A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

It is not yet understood how children acquire the meaning of numerical symbols and most existing research has focused on the role of approximate non-symbolic representations of number in this process (see Piazza, ("Trends in Cognitive" 14(12):542-551, 2010). However, numerical symbols necessitate an understanding of both order and…

Students benefit from learning multiple procedures for solving the same or related problems. However, past research on comparison instruction has focused on comparing multiple formal procedures. This study investigated whether the benefits of comparing procedures extend to comparisons that involve informal and formal procedures. We also examined…

An account is made of the relationship between the convergence behaviour of a sequence and the accumulation points of the underlying set of the sequence. The aim is to provide students with opportunities to contrast two types of mathematical entities through their commonalities and differences in structure. The more set-oriented perspective that…

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…

Upon entry to New River Community College (NRCC), placement tests are administered to students enrolling in curricula and to students enrolling in English and mathematics classes. Based on preestablished cutoff scores on the placement tests, students are advised by counselors to take appropriate courses. In 1990, NRCC tracked students from…

This bulletin lists materials available in the fall of 1963 to assist educators in their selections of programmed instruction materials, and updates the inaugural issue, "Programs '62." Since the 1962 edition provided a number of first analyses of programmed material available, some of the present statistical data have been related to last year's…

This bulletin lists materials available in the fall of 1963 to assist educators in their selections of programmed instruction materials, and updates the inaugural issue, "Programs '62." Since the 1962 edition provided a number of first analyses of programmed material available, some of the present statistical data have been related to last year's…