wielsonf

[wielsonf]

the not so hidden curriculum

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.

https://www.youtube.com/watch?v=32f9qAd0TDc  https://helpfulprofessor.com/hidden-curriculum/ 

[wielsonf]

satisficing slot shortage

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

ᵖˢ. ˢᵃʷ ᵗʰⁱˢ ᵖᵒˢᵗ ⁱⁿ ᵖᵃˢˢⁱⁿᵍ, ʳᵉᵃᵈⁱˡʸ ᵏⁿᵉʷ ⁱ ʰᵃᵈ ᵗᵒ ᵖᵒˢᵗ ˢᵒᵐᵉᵗʰⁱⁿᵍ ᵃᵇᵒᵘᵗ ⁱᵗ

[wielsonf]

why qualitative research matters to teaching (mathematics)

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,

for this course, i posed this question: how do teachers facilitate collegiate calculus learning through creative interventions?

in an attempt to answer this question, i had to look back at what is happening and what research tells us about calculus learning.

for one, most mathematics learning theories are based on existing ones from classical learning theories, like constructivism, positivism, and behaviorism. since the start of the 21st century, one of the main motivations of mathematics education research is rationalizing a theory for mathematics in consideration of its unique nature as a subject matter.

next comes becoming aware of challenges and factors in teaching and learning calculus, how do teachers intervene, and how important their role is.

as of yet, i think the question can't be answered by a simple survey, answered using a likert scale. we have to go on the ground and diligently ask calculus teachers and instructors in college the existing literature still resonate with the challenges they face and what they do about them in order to help their students. the quality of administration and prestige of the institutions they serve affect their students, but in reality, educators are at the frontline facing the students and implementing interventions as they go along day by day. their experience is a vital part of understanding the problem.

we should break down such a complex question into easily digestible and directly answerable ones that help us understand sac (structures-agency-culture): ask where the teachers come from, what kind of pool do they dive in to teach calculus, what restrictions they are put in, what the students are like, what they do to help the children [sic], and in what way do their interventions affect the students.

with the pisa results just released, now more than ever, we need to act as fast as we can to implement changes from the ground up.

why are we, everyone at school, so miserable in one way or another? this, i can definitely say, is my magnum opus.

i will die on this hill.

[wielsonf]

not just math anymore

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

caught by a system that's never consistent, always dependent, and never complete. my search for an axiomatic system to live by only led me astray, far from what i have been trained all along.

at school, my vocation has always been affected by factors not really my own doing:

a salary that my peers and i don't deserve (we deserve more),

students who are eager to learn but sometimes miss the mark (not really their fault if you think of where they came from - hometown, school, basic education [i said what i said]),

a structure that worked in the past that doesn't any longer,

and just millenial and gen z hopelessness, that's mostly it.

this is not to say that everything i did was to no avail; very far from it. my constant search for truth led me to what i am studying now (doctor of education at the ateneo de manila university); still related to my work and, just as i could, still relate to how we teach math. that feeling of being led astray only transported me to the edge and into the other side of the coin that's teaching whose faces are math, its theory and applications on one side, and education on the other. what made work difficult only made me want to collide with it, head on.

in order to tackle and try to solve any problem, understand it first.

what made us, educators, beg for salary increases when we are the foundation of any thriving society?

what made our students, uh, like this?

why are we keeping traditions when they don't serve us anymore?

why are we sad?

i don't have all the time in my seat at starbucks uplb so let me indulge you with a look at an attempt to understand these questions, at least one of them.

all these questions arise from society, with all its intricacies and faults. as such, following margaret archer's transformational model of social activity, these questions reside within the complex interplay of structures from which they arise, the human agents that act and affect everything everywhere all at once (un)wittingly, and the culture that these humans live by.

definitely, math cannot answer these questions; pen-and-paper is not enough anymore.

[wielsonf]

adopting a critical realist perspective in mathematics teaching and learning

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.

the transformational model of social activity (tmsa) encapsulates all the ideas of cr. the interrelationships of the philippine education system and a university existing policies on delivery and assessment modes (structure); the teachers, students, administrators, officers in governing bodies, and even politicians (agents); and the country’s, universities’, or localities’ beliefs and history all affect not only the challenges and barriers to learning calculus, but also possible, applicable, and implementable interventions to mitigate them. the structure, agents, and culture are distinct but not independent of one another; they depend on and influence one another, too.

[wielsonf]

positivist and postmodernist epistemology in mathematics teaching and learning

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.

a delicate balance between positivism and postmodernism is accorded to researchers in mathematics education by critical realism.

[wielsonf]

parking this space

for when twitter goes dark