I would be very cautious about pushing too much. My older son was always very slow with work early on (he was on the Asperger's end of the Autism spectrum, but doing great with a GF/CF diet and Armour thyroid) . The teachers were concerned as he really had difficulty completing tests, worksheets, etc on time in class, although he knew the work. Overtime, he did improve and we really never pushed it. My younger son was ADHD before the GF/CF diet and improved quite a bit, but the problem didn't totally resolve until very recently when he started taking Armour thyroid - he know has so much more attention and the struggle to get homework done is dramatically less - he would start once he got home from school, get distracted and often not finish until after 10 pm some nites. But, again, I didn't push the issue - but telling them that they can do x when they are done can hel, as well as asking them if they needed any help - but I never said to do the work faster or sooner really, as I think they truly are physically and cognitively limited as to how fast they can do work. Over the years, I've gotten grief from teachers that thought I should help them more and I have heard enough times to last a lifetime that teachers can see my kids can do the work, but they just don't do well on tests for the same material, yet they get top scores on standardized tests and have very high IQs. But, I feel that my kids have to do the best they can with their own efforts and timeframes, so they learn to deal with their limitations on their own as they get older. And, I've seen this work fairly well as my kids are gradually doing better.
So, if you've not considered the GF/CF diet or had him tested for hypothyroidism - a full panel including TSH, Free T3, Free T4, as well as antibodies and possibly even getting a sonogram to see if he isn't at the first stages of autoimmune thyroid disease as was my oldest son, then I would highly recommend that. It has been extremely useful for me to be able to encourage my kids by letting them know that I know they're doing their best and that it's not their fault when they have some of these difficulties. BUT, this is something that they do have to deal with. I am just thankful that they have recognized the benefits of the diet and the replacement thyroid hormone.
Also, you can get tested to see if he is having an immune reaction to gluten and dairy at: www.enterolab.com
And for the thyroid you can also order your own tests. https://www.healthcheckusa.com/testdetails.asp?productid=22 (TSH, Free T3, Free T4)
http://www.healthcheckusa.com/lab_tests/Thyroid_Screening...
http://www.healthcheckusa.com/lab_tests/Thyroid_Screening...
They send you a lab form to take to a local Labcorp clinic at your convience - you get results in 5-7 days. It couldn't be easier and saves on at least one doctor appt. If you just want your doctor to run the tests, please make sure they run all of them. Most doctors use old/inaccurate tests and don't test for antibodies.
I have found it's extremely helpful to go to doctors with these test results in hand - very few doctors are knowledgeable in this area, so it takes a very proactive mother to get kids like this the help they need. And, note I am not advocating self treatment for thyroid problems, it's just that I've learned that few doctors will even consider this for kids, but when you have proof in hand, they will treat. I am also so emphatic about this because my older son had low thyroid symptoms over 6 years ago, but the doctors wouldn't listen to me, so he wasn't diagnosed until a year ago. So, he suffered needlessly (struggling with school work and being very tired) for 5 years!