Thanks for your comment, Benjamin.
The traditionalist view of what constitutes ‘core mathematical knowledge’ certainly leaves a lot to be desired. The curriculum is packed with mindless facts and methods that actually inhibit students’ mathematical reasoning. At the same time, we should be careful not to dismiss the premise of core knowledge altogether. There are certain things that students should learn regardless of their background or interests —no education is complete without a firm grasp of, among other concepts, regular polygons, integer addition and fractions. That said, the way in which students interact with mathematical truths should take account of their individual needs, preferences and even their beliefs (if you can tolerate a shameless plug, see EdTech’s Culture Problem).
The key is to teach these concepts with understanding, which constructionism sets out to do. Discovery-based approaches sometimes go too far in their expectations of what children can learn for themselves, but Papert’s work is compelling because it acknowledges the need to embed supports within these exploratory contexts.