If you're studying for N3, then there are a few things you should already know.

First, when I say crazy grammar jargon like "volitional form," you should assume that I'm talking about verbs ending in ～よう or ～ましょう.

Second, you should know how to conjugate volitional verbs, as well as their varied nuances.

Need some review?

The short version: We use ～よう and ～ましょう to say (1) let's VERB or (2) I think I'll VERB.

The long version: The following two lessons...

[NDL #54] - I think I'll... go to sleep.
[NDL #55] - Yo, hey. I think I'll... tell you my plans...

Now, if ～よう means "I think I'll VERB" in some cases, then it should make sense that adding と and しない or しません, "don't do," to the end of it gives us "doesn't even think about VERB-ing," "has no interest in VERB-ing."

That also just so happens to be our lesson topic today:

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JLPT N3: ～ようとしない (doesn't even think about ～ing)

An example:

イワンさんは見たことのない食べ物は決して食べようとしない。
イワンさん　は　みた　こと　の　ない　たべもの　は　けっして　たべようとしない。
Ivan-san won’t even consider trying food that he’s never seen before.
Literally: “Ivan-san + は + saw + thing + の + doesn’t have + food + は + never / by no means + doesn’t even think about eating.”

Ivan has always been a bit closed-minded.

Let's break this down:

V-よう ＋ としない
doesn't even think about VERB-ing; won't even consider VERB-ing

We use this grammar form when talking about how other people make absolutely no effort and/or show absolutely no interest in doing something they should or would be expected to do.

Above, we saw:

食べる（たべる // to eat）
↓ 🐳 ↓ 🐳 ↓
食べよう（たべよう // let's eat; I think I'll eat）
↓ 🐳 ↓ 🐳 ↓
食べようとしない（たべようとしない // doesn't even think about eating;won't even consider eating）

Makes sense, yeah?

*You nod head.*

Oh, what a relief. I don't know how else to explain it.

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[Bad student] doesn't even think about reading the next three examples.

うちの犬は、雨の日は散歩に行こうとしません。
うち　の　いぬ　は、　あめ　の　ひ　は　さんぽ　に　いこうとしません。
Our dog has no interest in going for walks when it’s raining.
Literally: “home + の + dog + は, + rain + の + day + は + walk + に + doesn’t even think about going.”

彼は人に言われないと、何もしようとしない。
かれ　は　ひと　に　いわれない　と、　なにも　しようとしない。
He won’t even think about doing something unless someone tells him to.
Literally: “he + は + person + に + not be told + と, + nothing (=what + も) + doesn’t even think about doing.”

妹は毎日遊んでばかりで、全然働こうとしない。
いもうと　は　まいにち　あそんで　ばかり　で、　ぜんぜん　はたらこうとしない。
My little sister just goes out every day; she doesn’t even think about getting a job.
Literally: “younger sister + は + every day + play (and) + only + で, + not at all + doesn’t even think about working.”

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To reiterate, ～ようとしない is used to talk about other people making absolutely no effort to do something.

We can never use ～ようとしない when talking about ourselves.

So don't use it in the first-person:

× わたしは漢字を勉強しようとしません。
× わたし　は　かんじ　を　べんきょう　しようとしません。
× I don’t even think about studying kanji.
× Literally: “I + は + kanji + を + studies / studying + don’t even think about doing.”

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That's all for this one.

If it's too hard, then I recommend reviewing the two lessons I linked to at the beginning of this lesson. Those should give you a firm-ish grasp of ～よう, thus preparing you take on the beast that is ～ようとしない.