[iCONADA Research Team] The Educational Lessons of Information Entropy: From ‘Zero-Gain Instruction’to Cognitive Iteration Through Higher-Order Thinking Skills

Amid the global wave of education reform, Benjamin Bloom’s (1913–1999) concept of higher-order thinking skills (HOTS) has emerged as a guiding principle for the next generation of education. Yet as we champion critical thinking, evaluation and creativity among students, what exactly are we resisting? And what are we really trying to achieve?

Information Theory, established in 1948 by American mathematician Claude Shannon (1916–2001), offers an unprecedented, cool-headed and profound mathematical metaphor for this paradigm shift in education.

Rote Learning: A Stagnant Pool With Zero Information Entropy

When Shannon defined information entropy, he described it as a measure of uncertainty within a system. The more probable and predictable an event is, the less surprising it is – and the less information it carries. When an outcome is completely certain, such as with a coin that has heads on both sides, uncertainty falls to zero and so does information entropy.

Looking back, the old-fashioned model of rote learning represents an extreme pursuit of precisely this state of “zero information entropy”. Under traditional examination systems and didactic classroom teaching, the standard answer is treated as the only and absolute truth. The student’s task is not to explore the unknown, but to eliminate all uncertainty and accurately reproduce the signals transmitted by the teacher and textbook.

From the perspective of information theory, such a completely predictable model of teaching produces zero information gain.

It succeeds in turning students into a kind of read-only memory (ROM) – free of noise, perhaps, but also devoid of vitality. When education eliminates confusion, ambiguity and suspense, it may also be declaring the death of intellectual flexibility and creativity.

HOTS and Cross-Entropy: Optimising the Dynamic Mind

In the fast-changing and increasingly complex world of the 21st century, this educational model of “zero uncertainty” is no longer tenable. The HOTS approach now being advocated is, in essence, an exercise in understanding and optimising cross-entropy.

In machine learning, cross-entropy measures the gap between a predictive model’s probability distribution and the actual distribution found in the real world. Applied metaphorically to education, the complex, dynamic and multifaceted nature of reality – a world without a single standard answer – represents the “true distribution”. The critical thinking demonstrated by students through analysis, evaluation and creation, meanwhile, represents the “predictive model” they construct to make sense of that world.

Higher-order thinking education no longer insists on absolute agreement over every answer. Instead, it acknowledges that a gap exists. The process of measuring and reducing that cross-entropy is, in many ways, the essence of higher-order thinking.

When students confront uncertainty, they must examine evidence, assess risks and devise creative solutions. In doing so, they continually measure the “cross-entropy” between their existing understanding and a complex reality. Through reflection and debate, they independently iterate and refine their mental models.

This is not passive knowledge acquisition. It is a dynamic cognitive system that evolves over time – a process of finding order amid complexity and uncertainty.

Conclusion: Giving Education Back to Wisdom

From Shannon’s information entropy to Bloom’s HOTS, we can see a remarkable meeting point between science and the humanities. The ultimate purpose of education should never be to achieve a perfectly static state of “zero information entropy”, turning students into standardised products rolling off an educational assembly line.

Educators of the new generation should instead become facilitators of the algorithms of thought, encouraging students to embrace uncertainty. The classroom should be a sandbox where mistakes are tolerated, cognitive gaps are examined, and ideas are continuously tested and refined.

Only by allowing room for uncertainty and intellectual divergence can students face the storms of an unknown future. Through the self-iteration of higher-order thinking, they can transform uncertainty into profound insight – evolving from“machines that memorise” into “creators of wisdom.”