​

​

Algebra 1 Teachers’ Classroom Circulation Patterns: A Lay of the Land

Mitchelle Wambua, Washington University in St. Louis

​

Maria Stewart, Oklahoma State University

​

Samuel Otten, University of Missouri - Columbia

​

Zandra de Araujo, University of Florida

​

Amber G. Candela, University of Missouri - St. Louis

​

​

​

​

Dr. Zandra de Araujo

The PDPD Team

zdearaujo@coe.ufl.edu

Dr. Samuel Otten

ottensa@missouri.edu

Dr. Amber Candela

candelaa@umsl.edu

Dr. Paul Wonsavage

wonsavagef@coe.ufl.edu

Dr. Mitchelle Wambua

wambua@wustl.edu

Dr. Maria Stewart

​

maria.stewart10@okstate.edu

Faustina Baah

fa6nz@umsystem.edu

Olumide Banjo

olumidebanjo@missouri.edu

The PDPD Project

This work was supported by the National Science Foundation (award #2101508) though any opinions, findings, and conclusions expressed here are those of the authors and do not necessarily reflect the views of the NSF.

PDPD Goals

Create (and study) instructional nudges that…

1. Increase student engagement
2. Foster conceptual understanding

Observations of Algebra Instruction

Teachers n=51 total n=46 complete (hopefully)

https://PracticeDrivenPD.com/

Pondering Teacher Circulation

• Student work time was substantial (and seems to be important)
• Teachers seemed to differ in their approaches to circulation
• What does existing research say about mathematics teacher circulation patterns and its relationship to learning?
• Not much (multiple searches with zero relevant results)
• There have been studies of detailed substance of teacher interactions during student work, but not broad patterns.
• Kikan-shido “between desks instruction” functions and international comparison (e.g., O’Keefe & Xu, 2006)
• Groupwork monitoring (Ehrenfeld & Horn, 2020)
• Spatial pedagogy (Lim et al., 2012) and faculty flow (Hargis, 2014)

Research Questions

1. How do Algebra teachers circulate and initiate discussions during student work time?

​

• What are Algebra teachers’ justifications for engaging in various circulation and initiation patterns while students work independently on mathematics problems?

Framing the Analysis

Circulation:

• Stationary: mostly stayed at one or two spots
• Mix: a fairly even combination of stationary and circulating
• Circulating: mostly moving between students or around the room

Initiation:

• Reactive: the teacher responds to student questions as they arise
• Mixed: a fairly even combination of reactive and proactive interactions
• Proactive: the teacher interacts with students without the student raising a hand or calling for the teacher

Framing the Analysis - Practical Rationality¹

¹Herbst & Chazan (2011)

​

Circulation & Initiation Frequency

Frequency of Circulation and Initiation Pairings

Independent Student Work Time

Group Work Time

Independent Student Work Time

Individual Obligation:

“So I'm walking around… I'm checking their progress to see if they are having any, you know, if they're doing you know look like they working but they're not really working because they're stuck.”

​

​

Disciplinary Obligation:

I look over their shoulders and make sure what they're working on is correct, and if it's not, I'll be like, hey let me show you how to do this next one… I don't want people to do an entire assignment wrong cause that's not helping anybody.

​

Independent Student Work Time

​

Interpersonal Obligation

​

At the beginning of the semester they're more reserved about asking questions, but by the end of the semester, they're pretty free to ask…sometimes if someone finishes something quickly and I see they got the right answer. I'll say so and so is my expert check with them, or they'll, I'll say, go see, you know, see? See how they're doing. See if you can, you know. Move them along a little bit something like that. But that's only if I think the student feels comfortable with it, because there's some that do not want other people near near them unless it's just the teacher, cause they're afraid that people will see what they don't know.

​

​

Independent Student Work Time

​

Disciplinary Obligation

​

I like to say, like, after the first 3 or 2 problems, bring your worksheet up to me. And I check those first 3 to make sure that we're not doing all of our problems incorrectly and that's usually the fastest way to kind of just make sure that everybody's on track because if I'm just walking up and down the rows checking it, I tend to miss somebody because some people might work a little bit slower than others

Independent Student Work Time

​

Individual Obligation

In this specific class, there's one student who was frequently absent, a very good vocal advocate for herself…there are probably a lot of times where she definitely wanted to feel like she was getting some one-on-one special attention, and so I might kind of need to work with that student.

​

​

Disciplinary Obligation

If I see, you know, everybody didn’t distribute to the second term, I might be looking at my next questions to pick, okay, what would be a good fit to fix that specific, you know, issue that everybody's having.

Group Work Time

Interpersonal Obligation

I check on them and say, did you check on [each others’ work]? did your answers match? Do you agree? Trying to get them to argue over who's right if they don't agree…it's all about questioning on my end and not giving them answers. So you got this, and she got this who's right? And why?

​

​

​

Individual Obligation

Sometimes I'll stay with a specific group for long. Like, if I know that group is really having a hard time.

Group Work Time

Individual Obligation

​

Walking around, answering questions, making sure they're focused and on task. If they don't have questions, at least they see that I'm there and they have that reminder, “Oh, teacher's coming, I better start working on what I’m supposed to work on.”

​

​

​

​

Group Work Time

Group Work Time

Discussion

Discussion

• Researcher observations versus teacher self-reporting
• Circulation patterns matched
• Initiation patterns differed — we observed more mixed; teachers self-reported more proactive

• Individual obligations
• Most common — all teachers are deeply attuned to individual student obligations regardless of their circulation and initiation moves

​

​

Discussion

• Institutional obligations
• Not common — was mentioned by teachers who self-reported mixed circulation and initiation patterns
• Could imply that teachers who sometimes circulate stay stationary when attending to institutional obligations

​

• Having students working in groups requires more obligation balancing work for teachers
• No teacher mentioned being stationary during group work.
• Group work brings in a new level of obligation - more interpersonal obligations mentioned by teachers who circulate in addition to the other obligations, which are still present.

Thank You!

​

What questions and comments do you have?

Read more of our work here: https://PracticeDrivenPD.com/

References

• Ehrenfeld, N., & Horn, I. S. (2020). Initiation-entry-focus-exit and participation: A framework for understanding teacher groupwork monitoring routines. Educational Studies in Mathematics, 103(3), 251–272.
• Hargis, J. (2014). A ten year study of faculty classroom observations. Transformative Dialogues: Teaching and Learning Journal, 7(2).
• Herbst, P., & Chazan, D. (2011). Research on practical rationality: Studying the justification of actions in mathematics teaching. The Mathematics Enthusiast, 8(3), 405–462.
• Lim, et al. (2012). Spatial pedagogy: Mapping meanings in the use of classroom space. Cambridge Journal of Education, 42(2). https://www.tandfonline.com/doi/pdf/10.1080/0305764X.2012.676629
• O’Keefe, C. A., Xu, L. H., & Clarke, D. J. (2006, July). Kikan-Shido: Through the lens of guiding student activity. In Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 265–272).
• Otten, S. (2024, June 13). Practice-Driven Professional Development Project – Incremental PD. Math Ed Podcast. https://www.podomatic.com/podcasts/mathed/episodes/2024-06-13T08_20_56-07_00
• Otten, S., de Araujo, Z., & Candela, A. G. (2025). The benefits of modesty: Considering incremental professional development for mathematics teachers. Education Sciences, 15(4), 473. https://doi.org/https://doi.org/10.3390/educsci15040473