Program in Mathematics Education – Featured Graduate Student Post

Grad Post.jpgI’m in the spotlight on my program website this week:
https://prime.natsci.msu.edu/

The page address is: https://prime.natsci.msu.edu/news-and-events/news/graduate-student-post-eryn-stehr/

Eryn Stehr arrived at MSU to pursue a doctoral degree in Mathematics Education starting with the Fall Semester of 2011. Her research interests focus primarily on “supporting teachers’ professional decision-making about their use of technology to support their mathematics teaching and learning.”

Eryn began her journey in higher education by attending Utah State University, where she received a bachelor’s degree in mathematics. Upon her graduation from Utah State University, Eryn continued her studies at Minnesota State University, Mankato receiving her master’s degree in mathematics.

Eryn Stehr With StatueWith two degrees under her belt, Eryn applied for – and received – a fixed-term position as a mathematics instructor at her alma mater, Minnesota State University, Mankato. In addition to serving as a mathematics instructor, Eryn also volunteered as a math coach at an elementary school.

Now, as a member of the PRIME program, Eryn spends nearly all of her time concentrating on her studies and working on her dissertation, which focuses on technology in the mathematics classroom. Specifically, Eryn will cover multiple dimensions of technology in the mathematics classroom, including:

– “Teachers’ conceptions about the nature of mathematics, the nature of mathematics teaching and learning, and the role of technology in supporting mathematics teaching and learning”

– “Teachers’ attention to features of mathematics-focused digital tools and resources”

– “Potential relationships between teachers’ conceptions and what teachers notice about digital tools and resources.”

Eryn Stehr Apple OrchardWhen Eryn allows herself some down time from studying and working on her dissertation, she indulges in walking, watching Netflix, and reading. In addition to these hobbies, Eryn is earnestly working on developing new hobbies such as playing the piano, cross-stitching, and genealogy. Accompanying her in many of her hobbies is her 15-year-old cat, Pell.

Upon graduation from the PRIME program, Eryn is hoping to work at a university close to her parents and family so she can balance her personal and professional lives.

Written by JJ Thomas

When they take the post down some day, here is the PDF version of the post: Graduate Student Post_ Eryn Stehr – Program in Mathematics Education

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Preparing to Write a Research Proposal

When I was working on my Depth paper for Comps, one of my committee members asked if I had filled out questions similar to the following to guide my thinking as I prepared to engage in research.

Judy Olson’s Ten Questions

From: CEP901a Educational Psychology Prosem; Judy Olson’s Ten Questions

Use the questions to write a proposal or paper, plan a research project, think about your future, or check up on your progress.

  1. What is the problem? (in the theoretical debate, the world)
  2. Who cares? (an argument about its importance)
  3. What have others done? (the lit review, but pointed as an argument)
  4. What is your approach? (your general approach, the new idea)
  5. What are you going to do explicitly? (your operationalization, investigation)
  6. What will happen? (or did happen, if you have results)
  7. What does this mean? (in terms of answering the problem)
  8. Who cares? (in what way is this important?)
  9. Where will you publish these results?
  10. What will you be doing in 5 years?

Judy Olson was Professor in the department of Psychology and the School of Information, and Director of CREW (the Center for Research on Electronic Work) at the University of Michigan. She has since moved to UCIrvine. She used these questions in a seminar for doctoral students in the School of Information (SI) during several terms in the late nineties. I [Raven McCrory?] was a doctoral student at the time (in education, contemplating a joint degree with SI) and was privileged to be in her seminars.

Dissertation Sketch

The following summer (2014) I was working on developing my dissertation proposal. It seemed to me that people often say that the process of writing a proposal is linear (i.e., figure out the problem, come up with a research question, then find a method that will answer the research question). But that seems (to me) to be an over-simplification of my process, anyway. My process of developing my dissertation research study was a cyclic, iterative process of getting to know what it was that I really cared about, how I could make it interesting / critical for other people, and how I could find answers to my questions in a way that worked for the question and for me.

So, I would work on the research question, think about the participants I could include, think about the literature I was reading and problems I saw referenced in that literature, etc.

Therefore – I tried to start out with a very lightweight summary of my interests, so I could use that as a way to focus conversations as I talked with my advisor and committee members. So I created this simplification that I called a “dissertation sketch” (see below for an example “sketch”).

  • What is the problem?
  • What is your purpose (briefly)?
  • What is your research question(s)?
  • Research Design
    • Give an overall picture of your plan.
    • What kind of data will you collect?
    • Who are your participants?

