The field of statistics has also changed - box-and-whisker plots, stem and leaf plots, scatter plots, etc. Math is not static.
What you showed me isn't exactly new, though "manipulatives" seems to cover a broad range of teaching methods from the logical hands-on to the down right silly.
Another is fractals -Benoit Mandelbrot, a mathematician at IBM, is an expert in processes with unusual statistical properties, such as those in which a random variable's average or its variance is infinite. His early work in the 1950's and 1960's suggested that the variations in stock market prices, the probabilities of words in English, and the fluctuations in turbulent fluids, might be modeled by such strange processes. Later he came to study the geometric features of these processes and realized that one unifying aspect was their self-similarity. In the mid-1970s he coined the word "fractal" as a label for the underlying objects, since they had fractional dimensions. Fractals are shapes or behaviors that have similar properties at all levels of magnification or across all times. Just as the sphere is a concept that unites raindrops, basketballs, and Mars, so fractals are a concept that unites clouds, coastlines, plants, and chaotic attractors. .
Well, I've yet to see somebody mathematically predict, with consistent accuracy, the movement of the stock market. :^) That said, this is application, not fundamental math IMHO. And, its much higher level than the 6th grade class that you teach.
The field of statistics has also changed - box-and-whisker plots, stem and leaf plots, scatter plots, etc. Math is not static.
I'll concede that these are also progressions to math. But none of this changes the fundamentals of math - addition, subtraction, division, multiplication, fractions, algebra, trig, and basic calculus. The basics must be understood before one delves into higher orders of math.
You can't calculate the volume of a sphere if you can't perform the basics. And the best way to learn the basics is through progressively drilling, applying, and building upon previously learned material. Yes, that includes 'problem solving', but your definition of problem solving and mine are completely different.