Isaac Nash, from Huddersfield, went missing after getting into difficulty in the water at Aberffraw, Anglesey, North Wales, on Friday lunchtime.
Police and the coastguard yesterday continued to search for the Kirkburton Middle School pupil, who was playing with his brother Xander when he got into difficulty.
His mother Zoe told The Yorkshire Post that her son was “always active” and was due to take his black belt in Taekwondo in March.
She said: “He was an amazing boy. I thank God for giving me an amazing, special boy for 12 years who packed his life to the full.
“He had an amazing day climbing Snowdon the day before with his dad and brother, Xander. On Snowdon he saw a man propose to his girlfriend at the summit and he was so excited.
“The police and coastguard have been fantastic, and they are continuing to search for our boy. We are taking comfort in hearing all the stories and seeing the pictures of our young man.”
A specialist underwater search team was called in to help check the estuary on Saturday, while family members and local people helped search the shoreline.
Yesterday the police helicopter continued the hunt with three teams of coastguard staff.
Isaac and his brother Xander had been playing in the water when they got into difficulty in rough seas and relatives tried to rescue them.
Anglesey coastguard manager Dave Brewer said it was understood the father of one of the boys managed to grab him while the grandfather tried to grab the other child.
He said: “The grandfather went in to rescue the other lad and a wave swept over. He managed to grab the rocks but lost grip of the child that is missing.”
Since his disappearance, a page set up on Facebook in memory of Isaac has attracted dozens of comments.
An event in tribute to Isaac is due to be held tonight in Huddersfield, with well-wishers urged to bring a lantern or balloon.
One Facebook post said: “R.I.P Isaac, we will all miss you so much, everyone is going to be there tomorrow for you and it will be a beautiful night celebrating all the good things you gave to us during your short time on earth.
“You had the biggest heart and could cheer anyone up, you made us laugh with your mischievous ways and beautiful personality, not forgetting your amazingly positive outlook on life, you’re safe with the angels now.”
Another post said: “RIP Isaac Nash you always knew how to put a smile on everyone’s face, som things will never be the same without you, you will be missed greatly by so many, in our hearts and memories forever.”
One Facebook user wrote: “Isaac was one of the nicest people I’ve ever met he always knew how to make everyone smile and he was loved by everyone he will be remembered by everyone as that lovely with a cheeky grin xx R.I.P.”
Coaches at Phantom Tiger Taekwondo in Huddersfield, where Isaac attended, put a message about the schoolboy online.
It said: “Isaac was a fantastic member of the club and a pleasure to instruct. He gave everything to his training, always looking for new techniques and ways to improve, and always with a smile.
“Not only did he work hard to improve his own Taekwondo, he showed himself to be a great teacher, always happy to help other students, both juniors and seniors, from white belt to black belt.
“Isaac was a loving brother, son and friend to many. He taught us all a great many things and he will be greatly missed by everyone at the club.
“Our love and best wishes go out to all of Isaac’s family and friends at this difficult time, we are here to help in any way that we can.
“Isaac, you demonstrated all of the tenets of Taekwondo, it was our pleasure to train with you and we will remember you always.”