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MATH... and Other Tales of Horror
This article, by Leslie Wilson, was originally published in the September-October 1995 issue of Home Education Magazine.
The very word strikes terror into the hearts of many. And you have to teach it. If you are now wondering why you ever started homeschooling, don't despair. There are many life-saving approaches to this most feared topic. Here are a few we've tried in our family.
I'll admit at the start to a grudging appreciation for math. I don't know where I'd be without it in cooking, checkbook balancing, store trips... However, that doesn't make it much easier to like, only to co-exist. I set out to improve this outlook for Jenny's sake as well as my own. That is why we eventually developed a very eclectic approach to math.
In the beginning, we relied primarily on the guidelines of a curriculum manual and a "hands-on" approach without a formal textbook. By using a list of goals for each grade as a checklist, we found that using math in everyday activities, supplemented by some of the more interesting workbooks, computer programs and other tools, was the least painful approach.
There are several excellent math packages available for elementary education (which is the only area on which I can speak from experience). These are discussed in detail in many curriculum manuals. The package we ended up with, Miquon Math, worked nicely with our Cuisenaire Rods and the Annotations Book gave excellent discussions of each math concept introduced. However, Jenny's learning style proved to be more free-wheeling than the structured approach of such programs. "Supplemental" soon became the operative word for our family math program. Difficult, multi-purposed and interwoven math concepts benefit from a close scrutiny from as many different perspectives as possible. Also real-life applications give an extra boost to hammering home a point. Here's a popourri of tools & techniques that have brought math to life in our home:
Workbooks: When you need to drill on a particular area these can be very helpful. Some we've discovered:
Key To... Books - These very inexpensive workbooks for grades 4-12 cover the topics of percents, decimals, fractions, geometry and algebra in a deliberative, thorough, unintimidating fashion. They are designed for students to work in at their own pace. Jenny often does more that the assigned pages, which is rare for her in math.
Math Wipe On/Off books, Press & Check cards or Wrapups - sometimes a gimmick helps sell a rather dull product (Oops! I was going to improve my attitude, wasn't I?)
Golden Step Ahead books - available at discount and bookstores, these cover the early grades primarily.
Good Apple & Fearon books - covering the basics in all grades as well as specialty areas like calculator math. Especially enjoyable are the visual delight worksheets of their "Hooray for Math Facts!" series - engaging number characters, dynamic twists to learning the basic skills. Each includes a detachable & copyable practice wheel and timed tests to retake to measure increasing competency.
Thematic Activity books put out by Good Apple, The Learning Post and Teacher Created Material, for example, help put math and all other subject areas into a melting pot of related treats which are often easier to digest.
Games: We often employ games (one of my favorite topics as you may know from my past articles), activities and simulations to put some life into bare bones math.
For early math skills, Jenny enjoyed story-oriented activities built around the plastic bear counters in the Three Bears Family Fun game. This included many bears, a colorful cutaway house gameboard and a story and activity guide book for moving the bears about the house and answering easy counting questions about the activities. Jenny often played with the set on her own, it was so enjoyable.
On and off over the years we've resurrected the Wonder Numbers Game, each time playing a different variation of our own. We especially enjoy imagining the board is the land of Mathematica, where interesting things can happen in different locations: side activities tied to certain squares, prime number "cities" where you draw a word problem card worth bonus points or a prize. We sometimes use felt numbers or bear counters or Cuisenaire Rods to collect as prizes. They are added up at the end of the game, or certain ones multiplied, subtracted, divided to find out the winner. Infinite variations are possible.
Activities like dominoes, flash cards, and games using math like Made for Trade (colonial history and math rolled into one) and Monopoly. We introduced her to it at age 7 by simplifying the rules. The practice gained with money and land transactions was invaluable for instilling the desire to build math skills. Another game that we have applied to all areas of study is our old original Trivial Pursuit gameboard. Instead of drawing the cards it came with, we use questions from categories on our Brain Quest game cards. Similar Q&A cards or charts could be used or made to extend the usefulness of an all-purpose gameboard. Sources for several Trivial Pursuit-style games are listed under the Resources sidebar.
