Mary,

We have to be careful here. We can call it the Coin Test for Kantian philosophy.

Kantian philosophy is called by Hegel the philosophy of reflection. The ego is taken as absolute and its internal subjectivity is the arena in which reality is reflected and dealt with. He also calls this subjective idealism. When a Kantian thinks of a coin he sees it as perspectives or 'respects.' In other words, he only grasps it by external reflection in which the coin is "for himself."  Hegel calls this knowledge for self the vanity or conceit of knowing. It makes someone feel important but it cannot give us the truth.

The Hegelian, on the other hand, recognizes the coin as it is "in and for itself" as a unity in difference. It is the same situation as for a magnet in which two poles (polarities) are united. The otherness of the other is respected in and for its own self. He doesn't consider it according to his external perspective or reflection but determines its content  according to its own being, in relation to its own concept. 

Hegel does not discard Kantian reflection, as he finds all philosophy is an organic unity at different stages of development, but he sublates it within his absolute philosophy so that the Organic Whole or Absolute Truth itself has reflection within itself or is Subject as much as Substance. In order to avoid confusion sometimes Kantian reflection is spelled differently from Absolute reflexion. The Absolute has its own being in and for itself, and as the Absolute Necessary Being (sum of all possibilities or contingencies) it is the source or creator of all contingent being and Nature, including finite mind or spirit. 

Mind comes from Mind, Spirit comes from Spirit. Materialism cannot explain how mind comes from matter, but Hegel's Absolute that is Substance as Subject, or reflected in itself and for itself, gives a rational explanation for where Mind comes from.

The Kantian denies his own M(Other) from which he comes as a mediated, not immediate being. This radical otherness must be accepted and comprehended in its proper medium of otherness. Scientific knowledge or the proper Concept of knowledge requires this type of knowing. The finite ego is not left out, but he is also sublated in the Absolute as an ideality, as is the fate of all finitude in the Infinite or Absolute.

The philosophy of reflection is finite understanding, which grasps truth only in its particulars or parts, which it then tries unsuccessfully to unify. For speculative philosophy, the truth is only the whole - the organic whole in the sense of being both its process of developing and the result of that development.

Just to add a word about the mathematization of science, mathematics is a formalism, a tool that the knower applies instrumentally to the known. In the Phenomenology, Hegel explains how this instrumentalism distorts knowledge or makes it impossible to arrive at truth. Mathematics also suffers the problem of being conceived as true apart from its proof, and therefore cannot satisfy Hegel's criterion for science of the organic whole. 

Further problems it cannot resolve: its severe limitations Godel has shown in his Incompleteness/Inconsistent Theory, and the chaos it leads to in practical application (it cannot solve an n-body problem for n>2) has led to the complete downfall of deterministic science.

Kant felt that Life could not be dealt with by science since it involves an internal teleological principle inaccessible to experiential observation. Hegel does not consider science to consist merely of observational experience, but to be essentially a rational system that needs the concept of Life to make sense of its observations.

Getting back to the points you were making. If we mark a point on a sphere or spinning coin, at a particular time and mark its starting place, we can trace the movement of that point as a circle as the coin rotates on its axis. What the point does is move away from its starting place and then returns to it. In this sense it is an unchanging (resting) change (restlessness). It is the same movement Hegel attributes to Spirit/God, that posits itself as different and then returns from that difference to itself, thereby establishing its own identity. 

Its identity (rest) is not a static but a dynamic (living, restless) identity - an identity in difference. Infinity is the movement that posits the finite as its determinations and then returns these predicates back to itself, as in the speculative sentence. If S is the subject and P is the predicate, to state the proposition S is P is to lose the subject in the predicate. With the speculative reversal the predicate is brought back to its proper place as a characteristic of the subject. The finite determinations in which the infinite is expressed seem to have a being of their own but are then sublated and brought back to that to which they referred, which is a self-conscious Subject or Identity and not a mere formalistic movement. Thus it is really the Identity of its identity and difference.