Without memorization and practice to gain knowledge there can be no critical thinking, no bright ideas, no higher level thinking--not in math, science, etc. Everything flows from knowledge. Knowledge is the basis for higher level thinking. Common Core is all about testing, not teaching basic arithmetic.
Kids need achievable objectives, and, because academic ability varies widely, the learning objectives should vary or be flexible from school to school, even from classroom to classroom. This works best at the school building level with individual teachers making the educational decisions, policies, and tests. Yet, top-down Common Core does not allow this. Every student gets the same. One size fits all is idiotic.
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| Varvara started piano at 4. She is 10 in the photo. |
To become better at anything, a student has to memorize and practice and memorize and practice, have passion and persistence to learn, and get expert teaching. The problem in American schools is that most students do not get expert teaching early on; hence, [hidden] abilities in many capable very young children are squandered, never discovered or developed, whether it be in music, art, math, science, literature, writing, etc. Zig Engelmann writes, "The genetic interpretation of giftedness and intelligence is a myth." Yet, it [IQ] seems to govern the education policy in our schools, thanks to the influences of Darwin, Binet, Piaget, Dewey, et al. Even though brain plasticity (that IQ can be increased within limits) has been known for years, yet teachers are told to treat all students the same, that is, in Common Core all students learn the same content. It is the "triumph of mediocrity." The US education system seems to relish mediocrity. Our kids are not dumb. Indeed, better teaching and teacher quality are important, but, according to Will Fitzhugh (Concord Review), "The most important variable in student academic achievement is not teacher quality, but the student's academic work." In short, students should produce high quality academic work, but many capable students do not. Paul Zoch (Doomed to Fail), "Let there be no doubt about it: the United States looks to its teachers and their efforts, but not to its students and their efforts for success in education." It's not the teacher's fault that your kid is lazy. "Your kids are your own fault," writes Larry Winget. The blame should go to the parent, too, not the teacher. Early on, parents should provide the environment for achievement and teach kids how to be successful in school. But, this should not be the message: "If you're not the best, you're a loser." If you're not brilliant, you're worthless (
Do all students come to 1st grade with the same background knowledge, the same vocabulary, etc.? So, what do we do in our elementary schools? To paraphrase Horace Secrist, a professor of statistics, "Pupils of different mentality, and of training, grouped together in a a single room were to be education, which resulted in inefficiency and regression to mediocrity." When I first started teaching, we tracked students in elementary school and junior high school--to put superior math students with other superior math students with an expert math teacher, etc., but, for decades, this has been taboo in public elementary and middle schools and often called racism. Elementary school classrooms are similar to the old one-room schools. They are the breeding ground for mediocrity. It is called regression to the mean. Mike Petrilli says, "The greatest challenge facing America's schools today isn't the budget crisis, or standardized testing, or teacher quality. It's the enormous variation in the academic level of students coming into any given classroom." Before it was condemned in the US [as racism], tracking actually worked well for almost all students. It isn't a perfect system, but it is far superior than what we have today (inclusion and differentiated instruction). "Academic ability varies widely," observes Charles Murray (Real Education). [Note. For math class, Singapore pulls out weak math students at the beginning of 1st grade and places them with an expert math teacher to catch them up. The program lasts through 2nd grade for kids who need it.] Indeed tracking, when done right, is an effective strategy to reduce variation in the classroom, which means that students [by achievement] go to different teachers for math and reading starting in 1st grade.
Do most infants have the potential necessary to become gifted? Does intensive early training and education work? Should we push children? Varvara started piano at age 4. She was "lucky" to grow up in an environment that developed her outstanding musical ability. Luck plays a much larger role in how much children achieve. Even so, there are no short cuts. Real achievement requires a lot of memorization, practice, good teaching, and luck.
For example, Varvara has a passion for Mozart because her teacher has a passion for Mozart. She understands Mozart because her teacher understands Mozart. She grew up in an environment that fostered, nurtured, and developed her abilities. She was lucky! Varvara gets many standing ovations, and when she plays, hundreds and hundreds and hundreds of notes flow effortlessly, without thinking, from her long-term memory to her fingers. It is a remarkable process. She has mastered not only the piano parts and how to play them, but she also knows the orchestra parts. I saw a performance, and she was having fun playing Mozart! She started piano at age 4. She has developed music ability far beyond that of most kids, but without early intensive practice and expert teaching (nurture), she would be average, if that. And, without the right environment, she may have never started piano in the first place. I want to make clear that practice improves performance, but it does not create talent. There has to be something there to begin with (nature).
Here is my point. Start Young! Very young children are good at memorizing stuff. But, in my view, American educators don't take advantage of this, not in math. Young children are novices; they are not experts; and they are not little mathematicians, but most average children can master arithmetic and algebra when taught and practiced well.
