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.     

谈工作记忆与类比推理

类比推理是一种特殊的推理形式,也是个体抽象思维的一种主要形式。有些心理学家着重研究与类比推理有关的问题,以期可以找到发展类比推理能力的有效策略,以提高学生学习新知识、新技能等的效率。经过大量研究与调查数据显示,工作记忆的各个子成分与类比推理之间有着密切的联系,工作记忆直接影响着个体类比推理能力的发展。因此,文章主要探讨工作记忆与类比推理的含义,以及工作记忆对类比推理的影响,希望能够为相关研究者提供参考。     

Children's beliefs about everyday reasoning

Two studies investigated children's metacognition about everyday reasoning, assessing how they distinguish reasoning from nonreasoning and "good" reasoning from "bad." In Study 1, 80 1st graders (6-7 years), 3rd graders (8-9 years), 5th graders (10-11 years), and adults (18+ years) evaluated scenarios where people (a) used reasoning, (b) solved problems with nonreasoning approaches, or (c) reacted appropriately but automatically to events. All age groups distinguished reasoning from type (b) nonreasoning cases, but age-related improvement occurred for type (c) cases. Study 2 tested 160 1st, 3rd, 5th graders' and adults' evaluation of good and bad reasoning processes, finding 2 developmental changes: initial improvement in discriminating thinking processes by 3rd grade, and emergence of an adult-like, process-focused (vs. outcome-focused) concept of thinking quality by 5th grade.     

Children's views of collaborative learning

Collaborative learning is a widely used and popular strategy in many primary schools. In this article, the authors review the nature and purpose of collaborative learning and present a summary of how one small group of Year 5/6 children view its effectiveness.     

The use of humour during a collaborative inquiry

Studies show that teachers and students use humour when communicating with each other in a science education context. This study investigates the use of humour during a collaborative inquiry laboratory task on an undergraduate chemistry course and an undergraduate physics course. Seven groups of students working on a collaborative inquiry task were recorded on video. The videos were analysed utilising an analytical framework based on conversation analysis. During the tasks, humour was used in a dynamic way and the role of humour changed as the inquiry progressed. As expected, humour was used to create a group identity and to regulate negative emotions such as anxiety, frustration, uncertainty, boredom and disappointment. Humour also had an integral role in collaborative decision-making, for example in proposing and evaluating new ideas. Awareness of how humour can contribute to the regulation of emotions and collaborative decision-making might help students and teachers to better utilise humour in inquiry and learning.     

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.     

Development of reasoning skills through participation in collaborative synchronous online discussions

This article investigates the effect of participation in synchronous online discussions on the development of individual reasoning as manifested in reflective essays. Students from a fourth-grade classroom engaged in a series of real-timeonline discussions. The format of the discussion was based on the Collaborative Reasoning approach which has clear guidelines and procedures. The results showed that compared to the students from the contrast classroom, the students who had experienced synchronous online discussions wrote essays with more satisfactory arguments, counterarguments, rebuttals, and textual information. In addition, they wrote longer essays which contained fewer irrelevant statements. These effects of online discussions were consistent between girls and boys and between shy and non-shy children. The students' uses of arguments and rebuttals, as well as the length of their essays, were adequately predicted by the frequency of their contributions in the discussions. The present study suggests that when an online chat is implemented with an instructional approach which has well-established procedures and effective moves, it can provide an intellectually stimulating context in which all students can learn to reason by interacting with one another.     

Using representational tools to support historical reasoning in computer-supported collaborative learning

Abstract

In this article the authors focus on how features of a computersupported collaborative learning (CSCL) environment can elicit and support domain-specific reasoning and more specifically historical reasoning. The CSCL environment enables students to collaborate on a historical inquiry task and in writing an argumentative essay. In order to support historical reasoning the authors compared two representational tools: a graphical representation (argumentative diagram) and a linear representation (argument list). As it is assumed that an argumentative diagram can support both cognitive and interaction processes, it was expected that using this tool would result in more qualitative historical reasoning, in the chat as well as in the essay. However, the results of this study did not show a significant difference in the amount of historical reasoning between the two conditions. A possible explanation can be found in the way the students make use of the representational tool while executing the task. The tool does not only function as a cognitive tool that can elicit elaborate activities, but also as a tool through which students communicate.     

