Monday, January 28, 2019

DNA, Not Nurture

Note. For decades, the problem in the U.S. classrooms has been that basic arithmetic is not taught for mastery in the early grades, which requires proper instruction, memorization, and a lot of practice because students are novices. Singapore starts multiplication in the 1st grade.

It takes good instruction and hard work to get good at anything!  
No matter how long or hard I practice-practice-practice, I will never approach the performance level of 11-year-old Chloe Chua (Click), the Junior Winner of the 2018 Menuhin Competition. Even though my musical ability is unexceptional, it does not prevent me from listening to and enjoying classical music. "Practice does not cause talent," explains mathematician Ian Stewart. The talent must already be there (DNA)The talent, ability, or skill can be developed only through excellent instruction, lots of practice, and feedback. In short, practice unleashes talent. It takes hard work!

Innate Intellectual Potential
"We are phobic about saying out loud that children differ in their ability to learn the things that schools teach. Not only do we hate to say it, but we also get angry with people who do. We insist that the emperor is wearing clothes, beautiful clothes and that those who say otherwise are bad people." (Charles MurrayReal Education) Thomas Sowell used this quote to open Chapter 9: Wealth, Poverty, and Politics.) 

I think there is innate ability potential, such as academic ability, athletic ability, musical ability, artistic ability, and so on. And, you can measure ability only through specific accomplishments or achievements (i.e., performances). Most of our abilities come from DNA. They are innate. Still, some kids are better at math than others, and much of that is DNA. But, some kids study more at math than others, work harder at math than others, or get more help in math at home or from a tutor than others. These are environmental influences. 

I think kids with higher IQs can have an advantage, but a high IQ means little unless the child wants to excel. Moreover, to be outstanding, the student must be motivated and persistent enough to practice a lot. In short, regardless of IQ, the student must work hard to achieve and excel.

"Monumental intelligence on its own is no guarantee of monumental achievement...Genetic potential alone does not predict actual accomplishment. It also takes nurture to grow a genius..."Most geniuses," says Plomin, "don't come from genius parents."  (Note. Quotes in this paragraph are from National Geographic "Genius," May 2017; Robert Plomin, Blueprint: How DNA Makes Us Who We are, 2018)

In addition to DNA, it takes nurture to grow an outstanding violinist at a young age. It requires hard work to get good at anything!

DNA Dominates School Achievement
"Performance on school tests of achievement is 60% heritable on average." asserts Robert Plomin (Blueprint). Although there may be other factors, it is still DNA (nature) over the environment (nurture) by a long shot in academicsSchool achievement is 60% genetics. Reasoning is 50% genetics and personality 40%, while spatial ability is 70%, and verbal ability is 60%, writes Robert Plomin (Blueprint: How DNA Makes Us Who We Are). What this means is that "genetics contributes substantially to differences between people," including cognitive differences, even in children of the same family. It is called genetic variation. The percentages are what is and do not predict what could be, says Plomin. They are not deterministic. Plomin does not say that intelligence is genetically fixed. He writes, "Genetic influences are probabilistic propensities, not predetermined programming." 

Environmental influences are "unsystematic, random experiences over which we have little control," says Plomin. They are broadly defined as "nongenetic" If the differences in school achievement are 60% genetic, then the remaining 40% of the variance is nongenetic (i.e., environmental influences). So, nurture is important, too, but not nearly as much as we used to think. In school, even if the inputs are the same, the outputs will be different because of genetic variation. Genetic variation also explains the reason that the achievement of children from the same family can vary substantially. "Equal opportunities do not create equal outcomes." 

In Asian nations, home tutoring and intensive early training flourish. Asian parents prepare their children for 1st grade starting at age 3, especially in arithmetic.  They believe that early math will give their children an advantage. Is it genius building? No, I think it is more genetics than nurture if a child learns Greek at age 3 and Latin at 8, like John Stuart Mill. Unlike Asian parents, most American parents don't push their preschool children. Perhaps, they should. "The bad news about helicopter parenting is that it works," writes Pamela Druckerman (The New York Times). "New research shows that hyper-involved parenting is the route to kids’ success in today’s unequal world."

