In Chinese, some verbs can be reduplicated to indicate that an action is done within a short period of time or to show attempts. And it could lighten the tone, mood and seriousness of the sentence. It is very common to use this kind of reduplication in spoken language.
The common forms:
For instance: 听，说，读，写，等，看……
（Here A represents the monosyllabic verb.）
A：我能看看你的书吗？(Wǒ néng kànkan nǐ de shū ma?) Can I have a look at your book?
B：好的，我给你看一看我的书。(Hǎo de, wǒ gěi nǐ kàn yī kàn wǒ de shū.) Okay, let me show you my book.
A：你能写一写那个报告吗？(Nǐ néng xiě yī xiě nàgè bàogào ma?) Can you write that report?
B：可以等等吗？我现在有点儿忙。(Kěyǐ děngdeng ma? Wǒ xiànzài yǒudiǎnr máng.) Can you wait? I am a little busy now.
Note that when say AA form, the second character is often pronounced as light tone.
“A了A” often refers to the action that has been done in a short time.
他看了看这本书，就还回去了。(Tā kànle kàn zhè běn shū, jiù huán huíqùle.) He looked at the book and then returned.
我们一起听了听她的新歌，都很喜欢。(Wǒmen yīqǐ tīngletīng tā de xīngē, dōu hěn xǐhuān.) We listened to her new song together and we all liked it.
我早上等了等你们，但是时间不早了，我就先走了。(Wǒ zǎoshang děngleděng nǐmen, dànshì shíjiān bù zǎo le, wǒ jiù xiān zǒu le.) I waited for you in the morning, but it was late, so I left first.
The common form:
For instance: 考虑，准备，休息，介绍，运动……
我想再考虑考虑。(Wǒ xiǎng zài kǎolǜ kǎolǜ.) I want to think again.
你准备准备，下一个是你唱歌。(Nǐ zhǔnbèi zhǔnbèi, xià yīgè shì nǐ chànggē.) Just prepare, you will be the next to sing.
我很想睡觉，我可以在这休息休息吗？(Wǒ hěn xiǎng shuìjiào, wǒ kěyǐ zài zhè xiūxí xiūxí ma?) I really want to sleep. Can I have a rest here?
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For 5 我们一起讨讨论论吧 the pinyin is wrong. It says cancanguanguan, but it should be taotaolunlun.
Hi Sabrina, thanks for your feedback. We just updated it.