Recently we've expropriated a poster-size blank map of the USA to use as a game board. Many variations of rules later, we came up with a method of moving from state to state by rolling a die and going 100 miles times the number that came up. A second blank die was labeled with various compass directions to tell us which way to travel. (Math note: combined the two dice give you a vector.) Then just lay down your ruler in the right direction, measure and move.
Reading: Math doesn't really come to life until you get into word problems. And an excellent source for word problems can be a good book. Often you'll find information which can be calculated out. Reading Lewis Carroll's Through the Looking Glass, you might come up with: All the king's soldiers and men had just been set loose in the forest to put Humpty back together again: all 4,207 of them except for 2 needed in a game. If all the soldiers had horses, except the two missing of course, how many horses and men were there altogether? What if only half the soldiers were on horseback?...
If you are reading history books, biographies or historical novels, try calculating how many years ago the events happened. How long did the period of the book extend?...
The Bible is an excellent source for math-related stories. We worked several nice sessions out of Joseph's dividing of the crops to save a seventh for the famine years using craft wheat for counters. Also converting Hebrew units of measure to the standard or metric system. And while you're measuring, ever try creating a model of the temple of Jerusalem? All the measurements are laid out in the book. All you need to do is introduce the concept of scale modeling for a really fun creation! And then there is the book of Numbers. What more need I say?
For relaxed math reading, we read together excerpts from the math section in What Your Fourth Grader Needs to Know (available for grades 1-6). I have enjoyed this book for helping to give a brief over view of all subject areas.
Then there is algebra. Even the name makes you feel like you're entering a foreign land. I'm sure that's the way a teenage girl named Wendy Isdell felt when she was inspired to write A Gebra Named Al. It is a delightfully whimsical approach to understanding algebra, chemistry and related topics in math and science. This contest-winning story is now a book published by Free Spirit Publications. There is also a teacher's guide covering science, math, general activities and vocabulary. Jenny, working on 4th grade math and science, loved the tale. We found ourselves looking up the periodic table of elements and playing around with algebraic expressions, although she's had no formal introduction to algebra yet. Somehow math seems less intimidating when you can first meet informally. A friendship is so much more enduring than a business relationship, especially when it comes to math.
And Writing: A recent idea we had is writing a short story with built-in math problems. You've heard of word problems, I guess these are story problems. Our topic will be, of course, a day in the life of an ornithologist named Jenny.
Art: We began learning about ratios to meet a need: Jenny wanted to draw realistic figures. To help, I showed her a technique for measuring sizes of body parts in terms of the character's head. For example, a bird's body may be 2 heads wide, 3 heads long, the tail 3 heads...
TV: Yes, TV: that two letter word. Have you tried the weekday PBS educational shows lately? Around here, we get instructional programming from 9 - 3:30. For a small fee, we can get a detailed listing of the actual classes being taught, usually in 15 minute segments. Math programs (by grade) include problem-solving series like: It Figures (4), Math Works (5) Solve It (6) and for economics on a down-to-earth level: Econ and Me (3-4).
Balances: Starting with a $3 plastic number counters & balance set, we have both developed a love of balances. We have constructed a simple one from scrap lumber which has been used to weigh and measure everything from Cuisenaire Rods to the plastic bear families.
Speaking of balances, Dr. Borenson's Hands-On Equations learning system is an excellent tool for teaching equation principles, highly recommended for 3rd grade and up.
Graphing: Here's an activity that works well with many areas of interest for Jenny: charting the eventual length of all the fish in her tank using an aquarium fish book; sorting her critter collection (plastic dinosaurs, stuffed dinosaurs, stuffed birds...) and making a chart of the total number of each classification; sorting and eating colored candy like M&Ms; graphing occurrences of different state birds (you may be surprised at how many times the Western Mockingbird pops up).
