate, near, far) and function type (linear, non-linear) seem to mediate the development of level of reasoning across grade level but the complexity of the task (simple, more complex) did not. Students used several strategies in each cluster of grade levels and the developmental trends of student level of reasoning associated with strategy use were not uniform and varied across clusters of grade levels, thus supporting a neo-Piagetian interpretation of the results.     

元认知与图式理论对英语阅读教学的启示

传统的图式理论将图式分为语言图式、内容图式和形式图式三大类。随着元认知概念的提出,众多实验证明对阅读策略元认知程度的不同是阅读能力强和弱的学生之间的主要区别,也成为了有效运用图式理论帮助阅读理解的重要因素。因此,图式理论应将对阅读策略的元认知这一维度纳入其分类之中。基于此,阅读教学中,教师应在阅读前帮助学生激活图式;在阅读过程中,帮助学生将图式具体化、形象化;在阅读后,对阅读进行拓展,帮助学生对已有图式进行完善,提高学生对包括阅读策略元认知在内的四大类图式的理解和运用,全面提高阅读能力。     

Relationships between formal-operational thought and conceptual difficulties in genetics problem solving

Seventy-one college general biology students were taught a unit in Mendelian genetics by the traditional lecture method. Emphasis was placed on meiotic formation of gametes, the Law of Segregation, and the Law of Independent Assortment. The Punnett-square model was used for all practice problems. Eight weeks later, a content-validated retention test was given to evaluate the students' retention of problem-solving skills. The test required students to use proportional reasoning (identifying ratios from the Punnett squares), combinatorial reasoning (identifying combinations of gametes from parental genotypes), and probabilistic reasoning (estimating gamete or offspring probabilities). Each of the 71 students was also given three Piagetian interview tasks to evaluate intellectual development in the areas of reasoning under question. The balance-beam task, the electronic switch-box task, and colored squares and diamonds were used to test for proportional reasoning, combinatorial reasoning, and probabilistic reasoning, respectively. Pearson correlations and factor analysis failed to show direct relationships among Piagetian tasks for the three kinds of reasoning and their corresponding occurrence in genetics problems. Some correlations were higher between different reasoning types than between similar types. Analysis of variance showed significant differences for all three reasoning types among concrete-operational, transitional, and formal-operational students with the retention test. Post-hoc analysis of ANOVAs indicated that formal-operational students had significantly more success in the three reasoning areas than transitional students, and transitional students had significantly more success than concrete-operational students.     

Complex problem solving in L1 education: Senior high school students' knowledge of the language problem-solving process

The solving of reasoning problems in first language (L1) education can produce an understanding of language, and student autonomy in language problem solving, both of which are contemporary goals in senior high school education. The purpose of this study was to obtain a better understanding of senior high school students' knowledge of the language problem-solving process. Fifty-three 11th-grade high school students solved standard, comprehension, and linguistic reasoning problems. Before solving the problems, the participants had filled in open-ended questions inquiring about their knowledge regarding the effectiveness of a chosen problem-solving strategy. Content analysis of the responses indicated four categories and nine subcategories. The implications of the relatively few responses in the category of explicit knowledge of the language problem-solving process are discussed in the light of the changing needs of L1 students.