Every few years I try this. It’s gotten to the point where I can no longer tell if this is actually helpful or illuminating, but below you’ll see the categories that I created when I tried to sort a bunch of mistakes that I’d logged on this site.

Enjoy, and please share any disagreements or alternate sortings that you see in the student work.

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*Mistakes Due To Limited Applicability of Models*

Recursive rather than Relational Thinking

http://mathmistakes.org/recursive-and-relational-thinking-and-the-feedback-each-deserves/

Circular rather than Rectangular Models of Fractions

http://mathmistakes.org/which-fraction-is-larger/

Non-commutative rather than Commutative Model of Multiplication

http://mathmistakes.org/write-a-story-problem-for-13-x-2/

Acting Out the Problem rather than Using a More Efficient Strategy

http://mathmistakes.org/91-mushrooms-7-people/

*Mistakes Due To Applying Properties of a Familiar Model in an Less Familiar Situation*

Linear properties applied in Non-Linear situation

http://mathmistakes.org/the-fundamental-mistake-of-trigonometry/

http://mathmistakes.org/value-of-absolute-value/

http://mathmistakes.org/overassuming-linearity/

One-Dimensional Distance applied in a Two-Dimensional Situation

http://mathmistakes.org/the-distance-between-11-and-45-is-7/

Additive properties applied in Multiplicative situation

http://mathmistakes.org/what-else-could-she-know-on-12×14280/

http://mathmistakes.org/5-and-12-x-2-and-14-7-and-34/

http://mathmistakes.org/people-often-use-additive-instead-of-multiplicative-reasoning/

http://mathmistakes.org/squaring-doesnt-make-equivalent-fractions/

http://mathmistakes.org/comparing-ratios-what-feedback-would-you-give/

http://mathmistakes.org/complex-number-mistakes-are-often-algebra-mistakes/

http://mathmistakes.org/they-are-not-similar-because-you-have-to-add-different-numbers

http://mathmistakes.org/scaling-by-12/

http://mathmistakes.org/cross-addition-isnt-a-thing/

Side-times-Side Formula for Finding Area Applied in non-Rectangles

http://mathmistakes.org/base1-times-base2-area-of-triangle/

__Area Properties Applied to Perimeter__

http://mathmistakes.org/perimeter-is-the-space-outside-of-a-shape/

Properties of some paradigmatic example of a shape applied globally [1]

http://mathmistakes.org/all-ramps-are-45-degrees-pythagorean-theorem/

http://mathmistakes.org/thats-not-an-array/

http://mathmistakes.org/using-a-bad-base/

Maybe: http://mathmistakes.org/a-third-34/

http://mathmistakes.org/triangles-and-3-gons/

Properties of a Fractional Parts of a Rectangle Applied To Other Shapes

http://mathmistakes.org/three-fifths-of-a-triangle/

*Mistakes Due to Quickly Associating Something In Place Of Another*

Squares Instead of Square Roots

http://mathmistakes.org/integrating-by-parts/

Multiplying In Place of Exponentiation

http://mathmistakes.org/two-cubed-is-eight-but-seven-squared-is-fourteen/

Addition In Place of Multiplication

http://mathmistakes.org/5-and-12-x-2-and-14-7-and-34/

http://mathmistakes.org/sometimes-kids-add-when-theyre-trying-to-multiply/

Changing the Numbers of the Problem

http://mathmistakes.org/mixed-up-numbers/

Operating on the “Answer” in an Open Sentence Problem

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[1] This is a very mushed-together category. I’ve fallen into the trap of giving geometry short-shrift in the face of arithmetic and algebra. In general, I understand geometry thinking less well than I understand arithmetic/algebraic thinking. That category of “Properties of Shapes Overextended…” needs some serious breaking-down.