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Teachers' Lounge Discussion: Problem-solving difficulties

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From: Loyd

To: Teacher2Teacher Public Discussion
Date: 2001122215:27:22
Subject: Problem-solving difficulties; making a table may help

My only full time classroom experience has been with 9th and 10th
grade math classes.  However, i have taught GED classes and also
tutored quite a few elementary and middle school students in small
groups of 1 to 3.  Here are a couple of things a I think can help.

1.  Make sure the students know their add, subtract, multiplication
and division facts before they enter the 4th or 5th grade.  I have
tried to teach many students who still didn't know all their
multiplication facts.  This slows them down so much in almost
everything they do.  For example, can't convert 24/36 to 2/3.

2.  Many students have trouble understanding when to use 
multiplication or division.   Some times they can get the correct
answer if the numerals are small.  or example, if you say eggs are 2
cents each, how much will 3 eggs cost.  They know that the answer is
6, but they often don't know that multiplication will result in the
answer.   One thing you can do is to make the problem harder with say,
eggs are 5 cents each, how much does 12 eggs cost.  Often they are
confused and give completely illogical answers.  I try to teach
students to make a table and make them take the time to complete:

Number of eggs                                 Cost
1 egg                                          5 cents
2  eggs                                       10 cents
3 eggs                                        15 cents

12 eggs.                                                 ?

Often they still don't know the answer, but if you continue to make
them complete the cable, they will usually see the solution is a
simple multiplication.  So, start with simple tables with small
numbers and then progress to ones with larger numerals.

The way I worked these type of problems during my life time was to try
to solve the problem and If I had trouble, substitute small simple
numbers in place of the larger more complex looking numbers.  Then ask
yourself what you did to solve the simple problem.  Do the same for
the complex problem.

For example, if you said Santa had to visit 10 homes in 10 hours, how
much time would he have for each home including the travel time.   
This problem is easy, but if you substitute numbers as follows:

Santa  had to visit 31,256,132  homes in 14 hours, how much time would
he have for each home including the travel time.  With this problem
you may get silly answers even if students use a calculator.  That is
why it is often profitable to substitute simple numbers to see the
procedure for obtaining the solution.  

3.  Division problems are just as difficult but if you can relate the
problem to life experiences, that can help.  For example if you bought
three pizzas cut into 8 slices each, how many slices will each person
get if there are 8 people to eat the pizza.  If they can work that
problem, you can progress to more complicate problems to make sure
they know to use division.  A student will often know the answer is
three slices each, but may not know they used division.  You can check
that by making a hard problem such as if there are 57 slices of pizza
for 19 kids, how many do each kid get.  

4.  Students don't understand subtraction vocabulary many times.  For
example, "take 8 from 9" is often misunderstood.  Often they will
write 8-9 fof that problem. One needs to express each problem in a
variety of ways for it to sink in.  

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