"The most effective parents, according to the authors [Love, Money, and Parenting]," writes Druckerman, are authoritative [not authoritarian]. They use reasoning to persuade kids to do things that are good for them." Of course, you can't reason with a 2-year old, but you can plant the seeds. Children want to do things that are good for them. The future rewards are children with college and postgraduate degrees that have a "huge financial payoff." In short, the result is successful children in a competitive world. But, to get those degrees requires intelligence and ability, which come from DNA, along with lots of study, practice, effort, and persistence. Amy Chua (Battle Hymn of the Tiger Mom) suggests that you don't get to Carnegie Hall without first-rate instruction, intellect and ability, motivation, and practice-practice-practice.  

Too often, we have thought that "nurture" was the primary (only) cause of school success or failure. If we provide the right environment in school and at home, then the kids will be successful. But, as it turns out, it is mostly genetics, not nurture. It does not mean that children with lower aptitudes in math can't learn arithmetic and algebra at an acceptable level, but the learning requires proper instruction, hard work, effort, persistence, motivation, and lots of practice. 

"I am sure that training can lead to some improvement," writes mathematician Ian Stewart (Letters to a Young Mathematician, 2006). But, Stewart's view is at odds with current education psychologists who think that practice is the cause of talent. It doesn't work that way because of genetic variation, which has been a thorn in education for decades. Genetic variation means that children do not have the same abilities to learn. It does not mean that children can't learn the basics of arithmetic and algebra. It means that some children learn math skills and knowledge faster than others. 

"Children differ in their ability to learn the things that schools teach," observes Charles Murray. Educators know this, but seem to ignore it and treat all children the same as if they have the same academic ability in the name of equity, but Thomas Sowell calls it the "fallacy of fairness." Often, the best students are shortchanged and underfunded. Indeed, all learners are different in ability, skill, knowledge, motivation, persistence, and so on. But, they are not treated that way. For example, the best math students should be sorted to a math class that moves through content much deeper at a faster pace. The sorting for math class can begin in 1st grade, but sorting rarely happens in elementary schools.  

Daniel T. Willingham, a cognitive scientist, points out that "practice is crucial to long-term retention. There must be sufficient classroom time or homework devoted to the practice of skills or knowledge that must be remembered." Indeed, instructional programs should be built on the mastery of essential skills and knowledge, both in the classroom and at home. It requires strong teacher guidance, memorization, and a lot of practice-practice-practice, not group work or minimal guidance methods favored today, such as discovery learning. Without the basics of arithmetic, both factual and procedural knowledge, in long-term memory, students are blocked from further learning in math. 

Zig Engelmann states, "Without a firm foundation in number facts [automated in long-term memory], children are held back from further learning. You learn only through mastery." Moreover, Daniel T. Willingham points out that "factual knowledge must precede thinking skill." 

"Why do schools downplay the importance of memorization and practice to improve math skills and knowledge? Why don't schools teach for the mastery of essential factual and procedural knowledge? The first goal should be the mastery of basics, not state test-based "proficiency."

Children are novices and need to drill-to-develop skills and knowledge according to abilities. Even Chloe Chau is a novice when she learns a new piece of music. Practice is imperative to learn something!

Students must have the intellect and ability to do college-level work. They need to study and practice a lot to be successful. How many students have the motivation and self-discipline to study and practice, if it is not stressed at home?  
DNA is what makes us who we are. 

1. DNA
Many believe that if we change the school and home environments, then we can revamp and equalize student outcomes. Really? The idea is liberal nonsense. Yet, it governs school policy. Here is another bad idea: Every student gets the same instruction regardless of genetic variation (ability) In Blueprint: How DNA Makes Us Who We Are, Robert Plomin asserts the opposite and makes a persuasive argument for the primacy of genes over the environment in shaping our intellectual abilities and personalities. Indeed, abilities vary. They vary a lot, as Charles Murray would say. 

