I Can't Make Up a New Problem!

After a student finishes his/her math homework or we work on division problems or problems with logarithms, or whatever, I ask them to make up three problems like these, that your teacher will give you on a test tomorrow (pretend), but you have to know the answers,. This is the usual response: I can't make up a new problem!

Why do I ask them to do this?

In making up a problem one has to think about what they are doing-What kind of numbers can I use? -What will the answer look like? Will it be an equation to solve or just simplify the math? -Have I done anything like this before? 'Can I make a graph of this?

Why is this a difficult assignment for them?

I am convinced that students are not asked to do this kind of thing in school. They are not asked to think about what they are doing. When asked what are you doing in school, most respond 'I don't know' or 'I don't know what you call it'. The game is just to memorize a method of solving a problem, then do 30 problems in their book, using this method. OR, They are given worksheets with lots of problems, where they are asked a silly question. The object is to come up with the answers, which then correspond to letters, then they must put the letter in its proper place, then these letters make up the answer to this silly question. They are also asked to do 25 examples of the same kind for homework, instead of giving them 3 problems that they must do 4 different ways! Or make up one for your friend to do or  for Mom and Dad to do.. When they get going, the hardest problems some students make up are guess my rule games!