Scholastic chess - kid struggling to play well in tournaments last few months

I'm wondering if any parents of young scholastic players have had this experience. My 1st grade son (this is his account) has a good teacher, plays online, is getting better online, but literally cannot make any progress on his OTB performance the past 4 months. He just doesn't seem sharp in the tournament games, and he is beginning to get discouraged. As a proxy for tournament performance, his rating is rattling around 850 or so, which is where it was after his 5th tournament in October!  

He loves chess and playing with his school team, but as I said, he's beginning to get bummed out, and I want to help him out of his funk. Words are great, but an even better cure will be to get him doing a bit better w/out undue pressure or stress.  Anyone other parent been here before?  

Possibly of interest:
Simple Attacking Plans by Fred Wilson (2012)
https://web.archive.org/web/20140708090402/http://www.chesscafe.com/text/review874.pdf
https://www.newinchess.com/Shop/Images/Pdfs/7192.pdf
Logical Chess: Move by Move by Irving Chernev (1957)
https://web.archive.org/web/20140708104437/http://www.chesscafe.com/text/logichess.pdf
The Most Instructive Games of Chess Ever Played by Irving Chernev (1965)
https://chessbookreviews.wordpress.com/tag/most-instructive-games-of-chess-ever-played/
Winning Chess by Irving Chernev and Fred Reinfeld (1949)
https://web.archive.org/web/20140708093415/http://www.chesscafe.com/text/review919.pdf
Back to Basics: Tactics by Dan Heisman (2007)
https://web.archive.org/web/20140708233537/http://www.chesscafe.com/text/review585.pdf
Discovering Chess Openings by GM John Emms (2006)
https://web.archive.org/web/20140627114655/http://www.chesscafe.com/text/hansen91.pdf
Openings for Amateurs by Pete Tamburro (2014)
http://kenilworthian.blogspot.com/2014/05/review-of-pete-tamburros-openings-for.html
https://chessbookreviews.wordpress.com/tag/openings-for-amateurs/
https://www.mongoosepress.com/excerpts/OpeningsForAmateurs%20sample.pdf

Chess Endgames for Kids by Karsten Müller (2015)

https://chessbookreviews.wordpress.com/tag/chess-endgames-for-kids/
http://www.gambitbooks.com/pdfs/Chess_Endgames_for_Kids.pdf
A Guide to Chess Improvement by Dan Heisman (2010)
https://web.archive.org/web/20140708105628/http://www.chesscafe.com/text/review781.pdf

Seirawan stuff

http://seagaard.dk/review/eng/bo_beginner/ev_winning_chess.asp?KATID=BO&ID=BO-Beginner
https://www.chess.com/article/view/book-review-winning-chess-endings
https://web.archive.org/web/20140627132508/http://www.chesscafe.com/text/hansen173.pdf
http://www.nystar.com/tamarkin/review1.htm

My first thought is he's getting bored or distracted. I've played casual game with beginner kids like this, who after 20 or 30 minutes of playing well will just start moving randomly at some point because they'd rather be outside running around or playing a video game. I don't know what time control the school uses though.

Also online ratings are more up to date because people play so much. Kids are notoriously underrated in their OTB ratings. Imagine him playing other kids like himself, who have improved, and can see it online after 100 games, but OTB they are limited to a few rated games a month, so even if they have improved a lot they can't see it after so few games.

If they're USCF rated games, you can search online for his opponents. Find kids with similar pattern i.e. same ratings after many months (which is very common) and show him (or explain to him it's normal).

If you're wanting to make your kid a very strong player though, I think this is a good way to start. A systematic program developed for kids. Instead of winning games OTB, you could make the achievement completing exercises or workbooks.

https://www.newinchess.com/The_Complete_Step_by_Step_Method-p-1933.html

I'm not at all familiar with early childhood chess, having coached high school kids who were serious-chess newbies, but 850 isn't bad and if he's reached a plateau - 4 months isn't that long - it might be because the things he does in chess are not adding to the knowledge he has. Does he have a program other than playing other kids at chess club?  Does he work tactics problems?  Does anyone go over endgames with him?

It may also be that other kids are improving, too and there's a closed group of players - the same kids in all the tournaments - whose overall rating may not go up much in such a young group.

Another reason they'd stagnate is they would convince themselves that if they memorized openings, especially opening traps, they'd win more.  So they did not study strategy and tactics - back then, in the '90's, our "Bibles" were Jeremy Silman's 1st Ed. of How to Reassess Your Chess - I bought copies for each of my players - and selected chapters of other books I photocopied like Nimzovitches chapter on Overprotection from My System and Kotov's chapter on Strategy and Tactics of Attack on the King from Keres' and Kotov's The Art of the Middle Game.

Little kids' books covering tactics, etc. may be worthwhile.