>be better of learning the basics of why (experiment design, independence, covariance, etc) and then the basics of how augmented with tools like probability too

>be better of learning the basics of why (experiment design, independence, covariance, etc) and then the basics of how augmented with tools like probability toolkits that do the math for you? This is how I learned statistics the first time. We started with experimental design and sampling and built up from that. By the time we'd actually started getting to the actual math and statistics we already had a pretty firm grasp of the principles behind what we were doing and why. The math itself by the time we started learning it really wasn't too bad, then we moved onto using R for stastics. I ended up having to take a second stastics course afterwards, the teacher taught it differently. There were people in my class that hadn't been through the other course. They struggled horribly with it. The material wasn't any more difficult, it was mostly the same material we'd been taught before(my degree was odd, I ended up having to take a few redundant, repeat classes to satisfy credit requirements). The teaching method made a huge difference, I even found some of the second course confusing despite it covering almost the same stuff.