Now that we are moving into more advanced graphing, measurements, computing averages and other useful topics, we are finding more practical applications which we all can appreciate. Jenny's current passion is conducting detailed bird tallies graphed by species and day observed, with monthly averages. She is even posting her results, finalized on an adult computer program, Graphtool, in her dad's office (where many bird fans reside).
In fact, Jenny's become so fond of graphing, she likes graphing her progress on periodic math quizzes. Hooray for... series has such quizzes in each of their books. I've recently created a timed quiz covering most 4th grade math skills which Jenny takes every few weeks. She posts her results in a table and graph we set up together in an Excel spreadsheet. She's actually asked to take the test more frequently so we can add another blip to the chart. By the way, best tests are posted on the refrigerator for everyone to ooh! and ah! over.
Incentives: Sometimes a little encouragement helps the math go down. Consider using stickers pasted to a do-it-yourself posterboard scene. Coated posterboards give a decent peel & replace surface or you can cover the finished scene with clear, vinyl adhesive. There are many other potential prizes for completion of assignments, tests well done... Mini-science kits makes great awards as well.
SOYP: My favorite approach is the Seat-Of-Your-Pants (SOYP) technique. Some examples:
- Trips to the store - Let them go in with a shopping list (not too long for the younger students) and a certain amount of money. Consider putting them in charge of store coupons (easy on the junk items, please). You may want to let them pocket the money saved as added incentive.
If they want and need help making choices, discuss the options available, give hints to figure out if there is enough money, how much change they'll get back... And be sure to let them take it to the cashier themselves. A small, quiet store is best for first trips. For our first outing, we went to a small bookstore for one book. We even rehearsed shopping at a store, one of our favorite simulations. We set up a number of reading books, comics, bookmarks, a play cash register and price tags for each book or sale shelf of books. Then Jenny enters the store with a certain amount of money (we use real or play money depending on what's handy). She carefully plans how many books she can buy using most of her money but never more. I, as cashier, do the final tally (to make sure her math is correct), give her change, bag the books and thank her for her patronage.
- Ordering from catalogs can be a grand adventure in math. Jenny's favorites are the bird catalogs: "Can we afford six Canada geese and a pair of ruddy ducks or should we get the canvasbacks instead? We are all into seed and plant catalogs in winter. It takes some real math juggling to figure out the most economical assortment of proper plants for your hardiness zone that will fit in your garden and mature at the right time. Pretty pictures help a lot. You may want to let them cut out pictures and description for projects when done with the catalog.
- Math and cooking. One of my favorite activities for fraction math, as those who read my bread article in the March/April issue know.
- Just watching the stars can be greatly enhanced with a simple star chart. Bear in mind, however, knowledge of simple geometry and calculating angles will be necessary as well as some solid geography and astronomy. This can lead into navigating by the stars which we read about in Christopher Columbus' log book. We even constructed a simple device to measure the angle a star is above the horizon using a protractor with a plumb bob (long string with a weight at bottom) tied to its pivot point.
- Building projects abound in our family. Ten-year-old Jenny can now take an active part in planning, measuring, cutting and assembling bird houses, feeding stations, and barns for our ever-growing bird population.
Sometimes the SOYP approach can put you in unexpectedly deep water when you get ahead of the text book (now where did I put that thing?!?). There are times you may be shaky on a topic yourself. While it's reassuring to be a step ahead of your students, free-wheeling studies don't always permit it. Just remember, it's okay to admit ignorance. Proceed slowly together with good reference material or an explorer's best tools: pen and paper and brain. Also remember encyclopedias, books or those great CD-ROMs like Encarta can provide succinct, easy-reading explanations on a particular math area. There are some excellent general math books for high school and college which give a good overview of all basic math topics. You may also want to check out the remedial math texts used by colleges.
Final Thought Math can be snuck into most any study, but don't feel obligated to drum the point in at every opportunity. Back off and let children discover on their own. I like to keep in mind the words of warning of one of my favorite critics, homeschooling mom Laura Weston: "Doing something for the sheer joy of it is the best lesson we can give our children."
© 1995 Leslie Wilson
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