I suspect he’s going to be hard to hold back, Mike. Sounds as though he’ll keep you on your toes from now on. It is unusual for a 3-year-old to add in the way you describe. Most children cannot do such addition before the age of 6 or 7, and then it isn’t always accurate.
You are right not to want to push him, but there are many ways you can encourage him without pushing. Take advantage of bits of conversation such as you described to provide an opportunity for you to slip in a relevant question. “If you gave one DVD to (a friend, a sibling), how many would you have?” Give him plenty of opportunities to relate counting to actual objects. Many children can count to 10 or 20, or maybe to 100. But if you lay out a number of blocks and ask them to count the blocks, they may touch some of the blocks two or three times and others not at all, ending up with an inaccurate number. Learning to do that correctly is called “one-to-one correspondence,” and it is an extremely important math concept.
Would you like a recommendation of one of my favorite math toys? Of course, so here goes. Buy a set of big dominoes and teach him how to play the game. It might not have helped me with subtraction, but that’s the way I learned to add! And how I loved playing the game with my dad!
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.