Abduction–induction (generalization) processes of elementary majors on figural patterns in algebra

The article deals with issues concerning the abductive–inductive reasoning of 42 preservice elementary majors on patterns that consist of figural and numerical cues. We discuss: ways in which the participants develop generalizations about classes of abstract objects; abductive processes they exhibit which support their induction leading to a generalization; ways they justify their generalizations in the abductive stage, and; the effects of figural and numerical cues in the manner they construct a plausible abductive generalization. Two types of abductions are explored, model-based and manipulative. A proposed abductive–inductive reasoning process for pattern sequences is presented and discussed in the concluding section.