# Types and Levels of Pattern Generalization

## Abstract

In this chapter, we synthesize at least 20 years of research studies on pattern generalization that have been conducted with younger and older students in different parts of the globe. Central to pattern generalization are the inferential processes of abduction, induction, and deduction that we discussed in some detail in Chaps. 1 and 2 and now take as given in this chapter. Here we explore the other equally important (and overlapping) dimensions of pattern generalization, namely: natures and sources of generalization; types of structures; ways of attending to structures; and modes of representing and understanding generalizations. In this chapter we remain consistent as before in articulating the complexity of pattern generalization due to differences in, and the simultaneous layering of, processes relevant to constructing, expressing, and justifying interpreted structures.

## Keywords

Individual Learner Direct Expression Pattern Generalization Structural Generalization Algebraic Thinking## References

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