Submissions for the Critical Analysis category should critically evaluate or analyze a piece of literature, a theatrical performance, a work of visual art, a historical moment, a philosophical argument, a social movement, etc. Submissions should not exceed 20 pages. Marissa Maldonado wrote the 2nd place submission in the Critical Analysis Category for the 2021 President’s Writing Awards.
About Marissa
My name is Marissa Maldonado and I am a passionate Native American student contributing to the realm of mathematics and STEM education. I am a thundering force of passion and curiosity, and I will never cease to represent my true self, nor will that be dampened by social norms within academia. I consider mathematics to be a genuine framework for my perspective on the human experience. I know that my passion in discrete mathematics will assist in developing productive academic curriculums in pure mathematics that will go on to help others see a more structured version of the world as well. The College of Southern Idaho’s previous president, Dr. Jeff Fox, once told me to “make my story survive”, so that is exactly what I am doing.
IDoTeach and Mathematical Pedagogy
Preface
There may have always been a slight serendipity to how I found myself working towards my bachelor’s in math through Boise State University’s IDoTeach program; at 21 years old, I find that my initial desire to earn an associate’s degree in computer science at 17 coincidentally led me to enrolling in more math courses than I ever had coding courses. I had laid out an ideal career plan for myself from the time I was rather young and took interest in front-end web development for designing sites and blogs online. The aspect that slightly guarded me from realizing my interest in science, technology, engineering, and math (STEM) was my continual interest in the arts – I wanted the power to design just as much as I wanted to build the framework for those ideas. I didn’t think it was possible to do both, but as I pursued my associates degree, I became entranced with all of the opportunities available at my junior college and began tutoring math and English as a freshman, followed soon after by taking on an internship as a web developer and graphic designer under the college’s Information Technology Department.
Throughout my three academic years there, I swiftly transitioned from an introductory algebra course to discrete mathematics to ordinary differential equations within a matter of six semesters. As time progressed and I became more involved on campus, I was elected Student Body Treasurer and I could feel my background in mathematics dominating the strategies I used within these jobs. It was empowering to have logic on my side and find underlying meaning in the numbers I encountered in such a way that it helped my community. It became increasingly obvious that my career path in computer science would always lead to me selling a product though, as marketing goes. There was not enough connection with others as I coded behind a desk tirelessly; yet the irony is that I found a strange amount of joy doing calculus III homework. I liked it so much that I asked my professor at the time how I could keep math in my life indefinitely, and he recommended I look into teaching upper-division courses in the future. It planted this seed in my heart, and I realized I could maintain the creative outlet I had always required through visual representation while still upholding core concepts of logic in mathematics.
With that being said: I deeply desired an undergraduate program that would support my complex and diverse goals as a student. When I perceive the world, I see a lot of variables existing as intertwined resources that can assist in pushing ideas forward. This required a balance between working directly with my community, finding professional development within my university, and studying a strong curriculum under passionate faculty. The IDoTeach Program checked all of my boxes, and although I never intentionally planned on teaching secondary education, I feel a deep sense of respect for students in adolescence as they navigate their growing world and changing identity. I knew that one day they may attend college and I want to know who is walking into my lecture hall. Simultaneously, I enjoyed coming back to the foundations of mathematics and renewing my perspective on any biases I have had within my own mathematics education. As I am gaining experience teaching in-person to high school classrooms, I am simultaneously applying these experiences in lesson development and student-based inquiry to my own upper-division courses in my mathematics degree.
Danielson Framework for Teaching
There is so much engagement and hands-on activity at the beginning of the student experience in mathematics, but as difficulty increases, courses have the ability to evolve into a silent classroom with only the squeaking of a whiteboard marker and the student’s pencils voraciously jotting down tedious notes. I am guilty for not minding such a class format at times, and, at one point, thought that was how math classrooms were supposed to be. Even within my first couple courses through the STEM education program, I began to recognize that I did not have to fit into this societal norm of what a math teacher should be, nor what their classroom should look like. With this realization came my pursuit to apply the Danielson Framework for Teaching (FFT) to my own pedagogy in mathematics (The Danielson Group). There are four pillars within FFT: planning and preparation, classroom environment, instruction, and professional responsibilities (The Danielson Group). This critical analysis serves as a philosophical representation for my connecting nodes of understanding within the diverse field of mathematics.
