# Ellis (2011)

*Generalizing-Promoting Actions: How Classroom Collaborations Can Support Students' Mathematical Generalizations*

The article *Generalizing-Promoting Actions: How Classroom Collaborations Can Support Students' Mathematical Generalizations* was written by Amy Ellis and published in the *Journal for Research in Mathematics Education* in 2011. The article is available from NCTM at http://www.nctm.org/publications/article.aspx?id=30191 and from JSTOR at http://www.jstor.org/stable/10.5951/jresematheduc.42.4.0308.

## Abstract

Generalization is a critical component of mathematical activity and has garnered increased attention in school mathematics at all levels. This study documents the multiple interrelated processes that support productive generalizing in classroom settings. By studying the situated actions of 6 middle school students in their teacher-researcher working on a 3-week unit on quadratic growth functions that can be represented by \(y=ax^2\), the study identified 7 major categories of generalizing-promoting actions. These actions represent how teachers and students can act in inter-action with other agents to foster students' generalizing activities. Two classroom episodes are presented that identify cyclical interaction processes that promoted the development and refinement of generalizations. The results highlight generalization as a dynamic, socially situated process that can evolve through collaborative acts.

## Outline of Headings

- Generalizing as a Situated Phenomenon
- Method
- Setting and Participants
- The Teaching Experiment
- Data Analysis

- Results
- Part I: Categories of Generalizing-Promoting Actions
- A note about the mathematics
- Publicly generalizing
- Encouraging generalizing
- Encouraging sharing of a generalization or idea
- Publicly sharing a generalization or idea
- Encouraging justification or clarification
- Building on an idea or a generalization
- Focusing attention on a mathematical relationships

- Part II: Interaction Cycles
- Excerpt 1: Developing an equation to find the DiRoG
- Excerpt 2: Connecting the DiRoG to the height and length of the rectangle
- Refining generalizations
- Students' ownership

- Part I: Categories of Generalizing-Promoting Actions
- Discussion
- Generalizing as Situated
- Generalizing as a Collective Activity
- Learning from the possible: Implications

## Also

- APA
- Ellis, A. B. (2011). Generalizing-promoting actions: How classroom collaborations can support students' mathematical generalizations.
*Journal for Research in Mathematics Education*, 42(4), 308–345. - BibTeX

@article{Ellis2011, author = {Ellis, Amy B.}, journal = {Journal for Research in Mathematics Education}, keywords = {Algebra,Classroom interaction,collaborative learning,constant comparison methods,functions,intermediate/middle grades,qualitative methods}, number = {4}, pages = {308--345}, title = {{Generalizing-promoting actions: How classroom collaborations can support students' mathematical generalizations}}, url = {http://www.jstor.org/stable/10.5951/jresematheduc.42.4.0308 http://www.nctm.org/publications/article.aspx?id=30191}, volume = {42}, year = {2011} }