In what image can I make my children?

What can we bequeath our children?
Will they be in our image? in the image of God?

In Karl Barth's extensive discussion of the imago Dei (image of God) (discussed some in a previous post) he goes on to compare Genesis 1:26-27 with Genesis 5:1-3

1 This is the book of the generations of Adam. When God created man, he made him in the likeness of God. 2 Male and female he created them, and he blessed them and named them Man when they were created. 3 When Adam had lived 130 years, he fathered a son in his own likeness, after his image, and named him Seth.

Barth then discusses how God has made possible history (the existence of human generations) and man has been blessed to control the physical mechanism by which a new generation is produced. But the "image of God" in man is only given by God, the creator.

The particular feature in the history of the human race is not given or actualised merely in the fact that it can renew and preserve itself by a continuous procreation of its kind. This history is a peculiar history in relation to that of all the other creatures because it is the history of a fellowship and intercourse between man and God.
But the possibility and continuity of this history as such is not assured by the fact Adam can be reflected in Seth; that man can become a father and have a son. Nor is it the human father who can transmit to his son that which will make him not only a living being but the subject and bearer of this history. Nor is he this himself in virtue of his existence as man, but solely in virtue of the fact that God has created him in and after His image.

The special feature of human existence in virtue of which man is capable of action in relation to God; his nature as a Thou which can be addressed by God and an I which is responsible to Him; his character as an I and Thou in the co-existence of man and man, of male and female-all this, and therefore the divine likeness, cannot be transmitted by the father to the son merely because he is the cause of his physical life.

The father can, of course, hope that God the Creator will so acknowledge the new creature to whom he as father has been able to mediate life that the son whom he has begotten may like himself be created in and after the image of God. But the realisation of this hope has not been left to his decision and action. How can he hope to be able to pass on what does not in any sense belong to him, but is his only because when He created him God willed to have mercy on him among all His creatures and to acknowledge him in this particular way? The actuality of the witness repeated in Gen. 5¹ is not guaranteed to all succeeding generations merely because there will be these generations........

There is no genealogical table of beings in the divine likeness, but from generation to generation the genealogical table aims at divine likeness. This divine likeness is the pledge and promise with which God accompanies the physical sequence of the generations and gives it meaning, thus giving meaning to the patience of God which makes it possible. The difference between likeness to God and likeness to Adam emerges clearly enough in the text and context of Gen. 5³.

Church Dogmatics 3.1, p. 198

This clearly illustrates that Genesis is not about the natural history of the animal and plant kingdom, or anthropology, or even human history, but about the character and the history of the covenant between God and man.