Decimals

When I was tutoring yesterday, we were working on decimals, multiplying and dividing decimals to be precise. While in teacher's college we went through the theory behind all of this, but when looking at it yesterday, I had a mini panic attack in my mind because I had forgotten it all and was not able to effectively communicate the theory to my student. However, thank God for textbooks because I opened it up and it provided a wonderful example and everything came flooding back!

When looking at my student's questions yesterday and when I learned the theory behind multiplying and dividing decimals, I reflected back upon my own learning of this material and realized that I never really learned the theory behind it, but I just did it, mostly by rote. Although I know many of our careers and jobs do not really need us to multiply or divide decimals, I wonder if any one in the working world now actually understands the theory behind it.

The question my student had to answer was (paraphrased because I can't really remember):
How come when you multiply 0.4 and 0.7, it will equal a smaller number/decimal?

Learning about this in particular was very enlightening when I was in teacher's college and was glad kids were able to learn how this actually worked, versus doing just everything by rote. However, there were some things that I also learned in teachers college especially in math and numeracy that was to a point disturbing. I say this because one of my students is in Grade 7 and is still having difficulties with her 4 times tables at times, and I am thinking back to my days in Grade 7 and I would think that I had a better grasp of the times tables and long division. For me, I find that as teachers we go so far to accommodate for some students but sometimes might be more detrimental than helping them. I feel that there are times for rote memorization and times for new strategies as well. It also could be because of my background as a CBC where my Chinese parents drilled the times table into my head after I could grasp the concept of multiplication. However, I think when I have kids I will do the same, because watching my student struggle yesterday with long division questions and sometimes even simple addition was frustrating and sad to me at the same time. It will be interesting to see how my tune will change when I actually get into the classroom myself.