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.     

Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks

Understanding that mathematics is founded on reasoning and is not just a collection of rules to apply is an important message to convey to students. Here we examined the reasoning presented in seven topics in nine Australian eighth-grade textbooks. Focusing on explanatory text that introduced new mathematical rules or relationships, we classified explanations according to the mode of reasoning used. Seven modes were identified, making a classification scheme which both refined and extended previous schemes. Most textbooks provided explanations for most topics rather than presenting “rules without reasons” but the main purpose appeared to be rule derivation or justification in preparation for practise exercises, rather than using explanations as thinking tools. Textbooks generally did not distinguish between the legitimacies of deductive and other modes of reasoning.     

Teaching Deductive Reasoning to Pre-service Teachers: Promises and Constraints

This paper broadly addresses the question of whether university students whose major does not require expertise in logic can improve their ability in deductive reasoning by taking an introductory course in logic. In particular, our study aims to evaluate a course in deductive logic offered by one of the authors in a department of elementary education. Two experiments were conducted by using a pretest-posttest design with an experimental and a control group as well as a follow-up test after 6 months on the experimental group. The results of the analyses showed that the course mainly succeeded in strengthening students’ general logical ability in the experimental group and these gains were retained 6 months later in the follow-up test. Promises and constraints of the study are discussed in the educational context. The names of the authors are listed alphabetically.     

Carving Metacognition at Its Joints: Protracted Development of Component Processes

Two experiments investigated the development of metacognitive monitoring and control, and conditions under which children engage these processes. In Experiment 1, 5‐year‐olds (N = 30) and 7‐year‐olds (N = 30), unlike adults (N = 30), showed little evidence of either monitoring or control. In Experiment 2, 5‐year‐olds (N = 90) were given performance feedback (aimed at improving monitoring), instruction to follow a particular strategy (aimed at improving control), or both. Across conditions, feedback improved children's monitoring, and instruction improved both monitoring and control. Thus, children's poor metacognitive performance likely reflects a difficulty engaging the component processes spontaneously rather than a lack of metacognitive ability. These findings also suggest that the component processes are distinct, with both undergoing protracted development.     

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.     

Spatial Visualization of Human Anatomy through Art Using Technical Drawing Exercises

Spatial visualization, the ability to mentally rotate three-dimensional (3D) images, plays a significant role in anatomy education. This study examines the impact of technical drawing exercises on the improvement of spatial visualization and anatomy education in a Neuroscience course. First-year medical students (n = 84) were randomly allocated into a control group (n = 41) or art-training group (n = 43). Variables including self-reported artistic drawing ability, previous technical drawing experience, or previous anatomy laboratory exposure were gathered. Participants who self-identified as artistic individuals were equally distributed between the two groups. Students in the art-training group attended four 1-hour sessions to solve technical drawing worksheets. All participants completed two Mental Rotations Tests (MRT), which were used to assess spatial visualization. Data were also collected from two neuroscience written examinations and an anatomical “tag test” practical examination. Participants in the art-training and control groups improved on the MRT. The mean of written examination two was significantly higher (P = 0.007) in the art-training group (12.95) than the control group (11.48), and higher (P = 0.027) in those without technical drawing experience (12.44) than those with (11.00). The mean of the anatomical practical was significantly higher (P = 0.010) in those without artistic ability (46.24) than those with (42.00). These results suggest that completing technical drawing worksheets may aid in solving anatomy-based written examination questions on complex brain regions, but further research is needed to determine its implication on anatomy practical scores. These results propose a simple method of improving spatial visualization in anatomy education.     

Sources of Individual Differences in Children's Understanding of Fractions

Longitudinal associations of domain‐general and numerical competencies with individual differences in children's understanding of fractions were investigated. Children (n = 163) were assessed at 6 years of age on domain‐general (nonverbal reasoning, language, attentive behavior, executive control, visual‐spatial memory) and numerical (number knowledge) competencies; at 7 years on whole‐number arithmetic computations and number line estimation; and at 10 years on fraction concepts. Mediation analyses controlling for general mathematics ability and general academic ability revealed that numerical and mathematical competencies were direct predictors of fraction concepts, whereas domain‐general competencies supported the acquisition of fraction concepts via whole‐number arithmetic computations or number line estimation. Results indicate multiple pathways to fraction competence.     

Deductive reasoning: in the eye of the beholder

This study examines ways of approaching deductive reasoning of people involved in mathematics education and/or logic. The data source includes 21 individual semi-structured interviews. The data analysis reveals two different approaches. One approach refers to deductive reasoning as a systematic step-by-step manner for solving problems, both in mathematics and in other domains. The other approach emphasizes formal logic as the essence of the deductive inference, distinguishing between mathematics and other domains in the usability of deductive reasoning. The findings are interpreted in light of theory and practice.

