the wiel to learn

(originally submitted as a final output in the ateneo's cepp 313 – education for faith and justice: moral and spiritual formation)

Introduction

As an educator and formator (who is Catholic), I hold a deep responsibility in shaping the character and moral growth of those around me. This vocation is not simply about:

being an expert in the field of mathematics,

developing my students’ logical and overall critical thinking skills,

encouraging my peers and colleagues towards excellence,

meeting the minimum expectations from me at the university,

but it is about driving and nurturing everyone I encounter to become ethically grounded and advocating for inclusion and justice for all through developing personal and communal growth. In embracing this ideal, I recognize the pluralistic nature of my whole experience: with faith on one hand and with the nature of academia on the other. With these, I frame my philosophy as an educator and formator in three levels: for myself, for my students, peers, and colleagues, and for the university.

For Myself: Looking in for self-awareness

My journey as a formator is rooted in my desire for a holistic understanding and continuous growth while keeping true to myself. A wide range of knowledge and constant improvement are necessary for me to fulfill my role in higher education effectively. This requires introspection and lifelong learning. As such, it is essential for me to practice what I teach: integrity, empathy, and humility.

Keeping true to myself requires me to always think, both consciously and subconsciously, of my background, values, and ideals in that they should inform what I do. Though my past did not enable me to be the activist on the streets that connotes the UP student, the spirit of activism, acting for social justice and reform whenever and wherever the situation calls for it, is inherent within me. That could be for me looking into the experiences and contexts of mine, looking around the same for my friends, family, and community, looking out for the same in other people.

Continuous growth is necessary to my vocation, but also for me to be truly living. Without it, what one has is stagnation which is a life sentence to me. Having said that, just continuous growth is not enough for me. It must be complemented with an ability to reach a comprehensive understanding of how the world works. This does not mean knowing-it-all but it is the ability to recognize that there is always a bigger picture in an open system where every little thing could affect something greater.

Personal integrity is important in my philosophy as it requires me to act with self-awareness and consistency. Otherwise, I will be ridden with guilt. While empathy usually connotes putting oneself in other people's perspectives, I extend this to my two different personas: one desires sustained excellence (the professional), the other knows when to stop (the introspective). My humility is guided by my personal mantra, “made from stardust ✨ ️”, from dust I rose, to it I shall return. This mantra grounds me whenever I forget myself in the life process.

For My Students and My Peers: Brewing with discernment

For my students, my role extends beyond their grades. Beyond teaching them calculus and methods of proof, my ultimate goal is to cultivate individuals who are grounded in the realities of the world and have integrity, capable of empathy, and living a life of service. As a consequence, I expect them to be the change they want to see in the world – a transformation of not only themselves but also their friends and family, their community, and soon enough, the world. Only through formation can this be achieved.

In practice, I give them space to breathe in my classes through managing time and scheduling day offs from both face-to-face and online sessions. This is a time for them to sleep, reflect, think, rekindle their hobbies and passions, and other things they may want to do. Similarly, in my classroom, I give them time to learn individually, with their classmates, and as a whole class. Learning and formation is possible even from the mistakes of others, emphasizing that mistakes do not make anyone less of a person but are opportunities to grow instead.

For my peers and colleagues, I extend the same essentials. With me learning from the breadth of their experience and them learning the possibilities from my ideas, we create a feedback loop, as shared responsibility for everyone’s continuous formation and growth. Our individual integrity forces us to into this shared responsibility for consistency in words and action. Our personal practice of empathy allows us to understand one another and most especially our students as a group. Our own and collective humility transform us by being able to see our mistakes, then correct ourselves and our processes and learn from it in the process.

For my peers, my students, and I to be lifelong learners striving for service, the whole university system and the forces that support and enable it to fulfill its mandate must create opportunities for us to develop our service mindset.

For the University: Looking out for others through service

The university’s motto of Honor Excellence has stood ground through the years, but as part of its mandate, the university should strengthen and espouse service to the people, the country, and the world at all levels of the university. Its history and culture of activism for the people, serving the people, and its students being Iskolar ng Bayan para sa Bayan should now become more concrete, structured, and inherent in the dealings within and outside the university.

