In contemporary philosophy, idealism and materialism describe metaphysical schools of thought that respectively assert consciousness (or mind or concepts or will) and matter as the fundamental substance of our world. I will not mislead you, Engels does espouse a form of conventional materialism. In addition to this however, he gives idealism and materialism new meanings, I think best illustrated by this section from section "III. Classification. Apriorism" The quotation follows a lengthy section, paraphrased from Eugen Duhring which I will not subject you to here, but the beginning may be confusing as a result.
>"What he is dealing with are therefore principles, formal principles derived from thought and not from the external world, which are to be applied to Nature and to the realm of man, and to which therefore Nature and the realm of man have to conform. But whence does thought obtain these principles? From itself? No, for Herr Duhring himself says: the realm of pure thought is limited to logical schemata and mathematical forms (the latter, moreover, as we shall see, is wrong). Logical schemata can only relate to forms of thought; but what we are dealing with here are only forms of being, of the external world, and these forms can never be created and derived by thought out of itself, but only from the external world. But with this the whole relationship is inverted: the principles are not the starting point of the investigation, but its final result; they are not applied to Nature and human history, but abstracted from them; it is not Nature and the realm of humanity which which conform to these principles, but the principles are only valid insofar as they are in conformity with Nature and history. This is the only materialistic conception of the matter, and Herr Duhring's contrary conception is idealistic, makes things stand completely on their heads, and fashions the real world out of ideas."
This quote can be difficult to parse so read it over again if you need to. Engels unequivocally states here that the distinction between idealism and materialism is one of METHOD, rather than metaphysical substance. The primary difference between materialism and idealism for Engels is not metaphysical at all, it is epistemological! It regards principles, ie, statements, laws of nature, empirical claims. Let's break down his definition of the "materialistic conception" into three points:
>The principles are not the starting point of the investigation, but it's final result.
>They are not applied to nature and human history but abstracted from them
>It is not up to nature to conform to these principles but rather it is up to the principles to conform to reality
Clearly, materialism for Engels entails a particular method of empirical investigation. You might say, a scientific method. The first two points regard how empirical claims are apprehended. Karl Popper explicitly excludes any specifications in this domain from his criterion, so Engels method already has a wider array of applications, but the third point--upon careful consideration--contains the rational embryo for falsifiability! If principles are shown to not conform to reality, what are we to do with the? Throw them out! In this one line, Engels has implied Poppers criterion forty or more years before it's advent! Admittedly, it is not spelled out in Poppers characteristic autism, but I think what it lacks in rigor it makes up for in elegance.