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…

This study investigated the effectiveness of an instructional program (schema-based instruction, SBI) designed to teach 7th graders how to comprehend and solve proportion problems involving ratios/rates, scale drawings, and percents. The SBI program emphasized the underlying mathematical structure of problems via schematic diagrams, focused on a…

The Knowledge Is Power Program (KIPP) is a rapidly expanding network of public charter schools whose mission is to improve the education of low-income children. As of the 2012-2013 school year, 125 KIPP schools are in operation in 20 different states and the District of Columbia (DC). Ultimately, KIPP's goal is to prepare students to enroll and…

This study illustrates the types of information microgenetic methods can yield. Ninety-seven 5-year olds who had not mastered number conservation were given training in conservation or in reasoning about conservation. Results elucidate how changes in thinking occur and demonstrate children's efforts to understand other people's reasoning. (SLD)

This study compared effectiveness of either a concrete-representational-abstract (CRA) or a representational-abstract (RA) instructional sequence in teaching fraction concepts to 50 middle school students with mathematics disabilities. On all achievement measures, students in the CRA group had overall higher mean scores than did students in the RA…

One hundred forty fourth graders were asked to solve proportion problems about juice-mixing situations both before and after an intervention that used a manipulative model or other materials in three experiments. Results indicate different approaches appear to be necessary to facilitate children's proportional reasoning, depending on the reasoning…

Children begin school with the ability to use their informal and implicit conceptual knowledge to guide their problem solving, but shift to the use of superficial strategies in their attempts to solve word problems as they progress through school. This paper describes a study designed to investigate the effects of an instructional sequence that…