5. Mental Block: Due to all of the problems
mentioned above, people (not just kids) often
get stuck when they try to solve problems, either
math or non-math problems. It is a normal and
natural human reaction – freezing in the face of
complexity and ambiguity. No one teaches how
to overcome such mental blocks, except maybe
say “have confidence”, which is not very helpful
when you are not confident and cannot see what
is going on. What is more important is for you to
have a way to solve problems EVEN if you do
not fully understand them, and you do not have
“confidence”.
Because of limited space, I will only briefly and
partially explain the method to solve word problems,
and show a short example--
a. One Idea. Read only one idea at a time.
b. Name Names. Simple names. Don’t use Xs and
Ys because then you need to not only understand
what you are reading, know what you have, but
also translate what you’ve done EVERY TIME you
read it.
c. Translate As You Go (TAG). Every time you read
an idea, or new information, translate it.
d. Do What You Can. Take what you have and do
the most you can with it, regardless of “why” or
“what does it mean?” It sounds simple and trivial,
but it’s a key activity.
e. Keep Doing It. Don’t worry about “what should
I be doing?” “What is the problem/question to
solve?” When you reach the end of the problem,
you’d find that you already know the answer to the
question asked!
Here is an example of a 5th-7th grade level problem, which most students find difficult to solve, and solutions
shown are often difficult to replicate to other problems of similar nature.
Q: Vivienne has 30 oranges, apples, and pears. 10% of those are apples. A third of the remainder is
oranges. How many pears does she have?
Often the solution is presented as such: P = ? × 0.9 × 30 = 18 where P stands for Pears.
The explanation is that pears are two thirds of the remainder, which is 90% of the original quantity. Indeed, it is an
efficient solution. However, it again relies on reasoning out the problem. Furthermore, it is an explanation based on
knowing the answer, not an explanation of how to find the answer.
The “TAG” way:
Sentence 1: Vivienne has 30 oranges, apples, and pears in total. (We stop here, after the first idea, and translate).
Translation 1: Oranges + Apples + Pears = 30
Note: we avoid X and Y as much as possible! There is no need for them and they just add more things to
remember.
Sentence 2: 10% of those are apples
We can translate it to math but first we have to understand that “those” means, “all fruits together”, or
“Oranges + Apples + Pears”, or “30”.
Translation 2: 10% + All fruits together = Apples
Translation 2b: 10% x (Oranges + Apples + Pears) = Apples
Translation 2c: 10% x 30 = Apples and therefore: 3 = Apples or Apples =3
We now “Do what we can” and use this information: Oranges + 3 + Pears = 30 or Oranges + Pears = 27
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