What Students See: (x − 5)(x − 7) = 0
Students panic over parentheses and negatives; mathematicians see 'something × something = 0.'
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2016-06-22-what-students-see-when-they-look-at-algebra--what-students-see-zero-product/ (CC BY-NC 4.0)Transcript
(x − 5)(x − 7) = 0. Solve for x. / Students: "OH NO a variable expression with parentheses — I hate parentheses — what if it comes out negative? I hate negatives — maybe I can expand the expression…" "WHY CRUEL WORLD I don't get why math has all these symbols instead of numbers — I used to like math…" "look — zero! the only thing in this equation I understand! I'll just say 'zero' and cross my fingers." / Mathematicians: "Something × Something = 0. ah — so one of these shady characters must be zero."