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.     

Manipulation of M demand of chemistry problems and its effect on student performance: A neo-piagetian study

It has been shown that student performance in chemistry problems decreases as the M demand of the problem increases, thus emphasizing the role of information processing in problem solving. It was hypothesized that manipulation (increase or decrease) of the M demand of a problem can affect student performance. Increasing the M demand of a problem would affect more the performance of subjects with a limited functional M capacity. The objective of this study is to investigate the effect of manipulation (increase) of the M demand of chemistry problems, having the same logical structure, on performance of students having different functional M capacity, cognitive style, and formal operational reasoning patterns. As predicted the performance of one group of students was lower after the manipulation (increase) in the M demand of the problem. This shows how even small changes in the amount of information required for processing can lead to working memory overload, as a consequence of a poor capacity for mobilization of M power.     

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.     

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.     

Manipulation of logical structure of chemistry problems and its effect on student performance

It has been shown previously that manipulation of the M demand (amount of information needed for processing) of chemistry problems affects student performance, which suggests that manipulation of logical structure of chemistry problems could also lead to significant changes in performance. The objective of this study is to investigate the following: Given the opportunity for training, what is the effect of increasing (manipulation) the complexity of logical structure of chemistry problems on student performance, and to what extent can cognitive variables explain changes in performance. Results obtained show that (a) even a small increase in the logical structure of a problem can change the role of cognitive variables (mental capacity and formal reasoning) to the extent that increase in logical complexity outweighs the advantage students may have gained through training on a similar problem; (b) the use of algorithms and training on particular types of chemistry problems could lead to a situation in which formal reasoning is the only cognitive variable that explains variance in performance significantly; and (c) after having solved very similar problems on two different occasions with improving performance, the improvement is not retained if the logical structure of a third problem increases considerably. It is concluded that when dealing with significant changes in logical complexity of chemistry problems, developmental level of students is the most consistent predictor of success. A model for the qualitative analysis of logical complexity of chemistry problems is presented.     

Video game learning dynamics: Actionable measures of multidimensional learning trajectories

Valid, accessible, reusable methods for instructional video game design and embedded assessment can provide actionable information enhancing individual and collective achievement. Cyberlearning through game‐based, metaphor‐enhanced learning objects (CyGaMEs) design and embedded assessment quantify player behavior to study knowledge discovery and application. CyGaMEs is grounded by analogical reasoning theory, cognitive task analysis and knowledge representation. A construct representation argument for validity using evidence‐centered design warrants CyGaMEs, its web‐based learning environment, Selene: A Lunar Construction GaME, its embedded assessment, and a learning dynamics approach to student, measurement and statistical models. Two studies (US volunteers, Study 1: n = 267, mean (M)_age = 15; Study 2: n = 90, M_age = 12) cross‐validate learning dynamics (learner progress, rate of progress and changes in that rate) for Selene's multidimensional goals while players learn and apply standard‐based science about fundamental geology and space science concepts. Gameplay data analyzed using regression, calculus and hierarchical linear modeling exhibit overall relatively high standardized rates of progress toward each goal statistically higher than zero. For example, adjusting for nesting within individual players, average rate of progress toward the goal of accreting lunar mass is a z‐score of 1.4 (99% confidence interval = 1.40_lower, 1.48_upper) or 1.4 standard deviations above zero.     

Categories in conflict: Combating the application of an intuitive conception of inheritance with category construction

The idea that characteristics acquired by an organism during its lifetime can be inherited by offspring and result in evolution is a substantial impediment to student understanding of evolution. In the current study, we performed a preliminary examination of how acquiring physical changes in a question prompt may differentially cue intuitive and scientific justifications of inheritance and evolution and how this varies based on how student learned the concept. Middle school students in a suburban northeastern district (N = 314) either learned about evolutionary change with a category construction task (with different levels of feedback support) or completed a worksheet. Three days later students responded to two free response scenarios (one where a physical change is acquired). Responses were coded based on student justifications for either science accuracy or intuitive nature. Specific reasons were coded by justification type with high inter-rater agreement (k > 0.93). Results showed that students were more likely to apply intuitive reasoning when a physical change was acquired (50%) than if the change was behavioral in nature (16%). Additionally, students who completed the category construction task provided significantly more scientifically accurate justifications about inheritance (M = 1.12) than control students (M = 0.47), and significantly less intuitive justifications (M = 0.67) than control (M = 1.13). Finally, category construction produced the most scientific reasoning when feedback was provided. Taken together, these results suggest that intuitive reasoning is differentially applied based on physical organismal changes, intuitive reasoning is less frequent when learning via category construction, and the category construction task is more effective for this population with the inclusion of feedback.     

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.     

