From my very first days teaching a C++ programming class, it was evident that I was in over my head. I had a solid understanding of the fundamentals, but the curriculum rapidly escalated into complex object-oriented concepts – a paradigm radically different from what I was used to in programming. Determined to keep pace, I delved into the textbook every night, attempted the end-of-chapter projects, and formulated my own questions. Yet, it seemed as if a veil obscured my understanding. I just wasn’t getting it.
Then, unexpectedly, something remarkable happened during the second month of the school year – I crossed a threshold, and everything changed.
I vividly recall the instant when I finally “got it”. I was lounging on my friend’s couch, petting their dog, Chewy. Even after two decades, the memory is etched in my mind – the house, the couch, and Chewy’s furry presence. This was my eureka moment! As soon as I grasped the concept, it was as though I had leaped several levels in my programming skills. Such moments, known as “threshold concepts,” have the power to reshape how learners perceive a subject, leaving them feeling invincible.
A threshold concept is a paradigm-shifting idea or principle that, when understood, fundamentally alters a learner’s perspective. My experience with object-oriented programming exemplifies this. However, the journey to apprehending a threshold concept isn’t always instantaneous. Some learners undergo a protracted struggle with these concepts, encountering frustration and doubt along the way. Knowing when these concepts are covered in a semester can inform intentional design.
…there are certain concepts, or certain learning experiences, which resemble passing through a portal, from which a new perspective opens up, allowing things formerly not perceived to come into view. This permits a new and previously inaccessible way of thinking about something. It represents a transformed way of understanding, or interpreting, or viewing something, without which the learner cannot progress, and results in a reformulation of the learners’ frame of meaning. The thresholds approach also emphasizes the importance of disciplinary contexts. As a consequence of comprehending a threshold concept there may thus be a transformed internal view of subject matter, subject landscape, or even world view. Typical examples might be ‘Personhood’ in Philosophy; ‘The Testable Hypothesis’ in Biology; ‘Gravity’ in Physics; ‘Reactive Power’ in Electrical Engineering; ‘Depreciation’ in Accounting; ‘Legal Narrative’ in Law; ‘Geologic Time’ in Geology; ‘Uncertainty’ in Environmental Science; ‘Deconstruction’ in Literature or ‘Limit’ in Mathematics1.
Incorporating threshold concepts can reshape how and when you teach certain content. For instance, when building up to a threshold concept, consider setting aside less relevant information to avoid overwhelming learners with excessive cognitive load. You can introduce these peripheral topics at a later stage.
How do you know if your curriculum includes threshold concepts? Sarah Kent at the University of Calgary identifies five characteristics that indicate threshold status:
- They contain troublesome knowledge that is alien and counter-intuitive – oftentimes containing a continual struggle to understand
- They are transformative because they lead to a radical conceptual shift and ontological shift
- They are irreversible – the learner is not likely to forget it or revert to pre-apprehension understanding
- They are integrative and reveal interrelatedness of phenomenon; broad connections can now be made
- They are bounded and circumscribe a domain
In my experience, threshold concepts often elude those who already possess in-depth knowledge of a subject (the “curse of knowledge“). However, if you can identify a threshold concept within your course, seize the opportunity to create a peak moment for your learners – a moment of profound understanding.
Learning about threshold concepts, ironically, is a light-weight threshold concept in itself! Embrace these transformative moments in your learning journey, and as an educator, recognize the potential of threshold concepts to reshape your teaching approach and elevate your students’ understanding. Crossing these educational thresholds can be as unforgettable as the couch, the house, and the faithful presence of Chewy.
