Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally explaining how…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics (STEM) domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally…

Children using robotics for engineering, science, technology, and mathematics (CREST-M) is an ongoing curriculum creation and evaluation project developing math-focused science, technology, engineering, and mathematics (STEM) curriculum units that incorporate storytelling with math and are designed to be engaging for students from backgrounds…

How should a wide variety of educational activities be sequenced to maximize student learning? Although some experimental studies have addressed this question, educational data mining methods may be able to evaluate a wider range of possibilities and better handle many simultaneous sequencing constraints. We introduce Sequencing Constraint…

Educational video games have the potential to be used as assessments of student understanding of complex concepts. However, the interpretation of the rich stream of complex data that results from the tracking of in-game actions is so difficult that it is one of the most serious blockades to the use of educational video games or simulations to…

Dual eye-tracking measures enable novel ways to test predictions about collaborative learning. For example, the research project we are engaging in uses measures of gaze recurrence to help understand how collaboration may differ when students are completing various learning activities focused on different learning objectives. Specifically, we…

The rule space model permits measurement of cognitive skill acquisition, diagnosis of cognitive errors, and detection of the strengths and weaknesses of knowledge possessed by individuals. Two ways to classify an individual into his or her most plausible latent state of knowledge include: (1) hypothesis testing--Bayes' decision rules for minimum…

Describes study designed to investigate the effectiveness of personalizing verbal math problems on division of fractions for fifth and sixth grades using microcomputer-generated lessons. Treatment and control group results are analyzed, and results support the hypothesis that the personalized context group was superior in problem solving and had…