"Then He came to Capernaum. And when He was in the house He asked them, 'What was it you disputed among yourselves on the road?' But they kept silent, for on the road they had disputed among themselves who would be the greatest. And He sat down, called the twelve, and said to them, 'If anyone desires to be first, he shall be last of all and servant of all.' Then He took a little child and set him in the midst of them. And when He had taken him in His arms, He said to them, 'Whoever receives one of these little children in My name receives Me; and whoever receives Me, receives not Me but Him who sent Me'" (Mark 9:33-37).
It is likely that the house they entered into belonged to Peter. The apostles were reluctant to answer Jesus' question about what they had been arguing about. They kept silent because they were ashamed of themselves and their desire for position and authority that was motivated by selfish pride. Their shame, however, didn't prevent this issue from coming up again later (e.g., Matt. 20:20-24; Luke 22:24). Nothing exposes the confusion of the disciples regarding the nature of Jesus' kingdom more than these episodes. They still believed that Jesus would set up an earthly kingdom! They evidently were convinced that someone would have to carry on the kingdom, even if He did die as He had foretold (Mark 9:31). Tragically, it's almost as if these apostles were brothers fighting over the inheritance before their father is even deceased!
"If anyone desires to be first, he shall be last of all and servant of all" - Jesus' words here clearly indicate that He knew the topic of their dispute. The apostles had hopes of learning which specific person would be the greatest in the kingdom, but Jesus would only tell them what type of person would be the greatest (i.e., one who is humble).
Jesus then took a "little child" up into His arms. The Greek term used here generally refers to a child under the age of seven. The fact that Jesus took the child "in His arms" would also indicate that the boy was very young.
"Unless you are converted and become as little children, you will be no means enter the kingdom of heaven" (Matt. 18:3). Jesus instructed His followers that they must turn from this sin of pride and personal ambition if they wanted to be a part of His kingdom. He does not want them to become childish but childlike. He wants their actions toward God to be dependent, obedient, trusting, and humble, as a small child's actions are toward his parents.
As a side note, this verse clearly exposes an error of Calvinism. Can anyone really believe that Jesus was saying here: "Unless you are converted and become as totally depraved, sinful little children, you will by no means enter the kingdom of heaven"? To ask is to answer! Clearly, Jesus did not believe that children were born tainted with the guilt of sin or else He would not have encouraged His followers to become like children (cf. Ezek. 18:20).
Jesus continued in Matthew 18:4 - "Therefore whoever humbles himself as this little child is the greatest in the kingdom of heaven" (cf. I Pet. 5:6). The one who is the most humble will be the greatest because he lives the most unselfishly and is the most like Jesus! A true view of Jesus' kingdom should lead to self-denial, love, and humility. It should be stressed that one does not have to be influential, educated, or rich in order to be afflicted with the sin of pride. After all, the twelve apostles were only common men.