Developing Model‐Based Reasoning

Key elements of the structure and function of models in mathematics and science are identified. These elements are used as a basis for discussing the development of model‐based reasoning. A microgenetic study examines the beginnings of model‐based reasoning in a pair of fourth‐ and fifth‐grade children who solved several problems about chance and probability. Results are reported in the form of a cognitive model of children's problem‐solving performance. The cognitive model explains a transition in children's reasoning from tacit reliance on empirical regularity to a form of model‐based reasoning. Several factors fostering change in children's thinking are identified, including the role of notations, peer interaction, and teacher assistance. We suggest that model‐based reasoning is a slowly‐developing capability that emerges only with proper contextual and social support and that future study should be carried out in classrooms, where these forms of assistance can also be part of the object of study.

Model‐based reasoning is a significant intellectual milestone because it bridges the worlds of personal, intuitive knowledge, on the one hand, and mathematical‐scientific theory, on the other. However, across disciplines, consensus is still forming about what model‐based reasoning comprises, and there is little knowledge about its ontogenetic origins or how it develops. We consider analogy as the core of modeling, because in model‐based reasoning a system in one domain is used to understand a system in another. To understand how models come to play a role in reasoning, it is important to initiate study of their origins. Accordingly, we report a microgenetic study examining the beginnings of model‐based reasoning in a pair of young children solving problems about chance and probability. In this study we are engaged in the enterprise of modeling the development of modeling. That is, we report our results in the form of a cognitive model of children's problem‐solving performance that explains a transition in reasoning from a tacit reliance on empirical regularity to a form of model‐based reasoning. It is important to note the two distinct meanings for the term model used in this article. The first describes how children come to understand and appropriate a system of reasoning exemplified in practices of modeling. The second describes a research tool, a model of human reasoning—specifically, how children in this study began to use models of probability to reason about uncertain events. In this report, we use the terms model or model‐based reasoning to refer to the former interpretation, whereas references to a cognitive model denote the simulation of children's thinking—in this case, implemented as a computer program.

Before describing the empirical work, we first identify some key elements of the structure and function of models. Next, these elements of modeling are used as the basis for generating some conjectures about the development of model‐based reasoning. We describe a task that we used as a window to understanding progression in student reasoning toward reliance on models as tools for thought. We present our rationale for developing cognitive models of student performance and explain some choices concerning the implementation of the cognitive model reported here. Finally, we turn to the children's performance on chance and probability tasks and explain how that performance illuminates both what children do not understand about models and the kinds of relevant knowledge that they are acquiring.     

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 INTERPLAY BETWEEN ADOLESCENTS’ PERCEPTIONS OF TEACHER‐STUDENT RELATIONSHIPS AND THEIR ACADEMIC SELF‐REGULATION: DOES LIKING A SPECIFIC TEACHER MATTER?

Although positive teacher‐student relationships are known to aid students’ academic self‐regulation, the emotional aspects of teacher liking are often neglected within research. The present study used a large sample of seventh‐ and eighth‐grade students (N = 1,088; M_Age =  13.7) in secondary schools in Germany to investigate whether the motivation students gain from specific well‐liked teachers (i.e., that students identify) can moderate the relation between their perception of teacher‐student relationships overall and academic self‐regulation (intrinsic motivation, identified, introjected, and external regulation). By means of latent moderated structural equations, students’ motivation based on liking one specific teacher was found to moderate the association between teacher‐student relationships and intrinsic motivation. The present study makes a contribution to the existing research on teacher‐student relationships and academic self‐regulation by investigating the role of students’ motivation related to the liking of a specific teacher. Results indicate that when early adolescent students can identify a well‐liked teacher, they tend to have higher levels of academic motivation. Hence, students’ motivation based on liking a single teacher compensates for generally low‐quality teacher‐student relationships and their respective impact on students’ intrinsic motivation.     

The four-card problem resolved? Formal operational reasoning and reasoning to a contradiction

To test the hypothesis that adolescents classified as formal operational, based upon use of proportional reasoning on the “Pouring Water Task” (Lawson, Karplus, & Adi, 1978) have acquired the mental structures necessary to comprehend hypothetico-deductive arguments of a pattern referred to as “reasoning to a contradiction,” while adolescents classified as concrete operational, based upon use of additive reasoning on the same task have not, a sample of 100 high school students were administered the task and three versions of a problem requiring use of reasoning to a contradiction before, immediately after, and one month after brief verbal instruction in use of that reasoning pattern. Results were generally supportive of the hypothesis as most of the concrete students failed the immediate and delayed posttest problems (62 and 80%, respectively) while most of the formal students succeeded (80 and 71%, respectively). Group differences were significant (p < .001) in both cases. These results suggest that, contrary to those who have argued that content plays a substantial role in logical performance, a general hypothetico-deductive reasoning competence exists in some adolescents and is applicable across a wide variety of task domains. Science instruction which aims to teach this competence is recommended.     

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.     

