So he's in 1st this year and the year is almost up. It sounds like they want him to finish the year in second and start third next year? What is your goal? (Is it to have him in 4th next year?)

Zen Scanner=so funny. BTDT many times. Sometimes it's frustrating because you as the parent get a message that it takes a year to teach kids something simple. You will likely be met with resistance when you offer to fill in the gaps.

Remain calm and open minded in that they likely do want to help but may have seen both successful and unsuccessful accelerations. They may want to start slow and just didn't communicate the entire forward plan in the interest of not getting too far ahead. Just keep requesting what you think is best and work with them.

I know it is difficult when they ask your child to explain something that is pretty basic. When I was lamenting this to a friend, she reminded me that we need to be able to explain ourselves at work. Putting pencil to paper to show work is a useful skill and it will be required all through school and in the workplace. It helps me to remember that when the teachers require explanations for things that seem basic. I just want to caution not to downplay the need to learn the writing/showing work process. Agreed that it is maddening to think that it takes an entire year to teach this.

My experience has been that the teachers believe what they see from the kid more than the parents talking. Maybe you can convince them of a trial in 4th grade next year. Make sure over the summer that he's ready to write out his work (book stores have some workbooks for story problems) and spot check 4th grade math online (ixl, aleks).