In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…

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…

Adaptive learning techniques have typically scheduled practice using learners' accuracy and item presentation history. We describe an adaptive learning system (Adaptive Response Time Based Sequencing--ARTS) that uses both accuracy and response time (RT) as direct inputs into sequencing. Response times are used to assess learning strength and to…

In this work is proposed that an adaptation tool that is for the automatic generation and personalization of courses of a general-purpose LCMS that is named A Tutor. A Tutor is a Learning Content Management System. The architecture of the adaptation tool that allows a personalized sequencing of LOs in A Tutor for the learner's learning goals,…

This study examined the ability of 59 2- and 3-year-old children to monitor goal-directed activities with respect to an anticipated outcome. The study focused on two skills: error monitoring and error avoidance through anticipatory monitoring. To elicit monitoring, a variety of simple tasks were presented to the children. In each, a successful…

The report is a review of research results which concern sequencing (procedures for validating the hypothesized ordering of the subordinate tasks in a learning hierarchy) and practical applications of learning hierarchies in instructional design. Indirect versus direct validation procedures are examined in detail. (Author)

This review of the literature on five learner control variables in computer-based instruction concludes that: (1) pacing left to learner control has been found ineffective because learners tend to procrastinate or to exit lessons prematurely; (2) sequence, or content flow, has been an ineffective variable left under learner control since…

The LARC (Listening and Reading Comprehension) Program, an experiential based story grammar approach to listening and reading comprehension is described, and a pilot study of its effectiveness with communication handicapped children is reviewed. The LARC framework translates children's own recent experiences into sequenced story episodes which are…

Compared were the characteristics of 60 learning disabled (LD) and 60 normal children (all between 8- and 11-years-old) participating in the Georgia Reading Research Program. The target group consisted of LD children who showed deficits in the psychological process of ordering/sequencing; while the LD reference group were average or above average…

The empirical relationships among about 90 reading objectives were examined. The objectives span late first-grade through the sixth-grade (nominally). The results of contingency analyses and correlational analyses are reported. The identification of learning hierachies is stressed. Such hierarchies are apparent in the early learning of reading…

This study was designed to examine relationships between three variables of analysis/integration skill in visual perception and the tendency to retain differentiated memories of sequential visual images in a sample of 206 university undergraduates. Correlation techniques and factor analysis were used to analyze relationships between the perceptual…

The paper describes a multisensory technique which involves an individualized, sequential plan of instruction for the handicapped student. The multisensory technique is explained to involve three tasks in its developmental sequence--identification, naming, and writing. The technique is applied to the case of a student whose errors on the Key Math…

A study of the growth of seventh grade students' writing ability after targeted discussions of children's literature was based on the assumption that active comprehension of a distinctive model of literature would provide an awareness of the structure of narrative prose that would transfer to the student's own writing. Eight students participated…

Using a developmental model, the author explains a hierarchy which describes how a young child learns to respond to various types of environmental stimuli and discusses some educational consequences of a reinforcement stimuli deficit. Development is seen to take place in succession beginning with the primary level, proceeding to the social,…

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…