General intelligence, human motivation, school performance, traits, and abilities widely vary and are primarily influenced by your DNA. Children are different, not the same. Plomin writes, "Socioeconomic status of parents is a measure of their educational and occupational outcomes, which are both substantially heritable."  

Nature, not nurture, is what makes us who we are.  

The goal of education is to grow the abilities of students. Not all abilities or skills are the same due to genetic variation, and there is a limit to the abilities we do have. Moreover, a one-size-fits-all is not the best pedagogical paradigm because students are not the same in academic ability. A better, more practical model is to sort students to match their academic achievement, primarily for math class, starting in the 1st grade. With effort, hard work, and the proper instruction, most students in the average range can make adequate progress in arithmetic, but some students will be much better than others as all learners are different.

"In large groups of children, academic achievement is tied to academic ability. No pedagogical strategy, no improvement in teacher training, no increase in homework, no reduction in class size can break that connection," writes Charles Murray (Real Education, 2008). Murray advocated that K-8 Core Knowledge should be taught to students. Also, he pointed out that "children differ in their ability to learn the things that schools teach." Murray also says that educators tend to ignore the facts (e.g., genetic variation, IQ) when they get in the way of progressive ideology.

In education, we need to recognize genetic variation.

Due to genetic variation, I can't do physics like Richard Feynmanplay the violin like Chloe Chua (click), write poems like Edgar Allan Poe, paint like Rembrandt, swim like Michael Phelps, create photos like Imogen Cunningham, and so on.  

Practice makes improvement, but we cannot "practice" ourselves into superhuman beings due to genetic variation. A person's ability to do something has limits.  Practice does not cause talent. The talent must already be there (DNA). Practice brings out the talent; it improves performance. And for a tiny few, the performance is truly remarkable, like 11-year old Chloe Chau. We are not all equally creative, musical, or athletic. Academic ability widely varies, too. We do not live in Lake Wobegon, where all the children are above average and equal in intellect and abilities. 

Note. A student with an IQ of 90 is not going to learn as fast or as much as a student with an IQ of 115.

Students can improve their IQ by scoring better on three subtests from the Weschler Intelligence Scale for Children (WISC), which are Information, Arithmetic, and Vocabulary. Unfortunately, these are not stressed in modern classrooms, so "academic learning has stalled," says Mark Bauerlein. He writes, "Why, we wonder, do so many high school students, college students, and younger workers seem so terribly deficient in basic knowledge and skills? Their reasoning abilities may have jumped forward, but their reading comprehension hasn't improved at all." Likewise, their mathematics achievement has flatlined, too. 

High percentages of students (74% to 88% from nine school districts around Tucson) coming to community college are sorted into remedial math courses. The lack of vocabulary study makes it difficult to comprehend complex texts, so students are placed in remedial reading courses. One professor pointed out that many of her students had difficulty reading the chemistry textbook to learn chemistry. In short, many incoming college students are unprepared for college courses and end up in remedial math, reading, and writing classes. 

"Intelligence is the capacity for abstraction."

2. Wrong Path: Strategies, not Knowledge 
"Teaching strategies instead of knowledge has yielded only an enormous waste of school time," writes E. D. Hirsch Jr. "Strategies are empty" without the knowledge to back them up. Background Knowledge is essential. Hirsch writes, "The fact that critical thinking and problem-solving skills are not easily transferable from one situation to another (because one always needs background knowledge about the situation)--is a finding that is not widely known outside of cognitive psychology." 

Critical thinking is domain-specific. 
A student cannot solve a trig problem without knowing trig. In math, critical thinking is called problem-solving. A student can't translate Latin without knowing Latin. AI means, it is just common sense. 

What kind of junk has been tossed into education by those who pretend to be experts? Education is loaded with bad ideas that slow learning and produce insignificant if any gains in academic achievement. One is critical thinking independent of content. Another is ignoring generic variation. 

Note. The vast majority (82%) of the innovations funded by the U.S. Department of Education failed to show any gains in achievement.   

