Expert: Ken Jensen - 10/31/2009

Question
Hi.

I am a student not a teacher but I have been wondering about something about the way math is taught.
You see one day I asked my friends this question :  (  ((1-(1/2))*(1-(1/3))*(1-(1/4)).....*(1-(1/99))(1-(1/100))) - (1/100)  ) = ?
and  we are in the 12 grade but most of them couldn't answer it while I asked student from the 5th grade some of them did. So I tried going to online chat rooms and ask people who are 18-17 years old but they are said that the question is too complicated while they must have studied fractions.

I think any teacher would see that the question is simple since all the numerators and the denominators cancel out until 1/100  - 1/100 = 0

I am not talking about why people couldn't answer this specific question I am just wondering why  a lot of the students forget all things they studied in the previous year.

Answer
Hamad,
You ask a very insightful question, one which researchers here in the U.S. are working on trying to answer.  First, I want to validate your perception that many mathematical concepts and procedures which are easy for 5th graders seem to be harder for 12th graders.  You would think that new math ideas would grow and develop on top of old ones and that a student would need to understand the old ones well for them to understand the new ones.  This does not, however, seem to be the case for most students.  If you ever have the opportunity to read some of the work of Jo Boler you might get some insight into some of this.  Dr. Boler, along with other researchers such as John Van de Walle, James Hiebert, and the work of NCTM seem to be telling us that math which is “learned” in the elementary grades is many times lost in the secondary grades when it is taught out of context.  To be mathematically literate means to be able to use the math that you are learning.  When the math is useful it seems to be remembered and then used later with more complex math.  The problem you posed is a good example of this.  The problem by itself does not have any use and where as an answer may be found by a 5th grader, the 12th grader is more likely to answer with the question, “why would I ever need to know that?” The reality is that most people would not need to know how to solve the problem you have posed.

I have begun to ask, “What does it mean to work on important math?”  To me math that is important is math that is used in life.  Understanding how to use the patterns in Algebra, ratios in Trigonometry, and distributions in Statistics to make predictions are skills that would make an individual mathematically literate.  For me the main purpose of math is to make predictions and we would all make better decisions if we had a better grasp of the math that underlies them.  I believe that a better grasp of the math would then minimize the occurrences of students forgetting what they have learned.  

Please respond with your thoughts on this

Ken Jensen