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| Your child may not be another Newton, but, at the least, she can learn arithmetic, algebra, and probably precalculus well. |
Most likely your child will not become an expert [genius] in mathematics, such as Newton, Leibniz, Euclid, Gauss, Descartes, etc., or go on to take calculus; however, your child, at the least, can become competent in arithmetic and algebra, even higher, with practice and expert teaching in the right environment. Some American children [we need more] will advance to calculus and beyond and even to STEM careers. We have a shortage and have been importing STEM talent for decades. The K-12 American education system has not been developing the future talent we need in science, mathematics and other STEM fields. Our system produces mediocrity at a time we need excellence. Everyone in education talks about excellence, but the progressive reforms haven't worked. Gee, there must be something wrong with the reforms!
But lurking in some children could be another Newton, an old soul. Newton learned Latin but not mathematics at the King's School until age 17, when his mother decided to make Isaac into a farmer, but he hated farming. So later, he returned to King's School to complete his education, then went to Trinity College in Cambridge, where he started as a subsizar--a student who did chores on campus to pay for his education, room and board, etc. Thank goodness Newton was no good at farming and that the headmaster at King's School convinced his mother to send Isaac back school.
Very young children can learn a lot more than we think or are prepared to teach. American children consistently underperform in math! Kids often say they want to go into STEM, but when they get to college, they don't.
There is no reason why typical kids at very early ages cannot memorize multiples, just as Zig's disadvantaged inner-city pre-first-graders (4 and 5 year olds) did in the 60s, or the addition and subtraction tables for auto recall that Singapore 1st graders master (6 year olds), along with the standard algorithms. But this takes daily practice, oral drills, persistence, etc.! It also takes expert teaching by teachers who know traditional math and are passionate about math and its power, which is the conundrum in America. Most American teachers are weak in both math and science. Some elementary teachers hate math or push it aside. For decades, memorization and practice have fallen out of favor in progressive classrooms. Schools of education push progressive ideas and reforms. This is irresponsible. We don't push kids because "experts" tell us that this is bad for them. Wrong! Parents should drill math facts at home before kids are school age. It is easy to show 4-year-olds addition on a number line. Early on, parents should provide the environment for achievement and teach kids how to be successful in school. Early arithmetic practice at home pays off. Cognitive science has been catching up to anecdotal evidence, which is correct.
Unfortunately, there are idiots in education who say long division is either useless or too hard for kids to learn. But, 3rd graders can easily learn it, iff they have mastered the times tables in long-term memory. [iff means if and only if ⇔]. There are idiots in education who say that memorization of math facts and learning standard algorithms early on are not that important. The progressive reformers are dead wrong! Their policies have led to stagnation in math and reading achievement; impoverishment of public schools, thanks to the costs of Common Core reform and testing; national indebtedness--17 trillion; and a decline in education, rephrasing Dinesh D'Souza (America). The progressive reformers, who see themselves as disruptive innovators, are responsible for the decline and stagnation in US education because of bad ideas.
One unique feature of America has been as a "wealth creator" because of its sound innovations and enterprise, says D'Souza, but our K-12 education system no longer produces enough well-educated and informed citizens. Instead, our education system produces many people who don't work and who are dependent on government. Many college students don't belong in college, and if they pick the wrong major, there is no way they can pay back student loans. College students, even at elite universities [e.g., Harvard], are not taught to think for themselves, says William Deresiewicz. They graduate with "no sense of purpose."
Knowledge is the key to innovation.
It's not that our kids can't do these things--memorize math facts, learn standard algorithms, and apply arithmetic in science to solve problems early on. Our kids are not stupid; they are not taught. Some are lazy! The education establishment doesn't or won't do the right thing. Reform math has screwed up arithmetic for decades; consequently, most kids learn very little substantive arithmetic that prepares them for algebra by middle school. They cannot move forward or excel. Our kids are novices, and novices need to memorize and practice, starting with traditional arithmetic. They also need to be challenged. Our system does not find talent (STEM), and when it is found, it does not support it ($) or offer a different and accelerated curriculum, not in elementary school or middle school. Taking algebra-one in 8th grade is not an accelerated curriculum. Taking AP Calculus is for average kids who are prepared. [AP calculus relies on graphing calculators, has no proofs, and skips important topics, unlike university courses for STEM kids.] US education policies squander talent.
Let me reassure you that there is nothing wrong with classic arithmetic when it is taught properly and explained well, but progressive reformers, such as Common Core reform math crusaders, trivialize it.
The standard algorithms [traditional arithmetic] should be taught first and be the primary methods for calculating. Students must memorize number facts and use standard algorithms at the same time. They should encounter a wide range of routine word problems. First graders should also learn perimeter and area, parts of measurement, geometry, and algebra. I know; I taught it.
1. See Multiple Models (Different Strategies)
Students are taught inefficient, alternative strategies (reform math) instead of tried and true standard algorithms to do arithmetic.
2. See SingleDigit
Don't calculate single-digit math facts; memorize them.
3. See PiagetianMyth
Constructivism does not work in the classroom.
3. See CommonCore
Common Core is part of the progressive agenda to downgrade American education. Every student gets the same. The government has taken over and controls education. Teachers are no longer in charge of education.
©2014 LT ThinkAlgebra.org