There is no generalized thinking skill or strategy that is independent of content. Indeed, as Immanuel Kant (1724-1804) wrote, "Thought without content is empty." Yet, schools of education continue to advocate "the popular falsehood that knowing how to think [strategies] is much more important than facts (Hirsch)." E. D. Hirsch Jr. points out, "Teaching strategies instead of knowledge has only yielded an enormous waste of school time." But, educators persist on "teaching kids to fish," when there are no fish in the pond. It is contrary to the cognitive science of learning and makes no sense for novices. "Learning how to learn" has been a failed pedagogy for decades, says Hirsch. Kids are novices and need to memorize stuff and practice a lot so that knowledge, both factual and procedural, sticks in long-term memory and is instantly available for problem-solving. In short, students need to accumulate a storehouse of knowledge in long-term memory to facilitate thinking. 

Domain Specificity of [Thinking] Skills
E. D. Hirsch Jr. (Why Knowledge Matters: Rescuing Our Children from Failed Educational Theories) writes, "Modern cognitive psychology holds that the skills that are to be imparted to a child by the school are intrinsically tied to particular content domains. Thinking skills cannot readily be separated from one subject matter and applied to other subject matters. The domain specificity of skills is one of the firmest and most important determinations of current cognitive science.

Hirsch continues, "Critical thinking does not exist as an independent skill. The domain specificity of skills is one of the most important scientific findings of our era for teachers and parents to know about, but it is not widely known in the school world." He says that thinking skills, such as critical and creative thinking and problem-solving, are not productive educational aims. "Thinking skills are rarely independent of specific expertise." Anders Ericsson and Robert Pool bluntly state, "There is no such thing as developing a general skill."

Thought comes from knowledge, not thin air. 

Note. Thinking skills are often called strategies, such as reading strategies. Strategies in math are often called "Standards for Mathematical Practice" in Common Core, state standards, and reform math. 

3. Bad Policies
In education, it is anathema to sort kids according to their achievement, but the policy makes little sense in terms of genetic variation. Instead of sorting math students according to their academic ability  (i.e., actual math achievement: below average, average, and above-average), progressive leaders have erected a stumbling block of fabricated equity and diversity ideologies using a one-size-fits-all concept that impedes learning. 

The reality is that academic ability, like athletic ability, musical ability, and so on, "widely vary." They vary a lot, as Charles Murray (Real Education) would say.  One cannot break the strong link between academic ability and achievement, such as in math or other academic subjects, explains Murray.

What progressive educators have done is to "equalize downward by lowering those at the top," observes Thomas Sowell (Dismantling America). It is especially evident in Common Core and state standards, and it is lousy policy, rotten to the core. Sowell calls it the "fallacy of fairness." Also, Sowell points out that we are distributing money from academics to social work (e.g., social-emotional learning or SEL is all the rage). SEL is the latest version of the failed self-esteem movement. It doesn't seem to matter that teachers aren't trained as psychologists. 

Knowing something implies some level of understanding. 
Educators should focus on knowledge, not understanding, which is ambiguous and difficult to measure. When we say a student's understanding is weak, what we mean is that his knowledge is inadequate and fragile. 

Practice produces improvement in performance, which is measurable, but, on the other hand, understanding is ambiguous, implied, and difficult to quantify. It is the reason I use the word knowledge, not understanding. 

Elementary school math predicts high-school math achievement, which, in turn, predicts college success. Knowing math content makes sense. 

Note. For more Chloe Chua, click violin or here.

Last update: 2-1-19, 2-3-19, 2-5-19, 2-11-19, 3-9-19, 
Some corrections were made on 4-3-19.

©2019 - 2020 LT/ThinkAlgebra  

College success starts in math

College success starts in math.
Singapore students learn multiplication in the 1st grade. Unfortunately, our schools do not stress early math literacy, which is a mistake. We need to accelerate learning for all children. Students need to get to precalculus in high school, but how do they do that? The one-size-fits-all of Common Core and state standards is the wrong path. The stress on thinking strategies instead of knowledge stalls achievement. 
"Precalculus is the baseline high school math course for bachelor's degree attainment," writes Paul Cottle.
How do students attain that level? Math can be a great equalizer for many students, primarily from lower-income families and minorities, but not through Common Core reform math and state standards. 

