Refocusing After Class

Teaching a class does something nutty to my energy. Typically when a class finishes, I’m restless and unfocused. It’s a bit like stepping off of a stage, even when I’m leading the class from the sidelines. I’m so focused on the students, and so conscious of managing the various aspects of the class — understanding, focus, mood — that it is challenging for me to re-focus on the tasks of the day.

My typical strategy is to surfing the web and look at Facebook and other social media until my class-related energy dissipates. The trouble is that those screen tasks are so absorbing and addictive that I have a hard time pulling myself away and my nice break wastes my time rather than helping me to refocus and transition.

That’s why I’m on a social media break. I started last Wednesday and I’m going until this Wednesday night. I definitely worry that I’m missing something, but I know I’m really not, and I waste a lot less time. But I still don’t have a good way to refocus after class…

Using Memory-work to Study Struggles with Mathematics

So I have this new project idea that I am obsessed about which involves collaborating with students to research struggles with mathematics. If you are interested, have a look at my draft. And if you have any suggestions or want to talk about memory-work (or collaborate with me), leave a comment or send me an email. Oh, and this is a real live draft so if you notice any typos or errors, don’t be shy about letting me know.

Working in groups in Calculus: So far, so …

I’m done with the first week of calculus, and happy with how the class is going overall. Thus far, we have reviewed functions, worked on translating between descriptions and functional notation, done the bottle calibration problem, and started modeling functions in Excel. Next week, we’ll finish the Excel work we started and have them do some activities to get familiar with the library of functions we want to be able to use in class. There’s a lot going on this first week, perhaps too much, because I also have them doing a writing assignment for monday and using Khan academy to review pre-calculus material. My worry is that I may be creating too much of a jumble for them and causing confusion.

I’ve also been having them work in groups. I don’t have specific groups assigned, and I haven’t decided if I will do that this semester. Right now, I don’t have enough sense of who they are to make good matches. I did assign roles in todays class — leader, recorder, reporter, but I am not sure what use they are making of the roles. I told them that the leader should be keeping the group on task and also making sure that the group hears from everyone. But I haven’t made as much use of the recorder and reporter, so I’m going to try to correct that next time. I also need to switch up those roles, but I’m not even keeping track of the roles I assign. Perhaps next week I’ll ask them what roles they think people take in group work and try to discuss this. I would also like to take with them about the creation and enactment of mathematical identities in groups and in classes (as in that article I read earlier in the semester), since I would love their perspective.

I asked them for feedback today specifically about working in groups — what went well and what they’d like to change. Some difficulties that came up were: not everyone feels comfortable talking, rest of the group is familiar with each other and one person feels a bit left out, more talking ideas out needed, group designations didn’t seem to apply/stick (but writer thought that might not be a bad thing), and people can stay under radar and let others have more input.

Good things identified were working well together even through disagreement (several said this), collaboration (several said this), helping generate and verify ideas, getting tech support from each other for laptop use, helping each other out, people listening to what others had to say, able to give each other different points of view and insights we may not have seen, feedback, and being able to work with people that are better at math than I am.

If any of you out there have ideas about how to help students form productive collaborative relationships with each other, I’d love to hear them!

Feedback from the first week — Math, Art, and Design

In my classes this semester, I’m going to be asking students to give me a little feedback each week, and my goal is to make this feedback into a dialogue of sorts between me and the students. So I had students in my two Math, Art, and Design classes tell me something good or interesting from the first week, a question or concern, and anything they wanted to change. Now I’m looking through those responses.

From both sections, I have collected a pretty comprehensive sampling to give you a good feel of the feedback. Not everything is in here, but most everything is represented. I was impressed by how much the students put into what they wrote and how open they all were to mathematics as a subject.

The Good/Interesting/Exciting:

  • I was terrified coming into this class. I feel excited now
  • Enjoyed questions of how infinity works or if it does
  • Making math fun, can’t wait.
  • I am excited for it.
  • Math is hard for me to follow and I liked when we broke into groups.
  • Groups/videos are good ways to break up the class (a couple of people said this)
  • Never thought about an infinite amount of something so deeply before
  • Videos were awesome (several said this)
  • Idea of exploring philosophical connotations of infinity was fun
  • Class more energetic than I expect and I appreciated it
  • Idea that numbers can go infinitely backwards was interesting
  • Vi Hart video was cool and made me want to do math doodles
  • Infinity blows my mind
  • Learned what infinity is and how to define it, that is quite epic if you ask me
  • This is by far already the most interesting math class I have ever taken.
  • Like the format [I project notes from a tabled PC using Windows Journal and then turn those notes into a PDF after class]
  • Theores we discussed were really eye-opening and I really enjoyed the personal, mental freedom to explore these concepts. Adding examples that we could imagine physically (eg hotel) helped
  • Liked amount and variety of different visuals, it made everything easy to understand
  • History of Galileo & Cantor going insane were interesting
  • Love the way this class is challenging my concrete mathematical brain with the “impossible”
  • I liked how people in the class created a discussion instead of just listening to the teacher talking
  • Concept of one-to-one correspondence became clear
  • My mind hurts. Just kidding…kind of.

