In this paper, the structure of non-mathematicians' knowledge of probability is argued. Based on the analysis of the conceptual model (teachers' model) of probability, it is hypothesized that the mental model (non-mathematicians' model) of probability might consist of three different understandings (views), the case view, the frequency view, and the subjective view. In people's explanations of probabilistic statements about some concrete events, the hypothesized views are identified, and it is shown that an individual's explanations are often based on two or more views. The relationship between mental models and problem solving processes is discussed. It is demonstrated that the view that a problem solver took influenced problem solving processes. There are some cases where the frequency view has advantages in problem solving. The implication of multiple views of probability for mathematics education is also argued.
In this paper, role of computer-based tools is discussed from a standpoint of situated learning theory, which considers learning as a process of enculturation to a community of practice. The authors propose utilizing computer-based tool for supporting collaborative learning and mention AlgoBlock, a tangible programming language developed by the authors, as an example of computer-based tools for facilitating learners' conversation and cooperation. AlgoBlock is a set of physical blocks. Each block corresponds to a command of a Logo-like programming language, therefore, learners can connect those tangible blocks manually to form a program and they can share commands and programs on physical work space. It works as an open tool that enables learners to monitor each other's intention, and to make use of eye lines and body movements as resources for collaboration control, thus this tool supports social interaction among learners. By using this tool within adequate classroom settings, the authors believe, learners can improve their skills for programming and logical thinking through conversation and cooperation. To show the positive effect of the tool on learners' collaboration, the result of observational sessions, in which elementary students engaged in group programming works using AlgoBlock, is described.
This paper discusses fundamental issues on representation and human interface problems, and proposes some methodologies for establishing macroscopic cognitive engineering to contribute organizational and social problem solving. Through experience of human interface evaluation and designs in information and telecommunication systems, we have been confronted with the need to develop systematic and macroscopic Cognitive Engineering (CE), understandable not only for individuals but also for organizations, for resolving representation and human interface (HI) problems, such as HM (Machine) I, HG (Graphical representation) I, HH (Human) I, HE (Environment) I, HT (Task) I, HJ (Job) I, HO (Organization) I, HS (Society) I, etc., from viewpoints of individuals and organizations or societies. It is important to research and develop for new CE methodologies to bridge between microscopic view and macroscopic view for harmonious development of cognitive artifacts and humans and organizations. As for CE methodologies, SPSC (Social Problem Solving CE), PRFC (Problem Representation Facilitating CE), MYTC (Myself-Yourself-Task Communicating CE), CMOC (Cerebellum Mode Operating CE), BECC (Behavior-Emotion-Cognition Systems CE), MMBC (Microscopic-Macroscopic Bridging CE), IECC (Internal-External Considering CE), CARC (Cognitive Artifacts Reflecting CE), and HDEC (Harmonious Development Evolving CE) are needed for solving fundamental representation and human interface problems.
This paper examines the structure of grammatical knowledge through analyzing the acceptability of English parasitic gap constructions. Judgments on 100 parasitic gap constructions are collected with questionnaires from fifteen native speakers of English. The judgments are analyzed by multiple regression analysis. On the basis of the analysis, this paper claims that plural syntactic constraints simultaneously bear with different weights on the acceptability of parasitic gap constructions. A linear equation that predicts the acceptability of a given parasitic gap construction is proposed. As a general implication, this paper suggests that syntactic constraints as part of the language faculty are additive and with different importance.
We propose an information-media theory of learning, and to incorporate the learning mechanism of human beings into machine learning. In the theory, a learning is regarded as communication by using multiple information-media, each of which includes a specific past experience forming imagery. This paper reports an experimental investigation of human learning processes dynamically selecting information-media, and raises a research issue on learning mechanisms dealing with multiple information-media. The authors perform psychological experiments, in which subjects learn the programming language Prolog, and are asked to solve some questions. The subjects are divided into three groups according to their textbooks: (A) one containing only the specification of Prolog language, (B) the specification and an information-media explained in sentences, and (C) those explained in sentences and diagrams. Their incorrect answers, protocols, and elapsed time for solving questions are analyzed to clarify timing introducing a new information-medium, their selected media, and the effect of diagrams. Based on the experiment, the authors constructed a cognitive model for simulating the behavior of subjects. The model is programmed in Prosit, by which each medium is handled as a situation. It confirms the information-media theory, and is a prototype towards a knowledge-intensive and robust machine learning mechanism.
Previous studies of human device operation learning seem to assume that subjects acquire mental models of the target system by means of instruction prior to learning sessions. The researchers assume that when subjects are not provided such models, they would learn procedural knowledge, which imply that they would not have mental models of the system. However, in the first experiment, we analyzed verbal protocols of subjects controlling a water tank system without prior knowledge about the system, and found that they spontaneously formed several mental models, and that these models which were used by outperformed subjects were equivalent to the target system functionally, rather than structurally. In the second experiment, we provided subjects with such a functionally equivalent model and showed that it was as effective as structurally equivalent one.