Common Core (CC) is not world-class math and fails to prepare students for college. The members of the math group (2009) that wrote the Common Core math standards were not qualified. None of the 15 original members had taught elementary or middle school, according to researcher Mercedes K. Schneider (Common Core Dilemma: Who Owns Our Schools). Moreover, all the members of the math group were affiliated with an education company or nonprofit, except for one. When the workgroup was expanded, most members worked for the state departments of education or colleges and universities. "There was a lack of current classroom teachers involved in decision making roles," writes Schneider. 

On the other hand, there were key members from ACT, Achieve, The College Board, and SAP (Student Achievement Partners) in the math group. They would profit from CC. 

The CC math standards were not "college-career ready" or benchmarked to international standards, as originally marketed to states. Instead, they were part of a much larger picture--"test-driven reform" (NCLB). The CC math standards were not world-class, and they did not prepare students for college.

High School Algebra-2 (called Intermediate Algebra at community colleges) might get you to community college, but it is a far cry from earning a bachelor's degree. In short, "getting into college or community college" is not the same as earning a degree or certificate. Getting a high school diploma does not qualify students for community college unless they have had a rigorous Algebra-2 course and reviewed the content before the college math placement tests. Also, Algebra-2 is not enough for students seeking bachelor's degrees.  

Unfortunately, many high schools deliver watered-down math courses to increase the graduation rate to over 90%, which doesn't help disadvantaged or minority students. A large number of lower socio-economic students end up trapped in remedial math classes at the community college level. Either they weren't taught acceptable algebra courses for mastery, or they didn't review the content sufficiently before the college math placement test, or both. Too often, so-called "college prep courses" were in name only, not in content. Sad to say, many "remedial" students drop out of community college and never earn a 2-year degree or a certificate. 

Algebra-2 is required for graduation in some states, such as Arizona, but is that a good thing? The course is watered-down so that more students can pass it and graduate from high school. Or, more likely, a much easier course is substituted for Algebra-2, so almost all students graduate. Both are pathways to remedial math at community college. In the real world, community colleges expect entering students to know Algebra-2, but many don't. 

College success starts in math. It begins in 1st grade. It is the great equalizer according to Muhammed Chaudhry, CEO of the Silicon Valley Education Foundation, who writes that schools should implement programs that equalize the playing field (equalize opportunities) by "fostering new opportunities for girls, for children of lower socioeconomic status, and children of minority racial backgrounds. Math, he says, is the great equalizer, but, in my opinion, we need to upgrade the curriculum to world-class, use explicit methods of instruction--not minimal guidance methods taught in ed school--and teach standard arithmetic early on, not reform math. We may be able to equalize opportunities, but we cannot equalize outcomes. Children are novices and need to memorize stuff and practice a lot so that the basics stick in long-term memory.

Elementary school math predicts high-school math achievement, which, in turn, predicts college success. Knowing math content makes sense. Content knowledge in long division and fractions in elementary school (K-4) jumpstarts young children for success in middle school (prealgebra & Algebra-1) and high school math (Algebra-2, Precalculus, Calculus), according to the Renaissance blog. Here's the catch. To learn long division and fractions, students must first learn addition, subtraction, and multiplication. Singapore students start multiplication in 1st grade. Our schools do not stress early math literacy, which is a mistake. Most elementary school teachers do not teach long-division and fractions for mastery. We need to accelerate learning for all children, but the current version of reform math taught via Common Core stalls achievement.  

"Precalculus is the baseline high school math course for bachelor’s degree attainment.” writes Paul Cottle. The high school course students should aim for is precalculus. Most of the students who take precalculus in high school complete a 4-year bachelor's degree in college. Students who want a bachelor's degree should take harder math courses such as precalculus or above and science courses such as chemistry and physics in high school, including AP courses in math and science. 

College success starts in math. 

Taking Algebra-2 in high school isn't enough. Students who covet a bachelor's degree should take precalculus in high school. We have known this correlation for decades, which is the reason that independent schools often require precalculus for graduation. 

