When and how did you know you wanted to study mathematics education? Gutiérrez: In my senior year of college, I was a biology major, had already taken my MCATs, was working at Stanford Hospital, and applying to medical schools. I was focused and knew exactly where I was going. But, at Stanford, they want you to be well rounded, so they make you take all of these courses in areas you might not normally study, such as ethics, society, and art. For every one of those mandatory areas outside of science, I found ways to make them work for my very narrow-minded view of only wanting things that would help me become a better doctor. For example, for the course in ethics, I took bioethics. But in order to graduate I still needed one last course to fulfill the art requirement. My advisor had heard of a good professor in art education, Elliot Eisner, who offered a course on the Artistic Development of the Child. I wanted to become a pediatrician and thought maybe I could have my patients draw their pain. While I was in that course, I remember fighting a lot with the professor. He was world-renowned and one of the founders of the field, so other students just looked at me wondering how I could argue with someone so esteemed. But there were views discussed that didn't map onto my experiences or my family's, and I wasn't worried about getting a bad grade because I was planning to attend medical school and was really just checking off a box to graduate. After many arguments and many office hours, that professor and I became close. He respected that I stood my ground on things, especially providing views that other students hadn't heard (at the time Stanford was three percent students of color). Toward the end of the course, he said to me, "You know, Rochelle, you could become a great doctor. You are analytic, meticulous, and passionate. But, why not try something really difficult…like education?" It should have been obvious. I had always loved puzzles, logic problems, and finding patterns all around me, especially in nature. In my free time, I was tutoring other kids in mathematics, working in programs like Mathematics Engineering Science Achievement (similar to Upward

Using a combinatorial bijection with certain abaci diagrams, Nath and Sellers have enumerated $(s,ms\pm 1)$-core partitions into distinct parts. We generalize their result in several directions by including the number of parts of these partitions, by considering $d$-distinct partitions, and by allowing more general $(s,ms\pm r)$-core partitions. As an application of our approach, we obtain the average and maximum number of parts of these core partitions.

Using a combinatorial bijection with certain abaci diagrams, Nath and Sellers have enumerated (s, ms ± 1)-core partitions into distinct parts. We generalize their result in several directions by including the number of parts of these partitions, by considering d-distinct partitions, and by allowing more general (s, ms ± r)-core partitions. As an application of our approach, we obtain the average and maximum number of parts of these core partitions.

FOIL is a well-known mnemonic that is used to find the product of two binomials. We conduct a large sample (n = 252) observational study of first-year college students and show that while the FOIL procedure leads to the accurate expansion of the product of two binomials for most students who apply it, only half of these students exhibit conceptual understanding of the procedure. We generalize this FOIL dichotomy and show that the ability to transfer a mathematical property from one context to a less familiar context is related to both procedural success and attitude towards math.