Arguably, content with clear boundaries, such as a sine wave function, can be easily separated and then re-embedded in other courses, where these connections are made, but this becomes more difficult for subjects with less well-defined bound- aries, for example taking a learning object about slavery from one context and embedding it elsewhere may lose much of the context required for it to be meaningful.

(Weller, M. (2014). The battle for open. London: Ubiquity Press. DOI: https://doi.org/10.5334/bam p. 70)

which spontaneously made me want to protest. It could seem like something simple as a sine function could easily be isolated and explained on its own. However, after having taught the basics of trigonometric functions more times than I really care to count, I’m not so sure. And I believe there is something to understand about how students construct knowledge, what students expect from a course and how courses, in general are designed that Weller is missing here, something that has bearing on how reusing content actually works. It’s mostly beside the point he is trying to make, and I’m sure others have pointed out similar things, but I haven’t seen an explanation of it. So let me try to explain what I see as the problem here:

A sine function is something that needs to be explained as a part of a math course including trigonometric functions. It can be used to model periodic phenomena. There’s a picture showing y=sin(x) in the header of this post. There are a number of pictures, exercises, interactive or just explained that can help students understand how it works. MathWorld has a pretty thorough explanation of the basics including a number of graphs that can be redrawn according to parameters chosen by the viewer. However, the explanation found there is far too complicated for the students I used to teach, and it wouldn’t be advisable to use it. My students had, for example, no knowledge of complex numbers, which would be needed to understand that page. In order to include a resource about the sine function in a course, I would have to check very carefully that my students had the right prerequisites to explain them. This would make finding resources very time consuming, but I suppose it could be done, and I could probably find a good resource at a more suitable level. This page doesn’t have much text but contains a very useful visualisation of the relation between trigonometric functions and the unit circle. It would have been a much better resource to use with my students, even though there are a couple of things that I would like to improve before using it. (The toggle between degrees and radians, the lack of gridlines or ticks for other angles than π/2 on the x-axis and 1 on the y-axis for example.) However, if I wanted to use this resource, I would still want to go carefully about it. Math students are usually working very close to a textbook. The course focus would be a textbook with exercises. Introducing a separate resource like this will cause confusion and/or not add very much unless it’s done deliberately. I would need to add questions and problems to solve with the help of this  resource. Those questions should preferably be phrased in a way familiar to the students. In short, it’s a lot of work for me as a teacher. A lot more than would be implied by the notion that a sine function is a small simple object that could easily be lifted out from and integrated to different courses. And in general, I think it is hard to single out pieces that can be turned into small neat educational resources to be reused within another course, at least within a subject as accumulative as mathematics. In fact, I think a module about slavery more likely to be re-usable, especially since students in the social sciences in general have more experience with handling multiple sources and voices in their course materials. But a key here is, perhaps, that a module about slavery would be a module, something that’s a bit larger than just a pretty picture of a function, and something that can be taken in as a whole. Because embedding small pieces in a way that works may actually be more work than creating small pieces that you can use yourself.