Zoom In, Zoom Out

A Study of the Abstract & Concrete in Computer Science in Pedagogical Context

Abstract

In this article I will discuss the contrast between the abstract and the concrete in the context of learning Computer Science. I will argue for the importance of abstraction in learning, with a focus in the aforementioned fields, discussing academic research papers as well as my personal experience being homeschooled, studying at Community Colleges, and finally at UC Berkeley. In doing so, I will try to recognize some of the potential pedagogical consequences and benefits of imposing abstracted information in the learning process as well as offer strategies for incorporating it in the classroom.

Context

The exact meaning behind the notions of abstract and concrete concepts is very much an epistemological one, with its contentious nuances relegated to the field of Philosophy. This is consequently a point of deliberation in the world of education; after all how much can you really zoom out (the abstract) and how much can you really zoom in (the concrete) when teaching? And what defines the barrier between the two? For the sake of this discussion, let’s say the idea of abstract knowledge can be thought of as the macroscopic arrangement of a concepts in the context of its placement in a mental model. For example, the internet can be thought of in the abstract as a collections of machines that are capable of exchanging information with each other (and that do). How this idea fits pertains to related concepts such as security, social engineering, router design and more is a part of the abstraction. Fundamentally it can be understood as black-boxing the concept to better understanding its general properties and integrations. Contrastingly, the concrete is the microscopic implementation of the concept. For example, the Internet consists of a network of machines designed around a seven layer protocol called the OSI model for the means of relaying information between nodes (servers) in the most effective way. Each layer characterizes a specific function and makes use of a protocol data unit (PDU). A server is particular grade of computer that is meant to be low powered with few peripherals (no monitor and keyboard) and uses a web application to relay data between the seeker and the data provider. This concrete perspective can be described into the very specifics, uncovering layer by layer leading right to bytes and bits, but while the degree to which something can be described as abstract or concrete is questionable, it serves our purpose to acknowledge and discuss the implications of the contrasting limits of the range itself.

Discussion

As a freshman at UC Berkeley, my disposition towards my courses was one of a constant oscillation between excitement towards the material and fear as to how the content was structured. While this was not necessarily a unique attitude, my atypical educational background as a homeschooler for the entirety of my pre-college education posited a myriad of challenges that collided with the models of teaching in a my university classrooms. Homeschooling is very unstructured, in that the school district expects a certain subject matter to be learned, and administers standardized tests to students by local schools to judge the efficacy of the student’s learning. Through the formative years of my education, the instruction was carried out by my parents to teach the basics of reading, writing, grammar, and arithmetic. Concurrently, and rather unbeknownst to me, a rapid acquisition of metacognitive skills also took place. Since tradition schooling systems prescribe information to be studied iteratively, without a structure to lean on, in the face of a vast corpus of information to choose from, the onus of what, how, and when to study is placed on me, the student.

Consequently one of the emphasized metaskills is the cliche “learning how to learn” which encompasses the ability to self-motivate oneself to learn, to source information around a topic suggested by the district’s curriculum (borrowed textbooks, book, encyclopedias, and later the internet), to dissect the information and seek the essential parts first (the abstract), to create a sparse but connected mental model, to incorporated associated concepts into that mental model, to revising the model as new and more concrete information was gathered, to determine the veracity of the acquired information, etc. The lack of structure required me to create my own structure, and through over a decade of revision, resulted in a fairly comfortable process to acquiring desired information.

With homeschooling, an emphasis on transfer was not merely for the utility or novelty, but as an essential aspect of keeping track of a massive catalog of knowledge. For example, an interest I explored in high school was atomic weapons, and thus I built a framework that incorporated the historical climate of World War 2 that brought about the weapons and combined it with a study of fission, uranium and plutonium isotopes as well as the biological implications of exposure to radiation, to generate a report detailing my interest as a means to study it further (subatomic particles and the Cold War were resulting studies). What this allowed for was a very deeply integrated model that fit in the different perspectives of a subject matter from the different lenses of study that could take place over a range of time. New information was not disparate but rather just another element in my mental model of the world. When the time came to take exams, the difficulty of them was inversely proportionate to how well connected my model was. Instead of memorizing the area of a circle, by understanding the abstract reasoning behind the problem, the formula for circle, sphere, ellipsoid and more could be derived. By understanding the conditions that surrounded the early start of American Government, the positions of the Hamilton vs. Jefferson debate could be inferred rather than rotely memorized. Thus even when initial conditions were different, as the Hendrickson and Schroeder “throwing darts in the water” study illustrates, because the students who learned the principle of light refraction understood what they were doing, they could easily adjust their behavior to the new task.

Contrastingly, traditional education programs have a particular emphasis on engaging students in collecting a wide gamut of concretized information. Throughout grade school, an emphasis is put on the abstract ideas, the fundamentals of reading, writing, arithmetic, logic etc, until the student is sufficiently prepared to tackle complex information ranging from perimeter optimization and complex algebra to the history of the Ancient Roman Empire, US Civil War and World War 2, or photosynthesis, cellular structures, and molecular interactions. Then through high school, students are given focuses to study in a structured manner that adhere to the curriculum standards of the state (College Prep, AP). These help to give students a concrete understanding of specifics within a domain, like English Literature, Spanish, Calculus, and Physics.