Example Sketch (keep in mind that these are very informal)

  • Sketch 1
    • What is the problem?
      • Both MET1 & METII recommend teachers develop a framework of technology choice and use.
    • What is your purpose (briefly)?
      • Develop a framework or a set of questions teachers could ask themselves as they look for tech or turn to fitting it into lessons.
    • What is your research question(s)?
      • Roughly: How can teachers intentionally develop their tech/math/teaching muscles? That is, how to develop a framework of tech choice and use?
    • Research Design
      • Give an overall picture of your plan.
        • Work with teachers on developing their frameworks, starting with a general framework. Ralph and I have done this to some extent in CEP 805, so that could give me a first step to working with other teachers. I could use the course now and next spring as one step of my project and then working one on one with teachers in their practice as a second step? Or could I contact our former students to ask about their interest in participation in such a study?
        • What we have done in the 805 is:
          • select literature that (hopefully) focuses teachers attention on types of learning and some characteristics that are important in integrating technology use;
          • asking teachers to answer several questions about tech tools they choose from a menu we provide;
          • giving more freedom in choice (teachers search and choose tech tools)  adding more questions to answer: asking teachers to search for tech tools and answer a larger set of questions
      • What kind of data will you collect?
        • Field notes / artefacts / video of development
      • Who are your participants?
        • Practicing teachers enrolled in CEP 805 and then
        • Practicing teachers in Michigan
        • Pilot phase:
          • students’ work from Spring 2014 CEP805 (not-publishable);
          • develop plan for Phase 1
        • Phase 1:
          • get IRB for permission next spring to more formally do this;
          • develop PD module from results
        • Phase 2:
          • implement PD module in phase with MI practicing teachers
  • Sketch 5
    • What is the problem? (in the theoretical debate, the world)
      • Both MET1 & METII recommend teachers (and PSTs) develop a framework of technology choice and use?
    • What is your purpose (briefly)?
      • Build a framework based on “best practices” for searching/implementing tech in math lessons based on practicing teachers who are (or consider themselves or are considered) tech experts.
    • What is your research question(s)?
      • How do “expert” teacher tech users choose and use tech?
    • Research Design
      • Give an overall picture of your plan.
        • Ethnography type observation of teachers who self-identify as tech gurus — how they choose it: strategy for searching and planning; how they use it: classroom norms, discourse, student activity & evidence (would hope to find variety in these characteristics)
        • Compare how these teachers use technology – are there important differences in their strategies or type of use?
      • What kind of data will you collect?
        • Getting a picture: Initial survey to identify  possible participants and to get an overall view of teachers’ self-identification of themselves as tech users
        • Field notes + screen capture/camera recording of teacher searching & planning; possible debrief after choosing a tech but before implementation
        • Field notes + video of implementation
    • Who are your participants?
      • Mathematics teachers who self-identify as tech gurus

Growth and Fixed Mindsets in Everyday Life

Growth and Fixed Mindsets

My students last year kept bringing up mindsets and then at National Council of Supervisors of Mathematics (NCSM), Jo Boaler was a keynote presenter and spoke about mindsets (see more at https://www.youcubed.org/category/teaching-ideas/growing-mindset/).

Mindsets in Mathematics

Jo Boaler spoke about the misconception that some people are born with a “math brain” and others are not. So some people are unable to math at all. She pointed out that there some people who really are physically unable to do math, but those represent fewer than 1% of the population. She argued that we need to support “growth mindsets” which basically means that we support the idea that anyone can learn anything if they work hard, have appropriate experiences, and give it time.

Mindsets in Everyday Life

Pretty frequently I tell myself I have a “___ brain” where lots of things can go into the blank: I am just not a social person, and nothing I can do will ever get me to the point where I can interact effectively with other people on an ongoing basis. My mind just doesn’t work that way. Or, I am an imaginative person but I am not a creative person. I can’t draw or paint because my mind just doesn’t work that way. Or, I’m not an organized person – I am scatter-brained and can’t keep up on notes or planning. 

So, I’ve started to try to talk back to myself and say: If I expect my students, who may feel the same way about math as I do about socializing, to change to a growth mindset, then I need to change to a growth mindset about all of these things too.

This realization was pretty amazing for me: All this time, I have thought I was born a certain person who just can’t do things like other people. And I realize that some of those things may never come easily for me (because I probably still will be an introvert who prefers a quiet reading chair in the evening as opposed to an exciting evening with friends) but I can work on these things and improve. I can reflect on my feelings and strategies, and I can talk to other people about their feelings and strategies, and get better at anything that I want to.  It feels freeing.

Learning how to read … In grad school

When I first arrived in grad school, I asked so many students: How should I read? What do I pay attention to? Am I spending enough time? Too much time? I’m drowning!

My advisor said to imagine floating in an ocean and then grab onto whatever pieces are floating past, close enough to grab. I felt more like I was tangled in vines – all connected somehow, all important, but all looked about the same.

