I have always taught my children that the main point of mathematics is to understand its concepts. In other words, it is more important to know how to arrive at an answer than it is to get a correct answer. Our ultimate goal in math is, of course, to get correct answers; however, if you have 20/20 correct but do not really understand why you did what you did to arrive at those answers, then are you truly learning anything at all?
I would rather see one of my students, hand in an incorrect answer but be able to explain to me what process he or she used to get the answer than hand in a correct answer but not be able to explain to me how he or she did the problem. If a student understands the concept, then an incorrect answer is usually due to a mere computation error; in fact, if given the opportunity to carefully review the problem, the student (if he or she truly understands the concept) is likely to catch his or her own mistake.
I find it quite helpful to ask a student to explain how to do a particular problem out loud, to another person. If someone knows what to do and understands why doing it is necessary, then he or she should be able to provide basic instructions and explanations to others. This shows that learning has taken place.
In an English grammar and punctuation class, this would translate into knowing how to construct a coherent and grammatically correct sentence but also understanding why it is coherent and grammatically correct. Anyone can memorize rote instructions. Knowing that a comma belongs in a certain place is one thing. Understanding why it belongs there is equally, if not more important.
Is it good that a student can memorize information and repeat it on a test? Yes, to an extent, it is. What’s even better, however, is a student who understands what he or she has learned enough to be able to converse about it, to explain it, and to apply it.
Sadly, many children nowadays are passed onto the next grade level because they have shown up to 180 classes and were provided a certain amount of information. A failed “no child left behind” system has backfired big time because kids who do not understand what they’ve been taught are shuffled off with their peers to higher levels of learning. Some fake their way through. Some wind up hating school. Others barely function because they are struggling to grasp new information when they still don’t understand the previous information they were given.
Education shouldn’t be about status quo. It shouldn’t be about a race for grant monies. It shouldn’t be about standardized test scores. I should be about children; in fact, it should be about each child, and helping him or her reach his or her full potential in life. It’s up to adults to make sure children are understanding what they’re being taught, for if they aren’t, they are not really learning.
Knowing things is good. Understanding what is known makes knowing worthwhile.
Writer Bio: Judy Dudich
Judy Dudich resides in the beautiful woods of Pennsylvania, where 24 acres of land and a home-office provide the perfect setting for her children’s home-education and her own homesteading and business ventures. Life is full of blessings (and challenges!) for Judy, as a wife, mother of 10 and Grammy to six. She is a published author, whose book, “I Surrender/A Study Guide for Women” continues to encourage and support others in Christian family lifestyles throughout the world. Judy has also previously worked in the online speaking circuit. Her passion for permaculture, re-purposing, foraging and organic gardening fills her days with learning and adventure that she loves to share.