Proportional reasoning and the linguistic abilities required for hypothetico-deductive reasoning

The hypothesis is advanced that a necessary, though not sufficient, condition for the acquisition of proportional reasoning during adolescence is the prior internalization of key linguistic elements of argumentation, essentially those used in hypothetico-deductive reasoning. This hypothesized internalization, which does not occur in all individuals, results in some who have acquired the ability to reflect upon the correctness of self-generated answers in a hypothetico-deductive manner, and others who have not. As an initial test of the hypothesis, 46 subjects (Ss) (mean age = 21.03 years) were classified into additive, transitional, or proportional reasoning categories based upon responses to a proportions task. Group differences were found in which proportional Ss performed better than transitional Ss who in turn performed better than additive Ss on a number of items testing Ss' abilities to identify, generate, and use the linguistic elements of argumentation. Further it was found that some Ss who were successful on the linguistic items failed the proportions task, but no Ss who were successful on the proportions task failed the linguistic items. This result supports the hypothesis that the internalization of linguistic elements of argumentation is a prerequisite for proportional reasoning and by inference other advanced reasoning schemata as well. Implications for science instruction are drawn.     

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.     

Relation of field independence and test-item format to student performance on written piagetian tests

In this study we have investigated the relationship between the field-dependence-independence (FDI) dimension as measured by the Group Embedded Figures Test (GEFT) and subject performance on the Longeot test, a pencil-and-paper Piagetian test, through the open or closed format of its items. The sample consisted of 141 high school students. Correlation and variance analysis show that the FDI dimension and GEFT correlate significantly on only those items on the Longeot test that require formal reasoning. The effect of open- or closed-item format is found exclusively for formal items; only the open format discriminates significantly (at the 0.01 level) between the field-dependent and -independent subjects performing on this type of item. Some implications of these results for science education are discussed.     

Scientific reasoning in elementary school children: Assessment and relations with cognitive abilities

The primary goal of this study was the broad assessment and modeling of scientific reasoning in elementary school age. One hundred fifty-five fourth graders were tested on 20 recently developed paper-and-pencil items tapping four different components of scientific reasoning (understanding the nature of science, understanding theories, designing experiments, and interpreting data). As confirmed by Rasch analyses, the scientific reasoning items formed a reliable scale. Model comparisons differentiated scientific reasoning as a separate construct from measures of intelligence and reading skills and revealed discriminant validity. Furthermore, we explored the relationship between scientific reasoning and the postulated prerequisites inhibitory control, spatial abilities and problem-solving skills. As shown by correlation and regression analyses, beside general cognitive abilities (intelligence, reading skills) problem-solving skills and spatial abilities predicted performance in scientific reasoning items and thus contributed to explaining individual differences in elementary school children's scientific reasoning competencies.     

The acquisition of formal operational schemata during adolescence: The role of the biconditional

To test the hypothesis that the basic “logic” utilized by individuals in scientific hypothesis testing is the biconditional (if and only if), and that the biconditional is a precondition for the development of formal operations, a sample of 387 students in grades eight, ten, twelve, and college were administered eight reasoning items. Five of the items involved the formal operational schemata of probability, proportions and correlations. Two of the items involved propositions and correlations. Two of the items involved propositional logic. One item involved the biconditional. Percentages of correct responses on most of the items increased with age. A principal-component analysis revealed three factors, two of which were identified as involving operational thought, one of which involved propositional logic. As predicted, the biconditional reasoning item loaded on one of the operational thought factors. A Guttman scale analysis of the items failed to reveal a unidimensional scale, yet the biconditional reasoning item ordered first supporting the hypothesis that it is a precondition for formal operational reasoning. Implications for teaching science students how to test hypotheses are discussed.     

