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…

Sequence of contextual information refers to the order of descriptions involved in the context component of items, such as sequence of events, sequence of intention and action, and sequence of effect and cause. To build on prior findings on how different sequences of contextual information could influence student test scores, we used eye tracking…

As learning trajectories gain traction in mathematics education, we seek to understand the ways in which teachers may use them in interactions with students. This paper reports on one group of elementary teachers' use of their emerging knowledge of a learning trajectory to examine key pedagogical practices. Findings suggest that a learning…

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…

A battery of memory tests was administered to 243 male university students. Factor analysis with oblique rotation of factors revealed five factors: (1) associative memory (particularly important in paired-associate tests), (2) short-term visual memory (the ability to derive information from briefly presented visual displays), (3) meaningful memory…

Sequenced writing assignments--a series of related writing tasks--offer students frequent opportunities to write and to acquire writing skills through redundancy, progressively more complicated cognitive and rhetorical demands, and a diversity of learning activities. The most frequently identified goal of sequencing is to move students beyond…

An examination of student papers from three universities on the same tasks revealed that expository writing tasks were less demanding cognitively than argumentative writing tasks and that argumentative writing tasks were less demanding than speculative tasks. Another finding was that when students were able to translate a generalized task into…

The effects of conservation activities on children's acquisition of Piaget's conservation concepts were investigated. One hundred and twenty-eight seven-to nine-year-old children in four classrooms were given pre- and post-evaluation measures of conservation ability. The experimental group completed a set of 42 self-directed conservation…

The implicit assumption behind personal writing assignments given at the beginning of a writing course is that personal essays eliminate the writing apprehension of having nothing to say. However, college freshmen find it very difficult to write about themselves and their own opinions because this writing involves abstract mental processes and…