In a message dated 95-07-01 02:16:27 EDT, firstname.lastname@example.org (Norm Krumpe) writes:
> >Once again, I want to stress that IMHO, yes, knowing the "times tables" can >be helpful, but there are concepts more basic than these which should be >understood before learning the times tables. > >Norm Krumpe >Indiana University of Pennsylvania >Indiana University at Bloomington > >
Let me digress a little with an analogy. Last night I went to play banjo with some friends. I"m not particularily good and always out of practice. When I want to learn a song, I need to have an overall idea of what the song will sound like. In addition, my left hand must know where to go on the neck to find the notes while the right hand must know which strings to pluck. For all of this to happen requires practice and the overall concepts. If I don't do some practice, I will hear the song in my head, but I won't be able to play it - I won't be able to communicate the song to other people. If I practice exercises night and day but don't have a song in my head, no one will want to listen to my endless rolls.
Learning math is much the same. Students must have some concepts in their heads and practice at the basic skills. I think time must be spent developing basic understanding and practicing skills in an integrated manner. To teach one without the other is to do the students a great disservice.
As a secondary teacher, I find it quite frustrating when students believe that calculators are essential when doing basic arithmetic. Part of learning to understand math is the ability to manipulate the numbers in their heads. Since I learned arithmetic before the time of the calculator, I developed an understanding of the basic algebraic properties before I was told their names because they made it easier to do the arithmetic in my head