Coaching Students to Use the Back of the Book Correctly

Question

My high school students' textbooks have a full answer key in the back. Nearly all of my students make at least one of these mistakes:

• Not knowing that the answers are in the back of the book. Hence they miss out on opportunities that their classmates have to assess their own work as they do homework.
• Checking the back of the book too early and too often. Hence they try to make their answer fit the back of the book without paying much attention to the question content.
• Plagiarising from the back of the book, either with or without an attempt to show some working out.

What guidelines can I give my students so that they can use the answer key in the back of their books correctly?

Note: I am not seriously concerned about my students improving their grade by copying the back of their homework book, since we write more than enough quizzes and tests. However, I want guidelines which can help students understand how they should and should not go about learning, and help me respond correctly when students are out of line.

Another note: This other question is similar, but I'm interested in secondary education and in teaching my students how to use the help given rater than circumvent it.

Answer 1

While the first point is fairly straight-forward to address, I suspect the other two will not be easy to change. The whole set-up of schooling (in the UK at least) generally favours getting the answer right, at least in the short term, so the incentive for the students is to use the book to obtain their answers rather than to benefit their learning.

I think it's likely that there will always be some students who are lazy, and no amount of effort on your part will make them want to use the answers correctly for their own sake. However, there are probably some other students who will rely on the answers too much for other reasons. Talking these through with the students might be helpful.

One reason might be a lack of confidence. If you are afraid of always getting things wrong, you are likely to keep checking how you are doing, to avoid making too big an error. The aim-of-the-game for you is to minimise risk, rather than to maximise potential gain. One thing such students might need telling is that textbooks can contain errors, because if they encounter a wrong answer they cannot match, they may well assume they themselves are wrong and lose hope.

Another reason might be a misunderstanding of what the aim of mathematics is. Many students will have picked up from their schooling that mathematics is about performing meaningless calculations rapidly and accurately, and that the rewards come for doing so. Even if they personally would prefer to take the time to build understanding, they may feel that they are not allowed to do so. It could help to tell the students that you value their understanding of the material, not just a line of correct answers. I'd be tempted to try and show that in action too, perhaps by giving them questions to answer of the form 'what have you learned in the last lesson/week/month', or by encouraging and allowing students to discuss their intuition with each other.

Answer 2

I would start by addressing the issue openly on the first day of class. This solves issue #1. I assume your evaluation method is primarily based on students solving problems for which they do not have access to the solutions (e.g. almost any exam format fits this characterization). I would explain that in order to be able to complete that task successfully, they have to practice that very task. Looking at the answers first for guidance or -- much worse -- simply copying the answers will not improve their skill level and consequently does nothing to prepare them for exams. (In theory, the primary concern for the students in the course should be increasing their skill level, but in practice, the primary concern for students in the course who engage in #2 or #3 is, of course, their grade.) Emphasize that the answers are meant as a diagnostic tool to help them instantly confirm whether or not they have mastered the given problem. I like to emphasize that even if they produced an answer on their own and the back of the book confirms that their answer is correct, they have not mastered the material if they cannot explain the thought process that underlies the method they used to obtain the answer. Of course, many students are not interested in putting forth the effort to achieve this level of mastery (whether it be disinterest / laziness or simply an accumulation of lack of understanding in earlier grades that makes such a level of mastery difficult for them to attain).

You also have to accept that no matter how clearly you communicate the proper use of solutions, some students are simply going to ignore your advice and will only learn "the hard way" after some failure. Keep in mind that failing and learning from failure is our natural way of learning, while trusting the directions of someone else to avoid a failure we've never experienced before is not natural. But if you address the issue in advance, then students who ignore your advice may have an epiphany later on when they do not do as well as they wanted to.

Answer 3

What guidelines can I give my students so that they can use the answer key in the back of their books correctly?

Here's what I do: Document it on the syllabus. Tell them explicitly on the first day of class. Occasionally remind them at the start of a class session (e.g., "Were there any homework problems you had trouble with, or were surprised by the answer at the back of the book?").

But that won't solve the problems that you list in the lead-up to your question; other classroom procedures also have to support these learning objectives. In particular: Not just grading on the correct final answer (which is what the possibility of "Plagiarising from the back of the book" sounds like).

In my community college classes (mostly remedial, i.e., 6th-8th grade level), I'm dedicated to grading the justification ("work") for any piece of mathematical writing line-by-line; the final answer is just one guidepost by which we can check whether the procedures are correct or broken. In order to accomplish this, I've had to reduce the amount of homework I grade, currently at "none", but commit to giving complete scored feedback on any tests. This sends the signal that the logical connections are the important thing (both to the work itself and communicating it to others), and copying someone else's answers and presenting them as if by magic won't be rewarded. This has to be a daily point of emphasis, and not everyone gets it, but it at least gets some traction with a good proportion of students.