Showing our work transforms thinking and solving problems in mathematics, science, business decisions, and personal growth. This truth hit home as I watched my sister struggle with my seven-year-old niece over homework towards the end of January 2025.
I sat quietly for thirty minutes, trying not to laugh as they went back and forth. My niece had solved her maths problems correctly but hadn’t shown any working out. Her frustrated mum insisted she write down her steps, yet neither truly understood why this mattered.
The scene transported me back to my college and university days. Those moments when complex physics equations would click in my mind, leading to correct answers—yet without showing our work, I’d lose most of the marks. Back then, it seemed unfair. Now, this approach hits like a lightning bolt of clarity.
“Let me explain something,” I finally said to my niece. “Imagine getting ten points for solving a problem. Eight of those points come from showing your working out. Only two points are for the right answer.”
Her eyes widened as I continued: “Sometimes you can get the answer wrong but still earn eight points because you’ve shown how you thought about it. That’s actually more valuable than just getting lucky with the right answer.”
I laughed, remembering my own struggles with this concept. “Trust me, I learned this the hard way – failing many assignments in college because I was too lazy to show my work, even when I knew the answer.”
A few days later, Seth Godin’s blog landed in my inbox with perfect timing. He presented a simple yet powerful equation:
Analysis = Facts + Interpretation
His message was clear: our interpretations lose credibility without showing the facts behind our analysis. We must demonstrate our thinking process for others to trust our conclusions.
This equation grabbed my attention like a familiar friend in an unexpected place. As a researcher with a PhD in computational fluid dynamics, I see equations differently. Each one tells a story from multiple angles. Just like Newton’s fundamental equation:
F = ma
Rearranging it to solve for force, mass, or acceleration reveals different insights. Godin’s equation transforms when we rewrite it.
When we rearrange for interpretation:
Interpretation = Analysis – Facts
This shows how our interpretations emerge from analysing facts, reminding us that without solid facts, our interpretations become mere guesswork.
When we solve for facts:
Facts = Analysis – Interpretation
This reveals how we can extract pure facts by removing our interpretive layers from analysis.
These arrangements illuminate different truths about processing information and understanding the world. The power of showing our work lies in revealing these connections.
Statistics was never my focus before my PhD until Hans Rosling showed me how understanding data transforms decision-making. His revolutionary approach to presenting complex data changed how I view information.
Today, we live in what I call the junk food information age. We crave quick answers and bite-sized summaries. AI tools condense research papers into bullet points. Social media reduces complex ideas to soundbites. We’ve become obsessed with answers whilst dismissing the thinking process that leads to genuine understanding.
Yet, just as my niece needed to learn the value of showing her work, we all benefit from seeing the steps behind conclusions. When someone presents an analysis without revealing their facts and interpretation process, they hide the eight points and show only the two.
Showing our work isn’t about proving we’re right – it’s about revealing how we think. When we skip this step, we lose the chance to spot errors in our logic or identify better approaches. More importantly, we lose the opportunity to help others understand and build upon our thinking.
This applies everywhere: in business decisions, political discussions, scientific research, and personal growth. When we share our conclusions and our thought processes, we create opportunities for genuine learning and meaningful dialogue.