We should focus on the mastery of basics, not learning for a state test.
- Practice builds conceptual knowledge and math skills.
- Thinking in math requires knowing math facts!
- "You learn only through mastery!" - Zig Engelmann
- Children need to do things that don't come easy for them.
Chris Hogan, Everyday Millionaires
Hogan blasts the myths about millionaires. He writes that net-worth millionaires are just ordinary people such as engineers, accountants, and teachers. (See the bottom of this post)
Low Standards, Inferior Methods of Instruction, Inadequate Teacher Training, etc.
After over 50 years in education as a classroom teacher, tutor, and a guest teacher, I believe that the educational establishment in government schools will do little if anything to correct the curriculum and the teaching of math in our classrooms. It is up to parents to force changes, but, since the "math wars" era, they have hesitated to criticize the teaching at their schools. Reform math hasn't worked. Smaller class sizes haven't worked. Putting more money and tech into the classrooms haven't work. Increasing teacher pay hasn't worked, either. The math standards are still below world class.
The raw truth is that ACT math scores are at a 20-year low (ACT) and only 25% of 12th-grade students are proficient in mathematics (2017 NAEP). But the test results don't seem to lead to constructive changes in the teaching of mathematics, starting with 1st-grade arithmetic. The problem is that math is not taught for mastery! It is taught to score better on a state test. Annual testing should be eliminated so that teachers can focus on teaching standard arithmetic for mastery. Knowledge is the basis for problem-solving in math.
What's wrong with learning in our classrooms? It is the teaching, along with fads and the hype over tech. Children need to be "rescued from failed educational theories."* The failed theories come from schools of education along with other methods, policies, and trendy fads that violate the cognitive science of learning. Today, we have rampant grade inflation, watered-down courses, and credit-recovery nonsense that boost graduation rates artificially, but at what cost? High School graduation has become more important than learning science and math. Consequently, many high school students are weak in math and science according to national and international tests. *E. D. Hirsch Jr.
Another red flag has been the explosion of "remedial math" coursework at community colleges. Also, we have more discipline problems in our schools due to the idiotic liberal policies and guidelines. Many U.S. high school students don't know enough math content to do problem-solving in math.
Contrary to the "constructivist" theory taught in schools of education, students should not be expected to figure out or grasp the basics of arithmetic on their own via group work, discovery activities, or other minimal guidance methods of instruction. Instead, children need explicit teaching and lots of practice because they are novices. Zig Engelmann points out, "Without a firm foundation in number facts [automated in long-term memory], children are held back from further learning." This is the situation in our schools. Kids aren't learning enough!
Thinking comes from knowledge, not thin air.
In many of today's progressive classrooms, thinking skills or strategies are highlighted, often at the expense of the mastery of content knowledge, which is domain specific. Knowledge is downplayed, a gross error. Moreover, problem-solving or thinking in math (logic with true statements) is different from thinking in science (observation and inference). Math is absolute; science is uncertain.
If you have learned something, then you remember it. If you forget something, then you haven't learned it as "learning is remembering," which is retrieving stuff from long-term memory. Remembering fragments isn't good enough. You don't know anything unless you have practiced, as Richard Feynman used to say.
The idea that practice at home doesn't benefit elementary school children is a myth. Students should practice basics for mastery at school as well as at home.
Homework
Kids need homework and lots of practice to master arithmetic because they are novices. We should make sure that students know the calculating skills necessary to do the applications and to solve problems. In short, applications should not be introduced at the same time students are just learning the calculations and the procedures needed to solve them. Also, engagement is not the same as learning. Teachers spend too much time on engagement and discovery learning activities and not enough time on mastering math content and associated skills.
The problem goes deeper. Many of the so-called innovations, reforms, or changes often hyped in our schools don't work, including the popular belief of using technology and software to tailor instruction to each child. A whopping 82% of the innovations funded by the U.S. Department of Education did not improve achievement.
K-12 education technology is thriving, but student achievement is not.
In some school districts, each student is given a tablet or laptop, which is a popular idea to bring schooling into the 21st century, we are told. Really? The basics of arithmetic have not changed: the sum of 3 and 4 is still 7, and the Pythagorean theorem always works with right triangles, etc. The K-12 education technology business is thriving and lucrative. But, are students getting better in math and reading? The short answer is no, according to government tests (NAEP 2017). Students stumble over arithmetic: they are not learning standard arithmetic for mastery.