As an educator and formator (who is Catholic) in this secular institution of higher learning, the irony is not lost on me that superficially, my context has contradictions, but we can learn from (all) religion(s) as revealed by Catholic formation and religious education. As a start, religious education, Catholicism, and Ignatian spirituality may serve altogether as inspiration of the formation of our people in light of the “breadth of mind, strength of character, and generosity of spirit” we desire from UP students when they graduate. Even if this inspiration is rooted in just one religious tradition, the results that it could offer us are still secular, universal, and a beginning of an enriched spirit of public service in the university.

As individuals, as a community, and as an institution of the Philippine democracy, the University must:

look in: look back in its history and present and how it navigated the respective times

brew: learn from the actions of yesterday and today, what worked and what could have been done better

look out: use the learning to prepare of possible futures, create roadmaps that seek to develop honor, excellence, and service in everyone inside and outside of the university.

The hidden curriculum allows students to develop soft skills beyond what the formal curriculum offers them to do so. Moreover, the school hierarchy itself exposes the students early on to the corresponding hierarchies that exist in society.

This structure, on the other hand, perpetuates and, possibly, inculcates to the students the faults in our modern society. Traditional gender roles, (c)overt caste systems, and racial biases may be evident in the language, narratives, and illustrations we use in class.

It is crucial that we emphasize the nuance of the hidden curriculum in school to mitigate the cons and utilize the pros of the hidden curriculum.

when we can't optimize, we satisfice (satisfy+suffice).

i personally do not like that anyone in the uplb faculty has to resort to this, but the teacher was left with no other ethical and moral choice, hence, the satisficing.

the issue of limited slots in courses is not new. i vividly remember being one of the summer students in 2010 ̶b̶e̶g̶g̶i̶n̶g̶ queuing for a slot in nasc 10 (forests as a source of life), a general education (ge) course and the lone ge out of ~27 offered that summer at the heart of the makiling forest reserve. from 160, the class size became 220 due to the teacher's prerogative, an institutionalized mechanism in the up system where a professor (in this case, a team of faculties-in-charge) may accept additional students on their own volition.

it has been at least a decade and this problem lingers. increase faculty items, decrease class sizes, more facilities - a few of the possibly many solutions a true national university deserve.

ariel m. bombio on facebook

the pioneer cohort of ed.d. and ph.d. educ at ateneo gbseald with dr. ma. assunta "achoot" cuyegkeng / screengrabs from markkie aribon and lavi subang of ed.d.

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i told the internet about why i am where i am now in a previous post. now, i am ready to share what invaluable knowledge i've got from one of my courses so far.

during my undergrad and graduate studies, just pen and paper is mostly sufficient to create new ideas, problems, and solutions, and do research in math, but that's not the only concern i have with life and work.

for the past half a decade or so, peers and i saw a decline in the perceived quality of students in calculus at the university of the philippines los banos. what was supposed to be tackled in senior high school, like algebra, trigonometry, and precalculus especially for those from stem track, wasn't adequately done so. when introduced to fundamental calculus concepts, they do understand the notion of limit, how lines and derivatives intertwine and entangle, and why area is an integral, but when it comes to crafting solutions and answering problems, this inadequacy becomes apparent.

in turn, it becomes necessary for us to ask why this is the case? how do teachers influence their students' calculus learning and what are they doing to adapt? has existing policies done us (dis)service in the philippine (math) education? and, why is everybody and nobody at fault here?

just thinking about possible solutions is not enough. we need to get our hands dirty, wreck some established norms, and possibly hurt some feelings in the process. qualitative research, i learned, has some of the answers.

as i mentioned in a previous post,

hi, i am wielson from the internet.

for the longest time, since 2009, i've been studying mathematics for itself, mostly without numbers, just logic and reasoning. i'm a novice graph theorist who never had training in it inside any classroom. i chose this topic because i was able to understand it on my own.

every day, i live in this construction charateristic of any theoretical undertaking in mathematics called axiomatic system that consists of truths we assume to be true without question (axioms, thus the term axiomatic), from which all logical statements (theorems) come through deduction, characterized by consistency, independence, and completeness (which happens to be incompleteness, a story for another day). set theory, calculus (or, more formally, analysis), euclidean geometry - all these are such systems. these are all closed systems in the sense that nothing can bend truth within each of them; in the case of euclidean geomety, bending the parallel postulate did not affect the truth within; it just gave birth to new axiomatic systems. axiomatic systems do not need statistics (not talking about the theory), any experiments, or interviews.