Muhammed Chaudhry writes, "Math scores better predict the likelihood a student will one day reach college and graduate into a successful career beyond." Indeed, math can be a great equalizer for many students.


©2019 -2020 LT/ThinkAlgebra  

Tuesday, January 22, 2019

Upgrade School Math

Upgrade K-8 School Math
Instruct for Mastery
To upgrade high school math, we first need to upgrade K-8 math, starting in grade 1.

Fifty-four percent of Singapore 8th graders reach the Advanced Level in an international math test (TIMSS), which is mostly problem-solving, compared to only 10% of U.S. 8th graders. While American students stumble over basic arithmetic and algebra, Singapore teachers introduce math and science far ahead of its national curriculum. Singapore teachers instruct students for content mastery, and they don't limit students to grade-level content. 

Upgrade School Math Content
To upgrade content, schools should boot the Common Core (CC) grade levels and embrace the Core Knowledge (CK) math guidelines that prepare most students for Algebra-1 by the 8th grade. Start with CK K-8 math guidelines, which are world-class. The CK math guidelines embrace the teaching of standard arithmetic for mastery with memorization and practice-practice-practice.   

Make the Right Move: Upgrade to Core Knowledge! 
Forget Common Core!

We can change the outcome for many children if we switch from Common Core grade levels, state standards, and annual testing to the Core Knowledge Math Guidelines for K-8 and adopt a mastery instructional approach for essential content (i.e., factual and procedural knowledge). 
Changing to Core Knowledge math would be a step in the right direction, but we must also acknowledge that school achievement is 60% DNA. Indeed, academic achievement is tied to academic ability.
Note. Read DNA!
Note. If schools follow the Common Core (CC) grade levels, then students won't be ready for Algebra-1 in middle school. Students need an excellent prealgebra course that includes right triangle trig no later than the 7th grade to be successful in Algebra-1 in 8th grade. CC does not get students to that level. In contrast to CC, the Core Knowledge (CK) K-8 Math Sequence prepares students for Algebra-1 by the 8th grade. The CK math guidelines are "content-specific, cumulative, and coherent." In 2011, I recommended the K-8 Core Knowledge math guidelines, not the Common Core. The CK math guidelines embrace the teaching of standard arithmetic for mastery with memorization and practice-practice-practice. 

Whole number operations and their standard algorithms should be taught no later than the 3rd grade, so that 4th-grade students can concentrate on fractions-decimals-percentages and begin prealgebra arithmetic such as exponents, order operations, negative and positive integers, square roots, graphing in the coordinate plane, solving linear equations and proportions, etc. But, students can't do this without learning basic arithmetic in the early grades. We need to prepare students much better and not restrict instruction to grade-level content. In short, students are not ready for future grade levels if the instruction is confined to the current grade level as is the case with Common Core and state standards.  

Starting in the 1st grade, educators should focus on the mastery of basics, not learning for the state or district test. 
Our elementary school math curriculum needs to upgrade content and change to a mastery instructional approach.  Children should learn math content, which includes calculating on paper, to solve math problems. But, today, we have a [thinking] skill approach, not a content approach. Reformers say that students should learn to observe, reflect, and analyze independently of content. Well, it doesn't work that way, retorts Mark Bauerlein. It is a radical view.

“The skills-not-content approach doesn’t produce the learning that its advocates promise,” writes Bauerlein. “Without a body of material which students have first studied and retained and to which they may apply their aptitudes, the exercise of thinking skills is empty and erratic.” (Bauerlein's Quote from Joanne Jacobs blog)

Educators have been led to believe that skills--such as training the mind to observe, reflect, analyze--are more important than content knowledge. In fact, the 21st-Century crusaders boast that knowledge isn't needed. This radical approach is dead wrong. Immanuel Kant (1724–1804) made clear that thinking without content is empty. Kids learn higher-level thinking skills when they learn math and science content. Thinking in math (logic from true statements) is different from thinking in science (observation/inference). Math is not a matter of opinion; it is a matter of fact. Math is absolute; science is uncertain. Also, as E. D. Hirsch Jr. (Why Knowledge Matters) points out, a generalized "thinking skill" doesn't exist. 

