Exploring teachers’ attention to students’ responses in pattern generalization tasks

Abstract

This paper explored the following: (1) teachers’ ways of attending to students’ written responses in pattern generalization tasks and (2) differences in the ways of attending to students’ responses associated with different factors. A questionnaire was developed to classify teachers’ ways of attending to students’ written responses. The questionnaire was given to a sample of 91 practicing mathematics teachers from different grade levels (grades 4–12). The structure of attention referring to “holding wholes, discerning details, recognizing relationships, perceiving properties, and reasoning on the basis of agreed properties” was used as a theoretical model. A mixed quantitative–qualitative approach was adopted to analyze the data. Analysis of data showed that teachers’ attention to students’ written responses seems to focus on distinguishing details of students’ responses in particular step(s) of the pattern without demonstrating awareness of relationships that could hold in different steps of the pattern. The analysis also showed that differences in the ways of attending to students’ written responses were associated with different factors. In particular, pattern generalization type (near and far generalization tasks), student strategy use (e.g., functional and recursive strategies), student reasoning approach (numerical and figural reasoning approaches), and teaching experience in particular school cycle were associated with significant differences in teachers’ forms of attention to students’ responses in pattern generalization. In contrast, the number of years of teaching was not associated with significant differences in teachers’ forms of attention to students’ responses. © 2018, Springer Science+Business Media B.V., part of Springer Nature.