Previously by Jeremiah Dyke: Math by Hand, Math by Calculator
Homeschoolers have a rare and terrific opportunity denied to most math students throughout the country. Homeschoolers possess the ability to finally relate to mathematics in both a meaningful and instructive way by creating applications to which a solution has relevance to the student; a solution worth deriving.
The typical public educator will complain that their students care nothing about how they derived an answer, they simply want to get there. However, what you normally never hear from those on the front lines of education is why they are asking this question, or, is it even a question worth answering? It is true that students may be apathetic toward how they derived their answers, yet, what we fail to understand is this reflects less so on them and more so on the quality of the question. Good educators have become masters at making questions relevant to their students. Students do much better when the application matters, in fact, if the question is interesting enough, they may be excited to answer it! Even something as simple as adding colorful pictures to a page of drill-and-kill exercises will make the students work harder than without them.
(Is it wrong to expect more from a math class?)
Thus, what we have is that students today are too far removed from the study of math. For most, math is simply a cluster of slightly varied problems to be done in repetition until mastered. At best, the student can hope that someone, somewhere, will ask them for help on their homework problems, as far as possessing the ability to solve a real-life problem…forget about it! So, page after page, worksheet after worksheet, drill after drill, students dull their pencils in hopes of never seeing their teachers' red ink. What nonsense is this? How are students to learn meaning by simply regurgitating steps — as if mathematics were a large set of multiplication tables to be memorized?
This is where the homeschooling advantage comes in!
My suggestion to a student or homeschooling parent is to eliminate every math problem from your textbook, and I dare say from your life, except those with a purpose i.e. those that involve a purposeful application. Make every problem, from k-12, a real life word problem. One that involves using math and analysis to reach a solution.
It's no longer what is "2 + 3"? Instead it's, "if I had two apples and added three more how many apples would I now have"?
It's no longer, what percentage is 12/15? It's, "If Edward always gets 100% on Biology tests, Bella, however, answered 12 out of 15 questions correct. What percentage did Bella get right?"(click for more twilight math)
Furthermore, there is no need to follow our state's math curriculum. Math need not be segregated into little subjects called pre-algebra, algebra, algebra II, geometry, etc. Follow your interests! If you, like Bill Friedman (son of David Friedman, grandson of Milton Friedman) find yourself enjoying probability more than other math subjects simply because it gives you an advantage in board games with your friends, then pursue it! You are simply filling your toolbox with more math skills, and, eventually you will find benefit in other branches of math.
Do this and not only will your students or children have a better understanding of mathematical principles, they will finally see the relevance in math and you know, they may actually start liking it!