A short web search only and you will find many utterances like the followings:
“Learning the "multiplication tables" is one of the first traumas that children usually face when learning arithmetic.”
“The dread rite of passage all children face: the multiplication tables.”
“Parents often remark that their children experience difficulty retaining their math’s times tables.”
“On a personal level, as a kid I found learning my multiplication tables terribly hard.”
If the mastering of this simple skill brings appearance of so negative feelings, then, evidently, there is something wrong with school math education. To improve the situation, we should find the causes of the difficulties and try to eliminate them. Even a brief analysis of the state of affairs allows ascertaining the next ten sources of the difficulties.
Cause #1. Pupils begin to learn the times tables while many of them have not mastered simple mental addition and subtraction totally.
Cause #2. Pupils learn the times tables without simultaneous learning the corresponding to them division facts.
Cause #3. To memorize the multiplication facts, many pupils use the learning by rote only, and the knowledge which has been crammed is forgotten very soon.
Cause #4. Criteria of the mastering the multiplication tables are ill-defined. Teachers and parents have no exact method to determine whether a kid has mastered the skills totally or not.
Cause #5. The memorized results of the times tables are not used in ordinary calculations on a regular basis. Because of that they are forgotten gradually.
Cause #6. Some educators suppose that pupils must learn the times tables up to 20 by 20. But some results (16 by 17, 19 by 18, etc.) are too difficult for kids to remember for a long time.
Cause #7. Many pupils have poor memory in view of the fact that the methods of teaching mathematics which are used at school do not encourage the development of their memorizing abilities.
Cause #8. Pupils are allowed to use calculators too early, and, instead of development of their independent computational abilities, their brains get a cripple wheel-chair for moving in the world of numbers.
Cause #9. The math curriculum of the first four grades is overfilled with great number of various topics, and because of that there is no sufficient time for required quantity of exercises.
Cause #10. The worst method of teaching the times tables is used very often – "Just shut up and learn them, or you'll fail!"
Possibly, this list of sources of the difficulties is not full. Maybe some of the causes will seem insignificant or farfetched to readers. So I will try to motivate and detail my considerations in the next articles.