This is the first time that I have ventured to encourage students to reflect freely and, in particular, visually, on their recent conceptual challenges and victories in their experience thus far in elementary calculus.

AIM:  I want students to reveal their thinking to me, and to examine affect and emotional stances, although through their own volition and on their own terms.  Thus, I aim to cede to students the necessary creativity in reflection that need not conform to conventional math reflection practice.

Rationale:  In setting the expectation, I wanted to bring attention to what students’ previous experience has been in the past with reflection, or with self-reflection.  Would they feel comfortable trying things “outside the box,” including other modes of attempting to reflect and to express what they sense and what they feel?

Methods:  In order to give some sense of structure to this reflection, I provided the attached  Visual Self-Reflection Prompt, but with encouragement that “any expression need not make sense to anyone else.  It only has to make sense to you, or it could be only an impulse that seems to feel right, and that may (or may not) lead to what you wish to express.”

The prompt initially included typical written reflection too, just to provide some familiarity in order to ease the bridging to other creative modes;  it then added the suggestion for reflection using any other chosen expression, particularly visual.  Again, only to provide some focus, I articulated recent seminal calculus concepts developed in the course upon which they might reflect, if they wish, and suggested that they could examine their inward stance towards these concepts in visual modes….

Student work:  Some excerpted anonymized reflections are posted here:  Visual Self-Reflection Expression.  These only show visual portions of their reflections, not the written format portion.

My reflection:    I view this as a starting step in an expanding dialogue that I may be fortunate to have with students.  Although some student reflections may appear antic, they may mean much more.  Some were revealing to me and insightful.  For instance, students  who outwardly do not appear committed or hardworking expressed the centrality of will-power; ironically, some high performing students expressed macabre disaffection.  Some visual representations were cryptic and abstract.  I wonder if I should ask more, or if I have the right to probe. Maybe. Furthermore, some students asked to take the reflection prompts home to reflect more deeply on them before sharing with me.  Thus I will make more observations, and I may share more later, especially in an attempt to further refine, support and appraise the possible development in students of visual representation and expression as a tool in self-reflection practice.

Luis

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