Search

Copyright of Computer & Education is the property of Tokyo CIEC and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Cognitive diagnostic assessments (CDAs) require a large number of items to measure the target attributes with high precision. An automatic item generation (AIG) system would help to reduce the cost and effort of item writing in CDAs. This study aimed to develop a valid AIG system for CDAs in linear equations of mathematics by designing an AIG system and examining two aspects of a generated CDA in cognitive diagnostic modeling: (a) the M-matrix, which specifies the set of attributes required by each item model and (b) the item discrimination index, which is computed from item parameters in the deterministic input, noisy-and-gate (DINA) model. First, we compared an original M-matrix to two alternative M-matrices by using information criteria, posterior predictive model checks, and item discrimination indices. Second, we examined the magnitude and variability of the item discrimination indices for every item model. No substantially large differences were found among the results from all of the M-matrices. The discrimination indices tended to be high in items that measured major attributes, and the variabilities of the indices were small within each item model, except for a few item models. These findings indicate the validity of our M-matrix and AIG system. Furthermore, they suggest ways to improve the AIG system. Research limitations and how future studies can help to enhance the AIG system are discussed. [ABSTRACT FROM AUTHOR]

Through the analysis of artificial neural networks and t-tests, we identified linear independence and linear dependence as the points at which students stumble in linear algebra. Furthermore, we developed mathematics websites in the fields of calculus, linear algebra and probability statistics that allow high school and university students to form concepts interactively, regardless of time and place. The websites were designed so that visitors can complement their knowledge with hyperlinks, regardless of their learning history. Teachers can also use the website to easily implement Peer Instruction in their classes. The website provides a useful structure for both students and teachers and is in line with the aims of the Digital Transformation in Education. [ABSTRACT FROM AUTHOR]

This article studies some central developments in the propagation and teaching of mathematical logic in 1930s China. Focusing on the emergence of a twofold disciplinary approach to mathematical logic, namely as a discipline studied and disseminated by Chinese philosophers on the one hand and mathematicians on the other, this paper explores one of the key turning points in the development of the academic notion of mathematical logic in China. Apart from casting some light on the teaching of mathematical logic in the framework of both philosophical as well as mathematical spheres of inquiry, this article also provides some preliminary insights into the circumstances surrounding the first systematic introduction of mathematical logic into the modern standardized system of education, which gradually took shape over the late-1920s and early 1930s in China.

In this paper, we aim to clearly explain the complex relation between advancement rate and intergenerational social mobility by formalizing a mathematical model. In order to derive general propositions that do not depend on the particular values of parameters, we simply assume that a society consists of four types of subgroups, namely, the combinations of high/low education and high/low class origin, and that a person with high education is more likely to enter the high class. We analyze two situations-first, the case where class origin has an effect on intergenerational mobility and second, the case where only educational qualifications affect mobility. The former is called the lexicographic order model; the latter, the educational credentialism model. By comparing these two models, we specify the condition that educational expansion leads to the formation of a closed society in terms of intergenerational social mobility. The models also show the relation between the equalization of educational opportunities and a decline in the rate of upward mobility. Moreover, we not only derive theoretical propositions but also attempt to verify the goodness of fit of the models by using nationwide statistical data. [ABSTRACT FROM AUTHOR]