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.     

Proportional Reasoning Ability and Concepts of Scale: Surface area to volume relationships in science

The National Science Education Standards emphasise teaching unifying concepts and processes such as basic functions of living organisms, the living environment, and scale. Scale influences science processes and phenomena across the domains. One of the big ideas of scale is that of surface area to volume. This study explored whether or not there is a correlation between proportional reasoning ability and a student's ability to understand surface area to volume relationships. Students' knowledge of surface area to volume relationships was assessed pre and post to a one‐week instructional intervention involving investigations about surface area to volume as a limiting factor in biological and physical systems. Results showed that proportional reasoning scores of middle school students were correlated to pre‐test and post‐test assessment scores, and a paired‐sample t‐test found significant differences from pre‐test to post‐test for the surface area to volume assessment. Relationships between proportional reasoning, visualisation abilities and success in solving surface to volume problems are discussed. The implications of the results of this study for learning concepts such as magnitudes of things, limits to size, and properties of systems that change depending on volume and surface are explored.     

Correlates of formal reasoning: Content and problem effects

Piaget's structural theory of formal thought suggests that a general construct of formal reasoning exists. The content of the task and type of problem employed are often ignored in Piagetian based studies but are important for generalizing findings to other studies and to educational problems. The study reported here examines content and problem effects of formal thought in 13-year-old adolescents. Specifically, three controlling variables tasks with different content and two question type tests (analysis and controlling questions) were administered to 120 seventh graders. Ability measures and personality dimensions associated with formal reasoning in the literature are used to clarify what formal reasoning is and how content and problem type are involved in formal reasoning. Significant main effects were found for problem and content effects (p = 0.001), and a significant interaction was found between the two (p = 0.001). Across the three tasks general ability, field dependency, and locus of control were consistently and significantly related to the controlling questions. However, only measures of field dependency were related to the analysis questions. Combinations of ability and personality factors were found to be uniquely related to each task, within each question type. Results have implications for a theory of formal thought and the teaching of the controlling variables strategy.     

The performance of college students on piaget-type tasks dealing with distance,time, and speed

Research was done to probe and extend Piaget's theory of the conception of speed. Specifically tested was the hypothesis that there is no hierarchical relationship in performance on the following Piaget-type tasks: conservation of distance, asymmetric series of speeds, one-to-many (circular) speeds, symmetric speeds, time, and proportional reasoning. The research also tested the gender-related performance on these six tasks. One hundred freshman and sophomore college students were shown demonstrations of equipment individually for each of the six tasks. A set of open-ended questions based on the demonstrations was administered to each subject in a 45-minute interview. Subjects were scored as “pass” on a given task if they manipulated objects in certain ways and gave specific types of explanations. A scalogram analysis of the data yielded a z-score of — 3.7 which indicated that subjects passed the task in a certain sequence. The tasks were found to form a unidimensional scale and to be increasingly difficult in the order listed above. A chi-square test for two independent samples showed a significant difference (alpha = 0.05) in performance between males and females on all speed tasks. No significant differences in performance between males and females were found for the distance and time tasks.     

Path analysis: A model for the development of scientific reasoning abilities in adolescents

A model was formulated and tested for the development of scientific reasoning abilities in adolescents. Piagetian theory provided the framework for choosing potential determinants of the dependent variable, scientific reasoning abilities. A model reflecting hypothesized causal relationships among determinants and with the dependent variable was developed a priori on the basis of theoretical and substantive reasoning. The hypothesized model was tested and revised using path analysis. Data from intact classes of middle-school (n = 101) and high-school (n = 89) students from an upper-middle-class suburb of a midwestern city revealed significant (p < 0.05) path coefficients for these variables and scientific reasoning abilities: age, I.Q., field dependence–independence, and experience. A path from locus of control to scientific reasoning abilities through field dependence-independence was also statistically significant. The revised model explained 61 percent of the variance in scientific reasoning abilities.     

