Theories of psychology and mathematics education recommend two instructional approaches to develop students' mental representations of number: The "exact" approach focuses on the development of exact representations of organized dot patterns; the "approximate" approach focuses on the approximate representation of analogue magnitudes. This study…

The primary purpose of the study was to determine if computer-based training programs promoted fluent and flexible use of reasoning strategies to solve addition problems using different tasks. Specifically, does participation in strategy training result in the fluent application of the target strategy on a traditional mental arithmetic task? Does…

In a 9-month training experiment, 64 first graders with a risk factor were randomly assigned to computer-assisted structured discovery of the add-1 rule (e.g., the sum of 7 + 1 is the number after "seven" when we count), unstructured discovery learning of this regularity, or an active-control group. Planned contrasts revealed that the…

Technology and mathematics. manipulatives have been brought together in a new format. This joining has resulted in virtual manipulatives that are available on the Internet for students. Virtual manipulatives have been defined as computer based renditions of common mathematics manipulatives and tools. Just as a physical object can be flipped,…

The framework of Tharp and Gallimore (1988) was adapted to form a ZPD (Zone of Proximal Development) Model of Mathematical Proficiency that identifies two interacting kinds of learning activities: instructional conversations that assist understanding and practice that develops fluency. A Class Learning Path was conceptualized as a classroom path…