Thinking in math requires knowing factual and procedural knowledge. You just can't "google" your way into critical thinking. You must know stuff in long-term memory. Critical thinking in math is called problem-solving. Students should start with routine problems first and build on them.     

Thought is domain-specific. 
You can't solve a trig problem unless you know trig. You can translate Latin unless you know Latin. Thinking comes from knowledge, not thin air. And, as Joanne Jacobs says in her blog, "You have to know something before you can think about it."

©2019 -2020 LT/ThinkAlgebra

Monday, January 14, 2019

Random Thoughts - 2019

Random Thoughts - 2019

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. 
Teachers, get out of debt, save for the future, and build wealth.
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. 

Kids Are Subjected to Failed Education Policies (e.g., Constructivist Theory)
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 learningToday, 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. 

Learning means remembering from long-term memory.
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. 

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 

Friday, January 4, 2019

Early Math

Early math is just as important as early literacy.
Algebra-1 is a middle school subject 
for students who are prepared!
Preparing for Algebra-1 starts in the 1st grade.
In the early grades, students should memorize math facts and learn the efficient, standard algorithms from the get-go. Practice-practice-practice and explicit teaching will prepare students for Algebra in middle school. As it stands now, the math standards from Common Core are not world class, so students start behind and stay behind up the grades. Students won't be ready for Algebra by the middle school unless we upgrade the curriculum to world-class and boot popular constructivist instructional methods and theory (Deweyism). The theory is wrong. 

Ineffective Teaching Dominates Math Instruction
Discovery learning and other minimal guidance methods that had been promoted by Dewey have been ineffective. Kids need explicit teaching from teachers who know math. Starting in the 1st grade, students should memorize math facts and learn standard algorithms from the get-go. And, they need to practice-practice-practice so that fundamentals stick in long-term memory for problem-solving. Practice may not be much fun or even dull, but it is critical preparation for algebra and higher mathematics, so ignore grumbling students and push Deweyism to the side. 

Social Process. Really?
John Dewey said that education is a social process: "Education is a process of living and not a preparation for future living." Dewey's idea that schooling is for socialization manifests itself in several ways in the classroom, including group activities, discovery learning, other minimal teacher guidance methods, collaborative learning, and so on. In short, the teacher no longer teaches.

Students sit in groups of 3 or 4, facing each other. They are encouraged to do group activities (socialize). In one group, I noticed that two students had words, but the teacher refused to separate them: "They must learn to get along with each other." But, at what cost? The fast learning of essential content is not the goal of the group work.

Note. Early Algebra is accessible to very young children through standard arithmetic. No manipulatives, no calculators, and no group work. 

Early math is just as important--perhaps more important--as early literacy.
Ian Stewart, a mathematician, explains, "Without internalizing the basic operations of arithmetic, the whole of mathematics will be inaccessible to you." Stewart is referring to math facts and standard algorithms by hand. Maya Thiagarajan writes that the East Asians are obsessed with math and advocate early math: "A strong math foundation must be built in the first 10 years of a child's life."

In contrast, many U.S. students are deficient in math skills, which starts in the 1st grade and rises up the grades into adulthood. U.S. math standards are not world class! In short, many students stumble over simple arithmetic. Likewise, adults often boast about their poor math skills. Many elementary school teachers fear math, which rubs off on their students. K-5 teachers are weak in both math and science, especially chemistry and physics. Children are great imitators. They learn by imitation, repetition, and practice. The attitude of their teachers rubs off on them. 

Elementary school science programs and textbooks lack math, something Nobel-Winning Physicist Richard Feynman pointed out as a significant flaw in the 70s. "None of the science books said anything about using arithmetic in science." He said that elementary school math textbooks were "universally lousy," too because they lacked sufficient applications and word problems. Not much has changed. 

