Some place emphasis on higher order thinking skills at the cost of lower emphasis on drill/practice. Others disagree. Personally, I agree that higher order thinking skills are necessary for effective application of mathematics to problems, but I do not want to ignore the fact that effective higher order mathematical thinking requires firm understanding of fundamental mathematical principles. Therefore, I would like to combine both… but I'm a bit unsure about the “how to”.

Is there any well-vetted way to find a good balance between both?
If there isn’t, can you provide some hints/tips that might help me?