Based on What is the learning goal anyway? I’m going to brainstorm potential learning goals of grad school reading:

  • Learn math ed theories
  • Learn math ed world values
  • Learn research methodologies
  • Learn the article itself for later use in research and arguments
  • Get to know the authors, aka, movers and shakers in the math ed world
  • Get to know the “cocktail party” conversation
  • Learn how to write
  • Learn about mathematics teaching and learning
  • Learn about students’ and teachers’ struggles and thinking

I’m sure there are many more. When I started reading for comps, I created a framework (based on other frameworks that had come up in different classes):

  • Abstract:
  • Stable URL:
  • Keywords: 
  • Type of article:
  • Theoretical Framing: 
  • Conceptual / Analytical Framing:
  • Research/paper purpose / research questions: 
  • Key terms / ideas / concepts:
  • Quotes from Text:
  • My Questions:
  • My Elevator Version / Summary:
  • Outline:

Another similar framing came from CEP956 (Mind, Media, and Society). It could be useful because the structure helped me look at the paper as more of an argument, which might have helped me learn better how to write.

  • Citation
  • Need
  • Purpose
  • Research Question
  • Theoretical Framework
  • Type of study and study details (i.e., sample, method)
  • Results
  • Conclusions
  • Limitations
  • Implications

What is the learning goal anyway?

In my years at Michigan State University, I have learned that having a learning goal is one of the critical elements of lessons and assessments, research plans, presentations, and guiding your own learning. (I think this post is supported to some degree by All About Models.)

Learning Goals in Mathematics Lessons and Assessments

For teaching, learning goals are important in helping a teacher choose relevant and focused questions, tasks, and discussions. Sometimes learning goals can be too restricting, closing off the potential learning and interpretations. Deciding what the true take-away from a lesson should be, is incredibly difficult! A teacher needs to think about immediate mathematical needs of her students, as well as future needs – in future math classes, of course, but also for the future adults the students will become. Those adults need to be able to make sense of their world, think critically as consumers and citizens, and put their mathematics thinking to use in their future profession. Once a learning goal is chose, thinking critically about the assessment is also important and really questioning whether the kind of learning and thinking does the assessment test for is relevant to the learning goals. (Which comes first, the assessment or the learning goals?)

Learning Goals in Research Plans, aka “research questions”

In my time on research projects, especially Preparing to Teach Algebra, I have seen again and again how important it is to work for a while and then re-read the research questions. The research questions indicate what you hoped to get smarter about before the project began – they indicate your learning goals for the research. Dr. Sharon Senk told me over and over: “I think you need to go back to the research goals: Does your current analysis help or should you reorient and what we hoped to find out?”

Learning Goals for Presentations

A large part of my job as a research is “disseminating results of research.” In class or at conferences, it is tempting to – and almost impossible to avoid – sharing everything you have learned with the audience. Because it all is amazing and interesting – and, yes, the audience would be enthralled if they had several days of time to chat with you. I try to fight against that need because I have been the perpetrator and the victim of such presentations. I remember serving on a Math Education faculty search committee. A candidate visited and shared her dissertation – it seemed like the whole dissertation – in a 50 minute presentation. She had over 50 slides, and only managed to talk through a couple of them, because each slide had tiny graphs and figures. I think it was frustrating to her, but also to us – we wanted to understand something she shared, but she talked very fast and it was difficult to see any details on the slides. In my mind, I think of that example as my reason to focus on only a handful of take-aways from a presentation. (I fail sometimes.)

Learning Goals for Guiding your Own Learning (as a grad student … and beyond?)

As a fifth-year graduate student, I have spent a great deal of time in the past four years completely overwhelmed by a program requirement or course assignment. It is easy to lose sight of the meaning of these learning opportunities, and I believe that many faculty are not focused on the learning goals and many faculty would disagree on the learning goals if they talked about them. I have tried to choose a learning goal that each assignment could support, and have successfully navigated each (so far). I would strongly recommend to other graduate students to think deeply about potential learning goals – what will you get from each project or assignment? Then re-evaluate you work regularly to see if the project is getting too big or if you are steering off-course.

That said, it is not always possible to reconcile your chosen learning goals with the learning goals of your committee, other faculty, or other graduate students. Try to argue for you perspective, but be open to other interpretations. And remember that at the end of your program, you will have to defend the choices you make. If you had no choice but to let others make choices for you, it could be difficult to explain – so make sure to talk to others to make sense of those “other” choices.

Navigating Grad School: Power and Communication

Over the past few years, I’ve spent a lot of time confront my own misconceptions about how to communicate with people who I feel hold power over me. Power can be real or imagined, but in grad school when you typically have about half a dozen “bosses” at any given time. I’m going to define “my boss” as someone who can tell me what to do and reasonably expect that I will do it or face unpleasant consequences like withholding money or dropping a grade or giving a poor evaluation. And then my boss is also someone I report to, who tells me I’ve done good or bad / right or wrong, and who – if they disagree with my choices or strategies – can cut me off in mid-stride and send me a different direction.