Planning and Preparation
Students deserve engaging and dynamic course lectures; even as a student myself, I thoroughly enjoy analyzing my own teachers’ lesson plans and seeing how that follows a larger philosophical component within the material. Something I desperately sought out in my pursuit of mathematics was some semblance of personal connection to the content. There is a beauty to the mechanical functions required in academia, and I loved that my curiosity continued even once lecture was over, but I knew there had to be more to my upper-division courses as I entered the fourth year of my degree. The FFT emphasizes a competence in knowledge and pedagogy (The Danielson Group), which is indeed necessary for a fulfilling classroom; yet even with competence, there is the possibility that such information does not have the correct mode of transportation to reach students. There must also be a curriculum productive enough to assess student outcome.
Future subjects I hope to teach are discrete mathematics and foundations of geometry. With this commitment involves the classroom metrics of student workload, breadth of content being covered, and recognizing which core concepts will best equip students for future applications of the subject. A large aspect of my mathematical pedagogy is the value in connecting proof writing abilities to student identity. Introducing students to proofs begins in high school geometry and has the ability to truly expand the metacognition of students as they prepare to enter college (Common Core State Standards Initiative). It is a skill to see the logic within one’s environment in the influence of their perception on the world. This relates to the idea of currere and the connection between subject and self (Pinar 6). When there is no discussion, no questions afterwards, it is then that the question must be asked of whether the curriculum was ever respectful to the notion of curiosity.
Although math exists as this intertwined being through virtually the entire human experience, I question if it is represented in its entirety to students. To avoid generalizations, I feel that technological applications can be a more accessible mode of learning in a classroom culture that used to strictly focus on rote memorization and the value of standardized testing (Robinson). Computer science also comes into play as students explore mathematical models – something that has been an enjoyable reconciliation to my previous career path. Design and user interaction can play a huge role in the efficiency of educational tools. A large part of such enlightenment in mathematics is sitting down and doing the work, and I hope for new discoveries in mathematics education to assist in building a less intimidating introduction to otherwise underrepresented students in the STEM field.
Classroom Environment
As I build an environment for my students where they are willing to be vulnerable in their learning, at all levels and abilities, I consider the work done by Maslow and his attempt to explain human motivation through the hierarchy of needs (Maslow). Now through the lens of a classroom: physical needs must be met in order to pursue further up the hierarchy and onto relational, personal, and intellectual growth (Maslow). When proper resources have been provided such that it builds a classroom environment capable of inquiry-based learning, this allows for a teaching structure that can offer a stable reality to students as they navigate their representation of self (The Danielson Group).
Throughout my experience in the IDoTeach program, I have come to realize there is a balance between structure and freedom in lesson plans such that the student is given a direction in which to go, but they have the opportunity to follow ideas elsewhere. When an IDoTeach faculty member is teaching a course, I know that there will be unique forms of engagement when exploring mathematical concepts in secondary education. As we analyze and take apart the details of lesson plans, I remind myself of my future goals in teaching upper-division courses and the value in “establishing a culture for learning” (The Danielson Group). I was initially fascinated by the idea of pursuing mathematics due to stumbling upon the concept of infinite knowledge as a senior in high school. And although it seems intuitive, it requires that I must practice math in order to learn it, and in order to learn it, I must practice it. I had this internal conviction that I must genuinely pursue both actions in order to move forward with my goals.
This applies to any topic a student may pursue, and it goes beyond the romanticization of grit and an overbearing academic workload. Sometimes intellectual growth comes from experience and connection with others – from the relationships we build in a classroom. It can come from perceiving passion in others and emulating that for oneself. There was a time in my college experience where I was an English and math tutor; as I passed my courses with good grades, I was permitted to tutor students in that subject. During lower-division math courses in my associates degree, I did not take into consideration the exact impact it would have on me to be coworkers with engineering and math majors at the end of their degree, passionately going back and forth, debating about proofs and quickly jotting down their concept maps on a whiteboard. I was a naive, sponge-like student who grew up to mirror such passion. Now I will stand in front of classrooms, finding reason behind logic, and hoping to connect with others as they dissect their own plane of infinite knowledge.
