(image from pxfuel.com)

Reflection assignments as an active learning strategy are commonly seen in humanities courses. The purpose of this writing is to share an example of how simple reflection activities can make a huge impact in two math courses.

MTH 251 Differential Calculus covers five units, with one exam for each unit, counting 14% of the final grade. Before students attempt to take the unit exam, they are assigned to read textbook readings, watch instructor-created lecture videos, work on Canvas-based homework assignment and Adaptive Learning based practice assignments in Knewton Lab online platform. After assignment due date expires, students are assigned to complete a weekly written homework reflection. The weekly homework and the weekly homework reflection together count for 14% of final grade in this course, weighing the same as each of the unit exams.

MTH 341 Linear Algebra I has ten weekly modules. Each week, students  read textbook assigned readings, watch lecture videos created by the instructor (Dr.   ), complete post-reading questions in quiz format, work on graded group discussion questions to solve math problems in small groups, complete written homework individually, and in the following week, complete a written homework response activity individually in discussion format.

The written homework reflection in MATH 251 and the written homework response in MATH 341 are both reflection activities designed to optimize student learning success, through comparing their own homework solutions with answer keys and evaluate whether they did it correctly or incorrectly and analyze where they did it wrong and how to get it right. The purpose of such weekly reflection is to help students develop meta-cognitive skills related to their learning. By looking back at students’ own work and learning from their mistakes, they develop an understanding of what is the proper way to solve a problem and what is not the proper way for solving a particular math problem. It also prompts students to plan for proper action in the future and exercises students’ executive functioning skills (CAST, 2018).

Here is what the instructions for the weekly reflection look like:
1. First answer the weekly prompt: Reflecting on the Unit 1 module, which topics did you struggle with the most?
2. Download the written homework solutions PDF: (Solution for each written homework in pdf format is attached here.)
3. Look over the solutions and compare to your submitted homework. Look for any problems where your solution differs from the posted solution.

• If your solutions had one or more incorrect problems then in the discussion board please discuss the following:
• why you struggled with certain problems
• why each solution makes sense now
• what will you do in the future when solving problems similar to these?
• what did you learn by making a mistake?
• what did you learn from looking at the solutions?
• If you are still confused about a problem, ask a question. DO NOT simply list which problems you got wrong.
• If your solutions are all correct then in the discussion board please discuss the problem that you found the most challenging. Describe what specific tasks helped you to complete that problem. Be as detailed as you can about your solution process.

Students not only posted their own reflections, but they also comment on or answer other students’ reflections as well. Additionally, the instructor and the four TAs in the course responded actively to students’ reflections, which makes the reflection more valuable since students get encouragement, praises, or corrections from the instructor and teaching assistants. Again, feedback from experts is critical in the success of a reflection activity (Vandenbussche, 2018)

Image 1: How reflection usually looks like and How reflection should look like (Image Source)

Many students were reflecting on what they did wrong and asked for help. Some were reflecting on their time management in completing the homework assignments. And we were glad to see students completing homework, evaluating their own work, analyzing where they did wrong, and planning for future improvement. Overall, the purpose of this assignment is accomplished!

(Image by Dave_Here)

A great benefit that comes from these weekly reflection activities is increased or sustained homework completion rate. For MTH 251 winter 2021 week 1 to week 7, over 85% of students completed the weekly homework and the reflection activity on average. For MTH 341 Fall 20 week 1 to week 7, over 90% of students on average completed the weekly homework and the reflection assignments. All math teachers love to see their students practice with homework assignments before they attempt to take the quizzes or exams! And evidence-based research tells us that deliberate practice with targeted feedback promotes mastery learning (Ambrose et al., 2010).

So, if it works in math courses, it will work in Chemistry, Biology, Physics, Engineering and other STEM courses too! If you’re interested in implementing this technique in your teaching and have questions about setting it up, feel free to contact us. We’d love to help you figure out the easiest way to set it up in your course.