Translation of algebraic equations and its relation to formal operational reasoning

A large proportion of science major college students are unable to translate even simple sentences into algebraic equations. Given the following sentence: There are six times as many students (S) as professors (P) at this university, most students write the following equation: 6S = P, referred to as the reversal error. In order to overcome the reversal error students need to operate in a hypothetico-deductive manner, i.e., performing a hypothetical operation that makes the group of professors six times larger than it really is (S = 6P). The objective of this study is to investigate the relation between student ability to translate sentences into equations, equations into sentences, and student performance in the following variables: formal operational reasoning, proportional reasoning, and introductory freshmen-level chemistry course. The results obtained show that as the student ability to translate sentences into equations and equations into sentences increases, their mean scores in Chemistry I, formal operational, and proportional reasoning increases. This study has found support for the hypothesis that students who lack formal operational reasoning skills (hypothetico-deductive reasoning) may experience more problems in the translation of algebraic equations.     

Hypothetico-deductive reasoning skill and concept acquisition: Testing a constructivist hypothesis

This study tested the constructivist hypothesis that the acquisition of domain-specific conceptual knowledge (declarative knowledge) requires use of general procedural knowledge. More specifically, it was hypothesized that use of a general pattern of hypothetico-deductive reasoning is necessary for the acquisition of novel domain-specific concepts. To test this hypothesis 314 high school biology and chemistry students were first tested to determine whether or not they were skilled in the use of hypothetico-deductive reasoning. Based on this test, students were classified as reflective, transitional, or intuitive thinkers. All students were then presented with a series of four concept-acquisition tasks. It was predicted that reflective (hypothetico-deductive) thinkers would acquire the concepts while intuitive (empirico-inductive) thinkers would not. Transitional thinkers were expected to be partially successful. These predictions were confirmed as skill in hypothetico-deductive reasoning (developmental level), but not age, was highly correlated with performance on the concept acquisition tasks (X² = 71.14, p < 0.00001). This result was interpreted to be supportive of the constructivist hypothesis.     

A Comparison and Evaluation of Two Methods of Organization for the Teaching of Reading

Abstract

In order to test the hypothesis that field independence would interact with level of guidance, students in five mathematics classes were randomly assigned to either a low guidance or a high guidance treatment group for a week of instruction. Both treatments used an inductive sequence of instruction on the topic of networks. Students were assessed on two aptitudes, field independence and general reasoning. Achievement was significantly better (p > .05) in the high guidance group than the low guidance group on both the posttest and the retention test. No significant interactions with the aptitude variables were found.     

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.     

What do tests of “formal” reasoning actually measure?

Tests of formal operational reasoning derived from Piagetian theory have been found to be effective predictors of academic achievement. Yet Piaget's theory regarding the underlying nature of formal operations and their employment in specific contexts has run into considerable empirical difficulty. The primary purpose of this study was to present the core of an alternative theory of the nature of advanced scientific reasoning. That theory, referred to as the multiple-hypothesis theory, argues that tests of formal operational reasoning actually measure the extent to which persons have acquired the ability to initiate reasoning with more than one specific antecedent condition, or if they are unable to imagine more than one antecedent condition, they are aware that more than one is possible; therefore conclusions that are drawn are tempered by this possibility. As a test of this multiple-hypothesis theory of advanced reasoning and the contrasting Piagetian theory of formal operations, a sample of 922 college students were first classified as concrete operational, transitional, or formal operational, based upon responses to standard Piagetian measures of formal operational reasoning. They were then administered seven logic tasks. Actual response patterns to the tasks were analyzed and found to be similar to predicted response patterns derived from the multiple-hypothesis theory and were different from those predicted by Piagetian theory. Therefore, support was obtained for the multiple-hypothesis theory. The terms intuitive and reflective were suggested to replace the terms concrete operational and formal operational to refer to persons at varying levels of intellectual development.     

The effects of instructional intervention on improving proportional,probabilistic, and correlational reasoning skills among undergraduate education majors

The main purpose of this study was to test the effect of instruction to improve the reasoning skills of undergraduates majoring in the field of education. The results of this investigation demonstrate the lack of proficiency in formal reasoning by undergraduate education majors in the areas of proportional, probabilistic, and correlational reasoning. However, after receiving three specifically planned interventions, students in the experimental group showed improvement in all three areas of reasoning (p ≤ 0.05). Also, it was noted that students with science and/or math in their backgrounds performed significantly (p ≤ 0.05) better in all three areas of reasoning on both pre‐ and post‐tests than did students with no science or math in their backgrounds. This study is among the first to show that background knowledge obtained from college level science and math courses correlates with better reasoning skills. Data from this study also demonstrated that interventions focusing on probability and proportionality improved the correlational reasoning skills of students. The results of this investigation indicate that deficiencies in reasoning abilities in the areas of proportionality, probability, and correlational reasoning can be successfully addressed even with limited classroom intervention. © 2000 John Wiley & Sons, Inc. J Res Sci Teach 37: 981–995, 2000     

