I thought a post might be good for parents new to KTM and this problem.
Kitchen Table Math exists because many K-8 schools don't ensure mastery of basic skills. Parents have to do the work at home. And, as one can see by other posts, it's not just a problem in math. Everyday Math, a common math curriculum, spirals through the same material each year in the hope that students at all levels will master the skills when they are ready. They assume that this works by definition. They tell teachers to keep moving and to "trust the spiral". It doesn't work.
One night long ago, I told my son to stop fooling around and do his EM math homework (from a workbook, not a textbook). Ten minutes later, I saw him doing other things and told him to do his math. He said it was already done. I looked at the workbook and saw only 4 easy problems. When I asked the teacher about this, she said that they will get a chance for more practice when they spiral back to the same material. They talk about how spiraling builds on previous knowledge and skills, but I saw only repeated partial learning. One parent complained that three of her kids were covering the exact same material and they were in three different grades. Either they knew the material already and were bored, or they were still confused.
Parents learn the hard way that it doesn't work. Many schools know that it doesn't work too because they send home blanket notes to parents asking them to work on "math facts". They must know that that some parents can't or won't. Unfortunately, this problem doesn't just stop at basic arithmetic. It continues with things like fractions, percentages, and solving equations. Parents are left reteaching their kids at home or with tutors. Some parents don't see this problem until 7th grade when their bright child gets placed into the "slow" math track. It's unlikely that the student will recover after that point. It could be an ability issue, but too many students respond well to curricula like Singapore Math (as with my son) at home or with tutors. KTM is loaded with examples of how parents had to help their kids.
When my son was in fifth grade, his teacher found bright students who still didn't know the times table. Some were still adding 7+8 on their fingers. She had to stop trusting the spiral to get students back up to speed. This caused her to skip 35% of the material that year, but the focus on mastery did work. However, she did not try to get the lower grade teachers to improve mastery of the basics.
This is not difficult material if mastery of basic skills is ensured starting in the earliest grades. However, the "trust the spiral" attitude pumps problems along until many gaps have built up and teachers can't possibly diagnose and address each one. That’s why Everyday Math includes things called "Math Boxes" to try to get students to fix themselves. This makes math seem much more complicated than it really is. Schools talk about critical thinking and problem solving, but they don't define them exactly and many students can't show them on state tests designed to match these teaching ideas. Those vague skills don't make up for a lack of mastery of the basics. The best students are the ones with the best mastery of skills.
Unfortunately, the new Common Core Standards won't force K-6 schools to fix the problems of mastery. The use of the word "fluent" in the standard is sparse and the word is undefined. The new tests, like PARCC, are unlikely to put much pressure on schools to achieve a level of mastery that will keep all career doors open in K-8. Kids will still be pumped along, and the onus for keeping kids on track will still rest with parents. My advice to parents is to not trust the spiral. You have to ensure that your kids master the material the first time starting in the earliest grades. You have to ask the school when and how they track in math. You have to ensure that learning gets done to meet this tracking decision. You have to realize that "proficient" is not nearly good enough. Even "exceeding expectations" might not be good enough. Schools will talk about how wonderful it is that they get so many kids over a low cutoff proficiency level, but this is not very meaningful for individual students. Many parents quickly figure out that their standards have to be much higher that the state standards. Schools care about statistics, but parents care about individuals. What’s good for schools is not necessarily what’s good for your child.