Well I lived in Japan for three years, I'm by no means an expert. With that disclaimer I would argue that the Japanese do not have a very technological culture. In fact, when I got back to the states it was amazing how different things were.
In japan I had a flip phone, I had never heard of a smart phone, and neither had my Japanese girlfriend. Droids blew us away, the iPhone was hot, but Japan had neither and if they did we had never heard about it. Also jobs that would be automated in the US are done by hand, this is in part a way to employ the overcrowded population, and tradition.
There's a thousand other small examples that make you pause, but they're too numerous to list here. All that said they're a very hard working and efficient society, but not at all like the many misheld beliefs westerners have.
Science, math and engineering is very well taught, the students at a young age will branch off into "clubs" and basically remain in them throughout their education. These are the typical clubs you think of in the us, the baseball clubs, math, soccer, chess..ect. Calculus is high-school level, and pretty uniformly taught. The good universities are on par with the US system, although most seek higher education outside Japan.
Their history education is abysmal, just strike up a conversation about WW2. Many will have no idea what you're talking about, as that's mostly glossed over. Those that know WW2 even happened had no idea about Pearl Harbor, battles for the Philippines, ect. This is just my anecdotal experience.