So, generally over the past four years I have had at least one boss per assistantship each semester, sometimes two. I have often continued on a project after my assistantship has ended, receiving hourly pay or volunteering my time. I consider the instructors of my courses as “bosses.” I also consider my advisor as a “boss” as well as committee members (to some extent, although advisor is “main boss”).

One of the difficulties with bosses is that most bosses in grad school don’t see the power they have for good or for bad and generally do not wield their power in thoughtful ways. On the other hand, it’s easy for me, as a grad student, to be overwhelmed with a sense of my bosses’ power. Partly because sometimes a boss is in a bad mood for a completely disconnected reason and uses their power to cause pain and distress, and to threaten dire consequences. And then the next day the same boss is happy and has forgotten all about what they said the previous day. So, as a grad student, it sometimes feels like walking in a mine field, trying to learn the rules when there aren’t actually “rules.”

It shows up in communication.

For example, emails. I can’t tell you how many days and nights I have stressed because a faculty member should have responded to an email and did not, and I don’t know if send a reminder is disrespectful or how they will react to it. Sometimes, if I send a reminder email the faculty member is thankful and responds quickly. Other times, I have sent reminders over months before getting an answer. And the question becomes: Whose responsibility is the communication? Ultimately, I pay the price when communication lines go down, so I am responsible. (I do recognize that faculty are so busy and have no way to accomplish all their tasks, much less respond as quickly as I want them to every time.)

Another example is communication in meetings. Faculty are not always sensitive to the power that their questions, jokes, or statements have on grad students. I remember in my first year talking to a 4th year student who was almost in tears because her advisor had made a joke that might mean she would fail comps. It’s easy for faculty to forget that we are often in situations that are high stakes, where we have little control, and where we don’t know the parameters because we’re doing it for the first time – that is, because we don’t know the parameters and because we haven’t seen successful and unsuccessful strategies, we don’t know whether our strategy is even close to reasonable.

A final example is communication about interaction. As a graduate student, it is difficult for me to tell the faculty around me when things are going well or poorly. Partly, I find it difficult because I am afraid and the fear is not always justified. Partly, I find it difficult because sometimes saying something has drastic repercussions. So, even though sometimes talking helps a situation, other times it makes it far worse, and there seems to be little consistency.

I try to think about what I can do when I am a faculty member and when I am an advisor. How can I create a situation where my students feel comfortable with helping me become a better mentor?

Meeting Paul Cobb

What advice do you have for new researchers?

Young researchers that go to research universities fixate on tenure and the checklist they need to complete to earn tenure. The first few years can easily become an identity-shredding experience. The wrong game is: “How can I get ahead?” Also, don’t write a proposal just to get a large grant. Think about your pre-tenure years, instead, as six years to work on something that you actually care about. Ask yourself: What you want to understand? What aspect of your practice do you want to improve? Because, if you care about it, you will work hard because it’s something you want to do. Don’t entirely forget about tenure – but don’t fixate on hitting a number of papers. Write quality papers that result from interest rather than weak papers resulting from “gotta”. As you plan, think about: Why did you come into this program to start with? What do you care about? Be aware of the danger of focusing on yourself in an ego way. Instead of thinking about how you can be a star, do work that you are interested in, task-involved, focused on doing good work. Also, in your first years don’t try to get a large grant but instead start with a small enough project so you can be intimately involved in all aspects of it.

What do you know about writing now that you wished you had known?

I wish I had know to outline, in detail, my ideas and argument. You should do this detailed outlining, pretending you are giving a presentation. You can use PowerPoint, for example, to create the outline. You should share your outline with others – meet with someone and talk with them through the outline. As you talk through the outline, pay attention to the structure of the argument: Does the structure make sense? Struggle with sentences: What is the next step in the outline? How do I say it appropriately? Instead of focusing on the question: What am I going to do next? focus on What do I want to figure out? Why am I doing this? What do I want to get a handle on conceptually? As you think about these questions, write a purpose statement for yourself: By the end of this, this is what I want to learn. This is what I’m doing to support that. This is why what I’m doing will help me reach my goal. 

As a grad student, how do I know when I should publish something?

As you publish papers, you will develop a better sense of when something is ready for publication, but there are no guarantees that you will be accepted. The main thing is, as you develop a reputation, you don’t want to submit a paper that is truly awful and then the editors know who you are and will remember how bad the paper is. But as a graduate student and new researcher, you have no reputation and you have no sense of when a paper is ready. So just try to publish it. If it gets rejected, or if it’s terrible, no one knows you and they won’t remember. Then you can develop your sense of when the paper is “good enough” that it won’t embarrass you, and when it is a “good fit” for the journal.