Tuesday, August 29, 2017

Why Learn Arithmetic & Algebra?

Why should students master Arithmetic and Algebra?
So, they don't live paycheck to paycheck and beyond their means.
So, they save and invest to become millionaires when they retire.
So, they are frugal, debt-free, and have a cash flow from investments to build wealth. (Kids need to learn Algebra-2 to get into college.)

Knowing math and having financial savvy can greatly improve your quality of life. Briefly, learning math and science opens the door to opportunities. Isn't this what we want for students? 

Why are you in debt and living paycheck to paycheck? That's stupid!
Arithmetic was deemed important because it was practical, but how many of us perform arithmetic when everything is calculated by machines? Most of us do not balance our checkbooks. We don't have a practical budget to track where the money goes; consequently, 78% of us live paycheck to paycheck and above our means, which is stupid. Most of us don't understand the science of money such as the miracle of compounding, which is exponential growth, not linear change. In short, most of us don't know enough arithmetic or simple ideas of algebra and cannot apply them even with a calculator. The concepts are not difficult. 

The difference is between those who know math and those who don't, between those who save and invest and those who spend and spend beyond their means. Income does not determine wealth. As your income increases so do your expenses. Cash flow from other sources (i.e., investments) determines your wealth. 

"Income is not wealth. Wealth is cash flow from other sources," write Tracy & Strutzel. Spend less than you earn and invest the difference in a good index mutual fund to start. 

Tracy & Strutzel point out that "successful people do not gamble" or buy new cars. They state, "The reason people don't retire financially independent is that they spend everything that they earn." 

The average American does not have cash. Nearly 70% do not have an emergency fund of at least $1000, much less 6 months of expenses should something happen. 

Unfortunately, most of us don't know how percentages work because of poor teaching. If we did, then we would never take out a seven-year car loan, pay the minimum on credit card purchases, or use "payday" or "title" loans, etc. We have been taught that debt is the normal way of life, and it builds a credit score, so we spend everything we make and then some. It is a dumb idea! 

In contrast, financially savvy people don't buy anything on credit or use credit cards unless they have the money in the bank to pay for it.  If you don't have the money in the bank, then don't make the purchase. They don't spend everything they earn. They budget and invest the difference.  

Financially savvy people buy an affordable car with cash. It's not a new car. Financially savvy people know math. For example, they know probability and don't buy lottery tickets. 

Student loans are another problem for young people. I had student loans, but I also had a job with enough income to pay them off.

You can become a millionaire by investing about $100 a month over an extended period. The investment would have to grow by a factor of 10000 over time. It would take 45.67 years of investing at least $100 a month in an index mutual fund that has an average annual return of 9.69%, which was the 50-year annual return in the stock market from 1966 to 2015. Even if your take-home pay is $1,666 a month to start, $100 a month is only .06 or 6% of your monthly take-home pay. You can become a millionaire only if you think that way. 

Also, as your income increases, you should increase the monthly investment to 10% to 20% or more of your monthly take-home pay. You can access the American dream, but not by living paycheck to paycheck and going into debt with credit cards and car loans, etc. If your take-home pay is $2500 a month, then 10% to 20% would be $250 to $500 a month. If you do this (10%) for 36 years, then you will have one million dollars, but you may need much more because nasty inflation kills off buying power over time. The only debt you might carry during this process is a reasonable mortgage, but after 30 years, it should have been paid in full. As your income increases, you should pay off the house mortgage within 15 years by making extra payments. Also, if you can't put at least 20% down, then don't buy the house.

We need to teach kids key financial lessons from 1st grade on up. One is that debt is not normal. If you want something, then save for it and pay cash. It is where arithmetic and algebra come into play. Easy credit with high-interest rates can kill your future. 


Wobegon does not exist.
Our educators and schools are loaded with wishful, Utopian thinking and illusions of fairness, most of which is absurd. "Fairness as the equal treatment does not produce fairness as equal outcomes," writes Thomas Sowell 

Many teachers don't know how to teach content because, they, themselves, have not mastered the content. Teachers who advocate flipped classrooms, personalized learning, tech as a panacea, and other schemes and fads don't know how to teach. 

The idea that children don't need to memorize or drill to improve math skills (i.e., practice) shows ignorance of cognitive science and of how children learn, which is remembering from long-term memory.

Many have the idea that new is better, so they must have the latest tech, newest car, etc. Why would you want a car payment, mortgage, or credit card debt the rest of your life? The "new is better" attitude has resulted in more lackluster achievement. Reformers preach "out with the old," even if it worked well, and "in with the new," even if it has no basis in evidence. Reformers seem to ignore the evidence. 

To Be Revised as needed.

©2017 LT/ThinkAlgebra

Saturday, August 19, 2017

Mechanics first Explanation later

Asian children are taught mechanics first with an explanation later, and it works!  We do it backward, and it doesn't work. Furthermore, the use of calculators masks weak arithmetic and algebra skills. And, it hurts our kids. Massive numbers of high school graduates are placed in remedial math at community colleges. Many community college administrators want to do away with the "algebra requirement" to increase the graduation rate. Why? Most kids don't pass the remedial algebra courses at Community Colleges either. 

In other words, the teaching of remedial (high school level) algebra courses at community colleges is just as poor as the teaching of algebra in high schools. Apparently, using calculators doesn't help much. Indeed, they are "absolutely unnecessary," writes W. Stephen Wilson.

Keith Devlin says that with all the cheap gadgets available today, the need for mastery of arithmetic has lessened considerably. I think he is wrong. Being able to do arithmetic well--especially fractions--is needed for Algebra. Kids are not little mathematicians or junior scientists. They are novices. They do not think like adults.

