Guilt-Free Homeschooling

Homeschooling families often have this lament: My child takes f-o-r-e-v-e-r to do math each day! Can anything be done??? Let’s consider for a moment exactly what the student is being asked to do, to see if we can understand why it takes so much time. (Please note: I will use he/him/his as generic pronouns; all of this applies equally to girls and boys.)

Beginning students are learning the fine art of manipulating numbers to learn the processes of adding, subtracting, multiplying, dividing, and learning new number-languages called fractions, decimals, percentages, measurements, and on and on. You, the parent/teacher, are probably performing calculations with a minimum of fifteen to twenty years’ experience, quite likely much more. What seems incredibly plain and simple to you may in reality be incredibly confusing to your student.

Nearly every math lesson will present the student with a new concept, or at least an expansion of a previously learned concept. This means that the student must 1) study the new idea to grasp its meaning, 2) compare this new information to his previous knowledge to see how they relate to each other, 3) experiment with a few sample problems to test out the new concept and prove his understanding of it, 4) proceed to complete the remainder of the lesson’s required problem set, which may include both problems from today’s new concept and problems from previously learned lessons as review material. Steps 1-3 can be prolonged and repeated through discussions with the teacher (you) to insure that the student understands the new material fully. Examples may be drawn on paper, chalkboard, or whiteboard. Manipulatives may be used for grouping and regrouping. Graphs, charts, geometric figures, angles, and other mathematical illustrations may be incorporated. Teaching a math lesson in a way that your student will understand it completely can take time. Once the lesson has been understood, the student must mentally review the concepts again with each problem to make sure he understands the process as he is working his way through all of the day’s assigned problems.

In contrast, a grammar lesson may ask the student to write a sentence using an action verb, and the student looking for shortcuts may respond with “Jim sat.” It has a subject and a verb, it shows action, and it meets all the requirements. However, math requires exactness. There are few, if any, shortcuts to be taken in math. Mathematical calculations have concrete solutions: one and only one answer. Every operation must be exact, every digit must be accurate, and every calculation must be done completely, in order for the outcome to be correct.
4321
+765
___6Wrong. Shortcuts do not work in math.

Some may argue that calculators provide shortcuts, but I will counter that calculators should not be used until higher math, and then only as a time-saving device by the student who is fully capable of doing the work accurately without the aid of a calculator. In the words of my favorite college math teacher, “[Calculators] are stupid. They are machines that can only do exactly what you tell them to do.” The student who accidentally pushes the wrong button will get the wrong answer. I know. I did it. On a final exam. My paper showed that I had executed the problem correctly, but in my haste to complete the problem quickly, I hit the wrong button on a very, very, very simple calculation and achieved the wrong final answer. My gracious teacher gave me partial credit for using the correct process, but his point was made forever that using a calculator does not automatically provide success. Every keystroke must be verified by an alert mind. My haste ruined what would have been a perfect score on my final — disappointing, to say the least.

Back when I was plugging my way through elementary math, I had a teacher who required perfection, not merely correctness. She was a bitter old shrew of a woman who had been encouraged to stay in a classroom long past her prime and had lost all compassion for the children placed under her authoritative control; but I digress. A math problem can be solved correctly without perfectly formed digits or immaculately aligned numbers, and the existence of erasure marks on the paper has little to do with the accuracy (or inaccuracy) of the answers. When my children began doing math problems that included multiple columns of numbers, I bought them spiral notebooks of graph paper to use for their daily assignments. They could write one digit in each quarter-inch box, and the boxes kept the digits perfectly aligned. My students could focus on the place values as they copied the numbers for the problems, and then successfully solve the equation without being sidetracked by wondering if a wayward digit rightfully belonged in the tens’ column or the hundreds’ column.

Math is a sequential subject: each lesson builds upon each lesson before it. If foundational skills have been rushed and are not fully understood, each subsequent lesson will become harder and harder to grasp. Do not push your youngsters to make progress in math simply for the sake of turning pages. Be certain that each student knows what he is doing before allowing him to move on to the next concept. However, many enjoyable games and activities can be used to reinforce math concepts and provide practice with fun — and using math means learning math, even if you are playing a game and having fun.

Let’s focus for a moment on your particular student. Does his learning style allow him to absorb new information easily when he reads it the first time? Or does your student benefit from an oral discussion with you and some Q & A about the subject matter? Perhaps your student is more hands-on and doesn’t really get the concept until he can play with some math manipulatives, moving them around, grouping and regrouping, sorting and re-sorting, counting and recounting? (That’s why they’re called “manipulatives,” by the way, because you can manipulate them.) And let’s not forget that kinesthetic student whose brain goes numb when his seat makes contact with the chair’s seat — he may need to be on his feet, stretching his muscles through every minute of his math lesson, but that physical action guarantees that his brain is revved up and tuned in — not at all what classroom models need you to believe. A student whose learning style is not being utilized will be a student who is easily distracted from the subject at hand. Touch his learning style and you will gain his attention.

One last consideration is the amount of work set forth in your student’s textbook. All textbooks are not created equal, and especially not math texts. The number of problems required with each day’s lesson may change from day to day in certain books, and it will surely change from year to year, but it especially changes from publisher to publisher. When my high school student was using a math textbook that assigned 30 problems per day, her friends’ math textbook from a different publisher assigned 100 problems per day for the same grade level. I repeat: All textbooks are not created equal, and especially not math texts. Our book’s daily 30-problem set offered a variety of problems, using a method of continual review over past concepts. The 100-problems-per-day book offered no such variety: all 100 problems were of the exact same type. Is it any wonder that students can become bored and tired of doing math?

Math does take time. Math will probably be the subject that eats up the largest segment of your homeschool day. However, if your student is sitting idly, hour after hour, staring at a math lesson but not completing it, there are most likely several causes at work.

1) A lack of foundational arithmetic skills. A child who cannot recognize specific digits for their representative amounts cannot perform addition. A child who does not know addition facts cannot perform subtraction or progress on to multiplication. A child who does not know multiplication facts cannot perform division. A child who does not know multiplication facts will not fully understand fractions and, therefore, will also not understand decimals, percentages, or measurements.

2) The student has not understood the lesson concepts or is confused by them. This is often due to the student’s learning style. This is not a disability, just a difference in how each of us takes in and processes information. Some people take in information through their eyes, some through their ears, others through their fingers, and still others through their larger muscles of arms and legs. Seriously. Touch his learning style and you will grab his attention.

3) The textbook may be too aggressive (moving too quickly for the student’s pace) or just plain too boring in how it presents the material. While much of math is often taught through drill, drill, drill, I do not know anyone who would choose to learn anything through repetitive and boring drills if there was a more interesting alternative available.

Allow enough teaching time and a variety of teaching methods to be sure your student understands each lesson concept completely. Allow your student to talk things out, work with manipulatives, or run a lap after every problem to keep his muscles-to-brains connection engaged. Allow your restless student to take breaks while working his math problems, knowing that you, too, would break up a long and tedious task into shorter segments, if it did not hold your rapt attention. Math does take time, but the flexibility of Guilt-Free Homeschooling allows you to conquer it with the methods that work best for your family.

For more tips, see also —

Looking for the “Hard Part”

10 Fun Math Exercises from a BINGO Game

Sugar Cube Math

Alternate Methods for Teaching Math

Topical Index: Math

Topical Index: Learning Styles