In our home-school, we’re pretty challenged by math. I was never a math whiz, but I understood it enough to make an A in calculus and then I waved “good-bye” to the math department for the much more hospitable climes of history.

I DID think that I could help a child understand 2 + 2, though. It’s simple, you just get out some toy animals or blocks and voila! The child understands.

Well, maybe not. Or maybe they understand today and forget it tomorrow.

I started out with some real misconceptions. Not all home-schoolteachers and kids face these challenges. But when you run upon them, they really bring you to a screeching halt.

Before I go into these, let me explain that, if you met my 7 y.o. daughter, you’d probably come away with the impression that she was very intelligent. She came to us from Russia when she was 2 1/2, and although she was late in speaking, she learned English VERY quickly. She is very extroverted and has a wonderful vocabulary for her age. Her manual skills have always been advanced, and she readily builds things. She has also demonstrated that she can spell words backwards as easily as forwards, although she also sometimes READS them backwards as well. She loves wolves and wild canines and says she wants to be forest ranger.

Yet she has lots of trouble with math. But perhaps our trials and errors will help someone else.

Misconception #1: COUNTING ON FINGERS I thought that all children instinctively knew how to count on their fingers. They DON’T. Not even in second grade. At our house we still can’t seem to just “look” at our hands and tell how many fingers we’re holding up without counting them. This may be a coordination or vision issue.

Misconception #2: LESS AND GREATER, BEFORE AND AFTER. I thought all children could grasp instinctively the fact that because 4 comes after 3, 4 is “1″ bigger than 3, or simply the fact that 4 is just bigger or greater than 3. NO. This sometimes causes great confusion. We’ve had to do LOTS of work with less and greater, and also before and after. I also had to clear up the idea that when I said “bigger” or “greater”, she thought I meant the font-size of the number. Thus a 30 pt. 3 was “bigger” than a 14 pt. 100.

The concept of “before and after” may also have been another issue, as our little girl likes to “rotate” images in her mind, so the concept of “before” or “after” was hard for her to grasp. Now she understands that she can’t “turn things around” in her mind.

Misconception #3. ADDITION AND SUBTRACTION ARE EASY A child, after some play with blocks, etc. should understand that when you add two numbers you get a BIGGER number, right? When you subtract, you get a smaller number. That makes sense to us, but not to all children. We still have problems grasping this simple concept. We often have to “prove” that two numbers equal another number with blocks. (I often get asked, “But HOW do numbers X + Y equal N?” or “But I thought Z + Z = N; how can X + Y = N, also?” We still have to do a lot of work with blocks. Not all kids are ready for abstract concepts at an early age.

Misconception #4: ADDING 1 IS EASY This seemed like a no-brainer. I though that children should be able to easily understand that if you add 1 to a number, you get the “next” number. No, this sometimes takes a lot of work. We’ve found the concept of stairs to work better than a regular number line. Once again, I think it’s a pattern-recognition problem.

Misconception #5: DIFFERENT USES OF NUMBERS
Most adults easily understand the difference between different uses of numbers, such as “1″ the numeral when counting vs. “1st” the ordinal number vs. “1″ as an amount. Not all kids grasp this quickly. (The idea that there was “1″ space between 3 and 4 caused us WORLDS of grief. She was confused because there’s no “1″ between 3 and 4, After all, “1″ comes before “2″. It was hard to help her understand that there are different uses for the concept “1.”

Misconception #6: COUNTING Any child can count, and a child who can count should be able to count starting at any number (i.e. 5, 6, 7) and count backwards easily. NADA. This sometimes takes LOTS of practice. The change from one ten family to another sometimes takes LOTS of work (39, 40…..49, 50….etc.)

Misconception #7: THE PATTERN 1,2,3,4… I thought a child should instinctively understand that the pattern 1,2,3,4……. is repeated over and over in math: 21, 22, 23, 24……. and 10, 20, 30, 40. But you can’t take that for granted.

Misconception #8: Children can understand mental gymnastics such as Math-U-See’s “9 wants to be a 10″ (and thus takes “1″ away from the other addend.) Not all kids can do the multiple steps required by concepts like this. The “Doubles + 1″ concept is similar. It involves understanding some slightly complex ideas about numbers and putting them to work all together. We’re still working on understanding that the sum of 6 + 7 is greater than the sum of 6 + 6. Once again, these concepts seem easy to adults, but can be hard for kids who still need concrete operations.

NOW FOR THE SUGGESTIONS & THE GOOD NEWS

Our daughter can now (2nd grade) count fairly well into the 100s. Sometimes we still have trouble with “before” or “after” numbers, though. It takes thought to remember which comes before or after. We know lots of math addition facts, although a few still elude us. We’re working hard on subtraction. It simply takes a lot of time and patience.

Multiplication, for some reason, is coming to her much more easily. I don’t understand it and I don’t even try.

HELPS
We’ve tried lots of things, so I thought I’d share some of our ideas with you. Some work and some don’t for us, but each child is different.

A) Regular workbook-repetition of Math facts. She can write math facts all day (if there are too many of them) and still not learn anything. When presented with a “math test” she would also just sit and cry because she couldn’t remember how to figure out a problem (although we learned how to figure out sums by drawing circles, counting on her fingers, number line, etc.) The abacus helped here, because it did empower her a little.

B) Flash Cards (regular & “triangle” style)- These helped us when used with just a few problems at a time.

C)Abacus- this helped. It’s small and portable and helps kids who have trouble memorizing the facts AND can’t seem to remember how to work them out any other way.