The Relationship of Content Characteristics of GRE Analytical Reasoning Items to Their Difficulties and Discriminations

In actual test development practice, the number o f test items that must be developed and pretested is typically greater, and sometimes much greater, than the number that is eventually judged suitable for use in operational test forms. This has proven to be especially true for one item type–analytical reasoning-that currently forms the bulk of the analytical ability measure of the GRE General Test. This study involved coding the content characteristics of some 1,400 GRE analytical reasoning items. These characteristics were correlated with indices of item difficulty and discrimination. Several item characteristics were predictive of the difficulty of analytical reasoning items. Generally, these same variables also predicted item discrimination, but to a lesser degree. The results suggest several content characteristics that could be considered in extending the current specifications for analytical reasoning items. The use of these item features may also contribute to greater efficiency in developing such items. Finally, the influence of these various characteristics also provides a better understanding of the construct validity of the analytical reasoning item type.     

Kindergarten reasoning and achievement in grades K-3

Performance of kindergarten children on reasoning (Piaget tasks of logical thinking), visual-motor integration, and verbal development was related to achievement scores in kindergarten, second grade, and third grade. Subjects were 52 children in the kindergarten classes of a middle-class, suburban/rural school. Reasoning and visual-motor integration were related to achievement on the Metropolitan Achievement Test at the end of kindergarten. For the 43 children remaining in second grade, there was a relationship between reasoning in kindergarten and achievement on the Reading and Math Concepts sections of the Iowa Test of Basic Skills. For the 38 children remaining in third grade, kindergarten reasoning was related to total and Vocabulary scores of the California Achievement Test. Kindergarten visual-motor integration and verbal development were not related to achievement test performance at the end of the second and third grade for these subjects. Early intervention programs that encourage the development of thinking and match the child's reasoning to his academic tasks may stimulate both reasoning and achievement.     

Cognitive Abilities among Twelfth‐grade Students: Implications for Science Teaching∗

The study investigated the differences related to formal reasoning abilities among students attending different sections of the upper cycle of secondary schools in Cyprus. The subjects of the study were twelfth‐grade students from 21 intact classes (227 boys and 242 girls). These classes were randomly selected among the 36 twelfth‐grade classes of four schools in a town of Cyprus. The sample of students represented the science section, the economic section and the “unified” section consisting of sections following common curricula in science and mathematics. Students’ performance on a standardized Test of Logical Thinking (TOLT) was used as a measure of their cognitive abilities related to control of variables, proportional, probabilistic, correlational and combinatorial reasoning. The students of the “unified” section had lower performance than the students of both the science and the economic section on all cognitive measures, and female students had lower performance than male students on cognitive measures related to control of variables and probabilistic reasoning. Multiple regression analysis between performance on TOLT and gender, section of study, and measures of school achievement showed that gender, section of study, achievement in mathematics, and grade point average, but not achievement in science and Greek language, contributed significantly to predicting performance on TOLT. Observed differences related to measures of school achievement either among the subjects of the three sections or between male and female students did not correspond to differences related to cognitive measures. Factor analysis of performance on the ten TOLT items (two items from each reasoning mode) produced a two‐factor solution. There were also significant differences in students’ performance between items related to the same or different reasoning mode. The results of the study cast doubt on the appropriateness of the existing curricula or their implementation and indicate that different theoretical perspectives should be considered when evaluating cognitive development.     

Formal reasoning performance of higher secondary school students: Theoretical and educational implications

The study investigated the structure and development of formal thought among tenth-, eleventh-, and twelfth-grade students. The subjects of the study were the total numbers of students attending the science, the economic, and the other sections of two higher secondary schools. Students' performance on a standardized Test of Logical Thinking (TOLT) was used as a measure of their cognitive abilities related to control of variables, proportional, probabilistic, correlational, and combinatorial reasoning. Students attending the different sections of study had significantly different TOLT performance, older students exhibited significantly better TOLT performance than younger ones, and boys performed significantly better on TOLT than girls did. The “rate” of development was, however, different for different reasoning modes and differences in school achievement between boys and girls did not tap differences in TOLT performance. Regression analysis showed that section of study, gender, grade level, and measures of school achievement contributed significantly to the prediction of TOLT performance. Factor analysis of performance on the ten TOLT items (two items from each reasoning mode) produced a two- and three-factor solution for the sample of boys and the sample of girls, respectively. The results indicate that different theoretical perspectives should be considered when evaluating cognitive development and that learning environments conducive to cognitive growth need to be designed and implemented.     

