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What boosts self-confidence?
Let me begin by sharing an interesting experiences I had back in college. So I attended a public speaking contest together with other contestants. Among them, a senior student always outperformed in the impromptu speech session with his creative ideas, smooth delivery, and forceful articulation.
At least, that's what I thought at the beginning, as I talked in a relatively slow pace (still do) and I lacked sufficient body languages and voice variation as per my speech training coach.
One time, I mentioned to my coach as to how great the senior student delivered speeches and asked if I needed to speed up my speaking like him.
My coach said, "no, you should keep your own pace". Then he went on telling me he had actually suggested the senior to slow down while speaking.
I was surprised.
He continued to explain how it's important to speak in a steady pace and make pauses when necessary to better attract audience's attention and deliver ideas more effectively.
Talking fast doesn't necessarily mean a person is strong at delivery, but sometimes, a way they protect themselves. They talk fast so that audience won't have sufficient time to think if an idea is well put.
So one lesson I've learned from this experience: you may think you lack self-confidence, but you can always act like you're not, and others actually can't tell the difference.

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Lower your expectation
The first time that I tried impromptu speech, I didn't finish my speech. I looked rather awkwardly on stage with my face went read and my mind went total blank.
I could saw some audience in the front, hoping me to find back my courage to continue. I felt grateful yet helpless, as I just couldn't come up with anything worth to be delivered
That, however, didn't stop me from trying. What made me different the second time was because I adjusted my strategy to lower my expectation from both inside and outside.
For audience, don't expect them to accept your ideas fully with no criticisms. Apparently, it's great to find someone that shares the same idea. But it's also okay if you can't. It'll then become a great opportunity to hear different voices and think about what's wrong with your idea so that you can make improvement.
For me, I've already experienced the worst situation once, what else can I lose? As long as I make efforts, I'll perform better than my first time. Just don't stress yourself with high standards that you can hardly meet at the moment. Make improvement little by little.

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Rise to the challenges
One of the reason that we were afraid of impromptu speeches at that time was that we couldn't guarantee the quality of our speeches due to insufficient time for preparation.
A crappy speech means it's more likely for audience to find loopholes. But what I've learned is that, what you fail to deliver in your 3-min speech can in fact complemented by answering further questions from your audience.
So don't be afraid that your ideas and opinions are challenged by others. Rather, it's a second chance to make your ideas fully explained and understood. So don't waste it.

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Improve your self-efficacy
Self-efficacy refers to how much and how certain that you believe in your ability to achieve a specific goal.
In other words, if you don't believe you can give an impromptu speech, you'll be less likely to give one, or you give it up right away.
However, if you have faith in yourself that even when you're at your lowest point, you're more likely to actively find ways to improve and practice hard to make a difference. And you won't give it up easily until you accomplish your goal.