D) Math U See or Toys- Great help, although the series lost her pretty quickly. We’ve also used toy animals, blocks, cars and anything we can lay hands on for addition/subtraction. The toy animals are great for multiplication. You simply build Z number of corrals or pens, then put Y number of animals in each pen. Then show that Z X Y would equal the same thing as Y X Z. With division, you give the child a handful of animals and Z number of pens and tell the child to divide them equally so that the animals get the same amount of feed. It’s fun and it’s actually worked…..although it didn’t seem to help with addition and subtraction.

E) Math Stories. These were fun, but she couldn’t seem to transfer the knowledge to help her on her math pages. If you want a copy of my math fact stories, email me. I hope one day to get them on the website.

F. Doing math facts while exercising or doing hopscotch. This has not worked well for us. I know it has helped other children.

G. Doing addition & subtraction using a number line or an illustration of stairs or steps. The number-line confused her for some reason. The “stairs” worked better, because they showed that some numbers represent larger quantities than others. We sometimes build “stairs” with Math U See blocks.

H. Math songs – we made up LOTS Of these and even made some Power Point presentations with animation for them. But they didn’t seem to help us learn our math facts. Once again, transferring knowledge from songs to the math pages didn’t happen.

I. Touch-Math. I invented doing this myself in school; they didn’t have a name for it then. It’s a way of count-adding and is, I know, sort of a last-ditch desperate attempt. I felt that I HAD to find a way to help her solve math problems that she didn’t know, and this worked (up to 5, anyway.) You simply imagine that every number from 1 to 5 has dots on it: 1 has 1 dot; 2 has 2 dots on the front points; 3 has 3 on the points, etc. Then, let’s say the problem is 7 + 3. The child touches the 7 with her pencil and says “7″ then touches the dots on the 3: 8, 9, 10, and gets the answer. It helps the child remember to start counting at the next number.

What’s worked best for learning facts? There hasn’t been a magic-fairy solution. We take a max of 3 math facts per day and work on them intensively. After a few days’ practice, we have a quiz. If those facts aren’t learned, then no cartoons. We have to write the facts we don’t know 5 times. (This gives incentive to learn.)

The next quiz a few days later involves those math facts and NEW ones.

Math Fact Families
In our house, just because we understand that 3 + 4 = 7. doesn’t mean we can always remember that 7 – 4 = 3. The light hasn’t gone on about this yet, although we’ve demonstrated how it works what seems like hundreds of times. We work all math fact families using both addition and subtraction, but I focus on learning the addition problems FIRST.

I pray that this information helps someone out there who is struggling to help their child. I’m NOT a mathematician. I don’t know mathematical concepts or advanced jargon. My husband IS, but because he’s so naturally good at math, he doesn’t even know where to begin to help someone to whom math isn’t instinctive.

Yet I saw something the other day that made me realize how valuable we Moms are. At the eye doctor’s office there was an African-American mother with her little son, an obviously delayed child. The child could not speak – he only made sounds- and the mother was teaching him sign language. With obvious love and animation, she would show him a sign and then he would try it….then his face would light up when she praised him. Professional workers and experts are great, but I’m not sure that anyone other than a mother could work like that with so much love, patience and tenderness. It would probably be much easier to write that child off intellectually and let him stay in a low state of development, but that mother was devoting her time to being sure he reached his potential.

That’s what lots of us are called to do.

I started out homeschooling with a shelf of 19th century (reprints and originals) textbooks and lots of wonderful ideas.

It seemed so easy. Our child seemed intelligent and had a great voculary. I was sure that all I had to do was simply present the information to her, review it a few times, and she was good to go. How hard could that be?

(I hear other home-school Moms out there laughing hysterically.)

Nobody told me that children have to be developmentally ready to learn and that people learn in different ways and at different speeds. No one mentioned learning differences and difficulties (I won’t call them disabilities.)

From the beginning…(no pun intended), I noticed that our daughter had a few problems with “beginning” and “ending” and with patterns. I dismissed this at the time. When given a pattern to repeat and she’d make a mistake, she’d tell me, “But I think it’s prettier THIS way.” I just chalked it up to a strong-will and really didn’t make much of it. I think now it was a sign of something else.

We started simple phonics when our daughter was 3, and I expected to have her reading simple stories by the time she was 4.

No dice.

Now, at 7, she can read simple stories, but she reads mostly by sight. Rod and Staff Phonics is pretty intensive (at least it seems so to me), but she still prefers sight-reading. When she tries to sound out a word, unless she actually has her finger under it, she may mix up the sounds. We have to really work at tracking left to right.

We also started with numbers, counting and using blocks and toys to add. Things just didn’t click. I thought that kids naturally counted on their fingers to add, but this didn’t even come to her intuitively. She still can’t grasp that the numbers on the left of the number line represent smaller quantities than those on the right of the number line, or that when you take 1 from a number, the answer is like counting backwards.

You name it, we’ve tried it: making Power point presentations and songs to learn math facts, using Math-U-See blocks (good, but she wasn’t really learning her math facts), lots of repetition, hopscotch-type games, adding toys and lots and lots of practice. What’s working best right now are flash cards with a triangle and 3 numbers on them: the sum at the top and the two addends on the lower corners.

I won’t lie and tell you that I haven’t had times of frustration and discouragement….especially when friends show me how their 3 year-old who can read and say, “He just picked it up by himself!”

Nothing I’ve done in my life, I think, has made me depend MORE on the grace and help of God….daily, hourly, and by the minute some days.