Disclosure of students’ mathematical reasoning through collaborative technology-enhanced learning environment

Education and Information Technologies - We focus on students’ mathematical reasoning in a technology-enhanced collaborative learning environment. We adopt a dialogical approach to analyze...     

Children's conditional reasoning part III: A design for research on children's learning of conditional reasoning and research findings

Educational Studies in Mathematics -     

Social interaction and the use of analogy: An analysis of preservice teachers' talk during physics inquiry lessons

Analogies have been argued to be central in the process of establishing conceptual growth, making overt connections and carryover into an intended cognitive domain, and providing a generative venue for developing conceptual understanding inherent in constructivist learning. However, students' specific uses of analogies for constructing arguments are not well understood. Specifically, the results of preservice teachers' knowledge gains are not widely studied. Although we would hope that engaging preservice science teachers in exemplary lessons would assist them in using and generating analogies more expertly, it is not clear whether or how such curricula would affect their learning or teaching. This study presents an existence proof of how preservice science teachers used analogies embedded in their course materials Physics by Inquiry. This fine‐grained analysis of small group discourse revealed three distinct roles of analogies including the development of: (a) cognitive process skills, (b) scientific conceptual understanding, and (c) social contexts for problem solving. Results suggest that preservice teachers tend to overgeneralize the analogies inserted by curriculum materials, map irrelevant features of analogies into collaborative problem solving, and generate personal analogies, which counter scientific concept development. Although the authors agree with the importance of collaborative problem solving and the insertion of analogies for preservice teachers' conceptual development, we believe much more needs to be understood before teachers can be expected to construct and sustain effective learning environments that rely on using analogies expertly. Implications for teacher preparation are also discussed. © 2003 Wiley Periodicals, Inc. J Res Sci Teach 40: 443–463, 2003     

Discussing the Greenhouse Effect: children's collaborative discourse reasoning and conceptual change

In environmental education the construction of appropriate knowledge is not enough, but is undoubtedly a fundamental component of individual and collective environmental responsiveness. The aim of this study was to investigate fifth graders' changes of conceptions about the greenhouse effect and global warming, due to socio‐cognitive interaction developed in small and large group discussions in an authentic classroom context during the implementation of an environmental education curriculum unit. We hypothesized that a classroom transformed into a community of discoursei.e. a learning environment which stimidates and supports giving verbal explanations, comparing and critically evaluating different points of view on the examined environmental phenomenon, would be a fruitful breeding ground for knowledge revision. The results show that classroom discussions, the core of the proposed learning activity, led the children, although at different levels, to the integration of new scientific knowledge into their conceptual ecology, based on the personal revision of pre‐instructional conceptions. As hypothesized, a high positive correlation was found between conceptual change and metaconceptual awareness of the changes in pre‐existing representations of the examined phenomenon. Some implications are drawn from the standpoint of environmental education.     

Explicit reasoning, creativity and co-construction in primary school children's collaborative activities

This paper describes research that explored the question of whether or not it is possible to characterise and teach a single type of educationally productive talk. We analysed and compared the quality of children's interactional strategies when jointly working on a reasoning task and a psycholinguistic task. The latter involved writing an integrated summary of three related texts. Sixth grade primary school children (11–12 years old) solved these two tasks as pre- and post-tests before and after training in the use of ‘Exploratory Talk’ (ET) to think together and argue as well as in strategies for producing summaries. After training, children improved substantially in the use of ET when solving the reasoning but not the psycholinguistic task. However, using ethnography of communication methods to analyse the talk further around the latter task revealed that both the number and quality of communicative events and acts increased importantly. These changes were accompanied by a significant improvement in the quality of the summaries produced. These findings suggest that the requirement for explicit reasoning in the definition and analysis of ET may be task dependent. To account for the common features of the educationally productive talk in the two settings, we propose the more inclusive concept of co-constructive talk to characterise the inter-subjective orientation, social ground rules and communicative actions that support effective collaboration, co-ordination and creativity.     

