Optimization Isn't Always Optimal
The Shaving the Legs Theory
Why cutting-edge instruction fails students who have not yet built the foundation it requires.
By J. Daniels | April 1, 2026
There is an article that circulates in running communities about shaving your legs.
The claim is legitimate. Less drag. Marginal time savings. Small biomechanical advantages that accumulate over long distances. For a trained runner operating near the limits of performance, the optimization is real.
The problem is not the advice.
The problem is that the advice reaches people operating at very different stages of development.
Someone training for a marathon reads the article and gains a small advantage. Someone who cannot run a mile without stopping reads the same article, shaves their legs, and discovers that nothing meaningful has changed.
The optimization worked exactly as advertised. It simply addressed a problem they did not have.
Education often makes the same mistake.
Schools spend enormous amounts of time searching for better instructional strategies. AI-assisted instruction. Project-based learning. Inquiry-based curricula. Critical thinking frameworks. Collaborative learning models. The research behind many of these approaches is legitimate.
The problem is not the strategy. The problem is that every strategy assumes something is already present underneath it. When that foundation is missing, the optimization cannot produce the result it was designed to produce.
The optimization did not fail. The sequence did.
The Cognitive Mechanism
Optimization works. It works in sequence.
Cognitive load theory, developed by John Sweller and published in Cognitive Science in 1988, established that working memory holds roughly four chunks of information at once. When foundational skills are not automatic, they occupy that space. When they occupy that space, the advanced strategy the teacher is applying has nowhere to run. The student is not failing the innovation. The student is at capacity before the innovation begins.
Kirschner, Sweller, and Clark documented this directly in a 2006 paper in Educational Psychologist: inquiry-based learning, discovery learning, and problem-based instruction consistently fail when students do not already have the foundational knowledge those approaches depend on. The strategies are not wrong. The sequence is.
The Fundamentals Are Never Cutting Edge
Nobody publishes a white paper about teaching multiplication tables. There is no conference keynote on phonics. Logical sequencing does not get a product launch.
The foundational skills that every advanced instructional strategy runs on are not new. They have not changed. Multiplying fluently. Decoding reliably. Ordering information logically. Recognizing and reproducing patterns. These are the same skills they were fifty years ago and they will be the same skills fifty years from now.
What changes is everything built on top of them. Critical thinking tools. Analytical frameworks. Creative problem-solving approaches. Technology integration. All of it sits on top of the same unsexy foundation it has always required.
The National Mathematics Advisory Panel concluded in its 2008 federal report that automaticity with basic math facts is a prerequisite for higher-order mathematical reasoning. Not a support. Not a helpful add-on. A prerequisite. The advanced work cannot happen without it being present and automatic underneath.
The leg shave saves seconds per mile for someone running the miles. It does nothing for someone who has not built the base.
Critical Thinking Is Not a Skill
This is the part schools get most wrong.
Critical thinking matters. That is exactly why it cannot be taught in a vacuum.
Critical thinking is treated as a teachable skill set. A transferable capacity. Something that can be developed through exercises, frameworks, and deliberate practice in isolation from content.
Daniel Willingham, professor of psychology at the University of Virginia, addressed this directly in American Educator in 2007: critical thinking is not a skill. There is no set of critical thinking abilities that transfer across domains regardless of content knowledge. The ability to think critically about something depends entirely on knowing enough about that something to think with.
Sweller's cognitive load research explains the mechanism. When a student has not automated foundational skills, working memory is consumed by the computation of those skills. There is no capacity left for the reasoning layer the teacher is trying to build. Teaching critical thinking to a student who cannot yet multiply fluently is not advanced instruction. It is instruction applied to a system that cannot receive it yet.
Critical thinking is an output. It is what happens when foundational skills are automatic enough that the brain has working memory available to do something original with them. You do not teach it directly. You build what it requires and it emerges.
What This Means for Instruction
The question is not which strategy to apply. The question is whether the foundation that strategy requires is actually present.
Assess the foundational skill. Not the grade level. Not the age. The actual skill. If it is not there, no advanced strategy will produce the result it was designed to produce. If it is there and automatic, the advanced strategy works exactly as designed.
The optimization is legitimate. The sequence is everything.
References
Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work. Educational Psychologist, 41(2), 75-86. National Mathematics Advisory Panel. (2008). Foundations for Success. U.S. Department of Education. Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257-285. Willingham, D. T. (2007). Critical thinking: Why is it so hard to teach? American Educator, Summer 2007, 8-19.