I., \
Good news! you don't know what you don't know about ADHD. You are describing one of the kinds of ADHD, without hyperactivity, and there is treatment and plenty of help out there that will help him!
Get him to a Developmental Pediatrician or a psychiatrist/ neuropsychologist evaluation combination and write a letter to your school district asking for an evaluation. He should also see an occupational therapist about the handwriting, and request that he be given something called the CHES (children's handwriting evaluation scale.) Your school should provide services for him in school that will make him more educationally functional. He should have assistance to remember the things he is forgetting, reminders, cues, extra time, and many other interventions to help him with this.
You should provide the lions share of what he needs because this is a medical condition (if that is what the qualified doctor finds.) That will include some combination many hours per week of: Cognative behavioral therapy, play therapy, social skills classes, Occupational therapy, speech therapy, and medical, educational, and behavioral interventions. It is a lot of hard work for your sons doctors, therapists, teachers, you and your son, but it does produce results and he can feel better.
ADHD (even without the hyperactivity) is a medical condition that comes about because of an issue in the brain. Brain cells do not touch. There is a tiny space between each one called a synapse. Our thoughts are carried through our brains via electrical impulses, and when they reach the synapes, our bodies produce neurotransmitters, chemicals, to carry the throught accross the space. It happens hundreds of millions of times a second. If your son does not produce enough neurotransmitters or the neurotransmitters on his brain cells are damaged, he cannot keep thoughts going with any reliablity, and he "forgets." He can't fix this without targeted help. His thoughts just stop, not all of them, but many of them....and that he can pay attention to something does not mean that he is doing this on purpose, it means that that part of his brain that processes the information he can do is not effected or is less effected. ADHD is manefested in the prefrontal cortex, which is the area of the brain that is in your forehead, and this area does many of the organizational tasks and executive function that he has difficulty with. You cannot punnish him enough for his brain to make more, or better use of his nuerotransmitters. It is counter productive to tell him that could do a good job yesterday, or last week, or any time that he did not loose track, when his brain helped him to carry that thought, and then to say that that success is evidence that his brain did not lose track when it happens, and yet, teachers and parents beat kids over the head with their success all the time as a reason that their brains were not reliable on the times that they lose track. If you do this, I would stop right now, it eats away at them and they really cannot control the chemicals their brains produce.
Find out for sure, get a diagnosis, get the school involved, and do some reading about what ADHD is and isn't. You don't know what you don't know, and it is probably nothing like you think or the popular myth you have heard about. Read anything by Dr. Mel Levine or Dr. Russel Barkely. Go to the CHADD website and get additudes magizine. Log on to www.wrightslaw.com and learn about school advocacy.
M.