Concerns/Questions/Changes Needed

  • Same as in every math class I will end up getting lost
  • I am worried that I won’t retain all of the info or not understand a concept (Note: we don’t have a text in the class, which I know can raise anxiety levels so I want to be careful about supporting students)
  • Would like a longer break
  • Still not sure how there can be different sized infinities
  • Is there really an accurate definition for the word “infinity”?
  • Would like to see more working on our own in future classes
  • Curious what our 40 point project will consist of
  • I’m afraid of math
  • Curious to know more about how mathematicians think
  • Like you said, I’ll believe whatever the math professor tells me — I’m not confident enough to expand that into skeptical math questions
  • How did the idea that things are infinity even become an idea? If everything we know is finite, why would we we think there would be more?
  • If we have established that the infinite hotel is impossible why did this guy’s theory stick so well with the other mathematicians?
  • What is bigger than infinity?
  • Might it have been easier for some to grasp if we had approached topic from something infinity small (since infinitely large things are so hard to grasp)?
  • How can you play musical chairs backwards to represent infinity+1
  • Topic of infinity piqued my curiosity but was also frustrating because there are no defined answers concerning it.
  • I don’t want to change the class, only my knowledge of math.
  • I need some processing time before I’m even ready to ask questions.
  • Can we do more with drawing/visual arts and math [likely in response in part to Vi Hart video]
  • I am a bit nervous because I haven’t taken math since high school [the majority of the class are juniors or seniors]
  • Dont’ quite understand infinity hotel, why did they all have to move one door down? Why couldn’t they just send guests to the end?
  • Confused as to how the “number” infinity works. Know it goes on forever, just don’t understand how to add “actual” numbers onto it.
  • Still unsure of why it takes a set and a proper subset to equal infinity.
  • I would like to change my lack of willingness to try to enjoy learning about math
  • Less math and more philosophical quandries

I won’t be doing this with the feedback each week (although I will do it sometime around the middle of the semester with a midterm evaluation). I see in this feedback some subject matter I need to address and that I need to give more time for group work. I plan to address some of the questions students raised in our next class together.

The low-energy class

All of us find ourselves in classes whose energy is low, and I had the first meeting of such a class today. It was our first class together, and it went OK, but I felt like I was really having to pull things out of the students and that most students avoided making eye contact. I find that faced with a class like this, I tend to get frustrated and anxious and I pull away from them, which doesn’t help establish that connection. So, I have my work cut out for me in the next class, growing a really solid connection with these students and getting them to open up. I’ll be having them give me feedback in the next class (on Thursday), so that may help, but I think I may also simply want to address the class energy directly and talk to them about it. I wonder how much of the distance between us has to do with power dynamics and trust. Any suggestions anyone has would be much appreciated!

First classes for Math, Art, & Design and Calculus

I have had my first class in Math, Art, and Design (MAD) and in Calculus, and I wanted to give a report on how those two classes went for me. In MAD I introduced the class and then started to talk about infinity, our first unit this semester. I showed a number of videos and then we went through the “Hotel Infinity” thought experiment together. Part of the reason that I start the semester with infinity is that there is so much richness to explore mathematically, but it is also an idea that we all share — mathematicians don’t have the market on infinity cornered and anyone can engage with the ideas. But I find it interesting that even though I want students to engage in the ideas their own way, I still struggle when their ideas are different from mine. I still have this deep internal belief that this is math class and there really is a right/best/most illuminating way to engage with the material. I constantly have to remind myself that differences of approach and opinion are OK, even though I chose the topic specifically to allow for these differences. I had the students give me some written feedback and it is mostly positive. I need to guard against going so fast and intensely that I leave people behind, and make sure that I give students ample time to work on their own. Honestly, it was wonderful reading the responses because brief as they were I felt people were putting their hearts into them.

I just moments ago got done teaching my first calculus class, with 16 people in it. Yay! I talked too much, and next class I vow to give the students more time to work. Once again, I adhere to the idea of giving students space and control, but it makes me anxious and I control my anxiety by preparing too much material and talking too much. I talked explicitly about two things that I think are important. First, I talked about the way that math is taught with the teacher presenting procedures and the students practicing those. Good teaching means doing a good job explaining, and being a good student means practicing. I told them that I want to open us up to something different, but that it’s risky and uncomfortable for all of us. For me, its uncomfortable because I’m violating the social contract. They have certain expectations of teachers and I’m not always going to meet those. For them, it is uncomfortable because I’m asking them to do something new and sometimes it will feel like I’m throwing them into the deep end and insisting that they swim. The other thing I talked about explicitly is working in groups, and I tried to draw out some of what they think helps and what can go wrong. I want to do more of that in subsequent classes.

First Day

Is there anything better or worse than the first day of classes? There’s so much potential in the air, but also so much anxiety. This semester I really want to be connecting with my students, but it’s so hard to be open for that connection because when you open yourself up you risk rejection. So instead of feeling really open, I prepare the heck out of my first classes so that nothing is left to chance and I can be certain everything will be great. But, of course, when I over-prepare I don’t leave any room for the students. Instead it becomes all about me and the hopefully great things that I can do.

So, as usual, I’m prepared, maybe even over-prepared. I can’t really stop myself, because these first moments are so important to me. But I’m going to spend a little while just thinking about what might happen and creating a little room for the students to come in and join me.