Here are some examples of how the early Church fathers approached the Abraham stories, and more specifically the Binding of Isaac in Genesis 22. Read through these and note how the Christian interpretation of the story tries to read the story as a way to understand why there was an "old" revelation ("Old Testament") and how it is related to the new revelation (Incarnation and crucifixion of Christ).

Also compare these to Paul's own reading – Paul focuses more on Abraham himself (as an individual proving his faith), while these (especially Clement – probably the most important one) tend to focus on the binding and sacrifice itself.

These texts and others from the early Church Fathers can be accessed at two websites:
 http://www.newadvent.org/fathers/
 http://wesley.nnc.edu/noncanon/fathers.htm
 
 

From On Christian Doctrine
http://ccat.sas.upenn.edu/jod/augustine/ddc1.html
Book I, Fundamentals of Christian Doctrine, on Things and Signs

Augusting is discussing how to read the Hebrew Bible in light of Jesus and the events that founded Christianity: The issue is how to make sense of the ideas, prophecies, and histories of the Hebrew Bible now that we have a new revelation. The issue here: if the Ram used by Abraham in lieu of Isaac for the sacrifice does not merely signify the thing itself (i.e. just a ram), what does it signify? What does it become a symbol of?

CHAP. 2.--WHAT A THING IS, AND WHAT A SIGN.

2. All instruction is either about things or about signs; but things are learnt by means of signs. I now use the word "thing" in a strict sense, to signify that which is never employed as a sign of anything else: for example, wood, stone, cattle, and other things of that kind. Not, however, the wood which we read Moses cast into the bitter waters to make them sweet,(3) nor the stone which Jacob used as a pillow,(4) nor the ram which Abraham offered up instead of his son;(5) for these, though they are things, are also signs of other things. There are signs of another kind, those which are never employed except as signs: for example, words. No one uses words except as signs of something else; and hence may be understood what I call signs: those things, to wit, which are used to indicate something else. Accordingly, every sign is also a thing; for what is not a thing is nothing at all. Every thing, however, is not also a sign. And so, in regard to this distinction between things and signs, I shall, when I speak of things, speak in such a way that even if some of them may be used as signs also, that will not interfere with the division of the subject according to which I am to discuss things first and signs afterwards. But we must carefully remember that what we have now to consider about things is what they are in themselves, not what other things they are signs of.

 
Book IV: The Christian Orator
CHAP. 20.--EXAMPLES OF THE VARIOUS STYLES DRAWN FROM SCRIPTURE.

In a similar vein to the above ideas about Scriptural Interpretation. Here he is talking about styles of writing in scripture and what they mean. Using a quote by Paul from the New Testament, Augustine reads back to the Old Testament to try to show how and why the new revelation completes and surpasses, i.e. makes void, the old revelation (i.e. the Jewish revelation and covenant). If this is correct, it would then mean that "Israel" -- i.e. Judaism -- is no longer valid, it is still "in bondage".

