What is the point of an answer key? A quite interesting question I had never really considered before. Maria Miller of the Homeschool Math blog has been exchanging emails with a translator of a Russian geometry book. Here is an excerpt I found most interesting:
I couldn't do that in Germany. I didn't have a text book and I didn't have an answer key. I had a thin sort of problem book which had problems for each day, but there were no examples or solutions. I had to struggle through with what I knew of mathematics to try to come up with an answer. In class, we discussed these. I never knew it was possible to discuss so much about mathematics. And, completely foreign to me, we were NEVER given the answer. After discussion, we reworked the problem and could discuss it more. The teacher might point out an error, but left us to solve it on our own. We could conceivably spend a two hour block on two or three math problems. I have never looked at mathematics quite the same way since.
It also reminds me of one of the goals of the Principle Approach...to free us through personal mastery of the subject matter rather than dependence on others for watered down materials, such as a textbook, workbook or teacher's guide. This is the most daunting aspect of beginning...that there is no text. No neat curriculum package that tells what to cover each day. Just you, your child, your bible and your knowledge of what you are about to teach. I do not act as an instructor in an American public school, who delivers instruction the child is expected to consume. Instead, I attempt to lead, guide, direct and, above all, inspire.
Through my guidance and modelling, I seek to make a connection to my child's heart so that she will discover the principles of each subject for herself. With this mastery, she can then judge right from wrong, whether that be in her daily choices, her math lessons or any other subject she tackles. For in life, there is no answer key. If you judge by someone else's standard without being able to judge the rightness for yourself, you will always be dependent on others, even for your ideas.
Related Tags: math, teaching math, Principle Approach, mathematics, teaching, pedagogy, homeschooling, home school
Teacher's guides are intended to save a teacher, clueless about the subject he teaches, from the embarrassment 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.This reminds me of how I was taught in Germany. We had no text books in any subject. We came to class and the instructor, largely through discussion and question & answer, guided us through the principles of what we were to learn. I did very well in math, which was strange considering how poorly I did with it in the US. At first, I chalked it up to the fact that the concreteness of the numbers and signs made it the one subject I could follow despite the language barrier. But there was more to it than that. In the US, I had always sat with the problem, looked at the sample problem, and tried to copy the steps to arrive at an answer that I then checked in the back of the book. I learned math by rote memorization and drill, without ever really comprehending what I was actually doing.
I couldn't do that in Germany. I didn't have a text book and I didn't have an answer key. I had a thin sort of problem book which had problems for each day, but there were no examples or solutions. I had to struggle through with what I knew of mathematics to try to come up with an answer. In class, we discussed these. I never knew it was possible to discuss so much about mathematics. And, completely foreign to me, we were NEVER given the answer. After discussion, we reworked the problem and could discuss it more. The teacher might point out an error, but left us to solve it on our own. We could conceivably spend a two hour block on two or three math problems. I have never looked at mathematics quite the same way since.
It also reminds me of one of the goals of the Principle Approach...to free us through personal mastery of the subject matter rather than dependence on others for watered down materials, such as a textbook, workbook or teacher's guide. This is the most daunting aspect of beginning...that there is no text. No neat curriculum package that tells what to cover each day. Just you, your child, your bible and your knowledge of what you are about to teach. I do not act as an instructor in an American public school, who delivers instruction the child is expected to consume. Instead, I attempt to lead, guide, direct and, above all, inspire.
INSPI'RE, v.t. To breathe into.
To infuse into the mind; as, to inspire with new life.
To infuse into the mind; as, to inspire with new life.
Through my guidance and modelling, I seek to make a connection to my child's heart so that she will discover the principles of each subject for herself. With this mastery, she can then judge right from wrong, whether that be in her daily choices, her math lessons or any other subject she tackles. For in life, there is no answer key. If you judge by someone else's standard without being able to judge the rightness for yourself, you will always be dependent on others, even for your ideas.
Related Tags: math, teaching math, Principle Approach, mathematics, teaching, pedagogy, homeschooling, home school
