Children's hypothetical reasoning about complex and dynamic systems

Children's hypothetical reasoning about a complex and dynamic causal system was investigated. Predominantly White, middle-class 5- to 7-year-old children from the Greater Toronto Area learned about novel food chains and were asked to consider the effects of removing one species on the others. In Study 1 (N = 72; 36 females, 36 males; 2018), 7-year-olds answered questions about both direct and indirect effects with a high degree of accuracy, whereas 5-year-olds performed at chance. Six-year-olds showed intermediate performance. Using food chains with clearer constraints, Study 2 (N = 72; 35 females, 37 males; 2020–2021) replicated these findings. These results indicate that the ability to think about hypothetical changes to dynamic causal systems develops between 5 and 7 years. Implications for science education are discussed.     

Children's conditional reasoning

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 — Affirming 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 fifth-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 consequent). No sentential connective other than negation and conditional appears in the premises. Test/retest reliability was 0.79.Experimental and control group pretest performance levels did not differ (=0.05). More than 78% of the answers on AA and DC, and fewer than 33.1% on AC and DA, were correct. Overall pretest mean scores were 54.3% and 53.8% for the experimental and control groups respectively.There was a significant difference (=0.01) between the experimental and control groups' posttest overall performance—74.7% and 55.4%, respectively.There was no significant change in the control group's pretest and posttest performance levels on any logical form, or for the experimental group's on AA and DC. However, on AC and DA the two groups' gain scores were found significantly different.Negation mode, unlike logical form, was not found to be independently influential in analyzing test scores, but interacted with logical form.There was a pretest/posttest increase of 3.5 in experimental group frequency (percentaged) of incorrect NEC answers (AA and DC). As NEC appeared infrequently on the pretest, this increase was interpreted as learning that NEC is an acceptable answer. Separating out this effect from the percentaged frequency of correct NEC answers (AC and DA) left a pretest/posttest average increase of 37.8. This increase was attributed to learning when NEC is correct.Teachers were excited at the beginning, frustrated in the middle, and felt competent and involved in the project at the end. They felt the teaching should be less condensed. The majority of the students reacted positively to most parts of the experimental unit. However, some thought the unit as a whole was too repetitive and boring.No correlation was found between learning logic through the experimental unit and standard school achievement as measured by the Stanford Achievement Test (SAT). High, average, and low SAT achievers of the experimental group did not differ significantly in their pretest and posttest gain scores.Results of the study call for further investigation of the value and usefulness of teaching various parts of logic as an ordinary part of the elementary mathematics curriculum.This study was supported by NSF grants Nos. GW 7659 and PES 74-018450 and by an AAUW International Fellowship. It was carried out at the University of California, Berkeley, in 1974/75 under supervision of Professor Leon Henkin.     

The rejection of nonscientific beliefs about life: Effects of instruction and reasoning skills

Nine hundred fifty-four students in a large university nonmajors biology course were pretested to determine the extent to which they held nonscientific beliefs in creationism, orthogenesis, the soul, nonreductionism, vitalism, teleology, and nonemergentism. To test the hypothesis that hypothetico-deductive reasoning skills facilitate movement away from nonscientific beliefs, the degree to which those nonscientific beliefs were initially held and the degree to which they were modified during instruction were compared to student reasoning level (intuitive, transitional, reflective). As predicted, the results showed that the less skilled reasoners were more likely to initially hold the nonscientific beliefs and were less likely to change those beliefs during instruction. It was also discovered that less skilled reasoners were less likely to be strongly committed to the scientific beliefs.     

Children's social reasoning about inclusion and exclusion in gender and race peer group contexts

This study investigated whether children's and adolescents' judgments about exclusion of peers from peer group activities on the basis of their gender and race would differ by both age level and the context in which the exclusion occurred. Individual interviews about exclusion in several different contexts were conducted with 130 middle-class, European American children and adolescents. Younger children were expected to reject exclusion, by using judgments based on moral reasoning, regardless of the potential cost to group functioning, whereas older children were expected to condone exclusion on the basis of group membership in cases in which the inclusion of these children might interrupt effective group functioning. On measures of judgments, justifications for those judgments, and ratings of the appropriateness of exclusion, the vast majority of children used moral reasoning and rejected exclusion in contexts in which only the presence of a stereotype justified it. As expected, however, older children (13 years) were more likely to allow exclusion than younger children (7 and 10 years) when group functioning was threatened, and they justified this exclusion by using appeals to effective group functioning.     