39. But now to come to something more definite. We have an example of the calm, subdued style in the Apostle Paul, where he says: "Tell me, ye that desire to be under the law, do ye not hear the law? For it is written, that Abraham had two sons; the one by a bond maid, the other by a free woman. But he who was of the bond woman was born after the flesh; but he of the free woman was by promise. Which things are an allegory: for these are the two covenants; the one from the Mount Sinai, which gendereth to bondage, which is Hagar. For this Hagar is Mount Sinai in Arabia, and answereth to Jerusalem which now is, and is in bondage with her children. But Jerusalem which is above is free, which is the mother of us all;"(2) and so on. And in the same way where he reasons thus: "Brethren, I speak after the manner of men: Though it be but a man's covenant, yet if it be confirmed, no man disannulleth, or addeth thereto. Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ. And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect. For if the inheritance be of the law, it is no more of promise: but God gave it to Abraham by promise."(3) And because it might possibly occur to the hearer to ask, If there is no inheritance by the law, why then was the law given? he himself anticipates this objection and asks, "Wherefore then serveth the law?" And the answer is given: "It was added because of transgressions, till the seed should come to whom the promise was made; and it was ordained by angels in the hand of a mediator. Now a mediator is not a mediator of one; but God is one." And here an objection occurs which he himself has stated: "Is the law then against the promises of God?" He answers: "God forbid." And he also states the reason in these words: "For if there had been a law given which could have given life, verily righteousness should have been by the law. But the Scripture hath concluded all under sin, that the promise by faith of Jesus Christ might be given to them that believe."(1) It is part, then, of the duty of the teacher not only to interpret what is obscure, and to unravel the difficulties of questions, but also, while doing this, to meet other questions which may chance to suggest themselves, lest these should cast doubt or discredit on what we say. If, however, the solution of these questions suggest itself as soon as the questions themselves arise, it is useless to disturb what we cannot remove. And besides, when out of one question other questions arise, and out of these again still others; if these be all discussed and solved, the reasoning is extended to such a length, that unless the memory be exceedingly powerful and active the reasoner finds it impossible to return to the original question from which he set out. It is, however, exceedingly desirable that whatever occurs to the mind as an objection that might be urged should be stated and refuted, lest it turn up at a time when no one will be present to answer it, or lest, if it should occur to a man who is present but says nothing about it, it might never be thoroughly removed.

(From The Epistle of Barnabus: http://wesley.nnc.edu/noncanon/fathers/ante-nic/barnabus.htm
Church father pages. http://wesley.nnc.edu/noncanon/fathers.htm)

On why Abraham's circumcision is a sign of real faith versus other nations that also circumcised at the time. Abraham's sacrifice (here the circumcision, the shedding of his own blood, and not the Binding of isaac) looks forward to and signifies Christ's own sacrifice.

9:33 Learn therefore, children of love, concerning all things abundantly, that Abraham, who first appointed circumcision, looked forward in the spirit unto Jesus,
9:34 when he circumcised having received the ordinances of three letters.
9:35 For the scripture saith; 9:36 And Abraham circumcised of his household eighteen males and three hundred What then was the knowledge given unto him?
9:37 Understand ye that He saith the eighteen first, and then after an interval three hundred in the eighteen I stands for ten, H for eight.
9:38 Here thou hast Jesus (------).
9:39 And because the cross in the T was to have grace, He saith also three hundred.
9:40 So He revealeth Jesus in the two letters, and in the remaining one the cross.
9:41 He who placed within us the innate gift of His covenant knoweth ;
9:42 no man hath ever learnt from me a more genuine word ;
9:43 but I know that ye are worthy.

From An Answer to the Jews  http://www.newadvent.org/fathers/0308.htm

This is from a polemical tract intended to show the Jews why Jesus is in fact the correct Messiah, and to prove the validity of the new revelation. In these passages, Tertullian is working with various verses from the Hebrew Bible connected to each other with key words (here "tree"). In so doing, he connects the Tree of Knowledge in Genesis 2 (Fall of Adam and Eve) to the wood used by Abraham to sacrifice Isaac, to the wood used to crucify Jesus.

A second time, in fact, let us show that Christ is already come, (as foretold) through the prophets, and has suffered, and is already received back in the heavens, and thence is to come accordingly as the predictions prophesied … And in the Psalms, David says: "They exterminated my hands and feet: they counted all my bones; they themselves, moreover, contemplated and saw me, and in my thirst slaked me with vinegar."(14) These things David did not suffer, so as to seem justly to have spoken of himself; but the Christ who was crucified. Moreover, the "hands and feet," are not "exterminated,"(15) except His who is suspended on a "tree." Whence, again, David said that "the Lord would reign from the tree:"(16) for elsewhere, too, the prophet predicts the fruit of this "tree," saying "The earth hath given her blessings,"(17)--of course that virgin-earth, not yet irrigated with rains, nor fertilized by showers, out of which man was of yore first formed, out of which now Christ through the flesh has been born of a virgin; "and the tree,"(1) he says, "hath brought his fruit,"(2)--not that "tree" in paradise which yielded death to the protoplasts, but the "tree" of the passion of Christ, whence life, hanging, was by you not believed!(3) …

