To get straight to the point, funnily enough I used Pavlov's Dog Experiment and 'Association' theory to teach my little Chinese Crested dog to count.
April was the only one in her litter who survived and the family who bred her didn't think she would make it. They went out the day she was born, leaving the tiny premature pup with her mother, sad and assuming when they returned she would be deceased.
Much to their surprise upon coming home they discovered dear little April latched on to her mother's teet fighting to survive. She would never grow to become the size of other Hairless Chinese Crested dogs, however she became a huge part of my life.
April entered my life at a difficult time, and I found her to be a nice distraction from what was troubling me. I took to spending time playing with her, and one day decided (as I'm sure all dog owners do) to teach her some tricks.
Holding a little doggy biscuit in my hand that she eagerly wanted me to give to her I asked April to speak. "Speak" I said and as I did this I had the doggy biscuit in between my thumb and index finger together and motioned them upward. She'd watch my hand as I did this, but seemed confused.
"Speak" I'd say again and did the same motion with my fingers. Again April looked confused. She was getting pretty annoyed. Finally after a few times she barked at me out of frustration. If she could speak I'm sure she'd say "Just give me the damn biscuit!"
As soon as she had barked at me I gave her the biscuit. Then I repeated the same thing until she barked again, instantly giving her the biscuit again. She now associated the word 'speak' and my pinched finger and thumb moving in an upward motion with barking once. I could stand outside far away from her and do the finger motion and she would bark. Or I could just say 'speak' and she would bark. I've even tried this over the phone.
I then wondered if I could do the same thing and have her bark a number of times. I'd hold up two fingers and say "Count to two" and move my fingers in an upward motion like I'd done before. She'd bark, then I'd move my fingers in an upward motion again saying "Count to two" and she'd bark again - then I'd give her a biscuit. We repeated this until she associated the two fingers with barking twice.
What was absolutely amazing is that I didn't need to teach her any further numbers after 3. I could hold up 5 fingers and she figured out that it meant she would need to bark 5 times in order to receive her treat. We could do this all the way up to 10.
Eventually I wouldn't even need to hold fingers up, she managed to memorise the numbers. Now that is amazing.
I also taught her to do the Mexican Wave among other tricks. Never underestimate the intelligence or special qualities of a dog, no matter how small or if they are the runt of the litter. I also learned through this that anything is possible if you put your mind to it.
April to this day however refuses to 'sit' on command. I heard that Einstein had difficulty performing basic functions also. Ha ha.