Playful fostering of 6- to 8-year-old students’ inductive reasoning

This paper focuses on a training program in inductive reasoning for first-grade students and presents the direct results as well as the longitudinal effects of the evaluation study. The training is based on Klauer's theory of inductive reasoning and on his “Cognitive training for children” concept (Klauer, 1989a). The training program consists of 120 problems which can be solved through inductive reasoning. The tools for the training exercises were selected to correspond with the age of the targeted cohort. The experimental group in the study consisted of 90 students, whereas the control group was made up of 162. An inductive reasoning test was used in the pre- and posttest as well as in the follow-up study (one year later). The test comprised 33 figural, non-verbal items (Cronbach α = .86). On the posttest, the experimental group significantly outperformed the control group by more than one standard deviation. The experimental group scored significantly higher in each skill area targeted by the training. The most noticeable development was found in system formation. No gender differences were detected on the pre- or the posttest. The effect size of the training program was d = 1.12. In the follow-up study, the experimental group still significantly outperformed the control group; however, their respective levels of development had not changed in this one-year period. Thus, the training effect proved to be stable over time independent of individual students’ original level of inductive reasoning. This study provided evidence that inductive reasoning could be developed very effectively at this early age.     

Use of reasoning to a contradiction in grades three to college

The primary purpose of this study was to test the hypothesis that an important intellectual acquisition during adolescence is the ability to generate arguments that involve reasoning to contradiction. Students in grades 3, 5, 7, 9, 11, and college were individually administered a four-card selection task that required them to, among other things, reason to a contradiction to falsify a hypothesis. Virtually none of the students spontaneously utilized this reasoning pattern on the initial task. Minimal verbal instruction in use of the reasoning pattern was then given followed by a logically analogous selection task. Performance on this task improved significantly with age from 12% success among third graders to 52% success among college students, providing some support for the hypothesis. Performance on an evaluation task showed similar rates of success; however, most students were able to correctly evaluate falsifying evidence when presented. This result suggested that, contrary to Piagetian theory, students from grade 3 upward comprehend the logic of falsification. It is argued that reasoning to a contradiction is a reasoning pattern of central importance in testing alternative scientific hypotheses and its use in students grades 3 through college could be enhanced through proper instruction and, if done, should increase students' ability to generate and evaluate competing hypotheses.     

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.     

The Effect of a Computerized Simulation on Middle School Students’ Understanding of the Kinetic Molecular Theory

The objective of this study was to evaluate the effect of a dynamic software simulation on the understanding of the kinetic molecular theory by 7th graders. Students in the control group (n = 62) studied a curricular unit that addressed the differences in arrangement and motion of molecules in the three phases of matter. The experimental group (n = 71) studied the same unit combined with a few computer lessons using a software simulation. The results indicate that the students in the experimental group scored significantly higher than those in the control group. Nonetheless, while both groups of students improved their understanding of the kinetic molecular theory, the overall achievements were very low. These findings suggest that the simulation improved the understanding of the 7th graders; however, it was insufficient in itself to promote meaningful learning. Statistically significant gender differences were not observed. This paper concludes with a discussion of the educational implications of this study.     

Comparison of Modeling Techniques in Counselor Training

Two techniques of videotape recorded modeling for training counselors to ask open-ended questions (OEQ) were examined. It was hypothesized that a pure video model, exhibiting only desired behavior, would result in greater learning than a corrective video model, exhibiting both desired and undesired behavior, given that both models contained cues to indicate whether the behaviors are desired or undesired. Eighteen undergraduate peer counselors were randomly assigned to either (a) pure video model, (b) corrective video model, or (c) no-treatment control. Pre and postmeasures of level of OEQ responses were obtained by simulated interviews with one of four research assistants trained as pseudo-clients. Results indicate: (a) treatment had a significant effect on percentage of OEQ (F (2, 15) = 3.75, p<.05); (b) only the pure model was significantly different from the no-treatment control (Dunnett's t (3, 15) = 2.58, p <.02); and (c) the pure model was not significantly different from the corrective model. The findings support, but do not confirm, the hypothesis of the study that a pure video model would result in greater learning than a corrective video model. The experimenters suggest that negative modeling examples may interfere with learning at this introductory level of training and that these results have implications for the training methods used by many trainers of counselors.     

The Unique Contributions of Verbal Analogical Reasoning and Nonverbal Matrix Reasoning to Science and Maths Problem‐Solving in Adolescence

Relational reasoning, the ability to detect meaningful patterns, matures through adolescence. The unique contributions of verbal analogical and nonverbal matrix relational reasoning to science and maths are not well understood. Functional magnetic resonance imaging data were collected during science and maths problem‐solving, and participants (N = 36, 11–15 years) also completed relational reasoning and executive function tasks. Higher verbal analogical reasoning associated with higher accuracy and faster reaction times in science and maths, and higher activation in the left anterior temporal cortex during maths problem‐solving. Higher nonverbal matrix reasoning associated with higher science accuracy, higher science activation in regions across the brain, and lower maths activation in the right middle temporal gyrus. Science associations mostly remained significant when individual differences in executive functions and verbal IQ were taken into account, while maths associations typically did not. The findings indicate the potential importance of supporting relational reasoning in adolescent science and maths learning.     

