Even though the Christian can always offer certain dates for the Gospels, it should remembered that there was a gap of time between the ascension of Jesus and when the Gospel authors actually wrote their individual biographies about the life of Jesus. Therefore, there was a period where the words and deeds of Jesus were committed to memory by the disciples and transmitted orally. Remember, the home, the synagogue, and the elementary school was where Jewish people learned how to memorize and recall information such as community prayers. As Craig Evans notes in his article on Jewish Scripture and the Literacy of Jesus, according to the Shema, which all Torah observant Jews were expected to recite daily, parents were to teach their children the Torah ( Deut 4:9; 6:7; 11:19; 31:12-13; 2 Chr 17:7-9; Eccl 12:9).
As Richard Bauckham notes, “In short, memorization was a mechanism of control that preserved the Jesus traditions as faithfully as the early Christians required. It was exercised to the extent that stable reproduction was deemed important and in regard to those aspects of the traditions for which stable reproduction was thought appropriate” 
How would Jesus have made his teaching memorable?
Jesus was a called a “Rabbi” (Matt. 8:19; 9:11; 12:38; Mk. 4:38; 5:35; 9:17; 10:17, 20; 12:14, 19, 32; Lk. 19:39; Jn. 1:38; 3:2), which means “master” or “teacher.” There are several terms that can be seen that as part of the rabbinic terminology of that day. His disciples had “come” to him, “followed after” him, “learned from” him, “taken his yoke upon” them” (Mt. 11:28-30; Mk 1). 
Jesus taught in poetic form, employing alliteration, paronomasia, assonance, parallelism, and rhyme. Since over 90 percent of Jesus’ teaching was poetic, this would make it simple to memorize. 
According to Webster’s Dictionary, an aphorism is “a concise statement of a principle or terse formulation of a truth or sentiment,” (“he who has ears to hear, let him hear” [Mark 4:9, 23; Luke 8:8; 14:35] or “he who has ears, let him hear” [Matt. 11:15, 13:9, 43]. The parables of Jesus also seem streamlined for easy memorization. 
If you followed Jesus twenty-four hours a day, seven days a week wouldn’t you expect him to repeat some of the aphorisms throughout his ministry? 
We also see an emphasis on the importance of remembering the words of Jesus:
Jesus says: “Listen carefully to what I’m about to tell you.” (Luke 9:44)
“Everyone then who hears these words of mine and acts on them will be like a wise man who built his house on rock.” (Matthew 7:24)
“Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything that I have commanded you” (Matthew 28:19-20)
“Heaven and earth will pass away, but my words will not pass away” (Mark 13:31)
“ It is the spirit that gives life; the flesh is useless. The words that I have spoken to you are spirit and life” (John 6:63)
“So Jesus asked the twelve, “Do you also wish to go away?” Simon Peter answered him, “Lord, to whom can we go? You have the words of eternal life” (John 6:67-68)
“Do you not believe that I am in the Father and the Father is in me? The words that I say to you I do not speak on my own; but the Father who dwells in me does his works” (John 14:10)
“ But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you everything, and remind you of all that I have said to you” (John 14:26)
“If you abide in me, and my words abide in you, ask for whatever you wish, and it will be done for you” (John 15:7)
Even after the ascension of Jesus, the apostles gave their eyewitness testimony to the words of Jesus. Hence, the Gospel writers could base their word on a “fixed distinct tradition about Jesus-a tradition that was partly memorized and partly written down in notebooks and private scrolls.” Therefore, the oral tradition eventually was written in the form of the Gospels, emulating the written Torah of the Jews and reflecting the general revelation of Jesus the Messiah. 
Even when we come to Paul, we see he employs rabbinical terminology such as “delivering,” “receiving,” “passing on” “learning,” “guarding,” the traditional teaching within his letters. This can be observed in the following passages:
Romans 16: 17: “Now I urge you, brethren, keep your eye on those who cause dissensions and hindrances contrary to the teaching which you learned, and turn away from them.”
1 Corinthians 11:23: For I received from the Lord that which I also delivered to you, that the Lord Jesus in the night in which He was betrayed took bread.
I Corinthians 15: 3-8 “For what I received I passed on to you as of first importance that Christ died for our sins according to the Scriptures, that he was buried, that he was raised on the third day according to the Scriptures, and that he appeared to Cephas, and then to the Twelve. After that, he appeared to more than five hundred of the brothers and sisters at the same time, most of whom are still living, though some have fallen asleep. Then he appeared to James, then to all the apostles, and last of all he appeared to me also, as to one abnormally born.”
Philippians 4:9: The things you have learned and received and heard and seen in me, practice these things, and the God of peace will be with you.
1 Thessalonians 2:13: For this reason we also constantly thank God that when you received the word of God which you heard from us, you accepted it not as the word of men, but for what it really is, the word of God, which also performs its work in you who believe.
2 Thessalonians 2:15: So then, brethren, stand firm and hold to the traditions which you were taught, whether by word of mouth or by letter from us.
So according to Paul, the church possesses a normative standard which he refers to as “tradition” or “traditions” (paradosis, paradoseis, 1 Cor.11:2 2 Thess 2:15;3:6). The manner in which it is passed on is expressed in the verbs paradidonai, ‘hand over’ (tradition) and paralambanein, “receive” (as tradition), 1Cor.11:23; 15:1,3; Gal. 1:9; Phil 4:9; 1 Thess.2:13; 2Thess.3:6. The young congregations are to “maintain” or “hold fast” or “uphold” these traditions; the verbs used are among others, kratein (2 Thess.2:15), katechein (1 Cor. 11:2) and hesteknai (1 Cor. 15:1).
It is also important to note the role of how the disciples were active participants of the life of Jesus. They saw the importance of bearing witness to the deeds and sayings of Jesus:
As Richard Bauckham says:
” The sense (not a properly one generic one) in which the witnesses of the Holocaust created a new literature of testimony, is much the same sense as that in which the witnesses of the history created the Gospels. Those witnesses understood the imperative to witness to a command of the risen Christ, but the parallel is sufficient to be suggestive. In both cases, the uniqueness required precisely witness as the only means by which the events could be adequately known. In both cases, the exceptionality of the event means that only the testimony of participant witness can give us anything approaching access to the truth of the event.” 
Conclusion: The first followers of Jesus had a strong motivation to pass on both the actions and sayings of Jesus with considerable accuracy. Also, we need to remember that in the early faith community there was a center (Jerusalem) which consisted of leaders (the apostles). Hence, there would be checks and balances in place to control the tradition.
 Richard Bauckham, Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony (Grand Rapids, MI: 2006), 287
 Paul Barnett, Jesus and the Logic of History (Downers Grove, IL: InterVaristy Press. 1997), 138.
 Reid, D. G., The IVP Dictionary of the New Testament: A One-Volume Compendium Of Contemporary Biblical Scholarship (Downers Grove, IL: InterVarsity Press. 2004), 460.
 These points are emphasized in James M. Arlandson’s wonderful set of articles called The Historical Reliability of the Gospels available at http://wap.bible.org/series/historical-reliability-gospels
 Robert L. Thomas, Three Views On The Origins Of The Synoptic Gospels (Grand Rapids, MI: Kregal Publications, 2002), 281.
 Birger Gerhardsson, The Origin of the Gospel Traditions (Philadelphia: Fortress, 1977), 11-14.
 Bauckham, pgs 499-502.