Appearing at regular intervals in YFile, Open Your Mind is a series of articles offering insight into the different ways York University professors, researchers and graduate students champion fresh ways of thinking in their research and teaching practice. Their approach, grounded in a desire to seek the unexpected, is charting a new course for future generations.
Today, the spotlight is on Tina Rapke, a professor and researcher jointly appointed to the Faculties of Education and Science.
Rapke’s research is focused on developing and testing classroom-based strategies for teaching and learning mathematics.
Q. Please describe your field of current research
A. Most of my research is about teaching and learning mathematics. I usually focus on situating and studying some cool strategies that I see in classrooms within the literature, and developing and testing strategies based on current literature. Actually, a lot of them are researched right here in York University classrooms.
Q. What inspired you to pursue this line of research? Who or what sparked your interest in this line of inquiry?
A. I teach mathematics courses, mathematics education courses, and publish in education journals. It seems natural to do research that allows me to satisfy several of my academic responsibilities. Developing teaching and learning strategies based on current literature, trying them out, and conducting research about them in my own and my colleagues’ classrooms lets me do just that. Plus, I had a really great doctoral supervisor that does similar things. I’ve learned from the best!
Q. How would you describe the significance of your research in lay terms?
A. The research I am involved with is about enhancing the learning and teaching of mathematics. Wow, that’s pretty vague.
Let me give you an example from my own postsecondary classroom. The literature on assessment has inspired me develop a strategy that involves students and their instructor developing exams. I really like the research concerning students as partners in learning and teaching in higher education. Anyways, students in my courses, through assignment work, create practice exams, provide full solution keys and write and evaluate each others’ practice exams. I then craft the “live/actual” exam by including some of the questions from the student developed practice exams. Students can then use their experiences of this process and their developed materials as a resource to prepare to write the “live/actual” exam. To see the full details of this process and to read student comments that evidence deep approaches to learning see one of my latest articles. I promise the paper is friendly to people outside of mathematics education!
Q. How are you approaching this field in a different, unexpected or unusual way?
A. I think there are two significant components to the research I am a part of. One is a focus on student thinking, and two, I’ve been mentored by and am surrounded by some amazing people. Ok, so let me talk about about student thinking. Some might say that in my projects, student thinking is viewed as a resource in the classroom and there is an emphasis on ways to elicit and build upon student thinking. To put it in another way, my research and teaching are inseparable from and formed by students’ thinking.
Oh boy, that was a lot. What am I trying to say?
Let me unpack this with another example from one of the courses that I teach at York University in the department of mathematics and statistics, which aims to prepare students for upper-level mathematics courses. The learning objectives of this course are about developing mathematical thinking. I have created an interesting strategy around the idea of reviewing after students take their exams.
After writing an exam, instead of handing back graded exam papers, I hand students back a photocopy of their exam that I took before grading it. I explain to students that they will be assigning a score to their original work and revising it on a question by question basis. The revising and grading of each question occurs after students completed an assignment where they consider, evaluate and provide feedback to anonyomized exam responses that I have selected. I select a few responses that I consider to be of high and low quality. I selected the responses in hopes to draw students’ attention to areas that I feel they are struggling (i.e. help them identify their own areas of difficulty) and to draw their attention to “good” ideas in hopes of offering students a “better” idea to pick up on. This does take a lot of time, but maybe you can try it with just one question you are particularly concerned with when grading an exam from you course.
Notice that this strategy is reliant on and shaped by student responses to exam questions, i.e. it is inseparable from and formed by student thinking. Furthermore, the development/adaptation of this strategy was inspired by some of the literature that talks about using summative tests in formative ways (see link.springer.com/article/10.1007%2Fs11125-014-9329-7).
My own experiences indicate that this process helps students make sense of the grade that I have assigned to their work before the process, and encourages further learning. Of course, we collected data and a colleague and I will be sharing students’ assignments and exams scores this summer at conference to make claims about how this review strategy can encourage learning.
Q. How does your approach to the subject benefit the field?
A. There is a very practical component to my research. Furthermore, I have been having a lot of fun doing work that focuses on student thinking. I love my teaching and my research. I hope others, after reading my work or chatting with me at conferences, will use some of the strategies in their own teaching, develop more research-based strategies and have as much fun and success with them as I do/have had.
Q. Every researcher encounters roadblocks and challenges during the process of inquiry, can you highlight some of those challenges and how you overcame them?
A. There is a certain “messiness” involved in classroom-based research. I better not go into too much detail here. What I will say is that things don’t always go as planned and that is what we should expect.J Just roll with it, or in other words, evolve with it. Find me around campus and I’ll tell you more “off the record.”
Q. How has this research opened your mind to new possibilities or new directions?
A. I am continually learning from and about students’ mathematical thinking. I am amazed by how focusing on student thinking can enhance mathematics teaching and learning.
Q. Are there interdisciplinary aspects to your research? If so, what are they?
A. Yes, I do research in mathematics and education.
Q. Did you ever consider other fields of research?
A. Yes, mathematics. I do publish graph theory results in mathematics journals.
Q. Are you teaching any courses this year? If so, what are they? Do you bring your research experience into your teaching practice?
A. In case you haven’t heard enough about my classroom-based research, my colleagues and I will be talking about co-teaching with each other at the Teaching in Focus conference here at York University May 19 and 20). We have had a great time co-teaching and developing other strategies together that focus on mathematical thinking that I have not outlined here.
Q. What advice would you give to students embarking on a research project for the first time?
A. Just “chillax.” Read lots and make your decisions based on existing literature.
Q. Tell us a bit about yourself.
A. I have two young children and a husband that I find to be hilarious. My mom lives with us, which allows for my husband and I to pursue our work. My husband and I are very thankful for having a live-in grandma! Our kids tell us that she is their best friend. One of my kids goes as far as to tell us that they are going to marry grandma – my husband teases my mom and suggests that she might consider someone who can buy her a drink. My family keeps me laughing all day long.
Unfortunately, my family is trying to ban mathematics education from our dinner conversation. Let’s just say it’s not working out so well for them.
Q. How long have you been a researcher?
A. Over 10 years but I consider myself an emerging scholar.
Q. What books, recordings or films have influenced your life?
A. I don’t read much outside of academia.
Q. What are you reading and/or watching right now?
A. My kids have a rule about only watching cartoons on our TV. I have become very good at tuning it out when reading academic pieces.
Q. If you could have dinner with any one person, dead or alive, who would you select and why?
A. I would like to have supper with myself in 20 years. I am excited about how much my perspectives will have changed and developed (and anticipating to feel a little humble and awkward about where I am now).
Q. What do you do for fun?
A. We are currently renovating my husband’s shop to include a poolside bar. Feel free to stop by for a pint and a chat about mathematics education.