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Japan flagTomoaki
I was embarrassed Last sunday morning, I went to the beach for walking. It was a sunny day and really warm. I got suntanned. While I was walking beside the beach, I spoke something by myself for a practice speaking English. I think that speaking by myself is one of the best way to improve speaking ability. At the time, I was concentrated on speaking and I didn’t know someone was walking behind me. When I looked behind and she was looking me with a wondering face. I was really embarrassed about it. Looking back that time, I should have used earphones and pretended to talk to someone by mobile phone. Thanks for technology, since then, I am able to speak with earphones confidently wherever I like.

Corrections · 3

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I Was Embarrassed

Last Sunday morning, I went to the beach for a walk. It was a sunny day, very warm in fact, and I ended up getting suntanned. While I was walking along the beach, to practice speaking English, I spoke aloud to myself. Personally, I happen to think that speaking to yourself is one of the best way to improve your speaking ability. However, at the time, I was focusing so intently on speaking correctly that I did not realize someone was walking behind me. When I happened to look behind me, and saw the inquisitive look on her face, I was so embarrassed about it that I probably turned red! Looking back at that time, I now see that I should have just put my earphones on, so that anyone who might see or hear me would simply think that I am talking to someone on the phone. Now, thanks to the widespread use of this technology, by using my earphones, even though designed for another purpose, I am able to speak out loud confidently wherever I like.*

Hi, Tomoaki. Good job! Whatever changes I made were to allow your sentences to sound more natural to my native ears, to clarify your thoughts, and for ease of reading. Sincerest apologies if I have misinterpreted. I hope that this helps you. Jonathan

*Different styles exist, but use one for your title. I use Title Case. Days of the week are proper nouns and need capitalization.  Some of your sentences were short, and while correct, I feel it better to combine them together. The English language can be funny in this way, but you cannot "speak with earphones." You can use them while speaking (or, as you pretend to!), but make sure that your sentences do not have, or can be interpreted to have, another meaning. In other words, "say (or write) what you mean, and mean what you say (or write). Although all the facts remain yours, with my edit of it, the reader is better able to understand what you were doing, what happened, and what you learned from it. Finally, I, too, agree that speaking aloud is important since you definitely need to train your mouth and tongue muscles to make foreign sounds. Keep writing and keep practicing!
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I was embarrassed

Last sunday morning, I went to the beach for a walk. It was a sunny day, and really warm. I got suntanned. While I was walking beside along the beach, I spoke said something to myself in English for practice. I think that speaking by myself is one of the best ways to improve speaking ability.
At the time, I was concentrated on speaking and I didn’t know someone was walking behind me. When I looked behind me and she was looking me with a wondering face. I was really embarrassed about it. Looking back that time, I should have used earphones and pretended to talk to someone on a mobile phone. Thanks for technology, since then, I am able to speak with earphones confidently wherever I like.
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I was embarrassed

Last sunday morning, I went to the beach for a walking. It was a sunny day and really warm. I got suntanned. While I was walking beside the beach, I spoke something by to myself for a in English to practice speaking English. I think that speaking by myself is one of the best ways to improve speaking ability.
At the time, I was concentrated on speaking and I didn’t know someone was walking behind me. When I looked behind and back, she was looking me with a wondering face. I was really embarrassed about it. Looking back at that time, I should have used earphones and pretended to talk to someone by mobile phone. Thanks for to technology, since then, I am able to speak with earphones confidently wherever I like.

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Specifying that the language you spoke is "English" earlier sounds nicer, but both will make enough sense.
I think you can also choose between "When I looked back," and "When I looked behind myself,"

Good luck with your speaking ability!

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