Furthermore, the maintenance of the tech in schools is costly, such as software licensing, hardware repairs and replacement, "ongoing training, technical support, and network upkeep," reports Benjamin Herord. Where does all this money come from? Does the cost justify the scant achievement? No matter the claims that are made, the software is not that good. Kids are not gaining in achievement.
We know that schools spend an enormous amount of money on tech with little to show for it. We also know that performance in math and reading has stagnated. Educators chase after the latest fads and trends. Still, the vast majority (82%) of the innovations funded by the U.S. Department of Education don't work. The progressive reformers have had a terrible track record. In my opinion, they have screwed up math education, starting with the NCTM standards of the early 90s. In schools of education, K-8 teachers are not taught the cognitive science of learning.
Indeed, school officials, school boards, administrators, policymakers, teachers, and concerned citizens should be skeptical of the "enticing and often extraordinary claims" made by software companies and the tech industry, but they are not.
The brightest college students don't want to be teachers; they want professions that recognize and reward their abilities and accomplishments.
I don't blame them. Teachers are not well respected. Teaching has become a very difficult job with little reward, recognition, or professional advancement. They are not miracle workers. Incidentally, a master's degree in education is not an advancement. It means little except for a bump up on the salary scale. Getting a master's degree in education or a National Board Certification does not make teachers better at teaching.
Perhaps, in my old age, I have grown doubtful about the teaching profession. I am sure there are many who disagree. Teachers should not strike or walk out of classrooms.
Frankly, I don't know how to disrupt the entrenched culture of the highly bureaucratic education establishment. I can guess. I do know one thing. Technology, itself, is not going to change the culture.
The economy is booming, but little praise is given to schooling since the 80s. But, linking the booming economy to schooling is correlation, not causation. Other prosperous nations link the economy to their education system. Also, many American educators are convinced that our education woes won't get better until poverty is eliminated. There is a link between education and poverty, but don't confuse correlation with causation.
The problem, I fear, is that the education that many children are receiving today will be insufficient to meet the demands of the 21-century. Many jobs will no longer exist because of the advances in Artificial Intelligence. Adults who lack sufficient math and science skills will be left out.
Moreover, some teachers are told not to teach something kids can look up on Google. It is part of an anti-knowledge or anti-intellectualism movement. The stress in the classroom has been on critical thinking skills, but the problem is that "thinking without content" in long-term memory is empty. Thinking is domain specific. In math, for example, critical thinking is called problem-solving. You can't solve a trig problem unless you know some trig and have had experience solving trig problems.
Intelligence, I think, is the ability to work with abstractions. In my Teach Kids Algebra program, some kids work with abstract ideas in math better than others. Numbers, operations, rules (a + 0 = a), variables, and equations are some examples of abstract ideas students meet in arithmetic. I fuse algebra to arithmetic.
Get out of debt, save for the future, and build wealth.
"Teachers are often notoriously underpaid, especially considering how hard they work and how important their jobs are. And yet, teaching is one of the three most common professions among America's net-worth millionaires. That's awesome. Teachers know not only how to work hard but also know how to plan ahead with a longer-term view," writes, Chris Hogan (Everyday Millionaires). Hogan warns against taking out student loans, home equity loans, car loans, and so on, all of which are debt instruments. You can't grow wealth if you are in debt or spend more than you make. Hogan blasts the myths about millionaires. He writes that net-worth millionaires are just ordinary people such as engineers, accountants, and teachers. If you don't have the cash to buy something, then don't buy it. And, only buy what you need.
I wish I had Hogan's book when I started teaching in the 60s.
From Chris Hogan's book:
"Millionaires live on less than they make, plan and pay cash, use coupons, use shopping lists and stick to them, drive older cars with no car payments." Credit card debt, car loans, home equity loans, and student loans are a bummer. Materialism has been a significant problem in the U.S.
The average new car payment in 2019 is $530 per month. Suppose you paid cash for an older car with no car loan and put most of the new "car payment" towards your retirement plan in a Roth IRA. Let's say you invested $500 after-tax money every month for 30 years in an index fund, such as the Vanguard 500 Index Fund that mimics SP 500 and averages 10% annualized. After 30 years, your Roth IRA would have accumulated approximately 1.14 million. Most anyone who knows compound interest (exponential growth) and works hard can accomplish this.
I introduce debt as a negative number in my elementary school algebra classes (TKA).
©2019 LT/ThinkAlgebra
