Entrance Slip # 7: "Flow”, engagement and the Thinking Classroom

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Throughout Mihalyi Csikszenmihalyi's talk, I was reflecting on moments where I have felt "flow." I found the chart introduced around 15 minutes into the video accurate because I have felt those variations before, and I have witnessed their manifestation in students as well. I have often witnessed students disengage when a problem presented was above their ability, or at least perceived to be out of their reach. Their unwillingness to try shows they are in the zones of worry, anxiety, and apathy; the work is unattainable so they choose not to try or become too overwhelmed to start. One strategy I believe we as teachers could implement to move past this is by making math more tangible for students. That is, we could introduce manipulatives where possible so that students can work to solve problems with concrete visualizations. In her talk during the BCAMT conference, Kathleen Jalalpour spoke about the importance of starting out with physical objects, moving to pictorial representations, and then shifting to formulas and pattern recognition, which starts with the students' own understanding instead of memorization. She spoke of how some students may be able to memorize well and find the patterns themselves while others struggle to find the patterns, are told to just memorize a "shortcut," and never really understand so they declare math too difficult and become opposed to the subject as a whole. While the talk was geared towards younger grades, Kathleen spoke about the usefulness of tools such as base ten blocks at a high school level as well. I will admit I was not a fan of the blocks from my own school experience, but I became one by the end of the talk. Of course, Kathleen also mentioned how this transition from concrete to pictorial to abstract can be a long process, but I think if it's possible to do, it will be worth it in the long run for students who are stuck in a cycle of not being able to engage with material, and hopefully work towards control/interest, and eventually "flow," as seen on Csikszenmihalyi's chart.

Another way in which I have seen Csikszenmihalyi's chart in action is the range from boredom to arousal or interest. I remember having a conversation in which the person I was speaking with said something along the lines of, "I find that you math people get so caught up in a concept that you can't fathom how someone would not think it was cool. You really need to introduce things to your students in a way that makes them understand why they should care and why it's cool." In that way, I believe the introduction of a concept is quite important. The introduction should include linking to previous content and concepts so that the student understands which skills are required and can shift from a worry/anxiety/apathy position to interest/boredom. Additionally, the introduction should convey why the students should care so they are shifted from boredom to interest. Providing historical background and real-world applications are two strategies that I believe would help in achieving this. After setting up this atmosphere that could lead to flow, we also need to provide appropriate problems and extensions just outside the students' current abilities so they continue to engage and enter that state of flow as they work. 

In Peter Liljedahl's slides, he discusses some more strategies to use when a lesson begins to steer away from achieving flow. I have previously encountered giving hints or extensions based on if the students were having trouble or finished early, respectively. However, I hadn't thought about rearranging groups. I'm not sure I necessarily agree with this method because I think it could lead to more disruption and potential feelings of inadequacy if students are say, paired with a group that has higher skills than them. They may feel that they're "not smart enough" to solve the problem on their own. Instead, I think I would have different expectations of different groups and guide them towards an attainable goal for their current level. There may still be feelings of inadequacy if the students compare themselves to what other groups were doing but hopefully I would be able to keep them preoccupied with the task at hand by making it interesting enough to maintain their attention.