Does anyone know what this is? Does anyone care?
It's called "Common Core" and it's what gave us that horrible math.
The first way was too direct and straight forward, we want to encourage non-linear thinking that doesn't rely on observation and definition which is against the post-modern new-think ideals.
As sarcastic as that sounds, it's actually the reason they used wacky methods to teach math. "Common Core" was created by Liberal Professors who had zero teaching experience and instead were attempting to implement their own new thinking ideology starting at the youngest age possible, to prevent parents from corrupting children with old modernist thinking ways. On the "Common Core" approval and review boards there was exactly one teacher, she taught kindergarten and was overruled every time she pointed out the methods wouldn't be realistically feasible for K-12 education.
So teaching our kids to be deductive is a bad thing? The best way to do Mental math is to simplify the problem which is what the "new way" does in that image vs. the almost non-mental "old way".
I'll tell you what the flaw is:
Once a person figures out the method that works best for them; all desire to learn an alternative method to reach the same end is lost.
The focus on number sense is a great concept but humans are inherently flawed.
It's like: You know that 7x7=49 but did you know that if you know that but knew that 7x3=21 and 7x4=28 and that 3+4 = 7 then (7x3)+(7x4) = (7x7)?
One it's so abstract with the attention span these days you lose them, they do not draw the deduction to connect the sum of 3 and 4 to the sum of the products. On top of the fact most kids just memorize doubles so they don't even care by the time you cover concepts like this. But there will be one kid who has been struggling the whole time who suddenly had an epiphany. This is coming from first hand experience.