This book takes a theoretical perspective on the study of school algebra, in which both semiotics and history occur. The Methodological design allows for the interpretation of specific phenomena and the inclusion of evidence not addressed in more general treatments. The book gives priority to "meaning in use" over "formal meaning". These approaches and others of similar nature lead to a focus on competence rather than a user's activity with mathematical language.
Curriculum Design and Development for Studens, Teachers and Researchers.- Experimental Design.- Concrete Models and Abstraction Processes.- Teaching Models.- Algebraic Syntax and Solving Word Problems.- Cognitive Tendencies and Abstraction Processes.- Mathematical Sign Systems. Meaning and Sense.- Solving Arithmetic-Algebraic Problems.- Widening Perspectives.- References. A Deep Sea of Luminescent Ideas.
Local Theoretical Models and Mathematical Sign Systems: A theoretical and methodological framework for experimental observations in educational mathematics.- Mathematics Education and Educational Systems.- Teaching Models.- Cognitive Processes.- Experimental Design.- Mathematical Sign Systems: A theory for interpreting experimental observations.- Concrete Models and Abstractions Processes: Teaching to operate the unknown.-Solving Problems with a "Just Acquired" Algebraic Syntax.- Cognitive Tendencies and Abstraction Processes in the Learning of Algebra (and Geometry).- Solving Arithmetic/Algebraic Problems.- Historical Analysis of Algebraic Ideas.
Offers a theoretical perspective in which semiotics and history are included
Adds to previous work with priority to a pragmatic perspective
Of interest to both practitioners and researchers in mathematics education