Contrary to the "constructivist" theory taught in schools of education, which lacks evidence, students should not be expected to figure out the basics of arithmetic on their own via group work, discovery activities, or other minimal guidance methods of instruction. Starting in the 1st grade, the fundamentals, which begin with math facts and standard algorithms, should be taught explicitly and learned through practice-practice-practice, so they stick in long-term memory for problem-solving. Without content knowledge in long-term memory, critical thinking (i.e., problem-solving in math) is empty. 

Knowing something implies some level of understanding. 
Educators should focus on knowledge, not understanding, which is ambiguous and difficult to measure. When we say a student's understanding is weak, what we mean is that his knowledge is inadequate and fragile

Math is not a matter of opinion; it is a matter of fact. 

The Abacus Problem --> The Calculator Problem
Richard Feynman writes, "With an abacus, you don't have to memorize a lot of arithmetic combinations: all you have to do is learn how to push the little beads up and down. You don't have to memorize 9 + 7 = 16; you just know that when you add 9, you push a ten's bead up and pull a one's bead down."  

That's the problem with calculators. The NCTM pushed calculator use starting in Kindergarten. First-Grade textbooks like Scott Foresman - Addison Wesley (2001) had "Explore with a Calculator" activities starting in Chapter 1. I used number lines extensively in the first couple of weeks of school as 1st-grade students started to grasp simple combinations. But, I did not want students relying on the number line or counters (cubes) to calculate. The number line and counters were put aside after the first two weeks of school and replaced with flashcards. I wanted students to memorize the combinations. 

Novices need to learn numbers, math facts, how numbers combine, and place value, that 12 is 1ten+2ones. The standard vertical algorithm, which lines up ones under ones and tens under tens, is efficient and the best model for place value.

In 1st-grade, the idea of "carry" is important. 

Credit: WolframAlpha
1. If you can't calculate it, then you don't know it. I developed this idea when I tutored high school students in precalculus. They would say that they understood the idea but had difficulty applying and calculating it. Thus, their knowledge and calculating skills were weak. Your knowledge of an idea, let's say of perimeter, is better if you gain lots of experience calculating perimeters of polygons. 

2. I substitute the word knowledge for understanding, which is ambiguous and hard to quantify. Knowledge of something implies, in my opinion, that you have some level of understanding, which is difficult to measure. Kids need background knowledge. Math is mostly knowledge of content and calculating. Mathematician Ian Stewart states it this way: "Math requires a lot of basic knowledge and technique." 

Reciting a definition of perimeter doesn't mean much. If you can't calculate perimeters, then your knowledge of perimeters is weak, hence the "implied understanding" of perimeters, is weak, too. 

3. Practice produces improvement in performance, which is measurable, but, on the other hand, understanding is ambiguous, implied, and difficult to quantify. It is the reason I use the word knowledge, not understanding. Also, I often use the word ability rather than talent because practice does not create talent. Ability, I think, is something you are born with, but it can be developed only through excellent instruction and practice-practice-practice. We can measure improvement, but talent or understanding is ambiguous and difficult to quantify. We are not all equally creative, and we do not all have the same abilities. Not all children who have an ability have the same opportunities to develop and enhance it. 

4. Mathematical Ability varies widely
In my opinion, all children are born with some mathematical ability, but math ability varies widely like any ability, such as the athletic ability or musical ability, and so on. Some kids are just better at math than others; however, this does not mean that the vast majority of students cannot learn arithmetic and algebra at an acceptable level with enough practice and good teaching. 

5. Focus on Performance
My conclusion is that we should focus on ideas that are measurable, such as the student's performance in arithmetic, algebra, basketball, chess, violin, or piano, etc. If you do well on an arithmetic test, then the implication is that you understand the math at some level. Still, you would expect a 6th grader's understanding of perimeter is at a higher level than that of a 1st grader because the 6th grader presumably would have greater knowledge of and experience with perimeters than the 1st grader.

Note. Reading: New vocabulary should be introduced before the reading lesson.  

To Be Revised: 1-4-19, 1-6-19, 1-12-19
©2019 LT/ThinkAlgebra