Teaching Math Without a Curriculum

Many people, especially new homeschoolers feel the need to have work planned out for them. I think primarily because they feel a worry about being sure they cover everything and in the proper order. I understand this. Also, I think many feel it saves them so much time to have lesson plans all laid out for them.

I would like to explain why I chose to not use any math curriculum with my children:

FUN and ENJOYMENT is my primary reason for not using a curriculum. I love math and I wanted my children to love it as well. It is probably one of the easiest subjects to teach with a curriculum. And we did not have the vast number of wonderful manipulatives that are available today. All I used were Cuisennaire Rods and things I found around the house or made on my own or just real things (rulers, money, clocks, etc)

For those that worry about knowing what to teach when or in what order I would suggest using the Typical Course of Study from World Book.

http://www.worldbook.com/wb/Students?curriculum

Just select the grade level that you are working with. Progress through in order. The order of some things is important, but many things like money, time, calendar can be taught whenever the moment presents itself or the child shows an interest. For example: My grandson Douglas (age 3 1/2) has just shown quite an interest in clocks. We realized he could tell when the little hand was between the 8 and the 9 that it was bedtime. He would say, "It is quarter to nine, time to go to bed." Then one morning he noticed the clock in this position and was very puzzled. So we explained how it works. We are now working on teaching him time to the quarter hour. It is not a push thing. Clocks are first mentioned in the Kindergarten list, but he is interested NOW. If he continues, I will probably by him a watch for his birthday, NOT a digital one.

OK...back to topic. Just use the Typical Course of Study as a kind of check list. If all of a sudden you realize you have never taught geometric shapes and the child is in THIRD grade, believe me the world will not end. Instead, just teach it. Because of their age they will grasp it very quickly and you can move on. But most likely, even if you have never consciously TAUGHT it, they already know it. Because you will naturally point some of these things out as you talk to, read to, or interact with the child.

I learned something I had skipped when my sister asked me if she could test Cortney who was at the end of "kindergarten" by her age. I don't care for testing for many reasons but I thought this would be OK because my sister would administer the test, it would be done in our home, if Cortney did poorly I would not have to tell anyone, I could watch...if I saw signs of stress I would have just call it quits. However, Cortney was one of those girls who liked bookwork so she thought this was very cool and she dug right in. When she was doing the math portion I saw the problem (what I had failed to teach her). She saw 3 X 5 = ___. She had no idea what it meant. I asked Kathy if I could read it to her. If I could say "you have 3 groups of 5" or even "3 times 5" Cortney would have easily come up with the answer. We had been doing this kind of math a lot. We had used manipulatives to understand it and then did lots of oral drill (usually while riding in the car). But I had never shown her how the problem would be presented on paper. WOW!!! enlightenment for me. Was this a big problem? NO. For one she scored way above her "grade level" on this test (OK, I admit...I used this little piece of paper to show Grandma that homeschool was working...LOL). Second, we simple got out paper and pencil and I would remember to show her how to work these things on paper and not just in her head.

How well she understood concepts, however, was made very clear to my sister and I one day while visiting their home. My nephew (4 years older than Cortney) was trying to do a homework problem. "The farmer had 1/2 a bushel of apples. He gave 1/3 of the apples to his friend. What fraction of a bushel did he have left?" Cortney had absolutely NO idea how to work it on paper, she had barely been introduced to fractions. But because I thought it was so important for my children to know HOW to use numbers and understand the concepts she was able to SHOW him the answer. She simply got out the Cuisennaire Rods. She grabbed a pile and said "This is a whole bushel." Then she divided it into half and said that is what the farmer had. Then she divided the half into thirds and set one pile aside for the friend. She instantly saw that 2/6 or 1/3 of the bushel was left for the farmer.

I could go on and on with examples. But I think the important thing here is PLAY with math. Let the child know there is no mystery to math. Math is logical and always the same. Two plus two will ALWAYS be four. Whereas, Pluto was a planet and now it is not??? LOL

Also, let them see that math is FUN. It is not just a dry workbook with page after page of work to be completed.

AND... YOU CAN TEACH IT. At least at the lower grade levels. I didn't get them a curriculum until they were ready for Algebra. But by then they already knew lots of Algebra. I told them when they first solved 1 + 1 = ___ they were learning Algebra. When I taught in the classroom, I went and got a Algebra text book from the upper grades and showed them some of the introductory lessons. When they are first learning about unknowns. The problems would be 6 + n = 8. I would substitute a ___ for the n and they could solve it right away. They were so excited that they could DO ALGEBRA. The upper grade teacher told me when he got the first class I had taught in the lower grades that they were the first students that were not afraid of Algebra. Most children are fearful of it as it is a "high school" class and must be hard, it even sounds hard.

But I taught children, my own and those in the classroom that math was fun and any time they found something that they did not understand we would figure it out together. I put more emphasis on them understanding the concept than getting the right answer. They loved it when I would give them the assignment of story problems and all they had to do was write out the number sentence not solve it. So all they had to give was 17 boys X 23 marbles each = _____ total marbles Many of them would want to solve it because they knew they could. I told them they were free, of course, to do this. However, I counted the work half wrong if they did do the work and got the wrong answer, so most opted to NOT solve the problems.

When I taught 3 & 4 grades some of the children knew their addition and subtraction facts very well. They had been drilled on them and memorized them well. However, they didn't understand what they were really doing. They didn't know when to use addition or when to subtract. I talked about it with the 1 & 2 grade teacher several times, but it finally became clear to her when her youngest sister entered my classroom. Poor Sara was lost in math though she was one of the fastest when it came to speed drill on the facts. But she had NO understanding of the why's and the how's.

So...PLAY with math. Give them lots of opportunities to make discoveries. Give them TONS of story problems so they learn how to solve them. Give them opportunities to really stretch themselves and let them use any method to solve a problem. I had one student that had lots of problems in school but could he solve math problems in the most interesting ways. I loved watching his mind work!

So...get lots of manipulatives...doesn't have to be expensive sets, just collect things:

rulers, yardsticks, measuring tapes (boys especially like those retractable kind like dad has in his tool box)

measuring cups, spoons, liters, gallons (great for use in the sand box or bath tub where spills don't matter)

scales - balance scale and weight scale

counters (LOTS!) these can be ANYthing from pretty rocks you collect, matchbox cars, Beanie Babies, buttons, WHATEVER but things you can have a LOT of -- even hundreds of beans

calendar

clocks

real money -- at least real coins. I used bills that looked like real money xeroxed and shrunk a bit. But I never found plastic coins I liked...so use real. Make up a money box to have on hand quickly

calculators - yes, I allowed them...at appropriate times

puzzles

GAMES - lots and lots of home-made games to drill every math concept until it is mastered

See Games For Learning website for lots of ideas for making educational games for all subjects.

http://www.angelfire.com/wi2/GamesForLearning

Make them aware of numbers, they are everywhere. Make them realize how many times a day you use math. So many children think they really don't NEED math, when are they ever going to use this stuff? Let them see you (better yet, let them help you) balance the check book, pay the bills, buy groceries, know how fast you are allowed to drive, know what temperature to bake the cake and for how long, find the distance to the library or Disney World or Grandma's. Point out numbers everywhere. Signs that tell population of the city as you enter. Signs that tell you how far to Chicago. Signs that tell you how much that new car would cost. Signs and numbers everywhere...see them and talk about them.

To get assistance if you wish to take on the adventure of teaching math without a curriculum, check out this yahoo group:

http://groups.yahoo.com/group/TeachingMathWithoutACurriculum/