Generally, in a Geometry test, you'd need to test proofs (Prove that triangle XYZ and ABC are congruent).

On the other hand, proofs depends depends on theorems which depend on postulates, which are annoying (and ultimately useless) to memorize.

For example, when I learned Geometry, I had to memorize that postulate 13 is called the "Parallel Postulate" (If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.)

Note, I didn't remember any of that, I had to Google it. That's why I feel that learning Geometry like this is useless. On the other hand, you do need to somehow document your steps.

How do others do it?

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    $\begingroup$ Hi @educator. Welcome to SE. What education level / grade are you testing? $\endgroup$ Dec 23 '18 at 6:43
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    $\begingroup$ As with many pseudo questions about pedagogy, it's really not about pedagogy (how to design/implement a test) but about content. A "this annoyed me" plea. $\endgroup$
    – guest
    Dec 23 '18 at 17:01
  • $\begingroup$ I think in geometry, what you are really learning is how to make structured arguments AT ALL. So, I don't really buy the kvetch about named theorems. And for what it is worth, I found that I learned what they were and just used them so often, that having a quick name was helpful. And I think this is common and is an objective (to make structured arguments, using smaller predicates). So I don't even buy your argument of arbitrariness. Plus there is the "don't use angle, side, side, because you make an ASS". ;-) Furthermore, you DO need to know what it is to apply it (so not arbitrary). $\endgroup$
    – guest
    Dec 23 '18 at 17:05
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    $\begingroup$ It's difficult to give any kind of useful answer to this question without knowing at what level you are teaching and in what country you are teaching. What is taught as "geometry", and how it is taught, varies widely from place to place and level to level. Certainly "geometry" is not synonymous with teaching things about similarity of triangles, although it might be in primary education in the US. $\endgroup$
    – Dan Fox
    Dec 23 '18 at 18:01
  • $\begingroup$ I ditto Dan Fox's comment. I am guessing you are in the U.S. since most other countries don't equate geometry with the teaching of proofs. (They're usually considered two separate subjects.) A lot will depend on the curriculum you are required to follow. $\endgroup$ Dec 27 '18 at 10:34

If you don't want your students to have to memorize facts for your tests, then give them open-notes or open-book tests.

If you want them to memorize some things but not others, then hand out a sheet of notes that you wrote (and which they have seen in advance).


Some ideas: a) Consider giving extra questions and the student can pick eg 5 out of 6 or 5 out of 7. The advantage is that if the students forgets a postulate or theorem, they can pick a different question.

b) Don't insist on using postulate names, but allow either postulate names or the wording of the theorem and be flexible about the exact wording. (as in one the other answers)

c) Speak to your colleagues or past geometry teachers in your school. They will have the best sense of what works in your population.

d) I don't believe it's useless to memorize theorems just because you forget them when you no longer use them. If students are doing classwork and homework, they should have the postulates and theorems at their fingertips without actually having to sit and memorize them.

e) Consider the idea (from the previous answer) of giving students a list of theorems to use during the test.

Good luck and please edit the question to tell us what level you teach and in what country.

  • $\begingroup$ @user683 Your perspective is legitimate, but the OP seems to have a different perspective which is also legitimate. The OP wants to be able to test students ability to do proofs without requiring so much memorization or penalizing them for not remembering every postulate name and theorem. I was answering the question asked and giving strategies to do what the OP wants to accomplish. $\endgroup$
    – Amy B
    Dec 25 '18 at 7:07

You could allow any answer that unambiguously refers to the postulate or theorem even if wording is inexact or the name of the postulate or theorem isn't given.


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