I will be thrilled if this works. Some observations.
Brilliant new educational ideas often don't scale up. They work as long as you have motivated, specially-trained teachers who want everyone to succeed. However this seems to have allowed for some of that in its design, and may get past it.
This is not the math drills beloved by education traditionalists, but it does involve repetition and seems a cousin to drill. They are wise to not call it that. It breaks the work into even smaller components. It is emphatically not the way many newer math approaches have gone the last sixty years. Traditionalists might want to be prepared to embrace this as at least a less-bad alternative.
Farther down the article we get into some unanswered problems. The creator of JUMP is pleased that it works from a "growth mindset." This is very fashionable these days but remains unproven, except in the fairly obvious - well, it used to be fairly obvious anyway - idea that anyone can get better at things if they work at it. It is good to keep children, or anyone, from being discouraged too early. Yes, it does feel bad when you compare yourself to others and aren't as accomplished.
The problem of the better students being bored is glossed over. Supposedly, they are going to be happy because the whole class is happy and we're all in this together. Who needs silly old grades! We're having fun! The whole class is doing better, and the other students are happy! Uh, does this actually happen? I remember my second son throwing himself on the floor in despair the first week of first grade, wailing "Can't we at least do the numbers up to TEN?" A friend who was a math teacher gave him the bad news that every year of his school career in math would start with review.
I also don't like that they think bell curves will go away if teachers don't expect them. Tightening the distribution is a fun phrase, but I mistrust it. Also, what happens later in school? Do we apply this tightening in Algebra 1, so that the class doesn't move forward until almost everyone has got it right? Are we going to have any real mathematicians in the future, or just a lot of people who have mastered fractions and decimals? Maybe that's a better outcome, but my initial prejudice is against it.
The better students might just glaze over and self-teach, which might be better anyway.
If this does actually work better, I cynically predict it will be undermined by the education establishment who want other things to be true. They want their previous methods of "discovery" and "inquiry" to prove out. They are sure that they will prove out. Those are just better ideas, gosh-darn it, and we are cheating children if we don't give them that experience, you fools. They will resist implementation of repetition and breaking things into smaller steps, because that is "selling students short," and not "teaching them to learn." If JUMP is brought in, they will try to relegate it to supplementary status. Failing that, they will introduce their old methods as a supplementary status because "lots of children learn better that way," sans evidence. The supplement will gradually encroach on the mandated new program, and when there is no improvement they will claim "See? It doesn't work. We had better go back to the "old" way." If you think that can't happen, that is exactly what did happen to drill.
The first part of the method might work, and even if it doesn't work totally, it might be better than what we are currently doing. Let's hold that second part at arm's length.