The Home Schooler
A Biblical Light on Education -
With Special Emphasis on Home Schooling
1) Scope and Sequence
2) Spiritual Olympics - Olympic Christians
3) Mathematics - What Do Our Children Need?
4) Mathematics - What Do Our Children Need? - Part II (Don't miss this article)
5) Dr. Cates' Itinerary
Scope and Sequence
expose to inferential questions
distinguish between real/fantasy
distinguish between fact/opinion
answer why/how questions
skills in listening to others
becoming aware of purposes of listening
listen for clear speech patterns
apply skills for listening in a group discussion
learn how to adjust volume control in various situations
listen for directions
listen with respect
learn to understand audience response
teach purposes of listening: to gather and recall factual and
listen for sequence of ideas
recognize main idea and details in listening response
experience listening to various media
write and respond from teacher dictation
use of complete sentences
phrasing; pace; pitch; tone; expression
Spiritual Olympics - Olympic Christians
1. Their mindset is to win no matter what obstacles come before
them. They don't always win every race and sometimes fail badly.
2. They are people of courage.
3. They enjoy what they are doing, and others know it.
4. They sometimes have great struggles and challenges in their lives.
5. They don't give up.
6. They are goal oriented.
7. They are not victims, but overcomers. (The stumbling blocks become stepping stones.)
8. They don't make excuses, but try harder the next time to correct their mistake.
9. They practice over and over. "You will never be able to...understand the deeper things of God's Word until you learn right from wrong by practicing doing right." Hebrews 5:14
10. They refine their skills.
11. They do their very best.
12. They go forth no matter what the circumstances. (Spiritual rain and storms.)
13. They are not distracted from their tasks. No matter what others are going around them, they are focused on the goal set before them.
14. When they retire from the front lines, they train others to become their best.
15. They are encouragers.
16. They have great empathy, but show tough love.
17. They don't let their students give up in adversity.
18. They are always looking for ways to improve their own skills,
and help others improve upon theirs.<9> Dr. Carl Selzer, a consultant of Cuisenaire/Dale Seymour and President of Learning Materials, Inc., has been a very dear, supportive friend of mine for years. He has authored or co-authored over 50 math books. Belonging to many state and national councils of teachers of mathematics and educational publishers, he has earned many distinguished awards. Dr. Seltzer is a well-known speaker at local, regional, state and national conferences. I feel that homeschoolers could benefit greatly from the advice and teaching that he so graciously has agreed to give in writing a series of mathematical articles for our paper. Thank you, Carl.
This is the first in a series of mathematics articles that I've agreed to write for " The Homeschooler". I sincerely hope these articles will be of a significant resource to you as you contemplate the teaching of mathematics to your child (children).
Mathematics may be defined as the science of pattern and relationships. As a science, the "mathematics classroom" should be a scientific laboratory where children experiment, explore, observe, draw conclusions, and verify results. Problem solving should be the main focus of any mathematics program.
Having defined mathematics, the next question is why do we study mathematics? I believe that we've been incorrectly answering this question. Traditionally we've answered the question, why study mathematics, as follows:
1) You need it in later math courses.
2) You need it for college.
3) You need it to function in the real world.
4) You need it for specific careers.
These reasons are not convincing to me, nor are they convincing to children. Actually, these aren't really the reasons at all. Rather, I'd like to suggest that we study mathematics because in mathematics we learn how to answer every important generic-type question. The skills obtained by answering these questions are applicable to almost every profession or career.
People need mathematics and mathematical skills and abilities when they encounter questions like:
1) How can this information be sorted, organized, grouped and
2) Does it follow? Can you verify that fact?
3) What are the possibilities?
4) What strategies are available?
5) What are the chances? What are the risks?
6) Can we simulate or model the situation?
7) A small part of the situation is visible, but what is "actually" there?
8) Why does this work?
9) Are these figures accurate? Do the books balance?
10) What's missing? What's extra?
11) Are these two things related? Does one factor influence the other?
12) What are the extremes? What is most likely? How much variation can we expect?
13) Is that reasonable? Do I have enough?
14) What are the ground rules? What limits do they impose?
15) Is there a different way to look at the situation?
16) What if? What are the possible consequences? Have we explored every possibility? Have we missed something?
17) How much is necessary to complete the task?
18) Does this problem behave like any other situation? What's the same? What is different?