Children's use of analogy during collaborative reasoning

This microgenetic study examined social influences on children's development of analogical reasoning during peer-led small-group discussions of stories about controversial issues. A total of 277 analogies were identified among 7,215 child turns for speaking during 54 discussions from 18 discussion groups in 6 fourth-grade classrooms (N = 120; age M=10.0, SD=0.6). Use of analogy was found to spread among the children in discussion groups and occur at an accelerating rate, primarily because of the increasing use of novel analogies. Relational analogies with shared surface features triggered purely relational analogies during the next 2 speaking turns, showing a trend of relational shift. These results provide distinctive new evidence for the importance of social interaction in an aspect of cognitive development.     

Children's and adults' knowledge and models of reasoning about the ozone layer and its depletion

A model giving the main domains of ‘process knowledge’ in solving problems in physics is proposed. In the framework of this model the strategies and results of using thinking‐aloud experiments to obtain the elements of ‘process knowledge’ in the problem‐solving activity in physics are discussed.

     

Children's reasoning about social, physical, and logical regularities: a look at two worlds

In 2 studies, 6-, 8-, and 10-year-old children were interviewed about 3 different types of regularities or rules: social conventions, physical laws, and logical necessities. In the first study, children were asked if regularities could be changed (by consensus) and/or be different in another world. In the second study, children were asked if regularities could be different in another country (on Earth) or on a different planet. Results showed that social regularities were distinguished from the other types, but physical and logical regularities were treated similarly. While the evidence for age differences was equivocal, it was clear that even first graders did not judge physical items as alterable on Earth. This fails to replicate a previously reported finding that children pass through a stage where all items are seen as alterable. Finally, a sex difference emerged, with boys more willing to judge physical and logical regularities to be alterable in another world.     

Relative expertise in an everyday reasoning task: Epistemic understanding, problem representation, and reasoning competence

Experts in cognitive domains differ from non-experts in how they represent problems and knowledge, and in their epistemic understandings of tasks in their domain of expertise. This study investigates whether task-specific epistemic understanding also underlies the representation of knowledge on an everyday reasoning task on which the competent reasoners have neither expert domain knowledge nor training. 180 people on jury duty were assessed for epistemological understanding about the nature of knowledge and knowing in general, understanding of the specific task of the juror, and level of argument skill and evidence representation on two jury cases. Epistemic construal of the juror task and task-specific competent reasoning was found related to general epistemology, argument skills, and representation of the evidence. Additionally, estimations of the possibility of certainty in general and in a juror task predicted the participants' expressed certainty about their verdict choices. Implications for developing everyday reasoning competence are discussed.     

Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role

This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore links between the students' mathematical behavior in solving these problems and their perception of their roles as learners. We develop a theory in which the tendency to visualize, coupled with the students' view of their role, can be used to account for their mathematical behavior. This revised version was published online in July 2006 with corrections to the Cover Date.     

Children's responses to everyday marital conflict tactics in the home

Mothers' and fathers' reports of marital conflicts in the home were obtained (n = 1,638 and 1,281 conflicts, respectively), including conflicts in front of the children (n = 580 and 377, respectively). Participants were 116 families with children 8 to 16 years old (M = 10.82 years, SD = 2.17; 58 boys, 58 girls). Children's emotional responses indicated distinctions between distressing conflict tactics (i.e., threat, personal insult, verbal hostility, defensiveness, nonverbal hostility, marital withdrawal, physical distress) and those that increased their emotional security (i.e., calm discussion, support, affection). Analyses based on cross-reporter informants of parental conflict and child responses strengthened confidence in the findings. Conflict tactics were related to marital functioning, and children's emotional reactions during marital conflicts were associated with their adjustment.     