Student gain in reasoning ability as a function of teacher reasoning level and teaching style preference

This study examines the effect of teacher reasoning level (i.e., concrete versus formal) and teaching style preference (i.e., inquiry vs. expository) on improvement in student reasoning ability. A random sample of fourth and seventh grade teachers and their students were selected to participate over one school year. Students completed a reasoning test in the early fall and late spring. Teachers completed two instruments in the Spring, a reasoning test and a teaching style preference questionnaire. Students of concrete operational teachers showed greater gains in reasoning ability than students of formal operational teachers while students of inquiry teachers showed slightly greater gains than students of expository teachers. Possible explanations are discussed as are suggestions for future research.     

On the effects of training inductive reasoning: How far does it transfer and how long do the effects persist?

Using the same program, two training experiments have been conducted in a Dutch and in a German elementary school. The common expectation was that training in inductive reasoning would transfer both on intelligence tests measuring inductive reasoning and on math performance. Furthermore, it was expected that the training effects would persist for at least some months after training had ended. In experiment 1 (N=34), a rather short training period turned out to be effective with respect to the intelligence test performance but not with respect to math performance. In experiment 2 (N=23), the amount of training in inductive reasoning was systematically varied. It could be shown that transfer on intelligence test as well as on math performance was linearly dependent on the amount of prior training. The training effects were found to persist between four and nine months after training.     

A Rasch Analysis of Raven Item Data

The Progressive Matrices items require varying degrees of analytical reasoning. Individuals high on the underlying trait measured by the Raven should score high on the test. Latent trait models applied to data of the Raven form provide a useful methodology for examining the tenability of the above hypothesis. In this study the Rasch latent model was applied to investigate the fit of observed performance on Raven items to what was expected by the model for individuals at six different levels of the underlying scale. For the most part the model showed a good fit to the test data. The findings were similar to previous empirical work that has investigated the behavior of Rasch test scores. In three instances, however, the item fit statistic was relatively large. A closer study of the “misfitting” items revealed two items were of extreme difficulty, which is likely to contribute to the misfit. The study raises issues about the use of the Rasch model in instances of small samples. Other issues related to the interpretation of the Rasch model to Raven-type data are discussed.     

Formal operational reasoning modes: Predictors of critical thinking abilities and grades assigned by teachers in science and mathematics for students in grades nine through twelve

To test the hypothesis that formal operational reasoning modes are predictors of critical thinking abilities and grades assigned by teachers in science and mathematics, in September 1986 the Group Assessment of Logical Thinking (GALT) and in December 1986 the Watson-Glaser Critical Thinking Appraisal (WGCTA) were administered to 101 rural students in Grades 9 through 12. The grades assigned by teachers were collected in May 1987. Construct and criterion-related validities and internal-consistency reliability using Cronbach's alpha method were established on the GALT. On the WGCTA, content and construct validities and internal consistency reliability using the split-half procedure, coefficient of stability, and coefficient of equivalence were established. The five formal operational reasoning modes in the GALT were found to be significant predictors of critical thinking abilities and grades assigned by teachers in science and mathematics. The variance in the five critical thinking abilities attributable to the five formal operational reasoning modes ranged between 28% and 70%. The five formal operational reasoning modes explained 29% of the variance in mathematics achievement and 62% of the variance in science achievement.     