19) Can it fit in the available space?
20) How fast is the situation changing?
21) Have we reached the maximum or minimum? Can things get better or worse? What's best?
22) Can the situation be visualized?
23) Can we create a scale model?
24) Will our proposed change really make a difference? How can we tell?
25) How do you know it's true? How can you be sure?
26) What is the result of this series of actions? Are the steps reversible?
These are surely not the only questions studied in mathematics, but will give you a good idea of what our children need to learn.
Next issue topic--What kind of mathematics for our children's future--a look at the REAL world.
Mathematics, Part II
In the first part of this series of articles, I focused on the real reasons why we study mathematics. In this article, I would like to examine how our world is changing, and how that will impact our children.
Our world is changing! In 1982, there were 32,000 robots in use in the United States. In 1989, there were 1,333,000 in use; and in 1995, that number leaped to 24,000,000. By the year 2000 it is predicted that there will be 100,000,000 robots being utilized in the United States, alone.
Why are we putting so many robots into service? To answer that question, let's look at a typical example. In 1985, QR Industries employed over 300 people making clamps for General Motors cars. If a clamp was 1/100 of an inch off, the company was severely penalized. In 1986, 5% of their clamps were rejects, so QR Industries had to improve the process or lose the contract. They robotized the assembly line, and now only one out of 10,000 clamps is rejected.
QR Industries now has 17 employees. The accounts payable clerks are gone. Many other office jobs are gone. All have been replaced by computers. Yet, one of the largest enrolled courses in junior and four-year colleges is ledger accountants, accounts receivable personnel, and accounts payable careers. Between 1950 and 1990, we have seen major changes in business but very little change in our business colleges.
Our world is changing! Today the largest employers in the United States, listed respectively by the number of people employed, is as follows:
2. Burger King
3. U.S. Government
Twenty-two of the top twenty-five employers are in the retail and service sectors. Yet, the food industry is quickly becoming automated. In Ohio, there is a fast food restaurant where you push the button to select a hamburger, another to indicate what you want on it, and another to deposit your money or insert your charge card. In thirteen seconds you get a hamburger cooked like you want it, untouched by human hands.
Why are fast-food restaurants moving to robots? Simple. Because fast food restaurants have gotten sick and tired of trying to attract quality workers that can do the level of work they want, for a price they are willing to pay. Yet, these restaurants will pay a German technician $30.00 per hour (that's over $60,000 per year) to keep the high speed laser cooker system working. If it goes out, they're out of business.
Our world is changing! What's happening in the service sector? It is becoming automated. How many of you use an Automatic Teller Machine? In 1982, there were no ATM's. In 1988, 55% of all customer banking transactions were done at ATM machines. Where are all the tellers? In 1990, their positions were reduced by 40%, in 1993 by 80%. In the year 2000, who knows? The banking industry is becoming automated! Oh,yes, but the banking industry is seeking employees. They're scambling to hire technicians to maintain those Automatic Teller Machines. And where are these technicians coming from? Not the United States. Why? Because none of our colleges or universitites are producing a single technician who can run the ATM system.
One of the fastest growing companies in the United States, according to the Wall Street Journal, is the Checker Robotics Company with main offices in Deerfield, Florida. Guess what Checker makes? Right, robots! Actually, Automated Roboticized Checkout Counters. Push your grocery cart to the check out counter, and a robot arm reaches out, picks up your 16-ounce bottle of Diet Pepsi, reads the bar code, packs it in a bag, and tells you how much you owe. It even packs the heavier items on the bottom and the lighter items on top--what a novel idea that is!
In 1985, all Checker employees were working in the United States. In 1996, 2% of Checker employees work in the U.S. Where did they all go? Answer--China, Korea, Japan, and Germany. Why? Because they could not find the labor force in the U.S. who could do the work.
In 1992, American industry imported 1,000,000 foreign-born, foreign-educated workers with no work experience. These people are serving as well-paid technicians at Citibank, Checker Robotics, and technicians for fast-food restaurants. Is your son or daughter being prepared for this?
Our world is changing! Look at what is happening in the information sector. According to the U.S. Department of Labor, by the year 2000, 11% of all workers in the United States will be in the business of collecting, analyzing, synthesizing, and retrieving data.