[The passage goes on to talk about how world is sunk in error and sin, but how with Christ there is a restoration -- "baptism" is rebirth from sin into a new blessedness that is made possible by the crucifixion]:

[The world} is freed in baptism by the "wood" of Christ, that is, of His passion; in order that what had formerly perished through the "tree" in Adam, should be restored through the "tree" in Christ? … This "wood," again, Isaac the son of Abraham personally carried for his own sacrifice, when God had enjoined that he should be made a victim to Himself. But, because these had been mysteries(26) which were being kept for perfect fulfilment in the times of Christ, Isaac, on the one hand, with his "wood," was reserved, the ram being of-feted which was caught by the horns in the bramble;(1) Christ, on the other hand, in His times, carried His "wood" on His own shoulders, adhering to the horns of the cross, with a thorny crown encircling His head. For Him it behoved to be made a sacrifice on behalf of all Gentiles, who "was led as a sheep for a victim, and, like a lamb voiceless before his shearer, so opened not His mouth"

From The Instructor  http://www.newadvent.org/fathers/0209.htm
Book I

(Note: name "Isaac" means Laughter: one who laughs)

Clement here mentions the idea of "type" which becomes central to Christian readings of the Hebrew Bible. The idea here is that the Hebrew Bible contains "types" that correspond to ideas that are now revealed with Jesus and recorded in the New Testament. The Hebrew Bible therefore is a revelation of God that "looks forward to" and "anticipates" or "sets up" the new revelation to come (i.e. the Incarnation of God in Jesus and His sacrifice). One of the most important types is drawn from Genesis 22:

That which is signified by the prophet may be interpreted differently,namely, of our rejoicing for salvation, as Isaac. He also, delivered from death, laughed, sporting and rejoicing with his spouse, who was the type of the Helper of our salvation, the Church,

(NOTE: 'SHE' HERE IS REBECCA, ISAAC'S WIFE; REBECCA BECOMES A "TYPE" FOR THE CHURCH)

This is a more detailed explanation of Isaac as "type" of Christ

The King, then, who is Christ, beholds from above our laughter, and looking through the window, as the Scripture says, views the thanksgiving, and the blessing, and the rejoicing, and the gladness, and furthermore the endurance which works together with them and their embrace: views His Church, showing only His face, which was wanting to the Church, which is made perfect by her royal Head. And where, then, was the door by which the Lord showed Himself? The flesh by which He was manifested. He is Isaac (for the narrative may be interpreted otherwise), who is a type of the Lord, a child as a son; for he was the son of Abraham, as Christ the Son of God, and a sacrifice as the Lord, but he was not immolated as the Lord. Isaac only bore the wood of the sacrifice, as the Lord the wood of the cross. And he laughed mystically, prophesying that the Lord should fill us with joy, who have been redeemed from corruption by the blood of the Lord. Isaac did everything but suffer, as was right, yielding the precedence in suffering to the Word. Furthermore, there is an intimation of the divinity of the Lord in His not being slain. For Jesus rose again after His burial, having suffered no harm, like Isaac released from sacrifice. And in defence of the point to be established, I shall adduce another consideration of the greatest weight. The Spirit calls the Lord Himself a child, thus prophesying by Esaias: "Lo, to us a child has been born, to us a son has been given, on whose own shoulder the government shall be; and His name has been called the Angel of great Counsel." Who, then, is this infant child? He according to whose image we are made little children. By the same prophet is declared His greatness: "Wonderful, Counsellor, Mighty God, Everlasting Father, Prince of Peace; that He might fulfil His discipline: and of His peace there shall be no end." O the great God! O the perfect child! The Son in the Father, and the Father in the Son. And how shall not the discipline of this child be perfect, which extends to all, leading as a schoolmaster us as children who are His little ones? He has stretched forth to us those hands of His that are conspicuously worthy of trust. To this child additional testimony is borne by John, "the greatest prophet among those born of women:" Behold the Lamb of God!" For since Scripture calls the infant children lambs, it has also called Him--God the Word--who became man for our sakes, and who wished in all points to be made like to us--"the Lamb of God"--Him, namely, that is the Son of God, the child of the Father.