(The following was written to the chairman of the math department at CDO High School in Tucson, where I have been a volunteer math tutor for 8 years.)
America has given three great gifts to humanity: liberty, the national park system, and public education. All three are under attack, but I will confine myself to the last.
I believe students must be able to do the following before entering high school:
- Multiplication tables accurately and fast, mentally, with no calculator.
- Addition and subtraction of all two digit numbers quickly–paper allowed. No calculator.
- Ability to add and subtract fractions, including those such as 5 1/8 -3 3/4. Paper allowed. No calculator.
- Ability to deal with negative numbers quickly and accurately. It is inexcusable for students well into ninth grade continue to give “14” for 5 – 9.
- Know the number of months in a year, days in a year, hours in a day, and minutes in an hour (yes, these are frequently not known.)
- Know all basic English and metric measures: these include ounces in a cup, cups in a pint, pints in a quart and quarts in a gallon. They should know metric and English units of length, area, volume and temperature and be able to convert between them. They should know sixteenths of an inch on a measuring tape. They ought to know what a cubic foot of water weighs; maybe then we wouldn’t have drivers going through flowing washes every summer. It wouldn’t hurt if they knew that 1:60,000 on a map is roughly an inch to a mile.
- Know the decimal equivalent of all fractions with a denominator less than 10. Be able to quickly and accurately convert mixed numbers to improper fractions and vice versa. It is inexcusable for a softball player to require a calculator to figure out her batting average.
- Be able to estimate square roots of numbers that aren’t perfect squares; many honors geometry students can’t estimate the square root of 5.
- Know common factors of common numbers, which basically means understanding the multiplication tables.
- Be able to estimate answers to common problems, including the proper sign and rough idea of the magnitude of the answer. A quarter or the price scanners in Arizona are inaccurate; cashiers frequently give the wrong change.
- Be able to work with large numbers using scientific/exponential notation.
American students need to be able to collect, format and interpret data at a basic level. We have a data driven society: today’s key issues cannot be addressed without understanding basic science and math. We have a society where conspiracy theories are not debunked, vaccinations are believed to cause autism, and where a majority do not believe in evolution despite absolutely compelling evidence. We have the highest percentage of non-believers in global climate change in the world. More people believe in astrology than in astronomy; few know what a year represents, and fewer still can find ten well known countries on a map. But my focus is on math.
It is impossible to use a calculator without number sense–some idea of what an answer ought to be. Calculators give several decimal places when three to four would be sufficient (and better, in the case of scientific work, where the appropriate number of significant figures has to be used). Inability to estimate an answer means that if a wrong button is pushed, the student will be unaware of it. Too many graduate without basic skills; 80% of the students entering Pima Community College need remedial math training. How many children in Pima County, Arizona, and America leave high school unable to do basic math? We don’t know: but from my experience in two affluent districts with high graduation rates, I would estimate the number well over 5000 annually. These students are being left behind not just other Americans but the Singaporeans, Indians, South Koreans, Chinese and Japanese, all of whom recognize that in this century, as in all others, education is the way out of poverty. They are strong competition, and if they succeed, this country won’t.
I believe if students had a solid background in basic math, they would be able to handle basic financial issues. One reason we have the current financial crisis is that many cannot understand interest rates, doubling times for debt and money and budgeting skills.
We require students to memorize the alphabet and the numbers. We practice writing and diction. We similarly must require memorization, practice and homework in math to learn these basic skills.
I have nearly daily arguments with students about banning all electronic devices in the classroom, except calculators. I have yet to be in any class in any school, and I am in school 5 days a week, where there isn’t surreptitious texting occurring. Seniors probably can’t be controlled, but 9th graders should not be allowed to have electronic devices near them in the classroom. How to do this will be difficult, but if we don’t stop the electromagnetic abuse, learning will continue to deteriorate. I am well versed in studies of human error and know that multitasking hurts learning and that interruptions require significant time to reconfigure one’s ability to concentrate. I think far too many are labelled as learning disabled, without seeing what happens with concentration, hard work and one-to-one tutoring. I am bothered by grading participation, which to me has shown up in high school as loud, wrong guessing. We need to bring back the concept of school nights, where there aren’t concerts or hanging out. In these days of instant, easy electronic communication, parents ought to be fully aware of how their child is doing and should be acting upon it.
In passing, I mention the deterioration of dress, language and civility among today’s students. I think that more formal dress correlates with better civility and a higher likelihood of learning. I am no longer shocked by what students wear, and I’ve grown to tolerate coarse language, perhaps because of my Navy experience, where I’ve heard everything these students have said and a good deal more. The lack of civility I have a more difficult time with. I certainly wasn’t always polite as a student, but there were significant consequences for rudeness that when I violated, I still remember to this day. The public displays of affection are nothing short of shocking.
Education requires society, not just schools and teachers. Parents must inculcate their children with the proper values, dress, behavior and desire to learn. My father was a high school principal, assistant superintendent of schools and superintendent in three cities. He and my mother accepted nothing less than my best work. Yes, education is underfunded, and we need to press for more. But that does not excuse us from doing what we can with the people we have. And we aren’t doing that. We need society to be taxed to pay for the public schools. We also need to stop promoting those who do not earn promotion. We need volunteers, as I have been for the past 8 years. And we need the schools to put them to use, in the classroom, library, before, during and after school and on weekends, which has not occurred. Six schools have never returned my offer to volunteer. This is unacceptable. We need competent teachers, and we need competent substitutes, which I hope to be. I decided to substitute for pay because I was not busy enough and was felt it unfair that I taught when a certified substitute got paid and did nothing. We need appropriate tests, where to fail them would be so egregious that nobody, even in the Arizona legislature, would pass the student on to the next level. (I would wonder how many legislators would pass such tests.) Teachers promote students to high school who are incapable of doing elementary school–yes, elementary school–math. Eventually, high schools and community colleges end up teaching remedial courses. This must stop. Watering down AIMS because it upsets people is unacceptable. Do we want educated students or don’t we?
America’s future at stake. I am among the 7% of Americans who has served this country in uniform. We need mandatory national service, some of which could be in the classroom, where we might find our next generation of teachers. I refuse to let public education fail without a fight, for if it does, we will lose the middle class and this country. I will continue to speak out on this subject; I will do all I can as a volunteer and as a substitute to teach students the skills that I have been blessed with, not just genetically, but through practice, hard work, and strict demands — timeless values – made by my parents.
