# Jansen, Herbel-Eisenmann, & Smith III (2012)

*Detecting Students' Experiences of Discontinuities Between Middle School and High School Mathematics Programs: Learning During Boundary Crossing*

The article *Detecting Students' Experiences of Discontinuities Between Middle School and High School Mathematics Programs: Learning During Boundary Crossing* was written by Amanda Jansen, Beth Herbel-Eisenmann, and John Smith III and published in *Mathematical Thinking and Learning* in 2012. The article is available from Taylor & Francis Online at http://www.tandfonline.com/doi/abs/10.1080/10986065.2012.717379.

## Abstract

Transitions from middle school to high school mathematics programs can be problematic for students due to potential differences between instructional approaches and curriculum materials. Given the minimal research on how students experience such differences, we report on the experiences of two students as they moved out of an integrated, problem-based mathematics program in their middle school into a high school mathematics program that emphasized procedural fluency. We conducted an average of two interviews per year for two and a half years with participants and engaged in participant-observation at their high school. In this study, we illustrate an analytic process for detecting discontinuities between settings from participants' perspectives. We determined that students experienced a discontinuity if they reported meaningful differences between settings (frequent mention, in detail, with emphasis terms) and concurrently reported a change in attitude. Additionally, these students' experiences illustrate two opportunities to learn during boundary-crossing experiences: identification and reflection.

## Outline of Headings

- Background
- Transition into Secondary School
- Students' Experiences in Secondary Mathematics Classrooms
- Boundary Crossing and Discontinuities
- Learning During Boundary-Crossing Experiences

- Methods
- Context
- Curricular shift
- Instructional shift
- Building shift: Introduction of tracking

- Participants
- Collection
- Data Analysis
- Meaningful differences
- Changes in attitudes
- Discontinuity

- Context
- Two Cases: Illustrations of Boundary Crossing
- Bethany: Pursuit of Opportunities to Develop and Use Her Own Solution Strategies
- Boundary crossing as a process of identification

- Ethan: Reflections About the Nature of Mathematics Content and Instruction
- Boundary crossing as a process of reflection

- Bethany: Pursuit of Opportunities to Develop and Use Her Own Solution Strategies
- Discussion
- Limitations
- Conclusions and Implications

## Also

- APA
- Jansen, A., Herbel-Eisenmann, B., & Smith III, J. P. (2012). Detecting students' experiences of discontinuities between middle school and high school mathematics programs: Learning during boundary crossing.
*Mathematical Thinking and Learning*, 14(4), 285–309. doi:10.1080/10986065.2012.717379 - BibTeX

@article{Jansen2012, author = {Jansen, Amanda and Herbel-Eisenmann, Beth and {Smith III}, John P.}, doi = {10.1080/10986065.2012.717379}, journal = {Mathematical Thinking and Learning}, number = {4}, pages = {285--309}, title = {{Detecting students' experiences of discontinuities between middle school and high school mathematics programs: Learning during boundary crossing}}, url = {http://www.tandfonline.com/doi/abs/10.1080/10986065.2012.717379}, volume = {14}, year = {2012} }