Note: If there is no need to learn the mechanics (procedures) of algebra because technology does the procedures faster, as Wagner & Dintersmith (Most Likely to Succeed) argue, then, using the same argument, there is no need to learn the mechanics of arithmetic such as standard algorithms because calculators can do the operations faster. But, oddly, Wagner & Dintersmith don't think that about arithmetic. They claim, arithmetic is useful and algebra and high school math are not. They also claim that "most college courses require only K-8 school mathematics, "especially arithmetic, ratio, proportion, expressions, and simple equations." 

According to Wagner & Dintersmith, arithmetic is needed because it is used in everyday life. Really? When was the last time you did long division, a decimal multiplication problem, fractions, proportions, percentages, arithmetic mean, or a financial calculation without a calculator? 

According to the National Math Panel, "To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills." 

They are interwoven! You have to teach more than just concepts. Students need to know foundational knowledge, both factual and procedural (mechanics).

"By the nature of algebra, the most important foundational skill is proficiency with fractions (including decimals, percent, and negative fractions)." We do not teach fractions well. "The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in Algebra can be expected." (Source: Math Panel, Critical Foundations of Algebra)   

In many K-8 schools, we seem to have a "steady diet of test prep." Is that a good thing? Wagner & Dintersmith (Most Likely to Succeed) think test prep is bad for kids because it hinders creativity and curiosity, but there is little evidence to support the claim. Rather, I think test prep is a poor substitute for a math curriculum and a waste of time. In my view, test prep is not the same as learning core arithmetic fundamentals in long-term memory. 

Wagner & Dintersmith write, "Clearly we want every child by a certain grade level to be an adept and passionate reader, to be proficient (without a calculator) at core math operations (e.g., division, fractions, estimation, and financial literacy), and be able to communicate well. Mastering these foundational building blocks requires repetition and practice.

I agree. Kids need to master basic arithmetic. But...

Wagner & Dintersmith also conclude that the mechanics of algebra and much of high school math is outdated and unnecessary. They explain, "Don't get us wrong about the need to drill on lower-level math operations. Any young adult needs to be facile with core operations (+, -. x ÷, %, fractions, and decimals," which are K-8 math. But, we also know "they will never have to solve a quadratic equation by hand." 

Today's college entrance tests, they say, "require students to master skills that are obsolete. Indeed, "80% of U.S. adults never use any math beyond decimals, fractions, and percentages." Wagner & Dintersmith assert that "the math needed for college courses does not require high school math (algebra, trig, or calculus)--except for STEM students. Most college courses require only K-8 school mathematics, "especially arithmetic, ratio, proportion, expressions, and simple equations."

Comment: The problem I see is that the core basics are not taught well in our K-8 schools, which seem to focus more on test prep than on learning core fundamentals. (By core, I do not mean Common Core.)
Wagner & Dintersmith want to toss out much of high school math as obsolete, especially the paper-pencil techniques, procedures or mechanics of algebra, trig, and calculus, replacing them with calculators, tablets, computers, and smartphones. While calculus concepts are useful, they say, the "mechanics [of calculus] belong to smartphones." They imply the same for algebra and trig. Kids should learn just the concepts, not the mechanics.

I think they are wrong! 

Comment: In the real world, students still need to pass the admission and math placement tests at colleges and universities. Unfortunately, a massive number of high school graduates have been placed in remedial Algebra courses at community colleges because they didn't learn the mechanics and weren't able to apply concepts.

Wagner & Dintersmith think that students should drill the procedures of arithmetic, but there is no need to drill the procedures of algebra, trig, or calculus because they are old-fashioned and nonessential. They argue that high school kids should use the latest technology such as WolframAlpha on their smartphone, tablet, or computer. Their main argument has been that no one will ever need to solve a quadratic equation or an integral on paper. 

According to Wagner & Dintersmith, arithmetic is needed because it is used in everyday life. Really? When was the last time you did long division, a multiplication problem, or a financial calculation without a calculator? Algebra and Calculus are not needed because they are not used, but neither is arithmeticNotice the inconsistency! The lack of numeracy among students and adults has been a perplexing problem for decades. Today, only 3% of adults can ace a math quiz without reaching for a calculator. The questions on the quiz featured multiplication, subtraction, percentages, and division.

Comment: What do Wagner & Dintersmith and many others have against algebra mechanics and quadratic equations? Physics is loaded with quadratic equations. To understand physics well requires a calculus background, but most beginning physics courses in high school and college are algebra-based. Kids need to know algebra, but many don't know it well enough. So, they struggle in the hard sciences, if they get that far.  

Also, I guess no one will quote Shakespeare either, so his plays should be eliminated from the high school curriculum. Latin is gone too. Gee, I thought the mechanics of algebra were embedded in the understanding of algebra concepts. "If you can't do it, then you don't understand it," says mathematician W. Stephen Wilson.

If there is no need to learn the mechanics (procedures) of algebra because technology does the procedures faster, then, by the same argument, there is no need to learn the mechanics of arithmetic such as standard algorithms because calculators can do them faster. 

I don't buy it!!!

In the real world, kids need to learn the concepts, but they also need to learn the mechanics (e.g., standard algorithms, distributive property, etc.) and solving routine problems. Most of the concepts in arithmetic and algebra are easy. Even 1st-grade students can learn some of the fundamental concepts of algebra via arithmetic. By 3rd grade, well-prepared students can learn the mechanics (technique) for solving simple addition or subtraction equations using inverses.
© 2017 LT/ThinkAlgebra