How can I teach my child to solve mathematical problems logically?

Answer:  Teach him or her to solve problems the George Poyla way:

George Poyla was a famous Hungarian Mathematician who wrote a clever book in 1945 called How to solve it.

Here’s a summary of his problem-solving method and some problems to solve using his various strategies:

TEACHING PROBLEM SOLVING STRATEGIES IN THE 5 – 12 CURRICULUM

Here’s a video (best to turn off the music!):