What Students See When They Look at Algebra
Five three-panel jokes contrasting an algebra problem, the panic students see, and the structure mathematicians see: zero-product property, vertex form, chunking, fractions as pieces, and polynomial vs. exponential growth.
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2016-06-22-what-students-see-when-they-look-at-algebra/ (CC BY-NC 4.0)Transcript
[Each joke: What's on the page / What students see / What mathematicians see]
[1] (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."
[2] y = 7 − (x + 5)². Find the graph's vertex. / Students: a scribbled, overwritten "why = 7 − (x+5)²" with arrows to 7, "5 — wait no, −5," x = −5, y = 7, "minimum? no! max?" / Mathematicians: "y = 7 − (some positive number), so, maximized at y = 7, when the thing in brackets is 0"
[3] ((7x − 1)/2 + 4)/7 − 3 = 8 / Students: the same equation written entirely in skulls and crossbones / Mathematicians: "[Something] − 3 = 8. eh, I'll worry about this bit later"
[4] (3x + 1)/8 × 2 / Students: the fraction written in Devanagari ("sanskrit"): "um… 2 gibberish / 2 gibberish?" / Mathematicians: a pie cut in pieces of size 1/8, with 3x + 1 pieces shaded × 2: "Twice as many pieces! So, 6x + 2."
[5] x² vs. 2ˣ / Students: two identical tangled scribbles / Mathematicians: Jack growing a bit ("Wow, Jack — you've had quite a growth spurt!") vs. a towering beanstalk ("Wow, beanstalk — you've had quite a growth spurt!")