Mathematics

Mastery-Based Grading Through the Lens of Ignatian Pedagogy

Eric Bucher
Mentor: Bin Yu (Department of Political Science)

Acknowledgment. I would like to thank my mentor Dr. Bin Yu for her guidance, support, and insight
throughout this project.

1 What is Mastery-Based Grading?
Our goal as educators is simple. But often simple to state goals are the hardest to accomplish. We want our students to learn. It is what pushed us into the careers that we are in and it is what drives us to pursue self-improvement every semester.

Often I find in my classroom that something gets in the way of true teaching, and that is evaluation. How do we
know when our students have truly learned something? What does that look like? In this article I will speak from
the perspective of teaching in a mathematics course.

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Statistical Inference

Max Buot, Ph.D.
Mentor: Nancy Bertaux, Ph.D. (Economics)

I attempted to incorporate the Ignatian mission into the Statistical Inference (MATH 312) class I taught in the Spring 2008 semester. This course is typically offered every two years, and is aimed at advanced majors in mathematics, especially those undergraduates who are interested in pursuing advanced degrees in statistics. Although the list of topics in MATH 312 is typical for such a course, my effort to include Jesuit values made it a unique pedagogical experience.

To be honest, I found the task of explicitly demonstrating the Ignatian mission in an upper-level statistics course to be challenging. In my view, fulfilling this responsibility would require creative and careful planning to ensure that the course remains true to its objectives: introduce abstract statistical theory, prove the main results rigorously, and apply the results to solve a wide array of data analysis problems.

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Mathematics and Democracy - Student Reflections on the Case for Quantitative Literacy

Minerva Catral, Ph.D
Mentor: Thomas Wagner, Ph.D. (Communications)

Acknowledgement. I am grateful to David Burns for his encouragement and guidance, and much thanks and appreciation are due to my mentor, Thomas Wagner, from whom I have learned so much this past year.

1. Hopes and Goals
One of the wonderful pluses in being at Xavier is that there is no lack of opportunity for growth--expansion outside one's discipline and comfort zone is a process that continues on. I came into the Ignatian Mentoring Program (IMP) bringing with me my own (limited) expertise in my chosen field of study, with the goal of getting a broader general view from interactions and discussions with colleagues who bring with them their own expertise in their respective disciplines. The hope then is that this widened perspective might translate to a more informed instructorship and a more effective teaching and learning environment in the classroom.

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Mathematics and Social Justice-Creating Awareness of Social Issues for Pre-service Teachers

Carla Gerberry, PhD (Mathematics and Computer Science)
Mentor: Laney Bender-Slack, EdD (Education)

Goals of the project:

For this project, I had two goals. The first was to infuse my class with the Ignatian pedagogy. The second was to use this pedagogy in order to raise awareness, in my pre-service teachers, about the issues facing those who live in economically poor areas.

The Ignatian heritage highlights reflection, discernment and solidarity and kinship. These are key elements of teaching for social justice. At Xavier, we strive to help students think about others in new ways. As future teachers, it is important for my students to have a heightened awareness of issues they will face besides just teaching their content. Their students will come to them with an outside life and that will influence who they are in class. For those who choose to teach in a high-needs school district, this will be even more important. Issues of homelessness and home life will be more prevalent. Being aware of this will enable my students to be more sensitive and understanding of their student's lives and allows them to stand in solidarity with them.

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Allocation of Charitable Resources: A Practical Illustration of
Quantitative Literacy's Role in Ignatian Discernment

David J. Gerberry, PhD
Mentor: Richard Mullins, PhD (Chemistry)

As the Jesuit values of Xavier University were a significant factor in my decision to join the
Xavier community, I was excited to participate in the Ignatian Mentoring Program (IMP) during
the 2014-2015 academic year. In my first years at Xavier, I felt that I had imparted the Ignatian
principles of discernment, compassion and care for the whole person primarily through one-on-one
interactions with students. While I plan to continue to do so, the IMP has shed light on ways
that I can incorporate Jesuit values directly into the classroom setting in a way that is genuinely
connected to the mathematical aspects of a course. I would like to acknowledge my mentor, Richard
Mullins, as I have benefited greatly from his guidance and experience.

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The Secrets to Peace and Joy: Change Myself by Love

Huizhen (Jean) Guo, Ph.D.
Mentor: Daniel Otero, Ph.D. (Mathematics/Computer Science)

I am a happy person. You may ask why I am happy.

Am I healthy? I am not very sick but I am not strong either. I always feel cold and wear much more than other people do. I need more sleep than other adults do. That is the reason I exercise on a regular basis.

Am I rich? I am certainly not poor; I have food to eat, clothes to wear, and a bed to sleep in. I am satisfied with my living conditions, but I am definitely not rich.

Do I have a happy family? My daughter and I often sing the song "I love you; you love me; we are happy family," and we do love each other and get along well, but my husband has not been living with us for many years, he is not eligible to work in the United States.

How about my work? I do enjoy teaching and my students, but my students do not seem to enjoy their classes that much and I have been working hard on that.

