I see absolutely nothing wrong with rote learning, and, unlike John Mighton, will apologize to no one for advocating it.  It’s the educrats who are wrong. 
Also, if there’s time, then sure kids can ‘discover’, however with proper memorization of the basic facts, discovery happens on its own.  I have experienced this many times myself. 
We are fighting for common sense to be used when educating children.  Too bad so much time and $$ has to be wasted proving common sense

“The teaching methods used in JUMP have been characterized by some educators as rote learning, perhaps because I recommend that teachers guide weaker students in small steps until they have developed the skills and confidence to do more independent work. But, as I will explain later, I always encourage students to take the steps themselves, and as much as possible help them understand why they took each step. This method of teaching, which I call guided discovery, is very different from rote learning. Even when students are capable of taking only the smallest steps, they are still actively involved in making discoveries and constructing their knowledge of mathematics, and are therefore led to understand math at a deeper conceptual level. As students gain confidence through their successes and as they become more engaged in their work, I encourage them to take larger steps and to work more independently.”

Guided discovery, is only as good as the teacher’s knowledge of the children he or she is working with. It is more or less what I was doing at home, because I had to incorporate the school’s curriculum, so in the end my child could do her homework on her own. The weakness of guided discovery, is what one child needs more of differs right across the span, and for some children, they need huge dollops at all stages. What often happens in a classroom, is the gradual reduction of achievement where each child has enough to obtain a 50 percent, and it is left up to the individual child to be encourage to work on their own, to obtain more than a 50 percent. I observed this quite often, when the school complained that I was working my child too hard on achieving more than a 50 or a 60 average. If rote practice is working a child too hard, on the basics, please explain why my child is getting a 75 % or higher on tests? It boils down to when a child is allow to learned on their own independently? For many of the education practices, it rests at 50 %, and when I was re-teaching, it rest on the 90 % to 95 % before I allowed my child to do her homework. Nothing more satisfying to see your child’s face glow without tears running down her face, to see her homework being done quickly and efficiently, and more importantly correct. Now that really motivated my child to learned at a much deeper level on her own, because a firmed foundation of 90 to 95 % was placed beneath her feet.

Essentially, what the school was complaining, that she was learning knowledge at a deeper and more advance their her follow classmates. What was and still is getting in the way, is her dyslexia that plays havoc with her learning. The rote learning as well as direct instruction, helped very much to hinder the dyslexia that strives to keep her in the 50 something average, to maintaining a strong B average, in grade school.

I really do not think that Jump Math’s success has more to do with guided discovery, but what is actually being taught. Like all good math curriculum, it is on the basics,, seeking a solid foundation for students to stand on, to do advance mathematics. So unlike the present math curriculum, and instruction, where practice and direct instruction takes a back seat, to cutting and pasting, and other kinds of busy activities to motivate the student to explore on their own. A recipe for students to become confuse, and decide on their own, they are poor students when it comes to math. Or as my 16 year old said today, cutting and pasting is the grade 9 math curriculum. She was trying to explain the latest on triangles in grade 9 math, to which she does not understand the point of the activities. Would it not be easier to label the triangles as she does? She has a system, that I taught her to prevent the dyslexia monsters from interfering. Not prefect, but it is successful 100 percent of the time, for deep conceptual math knowledge, as well as memorizing the rules. A triangle always has the sum of 180 degrees. Would it not be easier to have students memorized the math rules, rather than allowing students to discovered this on their own? By the way, the idea of labeling system, came from the Jump Math and other good quality math programs. All I did, was reconfigured it for my child.