Here is my colleague at Mathnasium of Mill Valley refers to a great article which explains problem with always rushing through math.
Yes, we are fans at efficiency, but with a culture of rush, rush, rush, it seems many students are missing out on the deeper importance of critical thinking, explanation, and problem solving. With these experiences when they are younger, the advanced coursework comes easier and more natural. Number sense is where it's at!
“Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity — to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs — you deny them mathematics itself.”
I love this!! While we definitely spend time helping younger kids with the structures of numeric fluency, we also get them to talk about their math. "How did you do this problem? Why did that work with #4 but not #5? How are #2 and #6 similar or different?" Drawing conclusions, making mistakes, and sharing their thinking through their Mathnasium instructor's socratic questioning helps our students grow!
To read more, visit the entire article here