Kazuaki Kojima

Experimental study of learning support through examples in mathematical problem posing

When using mathematics to solve problems in everyday life, problem solvers must recognize and formulate problems by themselves because structured problems are not provided. Therefore, in general education, fostering learner problem posing is an important task. Because novice learners have difficulty in composing mathematical structures (solutions) in problem posing, learning support to improve the composition of solutions is required. Although learning by solving examples is adopted in general education, it may not be sufficiently effective in fostering learner problem posing because cognitive skills differ between problem solving and problem posing. This study discusses and experimentally investigates the effects of learning from examples on composing solutions when problem posing. We studied three learning activities: learning by solving an example, learning by reproducing an example, and learning by evaluating an example. In our experiment, undergraduates were asked to pose their own new, unique problems from a base problem initially presented after the students learned an example by solving, reproducing, or evaluating it. The example allowed the undergraduates to gain ideas for composing a novel solution. The results indicated that learning by reproducing the example was the most effective in fostering the composition of solutions.

Evaluation of a system that generates word problems through interactions with a user

In mathematical learning, it is important to give learners a number of problems that have various features in both surface problem situations and deep mathematical solution structures. In this study, we implement a system that generates various word problems by using episodes, which are knowledge regarded as cases of problem generation. Our system interacts with a teacher as a user to acquire the common knowledge needed to generate word problems. We performed experimental evaluations to verify problem generation by our system, with the results indicating that our system can successfully expand the variety of problems from the initial ones stored in the system. We also found that our system needs interactions with a knowledgeable user because novice users cannot necessarily provide the system with effective knowledge.

Development of a Usability Questionnaire for Automation Systems

In this study, we positioned automation systems as the third-generation artifacts and developed a generalized usability questionnaire with 18 questions for automation systems as daily used artifacts. This questionnaire could be used to evaluate various types of automation systems and is useful for the development and improvement of automation systems as artifacts used in our everyday life.

Learning Mental Models of Human Cognitive Processing by Creating Cognitive Models

We investigated how creating cognitive models enhances learners’ construction of mental models on human cognitive information processing. Two class practices for undergraduates and graduates were performed, in which participants were required to construct a computational running model of solving subtraction problems and then develop a bug model that simulated students’ arithmetic errors. Analyses showed that by creating cognitive models, participants learned to identify buggy procedures that produce systematic errors and predict expected erroneous answers by mentally simulating the mental model. The limitation is that this benefit of creating cognitive models was observed only in participants who successfully programmed a computational model.

Use of a Cognitive Simulator to Enhance Students' Mental Simulation Activities

We developed a cognitive simulator of the dual storage model of the human memory system that simulates the serial position effect of a traditional memory recall experiment. In a cognitive science class, participants learned cognitive information processing while observing the memory processes visualized by the simulator. Through the practice, we confirmed that participants learned to predict experimental results in assumed situations implying that participants successfully constructed a mental model and performed mental simulations while running the mental model in various settings. We discuss the possibility that a cognitive model can be used as a learning tool and, more specifically, as a mediator tool connecting theory and empirical data.

Supporting Mathematical Problem Posing with a System for Learning Generation Processes through Examples

Problem posing, by which learners create new problems by themselves, is an important activity in mathematics education. However, novice learners have difficulty in posing problems, particularly when formulating appropriate solution structures of problems. Although they are provided with example problems that can serve as hints for composing novel problems, they do not necessarily understand the key ideas used to generate the examples. To improve problem posing for novices, this study discusses an approach that supports learning from examples as a production task. We propose a method of learning from examples through imitation, where a learner reproduces problems identical to given examples. We implement a system that presents examples of problem posing and supports learners in understanding the examples by having the learners reproduce them. We conducted an experimental evaluation in which learners learned from an example that embeds useful ideas to alter solution structures in the system. The results demonstrated that the learners successfully adapted the example when posing their own problems if they learned the example by the reproduction method. Thus, learning from examples through reproduction appears to be effective in the domain of problem posing as a production task.

How do equity norms evolve? An evolutionary game theory approach to distributive justice

The Nash demand game (NDG) has been applied to explain moral norms of distributive justice. In NDG, two players simultaneously make demands and receive them unless the sum of the demands exceeds the amount of the resource. Otherwise, they obtain nothing. This paper proposes the demand-intensity game (D-I game), which adds an “intensity” dimension to NDG in order to discuss various scenarios for the evolution of norms concerning distributive justice. We show basic analyses of the D-I game in game theory and then evolutionary simulations. Descriptive/evolutionary approaches show that three types of norms could evolve mainly depending on the conflict cost in the game: egalitarianism, “wimpy” libertarianism and libertarianism in decreasing order of the cost. Although the wimpy libertarianism is classified as the libertarianism in the sense of claiming the full resource, it can achieve an egalitarian division without conflict cost as a result.

Experimental investigation of misuse and disuse in using automation system

In this study, we experimentally investigated human use of automation systems and the selection strategies of such usage. We used two different types of tracking tasks. As a result, we found that the participants neither tended to misuse nor disuse the automation system. Also, we confirmed that they tended to select to use the automation system depending on their manual performance rather than the system performance. Moreover, we found that there is a relationship between the tendency to use the automation system and the selection strategy.

Empirical Investigation of Cognitive Load Theory in Problem Solving Domain

The cognitive load theory has been mainly investigated in declarative knowledge learning, typically learning with hyper-media material. In this study, the preceding findings are examined in problem solving domain with a different type of experimental task such as Reversi game. The experimental results were consistent with preceding studies, showing that extraneous cognitive load is harmful to the learning process, but the effects of intrinsic load are subject to debate. Additionally, the participants correctly evaluated each cognitive load, using a questionnaire. In addition, it was confirmed that the subjective evaluation predicted learning outcomes.

The Use of a Maverick in Collaborative Problem Solving: Investigating the Implicit and Explicit Process

The present study focused on the implicit and explicit search processes for easing an impasse during collaborative problem solving. In this study, an attractive actor or an anomaly cue, a ‘maverick,’ appeared to aid the participant in a rule discovery task. Problem solvers works on the task in which autonomous agents play the roles of collaborative partners. We collected verbal responses and eye movement data throughout the task to capture the implicit and explicit cognitive processes used by participants in interacting with the maverick during the search activities. The results indicate that for successful problem solvers, (1) an anomaly cue(maverick) in the group explicitly facilitated an adequate search process, and (2) an implicit search process may exist from an early stage and may develop during the learning process through incubation. Additionally, we observed through case studies that participants actively use the anomaly cue(maverick) as a reference to ease impasses.