Though he never states this explicitly, it is clear that the method he advocates for the teaching of each individual subject, parallels the method by which he chooses his entire course of study. Each subject is taught separately (in simple parts) and is followed by a subject that bears an obvious logical connection to it. With his carefully planned out curriculum, Locke aims to present a rational pattern to knowledge and to tailor academic learning to the developing mind of the child.
Locke claims that natural philosophy can never be a science. He means that we can never really have a systematic body of knowledge in natural philosophy. Locke is working with a very strict definition of knowledge here. Knowledge is the perception of a connection (either agreement or disagreement) between two or more ideas. The connection that needs to exist between ideas in order for them to count as knowledge is very strong. In the case of disagreement, the connection must be one of logical inconsistency. A square circle is an example of two logically inconsistent ideas. A married bachelor is another such example. In the case of agreement between ideas, the connection needs to be a necessary connection. That is to say, in order to know that A caused B you need to know that given A, B could not have failed to happen. Another way to put this is to say that in order to know that A caused B, you need to be able to deduce B given only the information that A, or derive B from A. As an example, consider one ball hitting another and causing the other one to move. In order to know that the first ball caused to second ball to move, you must know that the second ball could not have failed to move given the fact that the first one hit it. Or, to put it the other way, in order to know that the first ball caused the second ball to move, it has to have been possible for you to have predicted with certainty that the second ball would move, as soon as you knew that the first ball hit it.
Given this strict definition of knowledge, Locke does not think that we can have any knowledge concerning natural philosophy (that is, we cannot make it into a science). All that we can do is go through the world and observe certain qualities regularly co-occurring. We can see, for instance, that gold is malleable, yellow, fusible, soluble in aqua regia, etc. This, however, does not give us knowledge of the nature of gold because we do not see any necessary connections that would explain why gold has all of these properties regularly co-occurring. We do not see any necessary co-existence between these properties. The kind of connection that Locke is demanding is the sort that we find between properties regularly co-occurring in geometrical figures. In those cases, we can deduce the properties and see why they are necessarily co-existent. For instance, if we want to know why the angles of a triangle always add up to 180 degrees, we can construct a mathematical proof that shows us why this is necessarily the case (that is, why it could not possibly have been otherwise).
Locke does consider the possibility that we could find a necessary connection between the observable properties and the microstructure of the objects they belong to. At IV.iii.11 of the Essay he states explicitly that if we had access to the microstructures (say, with a very powerful microscope) we would be able to deduce from it the observable qualities to which it gives rise. In other words, we would see the necessary connection between the microstructure and the observable qualities, and would therefore have knowledge of the nature of things. In section thirteen, however, he reigns this fleeting optimism in. Even if we did gain access to the microstructures, he tells us, there would still be an insuperable obstacle to our knowledge. The problem is that while there is a necessary connection between the microstructure and the primary qualities we experience (i.e. shape, number, texture), there is no necessary connection between the microstructure and the secondary qualities that we experience (i.e. color, sound, taste, smell, feel). There is no reason, Locke claims, why such and such an arrangement of matter should give rise to the sensation of sweetness or of blue. It is simply God's arbitrary decision that forges these connections. God could easily have set things up differently, so that, for instance, the microstructure that now gives rise to our sensation of yellow could actually give rise to the sensation of blue or even to the smell of chocolate. Given that a large percentage of what we observe about the world is secondary qualities, this is a pretty considerable obstacle to knowledge.