Life without answer keys?

Recently I've been exchanging emails with Alexander Givental, who has translated the famous Russian book Kiselev's Geometry into English.

He's raised some interesting points regarding answer keys. I will just quote him directly from his emails to me. The discussion concerns geometry problems (please see the earlier post for examples).

"What is actually accomplished by supplying any solution at all? Ideally a student should be able not only to find a solution himself, but also be able to check that his solution is correct. With the aid of a written colution, the exercise is rendered useless for both purposes. Furthermore, a beginning student who finds a more complex solution (or may be even the same solution but eplained differently) may decide - incorrectly! - that his solution was wrong.

So, comparing your solution with your classmate's, teacher's, or parent's one makes sense, but with the one written in a silent book - very little. That's why, I think, no one bothered to write solutions for "Kiselev".

There is one general problem with solution books: there are many ways to describe the same solution to a problem, and there may be many solutions to the same problem; so it requires just as much expertise from a reader to figure out if his own solution is correct by reading somebody else's solution as it would without it. That is why collections of problems *with* solutions (which do exist in geometry), typically deal with higher range of difficulty than Kiselev's problems, are written in a very concise style and intended for highly experienced readers. BTW, for more than a hundred years of systematic use of Kiselev's book in Russia, it didn't occur to anyone to publish a solution manual. This should tell you something.

Teacher's guides are intended to save a teacher, clueless about the subject he teaches, from the embarassment in front of the class. They don't make him less clueless for, if they did, then teacher's guides would be used in place of textbooks. With or without teacher's guides,
a clueless instructor - teacher or parent - is of little help to the student. Conclusion: teacher's guides are obstructions to learning - for the instructor, and therefore for the student."

I agree with some things here. Being able to check that your solution is right is indeed desirable. After all, real life situations won't come with an answer key either. You need to be pretty sure about your solution then.

But, I'm sure answer keys save many homeschooling families many frustration tears.

Maybe it would work if every parent had someone to turn to in moments of problems - support. It could be another person, or internet message board.

Maybe the existence of answer keys reflects the culture and the times: we want everything fast and easy. Even answers to math problems. No one wants to ponder on a math problem for more than ___ (fill in) minutes.

What do you think?

See also Challenging problems in math education


Rachel said…
I would definitely agree with some of what he said. During my homeschooled highschool days, I wouldn't have survived without the Saxon solution manuel. However, I do agree with him about needing to have significant knowledge of the subject in order to tell if your answer is really wrong when it is just in a different form.
Stephen said…
I don't want to have a solution in a teacher's guide. I want all the solutions in the text for the student. I recall deriving the Pythagorean Theorem. Very cool. Only much much later did i learn that there are more than 100 such proofs.

It's one of my complaints about Suzuki Violin. The student's book doesn't have it all. It should be noted that i don't have many complaints about Suzuki.
Sherry said…
Most of my students are not that interested in math. They are studying algebra and geometry because I think they should be familiar with those subjects. They would not be excited and pleased to figure out a new solution to a math problem; they would be frustrated that they had spent so much time on something that didn't interest them that much. Of course, they probably wouldn't spend the time in the first place.

So, we use a solution manual.
Anonymous said…
I would have to agree with most of the quote however a solutions manual is invaluable when the directions are not at all clear. Working the problem backward can sometimes bring a better understanding of what was asked.

Maria Miller said…
I wonder how textbook publishers would like hearing that: that parents need the solution manual to figure out what the problem was asking!

I've heard it mentioned that solutions manual is necessary because of all the grading work - which raises another question: is all that grading teachers and moms are doing really that necessary for good math learning? How much of the grading is done just for the system's sake?
Hanley Family said…
I agree, I think. Answer keys have problems with them. My dad once came up with a solution not on the answer key. He and the instructor spent a long time testing it and the teacher finally named the theorem after him. It wasn't until he was in college studying electrical engineering that he found that little theorem again.

With a good understanding of a subject, you do know when your answer is right and you know how to check it. Unfortunately, I don't have that good of a mastery to, say, see where my daughter made a mistake in calculus. But I have a few years to learn, I guess : )
Hanley Family said…
I know I just commented, but I ended up posting on this, as well. After thinking about it, it started reminding me of how I was taught math in Germany.
Anonymous said…
I believe that sometimes you yourself is not very sure of your solutions so i do agree that key answers are very useful to the reader or student because it is necessary to check on his solutions right away. I agree also that there are many solutions to one question, at least in the answer key you learn one or more if you are doubtful of your answer.


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