4 min read


Can Dogs Understand Simple Mathematics?



4 min read


Can Dogs Understand Simple Mathematics?


Do you remember learning to add and subtract when you were a child? First, you learned to count and sort. Then you learned to take groups of objects and count them out together. You may have even learned to count on your fingers. Teachers may have provided you with an abacus or even counting blocks. 

Now think of our dear dogs. They can't really count on their toes and they do not have words to call out numbers. They can, however, demonstrate abilities to recognize patterns and quantities. Scientists are beginning to believe that they can actually count and do simple math.  As we learn more about the abilities of our dogs, we can appreciate the intelligence they bring to the roles they fulfill as our working and social companions.


Signs Your Dog May Understand Simple Math

Becoming a good observer of your dog will help you to understand what your dog is feeling. Dogs communicate with their bodies and facial expressions. Well trained dogs enjoy the rewards and praise that have been developed in their relationship with their owner. As you work with your dog to perform tricks and respond to your signals, you may find your dog appearing confident and approachable. You might even see expressions that give you cause to consider that your smart dog is happy and enjoying the interactions with you.

With dogs, the tail will tell you much about their disposition at any moment. When your dog is feeling approachable and relaxed, you will see a tail that is down and relaxed. Your dog may show alertness as you are working and training with the animal. They will be using their problem-solving skills to understand what you are working on with them. 

Their tail will be horizontal and may move a little from side to side. If the activity is one that has the dog feeling playful, you may find your dog in the play position, with tail and hindquarters up and the front legs down, as if bowing.

Pay attention to your dog's ears and mouth. If your dog is relaxed, you will see the ears up and relaxed with a slightly open mouth. When the dog is being attentive to you and alert, you will see the ears up and forward and the mouth will be closed. You will also note that the dog is posed with a slightly forward stance and upon the toes. Dogs are often alert when they are deciphering quantity or working out simple problems in their minds. 

Body Language

If your dog is working to solve a basic problem, watch for the following:

  • Wag Tail
  • Low Tail Carriage
  • Tail Up
  • Play Bowing

Other Signs

More signs that your pooch is paying attention to numbers are:

  • Forward-Pointing Ears
  • Closed Mouth
  • Smooth Nose

History of Dogs and Math


Scientists have been learning about how math skills have evolved in the animal kingdom. As we look across species, there have been surprising discoveries of math abilities among insects, fish, salamanders, dogs, monkeys, lions, and chimpanzees. Scientists have different notions as to how it is that different species use patterns and math. 

Some believe that this is an outcome of life having a common beginning. Others' believe that the ability evolved from having similar problems to solve. This is called convergent evolution, which is a shared deep evolution of number sense. The importance of number sense for survival is evident in the discovery that wolves have an even better ability to detect quantity than the domesticated dog. 

Animal behaviorist, Stanley Coren, describes three kinds of intelligence in dogs. There is the instinctive intelligence from breeding, the adaptive intelligence that comes from learning experiences in the environment, and the working obedience that comes from training. Some breeds of dogs are more intelligent, such as Border Collies and Poodles. Basically, your dog is as smart as a two-year-old and can be trained to be a valuable assistant and companion.

Science Behind Dogs Solving Simple Math


Studies on the math abilities of dogs demonstrate they can learn simple math. The studies were first conducted with a similar method to studies of the ability of babies to detect quantity.  

The dogs were presented with two bowls. A treat was dropped into the bowls. More treats would be dropped into one bowl than the other behind a screen. The experimenter would then quietly remove a treat. When the screen was removed, the dog would spend more time looking at the bowl in which the number of treats was altered. 

The scientists concluded that the dogs spent more time looking at the bowl with the unexpected amount because they had an expectation of number.  In other words, the dogs had an innate sense that 1 + 1 = 2.  When the study was replicated with the experimenter adding an extra treat to the bowls, the dogs also spent more time staring at the unexpected quantity. 

Another study determined that dogs could reliably distinguish between no treats and one treat but they were not reliable with counting greater than one. Other scientists believe that dogs can count to four or five. While there is a natural sense of quantity that helps dogs to solve problems in their daily lives, simple math,  as with humans, may need some schooling!

Training Your Dog to Count


Teaching your dog can be a fun exercise for both you and your pooch. For supplies, you will need three objects for your dog to count, such as tennis balls or toys. You will also need to establish three targets onto which you place the numerals 1, 2, and 3. The target is something your dog will hit to show the number. Of course, you will need plenty of small treats.

You must first make sure your dog knows how to touch or point on command. You might need to train this skill first.

Start with one. Place one tennis ball on the floor, say, "One", and point to the target for 1. When your dog points to the target for 1, give a reward and praise. Repeat this practice until the dog consistently touches the 1 target when you say, "One".

Now go to two. Add a tennis ball. Say, "Two" and point to the target for 2. Again, praise the dog for pointing to the target for 2 and practice until the dog does it consistently.

Practice going back and forth between one and two.

Now you can add three, using the same procedure.

Like all of us, once we learn to count, you can continue to work with your dog to add combinations of targets and commands. That being said, remember to keep training intervals short and fun!

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Written by a Cavalier King Charles Spaniel lover Pat Drake

Veterinary reviewed by:

Published: 04/04/2018, edited: 04/06/2020

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