Identifying patterns of students' performance on simulated inquiry tasks using PISA 2015 log-file data

Previous research has demonstrated the potential of examining log-file data from computer-based assessments to understand student interactions with complex inquiry tasks. Rather than solely providing information about what has been achieved or the accuracy of student responses (product data), students' log files offer additional insights into how the responses were produced (process data). In this study, we examined students' log files to detect patterns of students' interactions with computer-based assessment and to determine whether unique characteristics of these interactions emerge as distinct profiles of inquiry performance. Knowledge about the characteristics of these profiles can shed light on why some students are more successful at solving simulated inquiry tasks than others and how to support student understanding of scientific inquiry through computer-based environments. We analyzed the Norwegian PISA 2015 log-file data, science performance as well as background questionnaire (N = 1,222 students) by focusing on two inquiry tasks, which required scientific reasoning skills: coordinating the effects of multiple variables and coordinating theory and evidence. Using a mixture modeling approach, we identified three distinct profiles of students' inquiry performance: strategic, emergent, and disengaged. These profiles revealed different characteristics of students' exploration behavior, inquiry strategy, time-on-task, and item accuracy. Further analyses showed that students' assignment to these profiles varied according to their demographic characteristics (gender, socio-economic status, and language at home), attitudes (enjoyment in science, self-efficacy, and test anxiety), and science achievement. Although students' profiles on the two inquiry tasks were significantly related, we also found some variations in the proportion of students' transitions between profiles. Our study contributes to understanding how students interact with complex simulated inquiry tasks and showcases how log-file data from PISA 2015 can aid this understanding.     

College chemistry and piaget: The relationship of aptitude and achievement measures

Cognitive performance on “An Inventory of Piaget's Developmental Tasks” (IPDT) was related to the Scholastic Aptitude Tests and performance in both college chemistry lecture and laboratory classes. The IPDT is a valid and reliable 72-item, untimed, multiple-choice paper-and-pencil inventory. It has 18 subtests grouped into five problem areas representing different Piagetian tasks. Subjects (n = 225) from two different levels of introductory chemistry courses participated. IPDT scores were significantly correlated with SAT and placement data. In overall Piagetian development, “A” students rated higher than others. Performance in classification and proportional reasoning problem areas correlated with course achievement, particularly for higher-level students. Weakest areas of development were indicated by subtest scores and are described with implications for course performance. Finally, Piagetian tasks were related to learning and instructional activities in introductory chemistry classes and are discussed.     

Field independence,task ambiguity,and performance on a proportional reasoning task

This study investigated the proportional reasoning abilities of 35 college science students. Using a projection of shadows problem, proportional reasoning was assessed under one of two experimental conditions corresponding to the type of information presented: (a) relevant only, or (b) relevant and irrelevant. Subjects were also measured on the cognitive style of field independence. Results showed that subjects in the relevant only condition performed significantly better than those in the relevant-irrelevant condition. Degree of field independence was related to performance only in the relevant-irrelevant condition. These results indicated an interaction between type of information presented in a task and cognitive style.     

Reexamining the Role of Cognitive Conflict in Science Concept Learning

In this study, we defined and quantified the degree of cognitive conflict induced by a discrepant event from a cognitive perspective. Based on the scheme developed, we investigated the relationship between cognitive conflict and conceptual change, and the influences of students' cognitive characteristics on conflict in learning the concept of density. Subjects were 171 seventh-grade girls from two city middle schools in Korea. Tests regarding logical thinking ability, field dependence/independence, and meaningful learning approach were administered. A preconception test and a test of responses to a discrepant event were also administered. Computer-assisted instruction was then provided to students as a conceptual change intervention. A conception test was administered as a posttest. In analysing students' responses to the discrepant event, seven types of responses were identified: Rejection, reinterpretation, exclusion, uncertainty, peripheral belief change, belief decrease, and belief change. These types were then ordered into four levels. The results indicated that there existed a significant correlation between cognitive conflict and conceptual change. t-test results revealed that there were statistically significant differences in the degree of cognitive conflict by the levels of students' logical thinking ability and field dependence/independence. Meaningful learning approach, however, was found to have no statistically significant effect on cognitive conflict. Educational implications are discussed.     