The reason I have joy and peace in mind is that I have faith in God's will, not my own will. God will lead my life. I love God and people as Jesus did. Because of my love, I am willing to change myself: changing my thoughts, perspectives, the way I look at the world, the way I look at other people. Just as the Bible says that all things work together to benefit those who love God, I would like to share what I have experienced spiritually with anybody who reads my article.

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Adding Explicit Ignatian Pedagogy to a Women in Mathematics Course

Christina Hammersmith, MS
Mentor: Stephen Mils, PhD (Chemistry)

The course and goals

My goals for this project were three-fold: infuse Ignatian pedagogy into a mathematics course, be explicit when the course has incorporated or addressed tenants of the Jesuit mission (thus increasing students’ awareness of them) and encourage solidarity and service to underserved communities within the STEAM fields.

Math 125, Women in Math, is a mathematical survey course that meets Xavier’s core Mathematical Perspectives requirement. The course introduces students to historical female mathematicians and explores topics in mathematics that influenced and were influenced by their work. The course is rooted in the Ignatian principles of Solidarity and Service Rooted in Justice by highlighting the lived experiences and mathematical contributions made by underserved members of STEM community. The only prerequisite knowledge for the course is basic arithmetic and algebraic skills, so the course has a secondary goal of showcasing mathematics as an exciting and varied field of study.

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Ignatian Pedagogy: Connecting Biology Majors to Mathematics

Hem Raj Joshi, Ph.D.
Mentor: Lisa Close-Jacob, Ph.D. (Biology)

Super goal:

• Facilitate Understanding in Personally Relevant Manner
• Magis - Novel Ways to Serve Students and University by Trying New Things
• Cura Personalis - Considering Needs of Students
• Challenging Students to Connect Topics

The discovery of the microscope in the late 17th century caused a revolution in biology by revealing otherwise invisible and previously unsuspected worlds. Mathematics broadly interpreted is a more general microscope. It can reveal otherwise invisible worlds in all kinds of data, not only optical (Cohen, PLOS Biology, 2004). For example, computed tomography can reveal a cross-section of a human head from the density of X-ray beams without ever opening the head, by using the Radon transform to infer the densities of materials at each location within the head (Hsieh, Computed Tomography, 2003).

The importance of mathematical and computational tools in every area of biological studies is well documented (Levin et. al, Science 275:334-343, 1997). Mathematical and computational challenges in population biology, ecosystems science, and epidemiology in particular have long been recognized. With new conceptual advances and technology, research initiatives that focus on integration of mathematics and biological issues are expanding very rapidly. There is a general and diffuse dissatisfaction with mathematics among the biologists (i.e. why I need math?). Today biology is becoming more mathematical, and all biologists need some mathematical skills to understand complex biological systems.

We would like to explore results from different biological experiments and connect them to relevant mathematics. To achieve this we will communicate with Biology faculty and develop a need based course (i.e. Teach mathematical skills that will be useful for biology majors).

Why should biology students study more math? There are two types of reasons:

Abstract reasons

• Improve logical/rigorous reasoning ability
• Ability to build models
• Better appreciation of mathematics and computation
• Appreciation and understanding of important phenomena: exponential growth and decay, limited growth...

Concrete reasons

• Ability to perform important mathematical operations
• Learn to interpret graphs
• Ability to analyze data: Statistics

Designing a New BioMath Course for Xavier University

As a first step we will modify the existing calculus-based math course, and it will be offered for the first time in fall 2005. This course will help biology majors to understand the importance of mathematical models in biological sciences and use the knowledge in biology research projects. In the future, we will develop an entirely new math course for the biology major.

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Ignatian Pedagogy in Collegiate Mathematics Education

Joy Moore, Ph.D.
Mentor: Leslie Prosak-Beres

During my participation in a Manresa Experience in the Fall of 2007, I was introduced to the concept of Ignatian Pedagogy. Considering myself to be a practitioner of culturally relevant pedagogy, I was struck by the similarities between the two pedagogical approaches. I became interested in viewing my classroom practice through the lens of an Ignatian pedagogical framework. I have always maintained a reflective journal of my classroom practice and so I decided to use that as a place to begin accounting my observations. I made journal entries during the Fall and Spring semester of the 2008-2009 academic year, presented here in summarized form. The courses discussed include MATH 120 (Elementary Functions), MATH 150 (Elements of Calculus I), MATH 201 (Foundations of Arithmetic for Early Childhood Education) and MATH 211 (Foundations of Arithmetic for Middle Childhood Education). 

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Statistics and Privilege

Grigory Sokolov, Ph.D.
Mentor: Haider Raad, Ph.D. (Physics)

Brief Introduction and Motivation.
Being a mathematician (half statistician, half probabilist) myself, I find myself at the very beginning of the journey to expand my teaching style and to view my subject as something more than just a framework to interpret and understand the world we live in. The beauty I see in a theoretical---and often abstract---mathematics is a thing that is challenging to express and communicate to somebody else, especially if they are a student. And it is also quite hard---at least for me---to connect and relate to the Ignatian values.

Teaching at a Jesuit school, one should seek to expand their views and embrace the opportunity to provide more to their students than merely the subject they teach (however abstract and seemingly disconnected from “real” life). In that respect, I am quite lucky---especially with my core-level classes---as statistics is a topic that shows up in virtually every aspect of our everyday routine.

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