How do pre-adolescent children interpret conditionals? (original) (raw)
Related papers
Conditional reasoning in context: A developmental dual processes account
Thinking & Reasoning, 2013
The way individuals interpret "if p then q" conditionals varies with content and context, often resulting in a biconditional reading. Surprisingly, truth table tasks reveal the existence of two different types of biconditional interpretations: equivalence, as for promises and threats, and defective biconditional, as for causal conditionals or indicative conditionals involving binary terms. The aim of this study was to determine how the interpretation of indicative conditionals is affected in children, adolescents, and adults, by restricting their context of enunciation to only one possible alternative for both the antecedent and the consequent. Moreover, we wanted to determine what is the exact nature of the biconditional interpretation induced by these restricted contexts. For this purpose, third, sixth, and ninth graders and adults performed a truth-value task on indicative conditionals presented either in restricted on non-restricted contexts. Restricted contexts had no effect on children who have a conjunctive interpretation of the conditional, but elicited a predominant defective biconditional reading in adolescents and adults. These results corroborate the developmental dual process account of conditional reasoning proposed by Gauffroy and Barrouillet (2009).
Child Development, 2006
In Study 1, 10-, 13-, and 16-year-olds were assigned to conditions in which they were instructed to think logically and provided alternative antecedents to the consequents of conditional statements. Providing alternatives improved reasoning on two uncertain logical forms, but decreased logical responding on two certain forms; logic instructions improved reasoning among adolescents. Correlations among inferences and verbal ability were found primarily when task conditions created conflict between automatic and controlled inferences. In Study 2, when the cognitive demands of the logic instructions were reduced, 10-year-olds made more logically correct inferences, but only when a conditional's consequents were strongly associated with alternative antecedents. Discussion focuses on the ability to inhibit invited inferences and the role of automatically activated memories.
Children's conditional reasoning
Educational Studies in Mathematics, 1977
This study stemmed from a desire to redress the distorted view of mathematics in the elementary curriculum, created by the current imbalanced emphasis on computational rules and some applications, but very little logical analysis. The study is intended to show that fifth-grade students can significantly improve their use of logical analysis through a suitable instructional unit taught under ordinary classroom conditions. Concrete teaching materials were developed, through several trials and revisions, to familiarize students with the distinction between the valid inference patterns-Modus Ponendo Ponens and Modus Tollendo Tollens (AA, DC), and the fallacious ones-AffLrming the Consequent and Denying the Antecedent (AC, DA). No formal rules were taught. The experimental unit was implemented four to five times a week for 23-25 sessions, by 4 ffffth-grade teachers in their ordinary classes. The teachers participated in a twelvehour pretraining workshop. A pretest/posttest treatment/no-treatment design was applied to assess resulting improvement in students' conditional reasoning ability. The sample consisted of 210 fifth graders in a suburban area, 104 in 4 experimental classes and 106 in 4 control classes. A written group test was developed, through trials and revisions. Test items are formulated with a reasonable hypothetical content. Each item includes two premises: the first a conditional sentence, and the second either its antecedent, its consequent, or the negation of one of these, thus determining the logical form: AA, DC, AC, or DA. The question following the premises is stated positively. AA and DC are answered correctly by 'yes' or 'no': AC and DA by 'not enough clues' (NEC). The test contains 32 randomly-ordered three-choice items, eight in each logical form (two of the eight in each of the four possible modes in which negation may or may not occur in the antecedent or consequen0. No sentential connective other than negation and conditional appears in the premises. Test/retest reliability was 0.79.
Theories of Conditional Reasoning: A Developmental Examination of Competing Hypotheses
Developmental Psychology, 2004
Children and adolescents were presented with problems that contained deontic (i.e., if action p is taken, then precondition q must be met) or causal (i.e., if event p occurs, then event q will transpire) conditionals and that varied in the ease with which alternative antecedents could be activated. Results showed that inferences were linked to the availability of alternative antecedents and the generation of "disabling" conditions (claims that the conditionals were false under specific circumstances). Age-related developments were found only on problems involving indeterminate inferences. Correlations among inferences differed for children and adolescents. The findings provide stronger support for domain-general theories than for domain-specific theories of reasoning and suggest, under some conditions, age-related changes in the roles of implicit and explicit processing.
Probability in reasoning: A developmental test on conditionals
Cognition, 2015
Probabilistic theories have been claimed to constitute a new paradigm for the psychology of reasoning. A key assumption of these theories is captured by what they call the Equation, the hypothesis that the meaning of the conditional is probabilistic in nature and that the probability of If p then q is the conditional probability, in such a way that P(if p then q)=P(q|p). Using the probabilistic truth-table task in which participants are required to evaluate the probability of If p then q sentences, the present study explored the pervasiveness of the Equation through ages (from early adolescence to adulthood), types of conditionals (basic, causal, and inducements) and contents. The results reveal that the Equation is a late developmental achievement only endorsed by a narrow majority of educated adults for certain types of conditionals depending on the content they involve. Age-related changes in evaluating the probability of all the conditionals studied closely mirror the developmen...