However what this style of teaching doesn’t provide is integrated concept map relating ideas learned in a first grade phonetics class to a high school level programming class. As Bransford et al. suggests, “superficial coverage of all topics in a subject area must be replaced with in-depth coverage of fewer topics that allows key concepts in that discipline to be understood…there must be a sufficient number of cases of in depth study to allow students to grasp the defining concepts in specific domains within a discipline. Moreover, in-depth study in a domain often requires that ideas be carried beyond a single school year before students can make the transition from informal to formal ideas.” (Bransford et al 20). Additionally research by Hmelo-Silver & Pfeffer in their paper “Comparing Expert and Novice Understanding of a Complex System from the Perspective of Structures, Behaviors, and Functions” suggested the distinction between a hobbyist’s and an expert’s understanding was that a hobbyist understands knowledge within a specific context, for example how to create a todo list web application using a framework like Django, while an expert understands the more abstracted principles of a subject allowing for complex reasoning such as appropriately deciding the right set of frameworks to use for their web application, understanding the speed and access tradeoffs between a relational database and key-value store, etc. With adaptive expertise (Hatano and Inagaki), experts can not only just make these types of decisions, but can understand how and why they made these decisions. To develop competence in an area of inquiry, students must: “(a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and © organize knowledge in ways that facilitate retrieval and application”. (Bransford et al). Accordingly to properly understand a subject, one must organize knowledge around deeply important concepts while concurrently conditionalizing the concepts into applicable contexts such that transfer and interconnectedness of one’s mental models is prioritized.

The different learning model in college changed the game for me, in that while I had the freedom to choose a course to study, the study of that material in accordance with the timeline of the semester resulted in a frustratingly constrained learning environment. Lower division Computer Science have bias towards students whose prior knowledge repository favors not just the abstract (computer science) but also the concrete (programming) — after all knowing how an applicable data structure can be suitable paired with an efficient algorithm to solve a specific task requires a smoothie of abstract ideas and concrete implementation. As a consequence I struggled to keep track of the information that I was iteratively taught — I knew what it was and how to use it, but not how it fit with the other concepts I was learning. To cope with this onslaught of seemingly disconnected information, I created a series of Field Guides for my courses that focused on structuring the course’s curriculum in both the structure and simplistic vocabulary that made sense to me. A public release of them proved to me that this model of learning offered some effectiveness to other students as well.

Computer science as a discipline of study is very much a interplay between the abstract and concrete. Classes are structured to give you an overview and a taste of selected content that is silo’d to the topic of the course. For example a security class shows you how to deal with implication of an insecure network without actually expecting a concrete understanding of networking, but instead black boxes the relevant elements that interact with the in-depth material from the from main class. In fact a subject like computer science requires you to understand the abstract first and then focus on the concrete information that is actually relevant to your interests. While it is not always important to know how to implement something, knowing that you can implement something is an important designation of an expert. If your interest is not Computer Vision, understanding RANSAC homographies has the marginal utility over using the Photoshop Panorama tool, just like running macOS instead of Linux for programming is sufficient if your relevant domain isn’t operating systems. However, while you don’t need to understand the bytecode that you computer runs to formulate complex programs (unless your are interested in systems optimization) this relegation relies on the notion that you must understand how and why a system can or needs to be optimized. That being said, understanding the context in which to apply the knowledge may be just enough until further study is required, resulting in a ad-hoc on-demand learning process.

This is of course not to say that incorporating more abstract into the concrete focused learning of the current education system is somehow the panacea to our education woes. Mathematicians such as Kline (Harrison & Treagust 513) insists that despite the desire to produce mental or analogical models of abstract objects and processes, the belief that we can do so is a myth. Doing so can lead to confused syllogisms like the shell question Harrison & Treagust study of molecular models illustrates. Nevertheless in the age of readily accessible information, maybe we are doing students a disservice by focusing primarily on the concrete information. Instead Herbert Simon states, “the meaning of “knowing” has shifted from being able to remember and repeat information to being able to find and use it” (Simon, 1996). The goal of education may be better off focusing on helping students to develop the tools, strategies, and resources to acquire knowledge (Preparation for Future Learning) that they can personally add to their cross-disciplinary models of the world promoting a deeply integrated “learning with understanding” approach. As Bransford et al. beautifully states, “fundamental understanding about subjects, including how to frame and ask meaningful questions about various subject areas, contributes to individuals’ more basic understanding of principles of learning that can assist them in becoming self-sustaining, lifelong learners”.


References

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Gentner, Dedre. 2010. “Bootstrapping the Mind: Analogical Processes and Symbol Systems.” Cognitive Science. doi:10.1111/j.1551–6709.2010.01114.x.

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Hmelo-Silver, Cindy E., and Merav Green Pfeffer. 2004. “Comparing Expert and Novice Understanding of a Complex System from the Perspective of Structures, Behaviors, and Functions” Cognitive Science 28 (1): 127–38. doi:10.1016/S0364–0213(03)00065-X.

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Schoenfeld, Alan H. 2015. “Essential Mathematics for the next Generation: What to Teach and How Should We Teach It.” Project IMPULS Symposium, 0–5.

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