Table of Contents

-1 Introduction. -2   The Context of Generalization. -3   Types and Levels of Pattern Generalization. -4   The Theory of Graded Representations in Pattern Generalization. -5   Gestures, Words, and Incipient Generalizations. -6 Variables and Algebraic Generalizations. - 7   Patterns, Generalization, and Arithmetic Learning. -8   Patterns, Functional Thinking, and Algebraic Learning. -9   Pedagogical Issues and Implications. -10 Conclusions.  ​

About the Author

Dr. Rivera is interested in issues involving visualization and algebraic thinking, in particular, generalization. His overall research program at San Jose State University falls under the category of psychology of mathematics education, which involves studying learning and teaching conditions that influence curriculum and instruction. He recently concluded a three-year longitudinal study on pattern generalization at the middle school level. Results of his findings are reported in various peer-reviewed journals, book chapters, and conference proceedings. He has recently published a book, Toward a Visually-Oriented School Mathematics Curriculum, that is a volume in the Springer Mathematics Education Library series. This year, Dr. Rivera will be completing a one-year longitudinal research study in a Grade 2 class. He intends to follow the same kids through Grade 3 during the next school year. Dr. Rivera's research is supported by a Career grant from the National Science Foundation.