I often wonder if students still need to learn basic number facts like multiplication tables. I'm told that they do, but I see so many that don't know basic multiplication facts.
Students, parents and even some of those affecting the direction of education seem to think that students don't need to "memorize" math facts. That's "old school" like when teachers used to hit students with pointers, (remember the wooden sticks with the rubber tips)?
Memorize multiplication tables? That's simply torture with no rationale or valuable outcome. You'd think it's Abu Ghraib or something! After all, we all have access to calculators pretty much all the time.
Pretty soon students probably won't need to write script/cursive. Oh wait...I think that already happened too. I guess being able to read script isn't important either.
Anyway, the analogy I use that seems to work for me is comparing knowing number facts to driving. Could you imagine if every time while you were driving and saw a sign you had to stop, interpret and then proceed? That analogy works if you assume that students eventually get their number facts correct after thinking about it (even though they often don't).
So I come to a red, eight sided sign that says "stop". Do I need to think about what to do? No. Am I even reading the sign? Maybe not.
I can drive from here to work and sometimes not remember anything about the whole ride. My brain helps me drive almost subconsciously.
When a ball rolls across the street, I automatically hit the breaks. No active interpretation needed. Ball = STOP! Street lights, merging into traffic, turning, whatever.
There was a time in my life that I needed to consciously decide what to do and how every moment through the process.
With mathematical facts, I just know them because I had to learn them. I think this is what many students are missing and why they stumble through math. They stop to think about every step in the process of solving mathematical problems. 6 X 7...uhhhhhhh. Damn! 36? uhhhhhhh. Ok 42.
Obviously these problems are may differ in different areas, schools,
etc.... but when I encounter a struggling student, I usually find that
the issue is with basic math.
If the simple processes could be truly mastered and internalized and become part of students thinking process, they would do much better.
I feel that the basic skills mastery is usually the difference between good students and bad ones.
-Working with fractions
-Operations with integers
These are the root of many of my students' problems. I usually hold pop boot camps several times throughout the year, and I think I've been able to do some good.
I'd love to know how others feel about this and what if anything they do to combat this problem.
Chris Robinson has an interesting blog post about number sense here, check it out.