The aim of this study is to investigate Danish pre-service teachers' (PSTs) mathematical and didactical knowledge of operations with rational numbers. This knowledge is studied through their collaborative activities to certain tasks related to the teaching of operations with rational numbers. An explicit model of the teachers' mathematical and…

While Educational Data Mining research has traditionally emphasized the practical aspects of learner modeling, such as predictive modeling, estimating students knowledge, and informing adaptive instruction, in the current study, we argue that Educational Data Mining can also be used to test and improve our fundamental theories of human learning.…

A new system of order analysis, developed by Takeya and called Item Relations Structure Analysis (IRSA), was described and used for examining the structural relations among a set of 24 items on the addition and subtraction of fractions. A diagraph showing 16 chains of items that had discernibly common features was generated by this method, and…

This report illustrates a network of procedures which can be used to solve problems involving the addition and subtraction of fractions. This network, which is based on a skills hierarchy, is used to classify seven levels of student competency. The determination of student competency depends upon the careful construction of error-diagnostic tests.…

The Proceedings of PME-XI has been published in three separate volumes because of the large total of 161 individual conference papers reported. Volume I contains four plenary papers, all on the subject of "constructivism," and 44 commented papers arranged under 4 themes. Volume II contains 56 papers (39 commented; 17 uncommented)…