Formal reasoning ability and misconceptions concerning genetics and natural selection

Students often hold misconceptions about natural phenomena. To overcome misconceptions students must become aware of the scientific conceptions, the evidence that bears on the validity of their misconceptions and the scientific conceptions, and they must be able to generate the logical relationships among the evidence and alternative conceptions. Because formal operational reasoning patterns are necessary to generate these logical relationships, it was predicted that, following instruction, formal operational students would hold significantly fewer misconceptions than their concrete operational classmates. To test this hypothesis 131 seventh-grade students were administered an essay test on principles of genetics and natural selection following instruction. Responses were categorized in terms of the number of misconceptions present. The number of misconceptions was compared to reasoning ability (concrete, transitional, formal), mental capacity (<6, 6, 7), verbal intelligence (low, medium, high), and cognitive style (field dependent, intermediate, field independent). The only student variable consistently and significantly related to the number of misconceptions was reasoning ability; thus, support for the major hypothesis of the study was obtained.     

The effect of grouping of laboratory students on selected educational outcomes

The purpose of this study was to discover if grouping students in the laboratory on the basis of their formal reasoning ability affected (1) their science content achievement, (2) their formal reasoning ability, (3) the learning environment in the laboratory, and (4) the relationships between individuals in a particular group. The laboratory groups for three physical science classes for preservice elementary teachers were arranged as follows: (1) one class with students of unequal reasoning ability grouped together, i.e., one highly developed formal reasoner per group (the heterogeneous group), (2) one class with students of similar reasoning ability grouped together (the homogeneous group), and (3) one class arranged in groups according to the desires of the class members (the student choice group). The three classes were compared using pre-and post-scores on content and formal reasoning instruments and scores for classroom environment and social relationships. Results indicated that the groupings as described had significantly different effects on science content achievement but not on any of the other questions posed above. The students in the class with laboratory teams grouped by student choice had significantly lower science content scores than the students in the classes with teams formed using either the heterogeneous or homogeneous grouping procedures. The difference between the heterogeneously and homogeneously grouped classes was not significant at the 0.05 level.     

Determinants of Complexity in Mexican-American and Anglo-American Mothers' Conceptions of Child Development

Complexity of parental reasoning about child development was studied in mothers who varied in ethnic background and biculturalism. Middle-class mothers from Mexican-American and Anglo-American backgrounds were compared on their level of concepts of development on a scale from categorical to perspectivistic reasoning. Categorical mothers interpreted child development as being caused by single constitutional or environmental factors. Perspectivistic mothers interpreted development as the result of the dynamic interplay between constitution and environment over time and accepted that the same developmental outcome could have multiple determinants. In a comparison among moderately acculturated Mexican-Americans, highly acculturated Mexican Americans, and Anglo Americans, the highly acculturated Mexican-American group scored as more perspectivistic than the other two groups, despite the fact that the Anglo-Americans were the most acculturated. When the 2 Mexican-American groups were subdivided into monocultural (Mexican or American) and bicultural subgroups and compared with the Anglo-American group, the bicultural subgroup of the highly acculturated Mexican-American mothers was the most perspectivistic. These results suggest a complex picture of diversity in Mexican-American mothers who retain values and beliefs from their own culture, as well as taking on values and beliefs of the American culture. Maternal intelligence and adherence to traditional cultural values were not found to correlate significantly with level of developmental reasoning.     

论证的形式模型概述及其在哲学上的应用

论证是一个用理由支持观点以及回应其所受攻击的过程.在过去的几十年里,论证已经成为哲学和人工智能研究领域中的一个重要主题.在哲学方面,十九世纪50年代和60年代图尔敏和佩雷尔曼对形式逻辑的批判,促进了非形式逻辑这一学科的产生,它研究推理和论证的非形式模型.在人工智能方面,论证的形式模型也发展成为常识推理和多主体冲突解决的基本模型.本文将讨论后一领域中所研究发展的形式模型如何能够用以澄清一些哲学领域、以及非形式逻辑领域中的理论问题和争议.本文的一个重要观点是,图尔敏和佩雷尔曼时代的形式逻辑只关注数学化的推理,但那些非数学化的推理形式其实同样也能够被形式化.     

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.     

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.