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To be entrusted with the development of a PhD student is the most important and gratifying aspect of my professional life. With this honor comes a tremendous responsibility to shape experiences that foster my students’ curiosities and passions for studying our field’s most complex problems, while concurrently developing their research abilities, knowledge and intuitions to design and conduct studies that generate novel findings. There are many students who become technically good researchers, however, relatively few develop the expertise and intuitions that result in their making significant advances in their field. It is therefore my responsibility to support my students’ development into careful and reflective researchers who are equipped to meet this challenge.
Students’ advancement under the mentorship of a faculty mentor is largely shaped by what they experience during collaboration with their mentor. This puts a heavy responsibility on the mentor to hold herself to high standards while crafting experiences for students that lead to their experiencing the power of collaboration, and the responsibility of making meaningful contributions to the refinement of research products. During interactions with my students I create an environment in which they become confident and comfortable in challenging my and each other’s thinking, and I convey that it is through having their thinking “pushed” that they improve. These intense collaborative experiences, that result from our striving for excellence in our work and products, is what frames our interactions.
Each new graduate student begins the graduate school journey with unique interests, talents and experiences. A good mentor will select experiences within the realm of her expertise that are developmentally productive for advancing that student’s knowledge of and ability to tackle important problems of a field. Gaining both the expertise and confidence to speak with authority relative to a problem in a field is an emergent process that results from deep reflection, focused study and ongoing research in a particular area.
I see my role as a mentor as facilitating each graduate student’s transition from viewing himself or herself as a consumer of knowledge to someone who advances knowledge. This dramatic transformation in students’ identities begins (if it begins) during their interactions with their graduate mentor. Rather than treating students as if they must prove themselves to me, I attempt to convey an attitude that all students are capable of performing at a high level. Then through regular interactions as we work on research problems and products, I provide direction and make demands to support them in succeeding and transforming into a better thinker, writer and researcher. This approach to mentoring has always been natural for me because this is how I was treated as a student. The greatest gift that my mentors gave me was to set high and meaningful standards for performance and then to support me in attaining those standards. Each new project or request to perform was followed by deep engagement that resulted in the refinement of my thinking, products and intuitions, and these in turn led to continued shifts in my identity as a scholar in our field. As a result, it is my imperative that all of my graduate students experience many challenge-support-success cycles prior to finishing their PhD.
During the first semester of working with a new mentee I engage the student in the current research in my project. We discuss the background literature and the rationale for my current research focus, and the specific findings that led to my current line of inquiry. Concurrently I select and shape experiences for my students to engage them in an aspect of my inquiry, beginning with their working with me to design and conduct small scale investigations in which they participate in discussions of the primary theoretical constructs, methods and tools for collecting, analyzing and interpreting their data. Subsequent to their investigation they present and defend their methods and findings in our mathematics education seminar. As my graduate students progress through our program I adapt my expectations and regularly reshape their experiences so that they become more and more knowledgeable of the complex problems of our field, and better and better equipped to tackle them. I regularly engage my students in discussion and reflection about critical problems that are worthy of investigation. I also work to support them in selecting a research focus for which they have passion and that has potential to have a significant impact in advancing the knowledge and practices of our field.
I expect all my PhD students to be dramatically transformed through their research and development experiences with me so that upon graduation they strive to assume a leadership role in our field. It is also my goal that they view their dissertation project as only an initial step in a lifelong pursuit of new knowledge that will assure the ongoing improvement of their effectiveness in whatever position and role they assume. This does not mean that I expect all my students to pursue the most competitive research positions, although it does mean that I expect them all to continually leverage their research knowledge and experiences to achieve excellence in whatever position they pursue. Through working with me they come to appreciate the important role that research plays in advancing both the practices of our field and their individual effectiveness as a mathematics instructor and curriculum developer.
All of my former PhD students are making unique and substantive contributions in their current positions—I am proud of them all, and take great joy in learning about their many accomplishments. As a few examples, one of my recent graduates, Kevin Moore, was hired to the top research position in our field in the year he graduated, while another student, Sean Larsen, accepted a mathematics education research position at Portland State University so he could work closely with mathematicians, and a third student, April Strom, elected to continue her position as a faculty member in a local community college. All three of these graduates have emerged as exceptional scholars, instructors, curriculum developers, and mentors in their own right and in their own setting. Because of her passion for improving teaching and learning for community college students, April Strom elected to retain her resident faculty position at Scottsdale Community College after graduating. Since completing her degree she has spearheaded and established a mathematics education research arm for the national organization of mathematics professors at two-year colleges. She also received an NSF research grant totaling $8.7 Million over a 5-year period. This is the first large NSF research grant ever awarded to a community college faculty member in the NSF Mathematics and Science Partnership program. Sean Larsen received a prestigious NSF research grant that was based on his dissertation project, and was recently invited to edit a special issue in a top journal in which he reports a sequence of studies from his dissertation and subsequent studies. Kevin Moore is hosting and is a lead presenter at an international conference in an area of research that was the focus of his dissertation.
When recruiting graduate students I make a special effort to target students who are from communities in which few students pursue advanced degrees (e.g., Irene Bloom, Nicole Engelke, Sean Larsen, April Strom), since I know first hand the many barriers that must be overcome to continue one’s academic pursuits after having attended a small rural school with low academic standards, and me being the only student from my graduating class to complete an undergraduate degree. I encourage all of my PhD students to reach out to students and teachers in rural and inner city settings with low academic standards. Opening academic doors for others who are less fortunate is central to my work. Since mathematics is often the barrier that denies students access to an advanced degree, my passion to improve the quality of mathematics teaching and learning in schools and universities stems from my desire to make education accessible to all U.S. citizens. When I learn how my former students are impacting the lives of others through their outstanding teaching (and many awards), research-based curriculum development projects, and graduate student mentoring I am very gratified to learn that my mentoring is making a difference that reaches well beyond the lives of my mentees.