## Abstract

*In many university mathematics courses, homework accounts for the majority of students’ interaction with mathematics content. However, we know little about students’ activity as they complete homework. This paper presents an empirically-based model of students’ activity as they complete an online homework assignment. I developed the model based on analyses of video recordings of nine Calculus II students completing an online homework assignment and follow-up interviews with the students about the homework session. In the context of the introduced model, I present two additional findings. First, students’ activity when solving online homework problems is cyclic and similar to mathematicians’ activity when problem solving. The online platform contributes to this by verifying answers and providing students multiple tries per problem. Second, students leverage their multiple tries per question and ability to submit parts of questions individually to obtain intermediate feedback. They use this feedback as formative assessment to guide their work on the remainder of the problem.*

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## Notes

- 1.
The students in Ellis et al. (2015) were at PhD-granting institutions selected as part of the Characteristics of Successful Programs in College Calculus project (c.f. Bressoud et al. 2015); details about whether the students were mathematics majors or whether the course was common for all science students were not provided. Subjects from Krause and Putnam’s (2016) study were enrolled in a mainstream calculus course.

- 2.
This paper is based on the same data set described in Dorko (2018) and refines the model presented there.

- 3.
As a result of this randomization, the numbers that appear in the student examples later on in the paper may differ from what is shown in this section.

- 4.
This branch of the model characterizes instances in my data in which students decided (via their own verification, not the online program’s) that their answer was incorrect. It is possible that a student might have worked on a problem, self-verified an answer, and then submitted it. I did not ask students if they self-verified answers that I knew were correct, so “self-verify” is not an explicit component of the model. I have described this branch as representing instances of students self-verifying their answers because students told me in the second interview that when they did not submit an answer and tried a different approach, it was because they sensed their answer or method was incorrect.

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## Acknowledgements

I would like to express my thanks to Kevin Moore for his help in preparing this manuscript and the RUME community for the opportunity to present a previous version of the manuscript.

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Dorko, A. Red X’s and Green Checks: A Model of How Students Engage with Online Homework.
*Int. J. Res. Undergrad. Math. Ed.* **6, **446–474 (2020). https://doi.org/10.1007/s40753-020-00113-w

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### Keywords

- Online homework
- Instructional triangle
- Didactic contract
- Problem solving