Reasoning about Conditional Sentences: Development of Understanding of Cues to Quantification
The previous literature has reported that when children are asked to judge the truth or falsity of universally quantified conditional sentences of the form If a thing is P then it is Q they typically give erroneous responses, e.g., responding “true” whenever there is a case of P and Q even if there are also cases of P and not-Q. Three experiments are reported that address possible sources of this error. Experiment 1 shows that the error survives on sentences that refer to particular things as well as to things of a particular kind, and further shows that articulating the necessity of the consequent (. then it has to be Q) eliminates the error for adults and reduces it for fifth graders, although it does not affect second grade performance. Experiment 2 shows that for second and fifth graders the error survives to problems that are not universally quantified and for second graders to problems that are not conditionals although are otherwise structurally similar. Experiment 3 compares various verbal formulations of such universally quantified conditionals: Second and fifth graders do not make the error when the quantification is expressed with the surface structure that makes its universality most explicit (all things . .); the error tendency is greatest when the indefinite article is used (if a thing . .); and formulations using any fall in between. We argue that such erroneous evaluations of universally quantified conditionals have more to do with the quantificational aspect than the conditional aspect of the problems; children interpret the indefinite article as existential, although they resist the error when the cue to universal quantification is completely clear. The error appears to result more from the surface-structure form of the stimuli than from an inability of children to appreciate the logic of universally quantified conditionals.
Developmental Review, 2009
This article presents a developmental dual-process theory of the understanding of conditionals that integrates Evans' heuristic-analytic theory within the revised mental model theory of conditional proposed by Barrouillet, Gauffroy, and Lecas (2008). According to this theory, the interpretation of a conditional sentence is driven by unconscious and implicit heuristic processes that provide individuals with an initial representation that captures its meaning by representing the cases that make it true. This initial model can be enriched with additional models (a process named fleshing out within the mental model theory) through the intervention of conscious and demanding analytic processes. Being optional, these processes construct representations of cases that are only compatible with the conditional, leaving its truth-value indeterminate when they occur. Because heuristic processes are relatively immune to developmental changes, while analytic processes strongly develop with age, the initial model remains stable through development whereas the number of additional models that can be constructed increases steadily. Thus, the dual-process mental model theory predicts in which cases conditionals will be deemed true, indeterminate, or false and how these cases evolve with age. These predictions were verified in children, adolescents and adults who were asked to evaluate the truth value and the probability of several types of conditionals. The results reveal a variety of developmental trajectories in the way different conditionals are interpreted, which can all be accounted for by our revised mental model theory.
Thinking about conditionals: A study of individual differences
Memory & Cognition, 2007
Recent studies have shown the existence of two qualitatively distinct groups of people based on how they judge the probability of a conditional statement. The present study was designed to test whether these differences are rooted in distinctive means of processing conditional statements and whether they are linked to differences in general intelligence. In the study, each of 120 participants completed three separate cognitive tasks involving the processing of abstract conditional statements-the probability-of-conditionals task, the conditional truth table task, and the conditional inference task-in addition to completing a test of general intelligence (AH4). The results showed a number of predicted effects: People responding with conditional (rather than conjunctive) probabilities on the first task were higher in cognitive ability, showed reasoning patterns more consistent with a suppositional treatment of the conditional, and showed a strongly "defective" truth table pattern. The results include several novel findings and post challenges to contemporary psychological theories of conditionals.
1975
This study stemmed from a desire to redress the distorted view of mathematics in the elementary curriculum, created by the current imbalanced emphasis on computational rules and some applications, but very little logical analysis. The study is intended to show that fifth-grade students can significantly improve their use of logical analysis through a suitable instructional unit taught under ordinary classroom conditions. Concrete teaching materials were developed, through several trials and revisions, to familiarize students with the distinction between the valid inference patterns-Modus Ponendo Ponens and Modus Tollendo Tollens (AA, DC), and the fallacious ones-AffLrming the Consequent and Denying the Antecedent (AC, DA). No formal rules were taught. The experimental unit was implemented four to five times a week for 23-25 sessions, by 4 ffffth-grade teachers in their ordinary classes. The teachers participated in a twelvehour pretraining workshop. A pretest/posttest treatment/no-treatment design was applied to assess resulting improvement in students' conditional reasoning ability. The sample consisted of 210 fifth graders in a suburban area, 104 in 4 experimental classes and 106 in 4 control classes. A written group test was developed, through trials and revisions. Test items are formulated with a reasonable hypothetical content. Each item includes two premises: the first a conditional sentence, and the second either its antecedent, its consequent, or the negation of one of these, thus determining the logical form: AA, DC, AC, or DA. The question following the premises is stated positively. AA and DC are answered correctly by 'yes' or 'no': AC and DA by 'not enough clues' (NEC). The test contains 32 randomly-ordered three-choice items, eight in each logical form (two of the eight in each of the four possible modes in which negation may or may not occur in the antecedent or consequen0. No sentential connective other than negation and conditional appears in the premises. Test/retest reliability was 0.79.
Basic Conditional Reasoning: How Children Mimic Counterfactual Reasoning
Studia Logica, 2013
Children approach counterfactual questions about stories with a reasoning strategy that falls short of adults' Counterfactual Reasoning (CFR). It was dubbed "Basic Conditional Reasoning" (BCR) in Rafetseder et al. (Child Dev 81(1):376-389, 2010). In this paper we provide a characterisation of the differences between BCR and CFR using a distinction between permanent and nonpermanent features of stories and Lewis/Stalnaker counterfactual logic. The critical difference pertains to how consistency between a story and a conditional antecedent incompatible with a nonpermanent feature of the story is achieved. Basic conditional reasoners simply drop all nonpermanent features of the story. Counterfactual reasoners preserve as much of the story as possible while accommodating the antecedent.