This study grew out of a need to investigate elementary students' multiplicative and proportional reasoning. Considerable documentation indicates that the concepts of ratio and proportion are difficult for students to acquire. In conventional classrooms, the typical focus is on the repeated addition model for multiplication and the development of computational skills. That treatment of multiplication, however, does not always lead to a full understanding of the operation. This study explores the understanding of and reasoning about multiplication, division, and proportion tasks among students in three different instructional programs. One reform program encouraged the use of reasoning procedures, another taught a variety of conventional pro...
This article investigates how students in third grade discuss and reason on multiplication when they...
Proportional reasoning has been recognised as a crucial focus of mathe-matics in the middle years an...
Proportional reasoning is one of four key areas of instruction for sixth and seventh grade mathemat...
This study grew out of a need to investigate elementary students' multiplicative and proportional re...
This analytic highlights students’ reasoning as they worked on five tasks which built towards the de...
The development of proportional reasoning has long been recognised as a central but problematic aspe...
This presentation reports the findings of a study that shows the effectiveness of targeted intervent...
Multiplicative reasoning permeates many mathematical topics, for example fractions and functions. He...
Multiplicative reasoning permeates many mathematical topics, for example fractions and functions. He...
This article investigates how students in third grade discuss and reason on multiplication when they...
This article investigates how students in third grade discuss and reason on multiplication when they...
Multiplicative reasoning permeates many mathematical topics, for example fractions and functions. He...
This article investigates how students in third grade discuss and reason on multiplication when they...
Proportional reasoning is required to operate in many mathematical domains in the middle years ’ cur...
The focus of this paper is on proportional reasoning, emphasising its pervasiveness throughout the m...
This article investigates how students in third grade discuss and reason on multiplication when they...
Proportional reasoning has been recognised as a crucial focus of mathe-matics in the middle years an...
Proportional reasoning is one of four key areas of instruction for sixth and seventh grade mathemat...
This study grew out of a need to investigate elementary students' multiplicative and proportional re...
This analytic highlights students’ reasoning as they worked on five tasks which built towards the de...
The development of proportional reasoning has long been recognised as a central but problematic aspe...
This presentation reports the findings of a study that shows the effectiveness of targeted intervent...
Multiplicative reasoning permeates many mathematical topics, for example fractions and functions. He...
Multiplicative reasoning permeates many mathematical topics, for example fractions and functions. He...
This article investigates how students in third grade discuss and reason on multiplication when they...
This article investigates how students in third grade discuss and reason on multiplication when they...
Multiplicative reasoning permeates many mathematical topics, for example fractions and functions. He...
This article investigates how students in third grade discuss and reason on multiplication when they...
Proportional reasoning is required to operate in many mathematical domains in the middle years ’ cur...
The focus of this paper is on proportional reasoning, emphasising its pervasiveness throughout the m...
This article investigates how students in third grade discuss and reason on multiplication when they...
Proportional reasoning has been recognised as a crucial focus of mathe-matics in the middle years an...
Proportional reasoning is one of four key areas of instruction for sixth and seventh grade mathemat...