I have never met a mathematician who feels that two-column proofs is the right way to teach high school geometry. Considering that little math taught in high school beyond basic algebra uses anything close to &#x27;absolute rigor,&#x27; introducing rigorous proofs should be left for college when one actually has a reason to learn proofs for advanced mathematics (set theory, analysis, etc).<p>Geometry is taught correctly when proofs are used as a tool to convey a deep intuition about a mathematical pattern. Check out Lockhart&#x27;s book [1] if you want to see what it&#x27;s like when done right, though there are many more examples. Two-column proofs are simply a tool for the lazy&#x2F;unknowledgeable teachers to fill a geometry class.<p>I am aware of Lamport&#x27;s work, and it&#x27;s a specific tool for a specific subfield in which there is a plethora of false results. Ignoring the fact that most of theoretical computer science research and most of math research more does <i>not</i> fall into the category that Lamport is critical of (distributed computing), these temporary issues about rigor in academic publishing should have no effect on high school pedagogy. Instead, we should listen to the world&#x27;s finest math teachers, who pretty much all agree that two-column proofs are awful. A quote from Lockhart [2]:<p>&gt; Geometry class is by far the most mentally and emotionally destructive component of the entire K-12 mathematics curriculum. Other math courses may hide the beautiful bird, or put it in a cage, but in geometry class it is openly and cruelly tortured. What is happening is the systematic undermining of the student’s intuition. A proof, that is, a mathematical argument, is a work of fiction, a poem. Its goal is to satisfy. A beautiful proof should explain, and it should explain clearly, deeply, and elegantly. A well-written, well-crafted argument should feel like a splash of cool water, and be a beacon of light— it should refresh the spirit and illuminate the mind. And it should be charming. There is nothing charming about what passes for proof in geometry class. Students are presented a rigid and dogmatic format in which their so-called “proofs” are to be conducted— a format as unnecessary and inappropriate as insisting that children who wish to plant a garden refer to their flowers by genus and species.<p>[1]: <a href="http:&#x2F;&#x2F;www.amazon.com&#x2F;Measurement-Paul-Lockhart&#x2F;dp&#x2F;0674284380" rel="nofollow">http:&#x2F;&#x2F;www.amazon.com&#x2F;Measurement-Paul-Lockhart&#x2F;dp&#x2F;067428438...</a>
[2]: <a href="https:&#x2F;&#x2F;www.maa.org&#x2F;external_archive&#x2F;devlin&#x2F;LockhartsLament.pdf" rel="nofollow">https:&#x2F;&#x2F;www.maa.org&#x2F;external_archive&#x2F;devlin&#x2F;LockhartsLament....</a>