When you said that the problem shouldn't be a variation of the "book problem" I would enforce it that way :
In the pool of problem, some must introduce new concept to work on. Students should be able to leverage their knowledge to solve them without to have been instructed how to do.
Some other problems should take a similar formulation than in "exercise book" with little variance to trap student that make "brainless studying".
Of course, students must be aware of such malicious questions.
Here is an example of theory and the 3 kind of questions : Theory :
The sum of 3 consecutive numbers can be computed by tripling the mean.
So : 3+4+5 is equal to 3*4
Question :
Type 1 : Calculate the sum of 345,346 and 347
Type 2: Calculate 5+6+7+8+9. Explain how you can calculate the sum of any 5 consecutive numbers.
Type 3 : Calculate the product of 17,18 and 19
Now, you can use the answer to know how the student may have acquired is knowledge :
-> Only type 1 OK --> Student make "brainless studying".
-> Type 1 OK and summed number in Type 3 --> Student miss some attention to question and didn't understand what he studied
-> Type 1 and 2 ok --> Student master the theory and is able to leverage it
etc.
Of course, it's time consuming but better for learners :-)
It's also nice to introduce some problem of lower grade without letting the student know !
They must able to find out how to solve them.
And also, putting some problems that can be solved can trick the student and show them what's real life. Students should be able to state: "not enough data to process it" or "Obtained answer is irrelevant" (eg. negative age).
I did never saw any puzzle in my maths exams and I think that they're good for assessment because the student must figure out how to translate it in mathematical terms to solve it.
I'm sure that students will disagree at first glance because exam would appear harder. But once they'll be used to, it will make only one difference : They will understand what they're doing and you will not have the following funny dialogue any more :
T - What's Maria's age ?
S - Minus ten.
T - Do you find it possible ?
S - Of course, it's maths ! All is possible !
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