References

Ambrose, S.A., Bridges, M.W., DiPietro, M., Lovettt, M.C. , Norman, M.K., & The Eberly Center for Teaching Excellence at Carnegie Mellon University. (2010). How learning works: Seven research-based principles for smart teaching. San Francisco, CA: Jossey-Bass

### Reflecting

How do you help your students reflect on your course and integrate what they’re learning into their subject knowledge and worldview? If you want your students to develop metacognition and self-understanding, or to articulate professional identity or a disciplinary perspective – reflection and reflective practice can help them integrate what they learn in your course into how they think.

### The Theory

The role of reflection in personal development and academic practice is widely acknowledged as a part of higher order thinking in general and also particularly in AACU’s VALUE rubric for Integrative Learning and rubric for Foundations and Skills for Lifelong Learning . The question is how we incorporate reflection in course design.

Adding reflection as a self-contained activity can be a great step, but we often add such activities as small items at the end of a course, or – from the student point of view – as an afterthought or the extra bit they need to do after they’re finished. Reflections done this way, though of potential benefit, can often easily lapse into superficial form-filling. A better approach is to build reflection into the course, and to scaffold student engagement with the process. This can be much more effective and changes how a student interacts with the reflective activity.

### An example: Current Problems in Sustainable Living (PS 399)

In PS 399 Current Problems in Sustainable Living (in the future to be offered as PS 374) Dr. Erika Wolters set out to engage students with the issue of their personal role in sustainability within the context of huge global political systems. The course description is as follows:

“Exploration of the role of individuals in sustainability practices and policies. Special focus is given to an examination of how individuals can make sustainable lifestyle choices in light of policy regulations, technologies, socio-economic conditions, and cultural values.”

### The Final Paper

Dr Wolters had set set up her course with three major papers alongside other activities and assessments. Originally, the reflective activity was contained in the final paper which required

“By the end of week 2, please select three personal behaviors […] that you will try to change in order to live more sustainably. Document your starting point and each step along the way. Your final paper will require you to discuss your step-by-step attempts where you were successful, where you met with unexpected difficulties, or any other surprises along the way. Place your personal sustainability experience into the context of your readings about individual actions and impacts.“

This paper sought to integrate practice, reflection, and critical disciplinary analysis. As Dr. Wolters and I discussed the course design and how to help students engage with this activity in an online environment, we were aware of two pitfalls to avoid: students reaching the end of the course and struggling to remember their experience and students spending all of their final paper recounting their experience rather than critically engaging with it.

### The redesign

The solution we came up with was to ask students to create journal entries throughout the course documenting and beginning to reflect on their practice. In the ten-week course, they identified their sustainable practice by week 2 and journaled about it in weeks 4, 6, and 8 before writing their final paper in week 10. The journal could either be in written or video diary format. There were any number of tools that could be used to support the video option, but using Canvas’ integrated tools and video recorder enabled students to do so easily and without the cognitive overhead of learning an external tool.

The journal could have been set up in a Canvas discussion board. This setup would have created a shared experience across the class in which students reflected and shared together. However, because the focus of this course was personal reflection, the journal activity was set up using the assignment tool. The video or text reflection was shared only with the professor. The reason for doing this was to create the opportunity for more personal reflections than the student might have felt comfortable posting in a forum.

### Work in progress

The course is still underway but halfway through I was able to catch up with Dr. Wolters to find out how it was going. Her key observations so far relate in large part to the changes developed through the availabilty of video as an option for this journal activity. She reported the following:

“I do think it is helping them think about the course differently. It is great having them undertake behavior/habit changes and reflect on the costs vs. benefits. It is really exciting to see how they are embracing the project!”
“[I]t is definitely helping me connect with the students differently. I really enjoy seeing and hearing them vs. just having the one-dimensional responses of the discussion boards.“
“[The video posts] were so much fun I responded with a video comment and then posted bi-weekly announcements as a video. It was fun! I definitely feel more connected to the students this way.”

### Interim Conclusion

Although this activity needs further evaluation, it illustrates a way to engage students with academic reflection through encouraging dialogue early and throughout the course. From the initial feedback it seems clear that from the instructor’s perspective it offers opportunities to connect with students throughout the course and enable them to engage with the topic.

### Image Credits

All images by Alan Levine (Flickr user Cogdog), used under a CC- BY licence.