How many of you can type -- not well, just type. Typing (or keyboarding) is an important skill, but what about the keyboard you are using or learning to use? Did you know the most frequently used letters of the English alphabet are "a", "e", "i", "o", and "u"? But on American keyboards, the most frequently used letters are not the most accessible. Not only that, but 72% of the keystrokes are hit with the left hand. Why? Because we made our old typewriters that way to slow down the pace so the typewriter keys wouldn't jam. It is doubtful that the left hand situation was even considered. Yet, we are still using the same old keyboard. Research shows that by simply changing our present keyboard, productivity increases by 36%. Yes, new keyboards do exist, and they recify this problem. So why do we still use the same old keyboard and continue to teach students the same old thing even when we know better?
Any computer manufactured in America since 1988 has two keyboards imbedded within. Word Perfect, for example, has two keyboards; the U.S. model and the rest of the world's model. Does this remind you of the metric system vs. the English measurement system? Changing how we teach math is a good parallel.
The fact that 44% of the jobs in America are going to be about the business of collecting, analyzing, synthesizing, storing, and retrieving data has nothing to do with this issue - nor should it! The world is changing, folks, and we must change with it.
In 1950, 60% of the jobs in the U.S. were unskilled. In 1989, 35% of the jobs in the U.S. were unskilled. In 2000, we estimate 15% will be unskilled. What are we doing about this?
One out of five students drop out of high school. Another one out of five graduate, but they come from what is known as the "general track"; we all know what that means. Another 20% go to college but last less than one year. What percent of Japanese students do you think complete college? It's not 100%; it is only 98%. In Germany, it is 96%. In China, it's only 92%. In America, it is less than 50%.
We live in a Global Economy, and the most important single resource product we have is our work force (our people). Today, North America, Europe, and Japan account for 20% of the world's poplulation. By 2010, it is projected that North America, Europe, and Japan will only account for 10% of the world's population. The rest of the world - the other 50% today and 90% in 2010 - have an average salary of 50 cents an hour. How can we compete with that? We can't!
It costs $9.80 to type one page of print in the U.S. and only $1.18 in China. We cannot compete with that. So we must work smarter! We must teach our childen
How to Think
How to Communicate Their Thinking
How to Reason Logically
How to Get Along with One Another
How to Solve Problems
To do this we must change the way we teach. Our methods of teaching mathematics are just about as obsolete as our typewriters. In the next article, we will examine how to do this.
Dr. Cates' Itinerary
Many of you would like to know when Dr Cates will be in your area again. Following is his itinerary. Included is a contact person and his/her phone number to get more information for that area's meetings.
December 8-11, Wilder, KY-Churchill Christian Academy, Bonnie Keys 606-781-3407
12-14, Easley, SC - Homeschool Conference, Jennifer Charron 803- 261-6471
January 14-19, Baltimore, MD - Homeschool Conference, Terry Rust 410-247-4119
22-25, Athens, TN - THEA Homeschool Conference, Susan Ward 423- 263-7026
January 31- February 4, Wilder, KY - Churchill Christian Academy, Bonnie Keys 606-781-3407
6-12, Kansas City, KS - Homeschool Conference, Kristi Jackson 816- 241-6616
14-18, Dallas, TX - Susan Foster (after 7:00 P.M.) 214-937-5026
March 10-12, Dallas, TX - Achievement Testing, Susan Foster (after 7:00 P.M.) 214-937-5026
13-15, Dallas, TX - Homeschool Spring Conference. (Same as above.)
17-20, Memphis, TN - Achievement Testing, Peggy Starbuck 901-452- 9877
24-27, Jackson, TN - Achievement Testing, Kathy Hayes 901-423-0942
April 3- 9, Wilder, KY - Achievement Testing, Churchill Christian Academy, Bonnie Keys 606-781-3407
11-20, Romeo, MI - Spring Homeschool Conference, Carolee Anderson 810-752-0980
24-26, Charleston, SC, Helen Reed 803-572-3924
May 1-5, Wilder, KY - Churchill Christian Academy, Bonnie Keys 606- 781-3407
6-9, Luling, LA - Homeschool Spring Conference, Jimmie McCall 504- 785-9142
10, Columbia, MO - Homeschool Conference, David Swartz 573-682-3635
16-17, Memphis, TN Homeschool Convention
19-24, San Diego, CA - Homeschool Conference, Monica George 619- 758-1775
27-30, Athens, TN - Wesleyan College, Susan Ward 423-263-7026