Young Children’s Ability to Produce Valid and Relevant Counter-Arguments

In collaborative problem solving, children produce and evaluate arguments for proposals. We investigated whether 3- and 5-year-olds (N = 192) can produce and evaluate arguments against those arguments (i.e., counter-arguments). In Study 1, each child within a peer dyad was privately given a reason to prefer one over another solution to a task. One child, however, was given further information that would refute the reasoning of their partner. Five-year-olds, but not 3-year-olds, identified and produced valid and relevant counter-arguments. In Study 2, 3-year-olds were given discourse training (discourse that contrasted valid and invalid counter-arguments) and then given the same problem-solving tasks. After training, 3-year-olds could also identify and produce valid and relevant counter-arguments. Thus, participating in discourse about reasons facilitates children’s counter-argumentation.     

Beyond inductive and deductive reasoning: The search for a sense of knowing

Examination of data from several mathematics education research projects has led the author to postulate a form of mathematical reasoning that learners engage in spontaneously and that is not inherently inductive or deductive. Transformational reasoning is generated through the learner's inquiry into how a mathematical system works. This sense of how it works may lead to a sense of understanding that may not be provided by inductive and deductive reasoning.     

Interwealth Contact and Young Children's Concern for Equity

This study examined young children's contact with individuals of high-wealth and low-wealth backgrounds and their behavior toward peers of these backgrounds in a resource distribution task. The sample included 72 ethnically diverse higher income children (M_age = 6.68 years, SD = 0.98 years). Contact with individuals of low-wealth backgrounds (interwealth contact) affected children's behavior indirectly, through social-cognitive reasoning processes. The more interwealth contact children reported, the more likely they were to reason about access to resources rather than their own wealth preferences in this context. This reasoning, in turn, was associated with more resources allocated to a low-wealth peer relative to a high-wealth peer. Thus, interwealth contact early in development was associated with more equitable peer interactions.     

What is the role of induction and deduction in reasoning and scientific inquiry?

A long‐standing and continuing controversy exists regarding the role of induction and deduction in reasoning and in scientific inquiry. Given the inherent difficulty in reconstructing reasoning patterns based on personal and historical accounts, evidence about the nature of human reasoning in scientific inquiry has been sought from a controlled experiment designed to identify the role played by enumerative induction and deduction in cognition as well as from the relatively new field of neural modeling. Both experimental results and the neurological models imply that induction across a limited set of observations plays no role in task performance and in reasoning. Therefore, support has been obtained for Popper's hypothesis that enumerative induction does not exist as a psychological process. Instead, people appear to process information in terms of increasingly abstract cycles of hypothetico‐deductive reasoning. Consequently, science instruction should provide students with opportunities to generate and test increasingly complex and abstract hypotheses and theories in a hypothetico‐deductive manner. In this way students can be expected to become increasingly conscious of their underlying hypothetico‐deductive thought processes, increasingly skilled in their application, and hence increasingly scientifically literate. © 2005 Wiley Periodicals, Inc. J Res Sci Teach     

Judgments and Reasoning About Parental Discipline Involving Induction and Psychological Control in China and Canada

This study examined judgments and reasoning about four parental discipline practices (induction or reasoning and three practices involving “psychological control”; Barber, 1996; two forms of shaming and love withdrawal) among children (7–14 years of age) from urban and rural China and Canada (N = 288) in response to a moral transgression. Children from all settings critically evaluated love withdrawal and preferred induction. Despite being perceived as more common in China than in Canada, with age, parental discipline based on shaming or love withdrawal was increasingly negatively evaluated and believed to have detrimental effects on children's feelings of self‐worth and psychological well‐being. Some cultural variations were found in evaluations of practices, perceptions of psychological harm, and attribution of parental goals.     

Evaluations of Conflicts Between Latino Values and Autonomy Desires Among Puerto Rican Adolescents

Puerto Rican adolescents (N = 105; M_age = 15.97 years, SD = 1.40) evaluated hypothetical situations describing conflicts between Latino values (family obligations and respeto) and autonomy desires regarding personal, friendship, and dating activities. Adolescents judged that peers should prioritize Latino values over autonomy, which led to greater feelings of pride than happiness. However, they believed that teens would prioritize autonomy over Latino values, which led to greater feelings of happiness than pride. Adolescents reasoned about autonomy desires as personal issues, whereas reasoning about Latino values was multifaceted, including references to conventions and concerns for others. Furthermore, judgments and reasoning depended on the type of autonomy desire and Latino value and sometimes, by participants' age and sex.