We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

During the semester break, 36 second-grade students accessed a set of resources and completed a series of online math activities focused on the application of the model method for arithmetic in two contexts 1) addition/subtraction and 2) multiplication/division. The learning environment first modeled and then supported the use of a scripted series…

This paper discusses Multi-Feature Hierarchical Sequential Pattern Mining, MFH-SPAM, a novel algorithm that efficiently extracts patterns from students' learning activity sequences. This algorithm extends an existing sequential pattern mining algorithm by dynamically selecting the level of specificity for hierarchically-defined features…

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…

This paper is a preliminary inquiry by a non-mathematician into graphic methods of sequential planning and ways in which hierarchical analysis and tree structures can be helpful in developing interest in the use of mathematical modeling in the search for creative solutions to real-life problems. Highlights include a discussion of hierarchical…

The general hypotheses derived from a series of six experiments in instructional theory were as follows: that the individually optimal reading sequence of juxtaposed, but mutally related, prose text depends on learning goal and pre-knowledge; that adult learners are able to approach this reading sequence through their own decisions; and that…

Turtle graphics is a popular vehicle for introducing children to computer programming. Children combine simple graphic commands to get a display screen cursor (called a turtle) to draw designs on the screen. The purpose of this study was to examine young children's abilities to function in a simple computer programming environment. Four- and…