to an extrovert who needs time to recharge sometimes, this realm of mathematics is a great escape from the world's, and mostly life's, problems, one captivating theorem or calculation at a time. as one can tell from the title of this post, my escape has been temporary; like a child in a game of tag running away from an it, sooner or later, they'd be caught.

and i was caught

the different backgrounds of the teacher (e.g., education and instructional quality), the student themselves (e.g., beliefs, attitudes, knowledge and foundations, economic background), and the university and the greater social context (e.g., public, or private; delivery modes; assessment and grading schemes) affect the learning of the students as well as their interplay as part of the social reality. in the same vein, the teaching practices are also influenced by this same interdependence and interconnectedness. as a social reality, we can view this phenomenon in the lens of critical realism.

critical realism (cr) distinguishes between the real and the observable, and advocates for a critical social science that describes, explains, and judges reality. it presents epistemological beliefs about reality, knowledge, and justifying the process of knowing. it also posits several features that make (social) scientific investigation possible and intelligible.

nowadays, many students in basic and higher education underperform in calculus and other mathematics subjects and courses. this reality transcends the changing circumstances, situations, and points of view of teachers and of students alike or any researcher’s own perspective. independence from observer’s perception exhibits the cr concept of ontological realism – the intransitivity of reality. associated with ontological realism is epistemic relativism, the transitivity of knowledge. in this context, the body of knowledge about mathematics teaching and learning is tentative highly depends on the context and the current environment of the study and in need of constant evaluation and reevaluation. these two concepts together justify judgmental rationality as it is sufficient and necessary for assessing different claims about the world.

two other concepts proposed by cr are the stratification of reality that distinguishes empirical experiences, actual events, and real causes in the world and the open system where causes do not necessitate future events but only provide tendencies. if the world were not stratified, that is, the three domains of reality would all be the same and causes are just the events and experiences, resulting in a positivist view. if it were true and that the students’ underperformance in calculus courses is a closed system, this phenomenon was only caused by their habits throughout the course of the semester or grading period and nothing more. this is entirely a naïve conclusion, disregarding any external influences on the event and other internal factors the student may not be aware of and thus failed to address, or that it could be a teacher factor, or a confluence of the classroom dynamics, policies that were implemented, and the external environment.

the literature clearly shows several factors affecting a student’s mathematics learning but not one reason justifies the event or the phenomenon. the student's performance and learning of calculus emerges from, say, their basic education, the learning interventions they have, their economic status, the amount of their free time, and others but these factors in isolation do not entirely explain the situation. the interventions teachers employ in their delivery of the course and the study interventions students try also affect the learning of calculus. the event is affected by the interdependence of these plausible causes. this cr concept of emergence is best summarized into the aristotelian adage of “the whole is greater than the sum of its parts.” the greater context of the contemporary times influences the overall phenomenon.

a researcher’s own epistemic consciousness influences their body of work and their research metatheory. it impacts the decision-making process involved in undertaking research, its methodology, methods, discussions, and conclusions.

for example, a positivist approach to studying calculus learning would presume that the classroom or a calculus course is a closed system, bounded by what happens in it without considering indirect factors which may affect calculus teaching and learning. a calculus student would be considered as a passive learner, a sponge absorbing the lecture. to a positivist, a probable cause of a student’s failure in first-year calculus could simply be the student’s inadequate preparation for the graded assessments in the course, without even considering the causes for this condition. in fact, even considering this metatheoretical discussion is “allegedly useless and sterile” to a positivist; positivists just do research mostly employing quantitative methods (sousa, 2010, p. 464).

on the extreme end of epistemological spectrum lies postmodernism, a rebuke to positivism. it argues that the truth of a claim is relative to agreement, negotiation, and consensus (sousa, 2010, p. 471). a researcher employing this relativist paradigm would use qualitative research techniques, “probably an instinctive reaction” to the positivist preference of quantitative methods. any research grounded in postmodernist epistemology would just be a report of the interviews made during the process and take it as fact.