After a brief survey on the main issues studied in literature about the development of proportional thinking, we present the results of a experimental study on proportionality focused on classroom discussions of three open problematic situations in different contexts. We concentrate on the report of pupils’reasonings which testify their different points of view. We stress the value of the ‘sharing of ideas’ for bringing pupils to understand -through argumentations of their classmates- the weakness of strategies such as the additive one and, more in general, for promoting thinking authonomy and critical scrutiny of own thoughts
Proportional reasoning is described as a sophisticated way of thinking and encompasses many intercon...
Within mathematics teaching, ways to help students resolve proportional reasoning problems remains a...
2010The purpose of this study was to identify characteristics of middle school students proportiona...
After a brief survey on the main issues studied in literature about the development of proportional ...
This study explores the development of students’ strategies from primary to secondary school when so...
The initial phase of the construction of proportional reasoning with students aged 12 to 13 is descr...
This paper focuses on the development of two phenomena that were so far studied separately: the use ...
This presentation reports the findings of a study that shows the effectiveness of targeted intervent...
We discuss two studies related to upper elementary school pupils’ use of additive and proportional s...
This paper outlines a study that was undertaken with a typical thirteen year old boy. This boy was e...
This case study explores how 12-13-year-old students encounter proportional reasoning while working ...
The ability to reason with proportions is known to take a long time to develop and to be difficult t...
Proportional reasoning is an important aspect of formal thinking that is acquired during the develop...
This study focuses on the transition from additive to multiplicative (proportional) reasoning. In pa...
Introduction: The research problem in this paper consists in reviewing the strategies used by the st...
Proportional reasoning is described as a sophisticated way of thinking and encompasses many intercon...
Within mathematics teaching, ways to help students resolve proportional reasoning problems remains a...
2010The purpose of this study was to identify characteristics of middle school students proportiona...
After a brief survey on the main issues studied in literature about the development of proportional ...
This study explores the development of students’ strategies from primary to secondary school when so...
The initial phase of the construction of proportional reasoning with students aged 12 to 13 is descr...
This paper focuses on the development of two phenomena that were so far studied separately: the use ...
This presentation reports the findings of a study that shows the effectiveness of targeted intervent...
We discuss two studies related to upper elementary school pupils’ use of additive and proportional s...
This paper outlines a study that was undertaken with a typical thirteen year old boy. This boy was e...
This case study explores how 12-13-year-old students encounter proportional reasoning while working ...
The ability to reason with proportions is known to take a long time to develop and to be difficult t...
Proportional reasoning is an important aspect of formal thinking that is acquired during the develop...
This study focuses on the transition from additive to multiplicative (proportional) reasoning. In pa...
Introduction: The research problem in this paper consists in reviewing the strategies used by the st...
Proportional reasoning is described as a sophisticated way of thinking and encompasses many intercon...
Within mathematics teaching, ways to help students resolve proportional reasoning problems remains a...
2010The purpose of this study was to identify characteristics of middle school students proportiona...