Using analogy to improve abstract conditional reasoning in adolescents: not as easy as it looks

Abstract reasoning refers to the ability to reason logically with premises that do not allow reference to knowledge about the real world. This form of reasoning is complex and difficult, and at the same time, it is critical for understanding science and mathematics. Two studies examined the use of analogy as a method to bridge reasoning with familiar content and abstract reasoning among older adolescents. The results showed that the ability to make an appropriate analogy depends on reasoning ability. Neither of the two procedures used resulted in an improvement in abstract reasoning. However, generating an inappropriate analogy actually decreased abstract reasoning performance among students who showed greater initial levels of reasoning ability. These results highlight the problems associated with using familiar reasoning as a basis for learning abstract reasoning skills.     

Children's application of simultaneous and successive processing in inductive and deductive reasoning problems: Implications for developing scientific reasoning skills

The research reported in this article was undertaken to obtain a better understanding of problem solving and scientific reasoning in 10-year-old children. The study involved measuring children's competence at syllogistic reasoning and in solving a series of problems requiring inductive reasoning. Children were also categorized on the basis of levels of simultaneous and successive synthesis. Simultaneous and successive synthesis represent two dimensions of information processing identified by Luria in a program of neuropsychological research. Simultaneous synthesis involves integration of information in a holistic or spatial fashion, whereas successive synthesis involves processing information sequentially with temporal links between stimuli. Analysis of the data generated in the study indicated that syllogistic reasoning and inductive reasoning were significantly correlated with both simultaneous and successive synthesis. However, the strongest correlation was found between simultaneous synthesis and inductive reasoning. These findings provide a basis for understanding the roles of spatial and verbal-logical ability as defined by Luria's neuropsychological theory in scientific problem solving. The results also highlight the need for teachers to provide experiences which are compatible with individual students' information processing styles.     

Children's learning and transfer of inductive reasoning rules: studies of proximal development

An initial study examined the relation between current developmental levels, as estimated by IQ, and proximal levels of development, as estimated by the efficiency of learning and transfer in assisted contexts. 8-11-year-old children learned to solve letter series completion problems with the aid of graduated sequences of prompts. Maintenance and transfer were later assessed using similar prompting procedures. Both IQ and age effects were found. Average-IQ (and younger) children required more assistance than high-IQ (and older) children to achieve the same mastery level on the original problem types. In addition to this difference in learning efficiency, average-versus high-IQ students, and younger versus older children, subsequently diverged in the number of prompts they needed as the transfer problems differed increasingly from the ones originally learned. In a second study, amount of assistance required in learning was found to be quite stable across moderately related tasks (letter series and progressive matrices). Assistance needed in maintenance and transfer appeared less stable but was also significantly correlated across tasks. Theoretical and clinical implications are discussed.     

Investigating and theorizing discourse during analogy writing in chemistry

Explanations of the role of analogies in learning science at a cognitive level are made in terms of creating bridges between new information and students' prior knowledge. In this empirical study of learning with analogies in an 11th grade chemistry class, we explore an alternative explanation at the “social” level where analogy shapes classroom discourse. Students in the study developed analogies within small groups and with their teacher. These classroom interactions were monitored to identify changes in discourse that took place through these activities. Beginning from socio‐cultural perspectives and hybridity, we investigated classroom discourse during analogical activities. From our analyses, we theorized a merged discourse that explains how the analog discourse becomes intertwined with the target discourse generating a transitional state where meanings, signs, symbols, and practices are in flux. Three categories were developed that capture how students intertwined the analog and target discourses—merged words, merged utterances/sentences, and merged practices. © 2011 Wiley Periodicals, Inc. J Res Sci Teach 48: 771–792, 2011