Avoiding The Adjective Fallacy

你正在读这篇文章，所以我认为你的英语很好。What’s wrong with these phrases?

Old little lady
Red big dog
Vietnamese spicy food

Do you have a logical reason for why they sound strange? Or are they just off?

You probably didn’t think, “In 3rd grade I mastered the Royal Order of Adjectives:

Determiner
Observation
Size
Shape
Age
Color
Origin
Material
Qualifier

在应用它们时，发现了几个错误。Old little ladyis incorrect because rules #3 and #5 are swapped — a childish mistake, really. The next…”

Ugh. Describing Gran Gran isn’t a logic puzzle. But guess what students learning English aretaught?

即使作为一个母语为英语的人，你能构建这个图表吗?你就是这样教别人英语的吗?

The Adjective Fallacy is trying to learn by mastering the formal rules.Just because a conceptcan严格定义并不意味着我们应该那样研究它。

We didn’t become good at English by studying a chart: we developed an ear for the language and know how itshouldsound. And “old little lady” sounds off.

Similarly, getting good at math doesn’t mean marching through a gauntlet of rules on every problem. It’s having a native speaker’s feeling about what works or doesn’t.

“303 x 13 = 5074” looks strange, but not because we computed the left-hand side. It’s weird because odd numbers can’t multiply to become even (intuition). The last digit of the result should be 3×3= 9. 5074 is too large, since 300 x 10 (similar numbers nearby) is only 3000. Our Spidey Sense is blaring that the computation looks wrong.

My learning goal is knowing enough to make rough predictions on my own. I want a horse sense for algebra, calculus, trig, and evenimaginary exponents,withoutscurrying off to apply an equation.

Rules aren’t inherently bad: they summarize, resolve ambiguous cases, and help us practice our weak spots. The question is how much to use them when starting off.

Learn enough rules to get started – don’t attempt to master them from the outset. See examples in a larger context and let the pattern-matching machinery of your brain get to work.

Learning Math

数学也是一种语言。Here’s a gut check:Would my current math study technique have helped me learn English?

如果一节英语课花一个月的时间学习形容词表，我们就会和老师进行一次谈话。但是在微积分课上花几周时间学习极限的形式理论是很典型的。我们是否可以承认，这么早地学习这么多细节，并不能培养流利性?

Pondering that question made me realize I had large gaps intrigonometryandcalculus. I could only describe concepts using the adjective chart I’d memorized with a furrowed brow. (I’ll describe my grandma, just give me a minute!)

Enough was enough: embrace approaches thatactuallyhelp you, like seeing the big picture first. In Calculus, that might mean seeing an integral in thefirst lesson:

That’s what Calculusdoes: break a shape into pieces (the derivative), and glue it together in various ways (the integral). If you like this style of teaching, check out thefull Calculus series.

A typicalcalculus syllabus在经过几个月的“打下基础”之后，我们将在第12周介绍积分。在我们分开学习形容词、名词和动词之前，最好不要使用一个完整的句子，对吗?(我的绝望可以解决能源危机。)

通往理解的道路并不总是最结构化的。

快乐数学。

Update: This concept is calledtacit knowledge, or “we know more than we can tell” (Michael Polanyi). Tacit knowledge is acquired through experience, and complements the explicit knowledge written as rules.

Learning Math

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