I kind of answered this question here albeit with a bit of a broader brush than specifically Anglo-Saxons. Defining 'science' in a medieval concept is a very tricky thing to do. Chemistry, for example, isn't really a field yet beyond specific applications: metallurgy and jewellery to give two. Anglo-Saxon moneyers become very adept at ensuring consistent levels of silver content in their coinage, for example. Technology does advance during the period though - development like the ox plow should really be considered as scientific advancement.

Science and scientific knowledge remain the preserve of the Church in this period, largely because they are the ones with the learning, understanding and access to the prepatory texts and theses. As I mentioned before, astronomy is actually very important, and one of the chief studies of medieval science. Partly this is because of the need to accurately calculate Easter, but also from an intellectual curiosity to better understand God's creation.