In our division, classes on the first day of school are only 15 minutes long. By the time students settle in and introductions are made, there is hardly enough time to wrestle and play with an interesting math problem. I saved that for the second day. Instead of going through the syllabus, however, I gave the time over to my students to reflect on the following questions:

- When I see the word ‘mathematics,’ I think of…
- A good experience with mathematics was when…
- A bad experience with mathematics was when…
- This semester, I expect to…

(The students completed the prompts in their new math journals, which I will hopefully get a chance to write about once the routine is more firmly established.)

The idea was to give students the opportunity to reflect honestly on their relationship with and views on mathematics. I plan to repeat the exercise at the end of the semester – it should be interesting and instructive to note any changes in perspective.

The majority of responses for second two questions were more-or-less predictable in a culture that equates grades with success and intelligence (or lack thereof): e.g., “…when I got 95% on a test” and “…when I got 50% on a test.” A small minority talked about a time when they were able to use mathematics in their daily life, like when they were able to find the best deal at the grocery store; a handful described a time when they solved a challenging problem, others when they had the opportunity to work on a problem with their classmates. In response to the third prompt, a good number of students (especially the older ones) answered “pass the class”; a small number, perhaps thinking that I was looking for a certain type of answer, wrote “listen to the teacher.” One student, IN ALL CAPS, wrote “I expect to… love MATHEMATICS WITH ALL MY HEART”:

Whether he was joking or not, what a challenge to receive!

The students’ responses to the first prompt (“When I see the word mathematics, I think of…”) were particularly interesting and thought-provoking because of their near-uniformity: the vast majority of students completed the statement with words such as “equations,” “numbers,” “problems,” “school,” “a teacher”… In other words, the vast majority of these students associate mathematics with its *products* or with related *objects* – and in particular, with products and objects that are typically imposed upon them, rather than those that students are involved in shaping. Not one student explicitly referred to processes* *or verbs*, *such as asking questions, looking for patterns, making connections, developing logical explanations, generalizing… What does this say about students’ (perceived) relationship with mathematics? Can this relationship be redefined in a culture that assigns higher value to tangible and visible products (answers, grades) than to processes?

I’m still ruminating about all of these responses and how I* *will respond to them through my teaching this semester. I would love to hear your thoughts.