What I wish I knew in the first two years

At the end of last summer, I had the pleasure of leading a pre-orientation for incoming graduate students. We had four three-hour meetings over the course week and our only main objective was to read through “Six ways to sum a series” by Dan Kalman.

When I participated in the pre-orientation as an incoming first year student, I believed that the purpose was to learn some math. (A kind of pre-wash before the real brainwashing took place.) I was good with that goal. As a bonus we even got the tried and true messages about impostor syndrome and growth mindset so I was rather content. But — as I moved into my first and second year, I realized that perhaps I had missed the point. I began to think that the purpose of the pre-orientation was to learn how to effectively work in groups and continually push yourself to become an independent learner. So, when I structured my lessons, I kept this in mind and moved forward ready to impart whatever minimal wisdom I could muster.

I began the week with five key messages that I wished my classmates and I had at the start. We would revisit these messages at the end of the week and hopefully keep them in the back of our minds throughout.

  1. No matter what your background you deserve to understand completely. Ask questions as soon as you are confused.
  2. If you are feeling like you are frustrated and struggling you are doing it right; these are signs of growth. Alternatively, if you are feeling comfortable, consider pushing yourself.
  3. Everybody’s voice is important. Listen to what your classmates have to say.
  4. Supporting each other academically and emotionally is an important aspect of first year. The older graduate students are here to help. Reach out to us.
  5. The only person you have to prove yourself to is yourself. Avoid comparing your progress to your peers.

At the end of the week, during a group discussion, the students expressed that “the messages, [especially the first two] empowered [them] to speak up, ask questions, and feel OK with being confused.”

The week was structured to begin with heavy group work and slowly release more of the responsibility to the individual.


Day One (“We’re kind of a package deal”):

Students began reading the paper. The instructions: “Read through this section with your group. Make sure that you are all staying together and understand what you are reading. A suggestion would be to read to a particular point and check–in with each other. In addition, be sure to keep track of all of your questions and your group mate’s questions.” It was really up to the students to decide how to proceed and I watched as they quickly took up all of the usual roles: the “I don’t need to write anything down, I got it” student, the “I don’t know what I am reading, but I’ll pretend just by staring at my paper” student, the “I’ll work on examples in the margins” student, and so on. I watched as they worked through the paper, keeping track of the questions going unanswered and the blank head nods that said, “I don’t quite know what you’re talking about, but, sure, I am good enough to move on.” All of these feelings were painfully familiar.

Throughout the time, we paused and answered questions as a group. I slowed us down and questioned how much we really understood of the paper. It was a rough first day, but played out exactly as I wished. This is what the beginning of first year felt like to me.


Day Two (“I have some questions.”):

Now that we felt the harsh realities of trying to do something at the pace of the fastest person in the group, it was time to forcefully grab a hold of our desire to understand and stand up for a more reasonable course of action.

On day two, students started by reading independently for fifteen minutes. The instructions: “Write every question that you have in the margins of the paper. Try not to spend too much time thinking about it. Just jot it down and read ahead. We will come back to it.” After a short break, in groups the students read the same section together, picking out all of their questions and answering them. Since they already thought about the questions, students were more willing to express the parts that were confusing and the questions that lingered. We progressed to feeling more comfortable with expressing confusion and answering questions without judgment. Day two was reminiscent of second semester for myself.


Day Three (“I think for myself, thank you very much.”):

Now for me the energy was buzzing. I am sure that for them the energy is that of pure exhaustion at this point in the week (they had been reading two papers six hours a day four three days now.) Nonetheless, I have enough energy for all of us.

Today, we spend even more time working independently. At first the instructions are the same as day two. “Read through the section making note of all of the questions that you have without thinking too hard about what the answer may be. Just get a feel for what you are reading.” But, today, the instructions come with a part two, after the 15 minute independent read: “Now, read the same section again. This time, really take the time to try and answer all of the questions that you wrote for yourself in the margins.” Finally, after a small break, the students worked in groups reading through the paper and answering any remaining questions. The conversations on this day were different. Rather than being focused on confusion, the conversations were filled with curiosity and explanation. They talked about how they had a question and were able to answer it themselves. They explained how. They asked questions beyond the reading. They moved along more quickly and with a deeper understanding. In my own mathematical journey, one could say this resembled third semester.


Day Four (“I can do this.”):  

The final day was for concluding what we learned so we spent the first half tying up loose ends and reviewing what we learned. The second half we spent reflecting on the week.  I pointed out that each day was structured so that they had more and more independence in their learning. I emphasized that each student is coming in with a different background and a different comfort level with working independently. The critical part being that everyone, no matter where the start can be successful. It is about pushing yourself to be more independent and striving for a deeper understanding. Then, I asked some key reflection questions related to our independence goals:

  • During the individual reading time was it difficult to focus on math? Were you distracted by how much was unfamiliar?
  • What percentage of your questions went unanswered each day?
  • How did the amount of independent time contribute to the overall group discussion?
  • Which day felt the most comfortable and why?

We had a very meaningful discussion in which the students reflected on their participation in their own learning. Taking away the importance of helping each other out, both to understand the material and to gain independence.  They reflected on their understanding saying that as the week progressed to more independence they could feel their understanding growing deeper.  Within their words, they emphasized the importance of working through their questions before meeting as a group.

I highly enjoyed watching them take learning into their own hands and certainly enjoy watching their continued growth throughout the program.

About Julianne Vega

I am entering my fifth and final year at the University of Kentucky, studying topological combinatorics. Prior to studying at UK, I was a middle school math teacher at a progressive, independent school in Alexandria, VA.
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1 Response to What I wish I knew in the first two years

  1. dan kalman says:

    Congrats on a well structured and apparently successful jump start for new grad students. It is particularly gratifying that you picked this paper for the students to work through. I hope that they found the topic interesting and enjoyed working through it.

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