Children's reasoning about disclosing adult transgressions: effects of maltreatment, child age, and adult identity

A total of two hundred ninety-nine 4- to 9-year-old maltreated and nonmaltreated children of comparable socioeconomic status and ethnicity judged whether children should or would disclose unspecified transgressions of adults (instigators) to other adults (recipients) in scenarios varying the identity of the instigator (stranger or parent), the identity of the recipient (parent, police, or teacher), and the severity of the transgression ("something really bad" or "something just a little bad"). Children endorsed more disclosure against stranger than parent instigators and less disclosure to teacher than parent and police recipients. The youngest maltreated children endorsed less disclosure than nonmaltreated children, but the opposite was true among the oldest children. Older maltreated children distinguished less than nonmaltreated children between parents and other types of instigators and recipients.     

Beliefs about truth and beliefs about rightness

Children's developing conceptions of what is right or proper are commonly studied without reference to concomitant changes in their understanding of beliefs, just as studies of young people's maturing grasp of the belief entitlement process ordinarily proceed separately from any examination of the value considerations that invest beliefs with meaning. In an effort to reverse these isolationist practices, a case is made for rereading the fact-value dichotomy that currently works to divide the contemporaneous literatures dealing with children's moral reasoning development and their evolving theories of mind. Findings from two research programs, in which children's beliefs about truth and rightness are combined, serve to illustrate the natural interdependence of these moral and epistemic matters.     

Preschool children's reasoning about ability

Young children's reasoning about ability was investigated among 155 preschoolers (M = 4 years, 10 months) across 3 studies. Results suggest that preschoolers are sensitive to mental state information when making judgments about another child's ability: They judged a child who finds a task easy to be smarter than one who finds the same task hard. Systematic patterns of errors on recall tasks suggest that preschoolers perceive positive correlations between (a) exerting effort and experiencing academic success, and (b) being nice and having high academic ability. Results from a comparison group of forty 9- to 10-year-olds (M = 9 years, 10 months) suggest that the preschool findings generally reflect emerging patterns of reasoning about ability that persist into later childhood, but that the perceived correlations between high effort and academic outcomes and between social and academic traits diminish with age.     

Children's ideas about evaporation

This article reports on research conducted as part of the Primary Science Processes and Concept Exploration (space) Project. The background to, and orientation of, space is briefly described.

Classroom‐based research into children's thinking about evaporation is reported. This work was conducted in close collaboration with teachers of the 5‐11 years age range with the intention of establishing the viability of the techniques for eliciting ideas and managing subsequent interventions within classrooms.

Children's thinking in relation to three main evaporation phenomena are discussed. Ideas about evaporation were categorized by reference to notions of conservation, change of location and change of form of the water.     

Commonsense reasoning about the physical world

This paper reports on a programme of research carried out over a period of twenty years by Joan Bliss, Jon Ogborn and others, and aimed at understanding how pupils and students reason about the everyday physical world. Our starting point was the science alternative conceptions literature, particularly force and motion, where the results puzzled and motivated us to make sense of the diversity of the findings. In a second step a Commonsense Theory of Motion was developed, which served as a framework for four other studies in the area of force and motion. These revealed that children were indeed using their everyday knowledge to explain these physical notions. The next step was to ask whether children also reasoned in a commonsense way about the physical world more generally, which led to the development of both a new theoretical framework and a further study to investigate these ideas. The findings showed that the physical reasoning schemes shown to exist were: movement, action/force/effort, container, carrier, support, fall, barrier, resistance, space, flow, break/not break, rigidity, stretch/squash and balance. The last section describes some ideas for future research in this area.     

Young children's reasoning about many-to-one correspondences

Young children's understanding of many-to-one correspondence problems was studied to illuminate the developmental transition from additive to multiplicative numerical knowledge. A many-to-one correspondence exists when a fixed number of target objects (greater than 1) is associated with each of a set of referents, as in putting 3 flowers in each of several vases. Two experiments examined effects of a brief training procedure that highlighted the iterative nature of many-to-one mappings. In Experiment 1, 5- and 6-year-old children did not benefit from the training, but a subset of 7-year-olds did. In Experiment 2, 7-year-olds showed training effects that extended to generalization problems. Patterns of performance across experimental and generalization problems suggested that some children had difficulty applying what they learned from training to the experimental problems.