Engaging students in a challenging (cognitively demanding) task and launching a mathematics lesson with a task before instruction are two characteristics of a reform-oriented approach to mathematics instruction often considered together. The authors systematically contrasted teaching with challenging tasks using a task-first lesson structure with…

An intervention experiment served to evaluate the efficacy of highly guided discovery learning of relations underlying add-1 and doubles combination families and to compare the impact of such instruction with minimally guided instruction. After a pretest, 78 first graders were randomly assigned to one of three intervention conditions: highly…

For young children, a found acorn, stone, or lichen-covered branch can be a touchstone of an experience in nature. Children, however, should also be taught to "leave no trace." As the National Park Service advocates, visitors to natural areas should "Preserve the sense of discovery for others by leaving all natural and cultural…

This paper reports the results of the improving thinking skills (ITS-1) intervention study on the thinking skills of low-achieving first graders. The intervention programme consists of 12 lessons, each lasting for 45 min. Lessons offer enriched-discovery learning activities and tasks to be solved through inductive reasoning. We used a…

A 9-month training experiment was conducted to evaluate the efficacy of highly and minimally guided discovery interventions targeting the add-1 rule (the sum of a number and one is the next number on the mental number list) and doubles relations (e.g., an everyday example of the double 5 + 5 is five fingers on the left hand and five fingers on the…

A concrete-semiconcrete-abstract (CSA) instructional approach derived from discovery learning (DIS) was embedded in a direct instruction (DI) methodology to teach eight elementary students with math disabilities. One-minute abstract-level probes were the primary metric used to assess student performance on subtraction problems (minuends 0-9). A…