Students’ reasons for preferring teleological explanations

The teleological bias, a major learning obstacle, involves explaining biological phenomena in terms of purposes and goals. To probe the teleological bias, researchers have used acceptance judgement tasks and preference judgement tasks. In the present study, such tasks were used with German high school students (N?=?353) for 10 phenomena from human biology, that were explained both teleologically and causally. A sub-sample (n?=?26) was interviewed about the reasons for their preferences. The results showed that the students favoured teleological explanations over causal explanations. Although the students explained their preference judgements etiologically (i.e. teleologically and causally), they also referred to a wide range of non-etiological criteria (i.e. familiarity, complexity, relevance and five more criteria). When elaborating on their preference for causal explanations, the students often focused not on the causality of the phenomenon, but on mechanisms whose complexity they found attractive. When explaining their preference for teleological explanations, they often focused not teleologically on purposes and goals, but rather on functions, which they found familiar and relevant. Generally, students’ preference judgements rarely allowed for making inferences about causal reasoning and teleological reasoning, an issue that is controversial in the literature. Given that students were largely unaware of causality and teleology, their attention must be directed towards distinguishing between etiological and non-etiological reasoning. Implications for educational practice as well as for future research are discussed.     

Balancing chemical equations: The role of developmental level and mental capacity

Why are some students able to learn to use the trial and error method to balance chemical equations while others are not? To test the hypothesis that formal reasoning is required to balance even simple one-step equations, while formal reasoning and a sufficiently large mental capacity are required to balance more complex many-step equations, a sample of science students was tested to determine level of intellectual development, mental capacity, and degree of field dependence/field independence. Students were then given classroom instruction in using trial and error to balance equations. As predicted, a posttest revealed significant correlations between developmental level and equation balancing ability for both simple and complex equations. Also, as predicted, mental capacity correlated significantly with complex equations but not with simple equations. Field dependence/field independence played no significant role in performance. Educational implications are drawn.     

The Influence of 16‐year‐old Students’ Gender,Mental Abilities,and Motivation on their Reading and Drawing Submicrorepresentations Achievements

Submicrorepresentations (SMRs) are a powerful tool for identifying misconceptions of chemical concepts and for generating proper mental models of chemical phenomena in students’ long‐term memory during chemical education. The main purpose of the study was to determine which independent variables (gender, formal reasoning abilities, visualization abilities, and intrinsic motivation for learning chemistry) have the maximum influence on students’ reading and drawing SMRs. A total of 386 secondary school students (aged 16.3 years) participated in the study. The instruments used in the study were: test of Chemical Knowledge, Test of Logical Thinking, two tests of visualization abilities Patterns and Rotations, and questionnaire on Intrinsic Motivation for Learning Science. The results show moderate, but statistically significant correlations between students’ intrinsic motivation, formal reasoning abilities and chemical knowledge at submicroscopic level based on reading and drawing SMRs. Visualization abilities are not statistically significantly correlated with students’ success on items that comprise reading or drawing SMRs. It can be also concluded that there is a statistically significant difference between male and female students in solving problems that include reading or drawing SMRs. Based on these statistical results and content analysis of the sample problems, several educational strategies can be implemented for students to develop adequate mental models of chemical concepts on all three levels of representations.     

Evaluating the effectiveness of a mindfulness coloring activity for test anxiety in children

The authors investigated the effectiveness of a mindfulness art activity compared with a free draw/coloring activity on test anxiety in children. The sample consisted of 152 students (50% female; M_age = 10.38 years, SD = 0.88 years) randomly assigned to a mindful (n = 76) or free (n = 76) group. Participants completed a standardized measure of anxiety and state mindfulness before and after the coloring activity, immediately before a spelling test, as well as a measure of dispositional mindfulness. Results revealed an overall significant decrease in test anxiety and an overall significant increase in state mindfulness following the interventions. Furthermore, although a significant negative correlation was found between dispositional mindfulness and change in state mindfulness pre- and post-coloring intervention, a significant positive correlation was found between dispositional mindfulness and pre-intervention state mindfulness, suggesting a possible ceiling effect. Explanations for these findings and implications for school personnel and future research are discussed.