Some assembly required: How scientific explanations are constructed during clinical interviews

This article is concerned with commonsense science knowledge, the informally gained knowledge of the natural world that students possess prior to formal instruction in a scientific discipline. Although commonsense science has been the focus of substantial study for more than two decades, there are still profound disagreements about its nature and origin, and its role in science learning. What is the reason that it has been so difficult to reach consensus? We believe that the problems run deep; there are difficulties both with how the field has framed questions and the way that it has gone about seeking answers. In order to make progress, we believe it will be helpful to focus on one type of research instrument—the clinical interview—that is employed in the study of commonsense science. More specifically, we argue that we should seek to understand and model, on a moment‐by‐moment basis, student reasoning as it occurs in the interviews employed to study commonsense science. To illustrate and support this claim, we draw on a corpus of interviews with middle school students in which the students were asked questions pertaining to the seasons and climate phenomena. Our analysis of this corpus is based on what we call the mode‐node framework. In this framework, student reasoning is seen as drawing on a set of knowledge elements we call nodes, and this set produces temporary explanatory structures we call dynamic mental constructs. Furthermore, the analysis of our corpus seeks to highlight certain patterns of student reasoning that occur during interviews, patterns in what we call conceptual dynamics. These include patterns in which students can be seen to search through available knowledge (nodes), in which they assemble nodes into an explanation, and in which they converge on and shift among alternative explanations. © 2011 Wiley Periodicals, Inc. J Res Sci Teach 49: 166–198, 2012     

Kohl berg's Cognitive‐Developmental Theory in Educational Settings: Some Possible Abuses

Abstract

Kohlberg's cognitive‐developmental theory provides teachers with a framework for understanding the change and development of moral judgment and decision‐making of their pupils. One major abuse, however, may be when teachers take the stage labels associated with the hypothesized stage levels of moral judgment as indicative of static student qualities or characteristics, by placing more emphasis on perceived and labelled qualities than on the actual moral reasoning of the student. This, it is suggested, together with some empirical examples, may obscure the developmental trend of the student's moral judgment or even affect the teacher's expectations and consequently student's performance, and fails to take into account such factors as environment and interpersonal interaction. A study is reported in which curriculum consultants exposed to moral development theory were tested to determine whether they would use Kohlbergian labels of stage content or actual moral reasoning when required to make assessments. Suggestions are put forward as to how moral development theory can be more closely linked to pedagogy.     

The Achievement Motives Scale (AMS): theoretical basis and results from a first try‐out of a Czech form

The achievement motive concept refers to a relatively stable personality characteristic in terms of a capacity to anticipate affects in achievement situations. The motive to achieve success (M _s ) refers to the individual's capacity to anticipate positive affects, and the motive to avoid failure (M _f ) refers to a capacity to anticipate negative affects in achievement situations. Based, among other things, on the conceptualizations of motives, a measurement was constructed to tap the two aspects (M _s and M _f ) of motivation. Over the years the scale has been translated to several languages and used in a number of studies. The Czech version of the scale is an adapted translation of the English one, and was administered to 179 pupils in the sixth grade in 1989. Further, the subjects were retested after an interval of 12 weeks. The analyses indicate that the psychometric properties of the Czech version of AMS are promising.     

Chinese Malaysian Adolescents' Social‐Cognitive Reasoning Regarding Filial Piety Dilemmas

This study examined the social‐cognitive reasoning of 52 Chinese Malaysian preadolescents (9–12 years old; M = 11.02, SD = 0.94) and 68 adolescents (13–18 years old; M = 14.76, SD = 1.39) in resolving filial dilemmas within the personal and moral domain. Preadolescents deferred to parental authority, whereas adolescents endorsed filial obligation reasoning to justify compliance in the personal domain. Both appealed to filial obligation, pragmatic, or welfare and safety reasoning to justify compliance but fairness or rights reasoning to justify their noncompliance, for the moral issue. Distinctions between authoritarian and reciprocal filial piety reasoning were revealed. Findings demonstrated complex decision‐making and cognitive reasoning processes among Chinese Malaysian adolescents as they negotiate their filial obligations and autonomy development.     

A study of the effect of HyperCard and pen-paper performance assessment methods on expert-novice chemistry problem solving

This study investigated HyperCard as a tool for assessment in science education and determined whether or not a HyperCard assessment instrument could differentiate between expert and novice student performance (balancing stoichiometric equations) in science education. Five chemical equations were presented by traditional pen-paper and by a HyperCard (Hyperequation) program. Thirty honors (expert) and 30 regular (novice) chemistry students were randomly divided into HyperCard and traditional pen-paper groups of 15 students each. Scoring was based on five dependent variables: performance scores, number of attempts, rate of attempts, time on task, and correctness. Correlation results indicated that students with high performance scores correctly balanced more equations, required fewer attempts to balance equations, and required less time per attempt than did students with low performance scores. MANOVA results showed that performance scores and correctness scores for both experts and novice were significantly higher on HyperCard compared to pen-paper assessment; the novice scores on HyperCard nearly equaled the expert pen-paper assessment scores. Significant interactions were found for time on task and for correctness. The results suggest that HyperCard can be a suitable tool for assessment in science education and that such an instrument can differentiate between expert and novice student performance.