The correct word to use in the blank in the sentence is "swam".
The sentence describes an action that happened in the past, so we need to use the past tense of the verb "to swim". The past tense of "to swim" is "swam", so we say "The children swam in the pool after school."
The word "swum" is also the past participle of "to swim", but it is not used in the simple past tense. It is used in perfect tenses, such as "The children have swum in the pool every day this week."
The word "swimming" is a present participle and is used to describe an ongoing action. For example, "The children were swimming in the pool when it started raining."
The word "swim" is the base form of the verb and is used for present tense or to indicate future tense. For example, "I swim every morning for exercise" or "The children will swim in the pool tomorrow".