At the present the simple multiplication skills of very many pupils are "good-for-nothing", and our children are getting worse and worse at the skills.
Myth #1. Pupils should learn by heart the times tables up to 20 by 20.
I can not even imagine some explanation to justify this immoderate demand. While the results of the times tables up to 9 by 9 are constantly using when we multiply or divide the numbers expressed by several figures, the other operations appear much more rarely in ordinary computations. So why kids must memorize by heart the results of 13 by 16, 19 by 17, etc.? If they have mastered the times tables up to 9 by 9, all such operations may be easily implemented by "pencil and paper". Maybe just this excessive demand provokes the considerable difficulties when teaching the times tables about which we hear so often.
Myth #2. Many kids do not have abilities to master the multiplication tables.
Indeed, at the present the simple multiplication skills of very many pupils are good for nothing, and our children are getting worse and worse at the skills. If the situation is not changed, then, maybe, very soon we will be forced to say that most pupils cannot perform simple multiplication. However, both my experience (35 years in the classroom) and my investigations (23 years of studies) show that every mentally healthy pupil can totally master all basic multiplication facts within the limits of 100.
Of course, there are kids who cannot learn math because they have not been taught to learn properly. Furthermore, there are persons who do not want to learn math at all. They do not try to memorize results, they do not work at lessons, they do not carry out homework themselves, but it is quite other problem. Nevertheless, I would like to lay emphasis once more – if a pupil wants to learn the multiplication tables, then we can help him/her to do this successfully. Good will of children and teachers is the main required condition for success in mastering the multiplication tables.
Myth #3. There are easy ways to learn the basic times-tables in minutes.
Do not trust educators who promise you easy and quick methods of mastering math basics. There are tips which can help to understand how to find the results of some operations, but there is not a magic potion which can help to memorize the results at once. In the past there was not a royal road for learning math as a whole (and the multiplication tables in particular), there is not one at the present, and I cannot imagine that such a road will appear in foreseeable future. To master any skill a pupil must perform certain quantity of exercises. Mastering the multiplication tables requires zealous work, maybe, arduous work. This work must include not only memorizing the results, but permanent application of them in different kinds of computations too. We can make this work interesting and productive, but we can not manage without it. And such a work requires sufficiently plenty of time to reach the desired goal (not minutes and even hours, undoubtedly).
Myth #4. We can manage without mastering simple mental computations because modern mathematics is a science of ideas, not an exercise in calculation. Being a wiz at figures is not the mark of success in mathematics.
I hardly can understand what some educators imply when they speak about New Math or Whole Math keeping in view reform of school mathematics. We can add new topics, shuffle them as playing cards, move them from one grade to another, but we can not manage without numbers when teaching math. Up to the point I have not seen at list one math curriculum which proclaims needlessness of mastering operations with different kinds of numbers, solving equations and so on. Meanwhile my practice and my long-lasting investigations show that pupils with unsteady simple mental computational skills (addition and subtraction within the limits of 20, multiplication and division within the limits of 100) have great difficulties while learning the other basic topics of arithmetic and algebra. Learning mathematics for pupils who have not mastered totally the skills is similar to learning reading without knowing the letters. Without a doubt, being a wiz at figures is not the mark of success in mathematics, but being an ignoramus at figures is the mark of failure in mathematics.