Instruction
The motivation behind my desire to integrate foundations of pure mathematics into secondary education curriculum lies in the fact that I felt rather unprepared for the majority of my mathematics degree, up until I pursued an emphasis in STEM education, in that there wasn’t an active conversation being had about how students would represent such tedious proofs they learn outside of homework. This is why students ask when they’ll use such information in the real world. I was one of those students and wanted to feel like I was valuing the time I put into my education! I challenged myself to relate logic problems on set theory to my daily life, and as I analyzed my thought process, I could see how these networks of connections had always been a part of me. My first proof-writing course was simultaneously taking effect on my cognition just as I was entering my term as Student Body Treasurer. As I prepared a budget analysis for the student councils and administration, I felt this intense comfort in that I understood how this set of data had a unique cause and effect that could never have been prepared for merely through rote learning and mundane worksheets.
This anecdote serves as a personal lens in how I came to love mathematics. These connections were made through experience, and teachers can format their classrooms to create such experience through engaging communication and philosophical forms of discussion (The Danielson Framework). There is value in following math standards and having structure, but allowing students to also have autonomy in their learning shows that they are active participants in their education and not simply a student ID number amidst a crowd. The challenging part about convincing a student, regardless of age, to care about mathematics is the necessity of what is deemed “busy work.” No matter how much I express my interest in philosophy and the personal interpretation of logic, assessing student progress with concrete data on their work will ultimately reveal how well they conceptualize theory and application. It is not about plowing through as many lessons as possible, but releasing the academic ego and truly assessing what framework of learning will best support students in their own endeavors.
Professional Responsibilities
Teaching is what grounds me in my curiosities. When I think of those who will attend my lessons, I know that I must represent my ideas in an organized manner in order to make an impact on students. I also enjoy the personal responsibility of looking after the cognitive growth of students and analyzing the work they do in accordance with the course curriculum. Their documentation contributed to my understanding of the world just as much as my lecture notes did theirs. Students have a right to communication with those who educate them and guidance on the work they do (The Danielson Group).
The aspect that I look forward to in teaching mathematics is the revisitation of ideas. As I mentioned earlier, when I was finishing up calculus III, I wondered how I would ever find the time to ponder on the subject again, yet here I am. Something that made my experience in relearning a math topic easier was my documentation. There was a peacefulness to nudging through old notes, adding unique information to new ones, and representing these ideas through artistic pursuits. With my background in graphic design, I enjoyed displaying information in cool layouts, so I began to make collages of relative math topics and philosophical frameworks using corkboard, some construction paper, and thumb tacks. It felt whimsical compared to the usual documentation I had in my coursework, but I honestly felt closer to the subject after beginning these creative math pieces. This pursuit is only a recent endeavor, but I think my experience in the IDoTeach program made me feel a willingness to try a new framework of learning for myself even if it did not follow the status quo of upper-division mathematics courses.
Now that I have been in my degree long enough that I have a decent foundational understanding of algebra, calculus, geometry, proofs, etc., I feel that attending seminars and colloquiums outside of my program are more of a cognitive playground for me. As the difficulty in my courses increases, I am able to make more connections between my education, career, and community such that soon enough I will also be able to contribute to larger bodies of work and push those ideas forward as well. Professional development in academia feels like I am contributing to more than just myself, but my educational curriculum and the students involved.
Mathematical Pedagogy
Truth be told: I grew up in a rural town in southern Idaho. I was very involved in extracurricular activities throughout high school, but I lacked any sort of drive to even begin thinking about applying for college. I had failed algebra II, modestly passing on the third try. Although I pulled myself up by the bootstraps for college out of sheer stubbornness to one day have a job I loved, I began as an unengaged student who sat in the back of the classroom. My teachers allowed me to stay this way, there was never any interjection of whether I could be something more. I say this beyond some heartfelt gesture, but as a lesson learned that the kids in the back of the classroom who won’t speak up are the ones who need such connection the most. It can be challenging to have students reflect on the philosophy of currere, the connection between subject and self, if they are not particularly aware of their own identity in the first place. This is where human connection and communication matters. A classroom can exist as a tool to lift students up and to believe that they can create valuable work as an extension of themselves. I have experienced this through the IDoTeach program at Boise State University and I believe that my story should survive.
Works Cited
Common Core State Standards Initiative. “High School: Geometry.” Core Standards.
The Danielson Group. “The Framework for Teaching.” Danielson Group, 2021.
Maslow, Abraham. “A Theory of Human Motivation.” Psychological Review, vol. 50, no. 4, 1984, pp. 370-96.
Pinar, William. The Method of Currere. American Educational Research Association, 1975.
Robinson, Sir Ken. “RSA Animate: Changing Education Paradigms.” YouTube, RSA.