Setting: The Homework System 36 

As mentioned in Chapter 2, the foundation of the homework system employed in this research consists of two salient principles: autonomy (Deci & Ryan, 1987; Ryan & Deci, 2000) and self-assessment (Andrade & Valtcheva, 2009; Paul Black, Harrison, Lee, Marshall, & Wiliam, 2004; Black & Wiliam, 1998; Heritage, 2009; Marzano, 2000; Reeves, 2011; Wiggins, 1998). At the beginning of the semester, I informed students that I would not be checking their homework. I explicitly told them that it was completely their own choice as to whether they completed the homework, how much of it they completed, and when they completed it. However, I did strongly encourage the students throughout the whole semester to engage meaningfully with the homework, as I believed this would increase their chances of success.

In addition to this, I also provided the students with homework tracking sheets for each chapter. These were intended for students to track how they were progressing with their homework. There was one tracking sheet for each chapter, on which there was a table with numerous rows and columns. The first column contained the chapter’s learning outcomes. The subsequent blank columns were for students to write in their homework assignment for each evening; they wrote the date along the top row of each column. I matched each assigned homework question to the learning outcome that it covered, and the students were to write the questions in the appropriate row for each learning outcome. After completing the homework, students were to track how they had fared with each question (see figure 1). If they did the question on their own and got it correct, they were to put a check mark underneath the question on the tracking sheet (see A in figure 1); if they got help with the question, they were to put an “H” (see B in figure 1); if they got the question wrong, they were to put an “X” (see C in figure 1); and finally, if they did not do the question, they were to put an “O” (see D in figure 1). As the chapter progressed and students completed additional questions for each learning outcome, they could look at their tracking sheets and see which outcomes they were consistently getting right, which they were getting wrong, and with which they were receiving help. In this way, the

for the students; it allowed them to clearly identify which specific mathematical concepts they were struggling with in each chapter.

Figure 1. Sarah’s homework tracking sheet for the radicals and powers unit

I actively promoted the use of the homework tracking sheets throughout the semester. I encouraged the students to use them, explaining explicitly on numerous occasions how the sheets could greatly contribute to their success in the course. During the first few months of the semester, I made an effort to give students time in class to fill out their tracking sheets if they so chose. As the semester progressed and students became more accustomed to the system, I gradually stopped doing this. I also improved the format of the tracking sheets to encourage more students to use them. First, I added a separate space underneath where the questions were written for students to put the check marks, X’s, H’s and O’s. I also added a quiz section. I decided to start giving daily practice quizzes to students as additional self-assessment. So columns on the new tracking sheets alternated between homework assignments and practice quizzes.

Appendix A shows this difference with the tracking sheets for the first and fifth chapters of the course. In this way, students could mark their achievement on the practice quizzes on their tracking sheets and directly see how they did on each outcome as compared to their homework.

In addition to merely filling out the tracking sheets, I encouraged the students to respond appropriately to the feedback. If students were consistently getting all of the questions for an outcome incorrect, the appropriate response would be to seek help with that concept. If students were getting help with all of the questions for a particular outcome, the appropriate response would be to attempt some new questions on their own. And, if students were consistently getting all of the questions correct for a certain outcome, then they could probably focus less on that outcome while doing homework or reviewing for a test.

Finally, I encouraged students to also use the self-assessment provided from the homework tracking sheets to guide their review for tests and the final exam. I pointed out that instead of simply trying to study everything we had done and complete massive review packages, they could instead use their tracking sheets to focus their studying on the learning outcomes with which they were still struggling.

3.2.2.

Rationale for an Autonomous Homework System

As mentioned in Chapter 2, the rationale for giving students complete autonomy over their homework was to maintain the integrity of the self-assessment that I was hoping the homework would provide. If the students had been forced to do the homework and tracking sheets, it is highly probable, as shown by Liljedahl & Allan (2013), that many of them would have cheated. Landers (2013) argues that as long as schools emphasize scores and grades, “it is not surprising that students will copy and cheat to complete homework” (p. 388). And indeed, early in the semester I caught a student trying to quickly fill in his tracking sheet with false information because he thought I was collecting them for marks (I only collected them to see who had completed them, and then handed them back unmarked). Making the homework and tracking sheets worth marks would have

to satisfy my requirements and not to self-assess their own understanding. Indeed, I would have had much more difficulty in determining which students had sincerely used the homework as self-assessment.

Furthermore, as mentioned, SDT posits that an individual’s perception of autonomy improves the quality of their motivation (Ryan & Deci, 2000) and that choice is central to autonomy (Deci & Ryan, 1985). Yet, the type of choice is important; action choices, as opposed to option choices, increase perceived autonomy (Reeve et al., 2003). The present study provided action choices, as students were able to initiate whether or not they completed the homework and also whether or not they treated the homework as self-assessment.