Tuesday, May 11, 2021


 Welcome to Cogitatus3 

"Study hard enough to become Smart enough."

Note:  Some content has moved to Cogitatus4. 

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Task Commitment & Self-Discipline

Michael E. Martinez (Future Bright) suggests that a pivotal element to predictive success in school or on the job is conscientiousness, which adds to IQ. "Conscientious people are achievement-oriented, pay attention to details, persist in solving complex problems, follow through when working independently," and other traits of task commitmentIQ is the key predictor of success, and conscientiousness adds to it. Unfortunately, American students tend to give up if they can't work a [math] problem immediately. Persistence and delayed gratification needs to be modeled at home and taught in the classroom. 

"Conscientiousness does not link to IQ. [The correlation is practically zero.] It adds its predictive power to that offered by IQ," writes Martinez. Thus, "beyond the IQ score, conscientiousness also predicts students' academic achievement." A related personal trait to task commitment is self-discipline, which predicts academic achievement better than IQ scores. Signs of task commitment include the "capacity for perseverance, determination, hard work, and dedicated practice." These are traits that should be instilled in children from the 1st grade on up, even earlier. 

If you want to get better at arithmetic (or any task), then you need the "capacity of perseverance, determination, hard work, and practice." 


Understanding does not produce mastery; practice does!

Calculating Skills Must Be Sharp & Automatic

Like physics, arithmetic is skill-based. To learn arithmetic well, specific factual and procedural knowledge must be memorized and practiced to automation. You cannot solve math problems without good calculating skills. A shortcoming in arithmetic leads to a weakness in algebra. Therefore, facility in the standard algorithms and supporting single-digit number facts, beginning with 1st-grade addition and subtraction, are vital for solving math problems and higher mathematics. 6-12-21

Scientific Integrity Lost

✍️ Today, I often hear "follow the science," whether it be Covid shots, climate, education, or other juicy topics that have been politicized; however, we should heed the stern warning of Richard Feynman, which he preached in lectures to students, that real scientists "bend over backward" to show that maybe their conclusions were wrong or inconclusive. 

Feynman writes, "I'm talking about a specific, extra type of integrity that is not lying, but bending over backward to show how you're maybe wrong, that you ought to have when acting as a scientist."

Furthermore, just because something is statistically significant doesn't mean it is consequential, useful, or correct. Science can change with the advent of new data or measurements. It's not absolute like mathematics. So, I am skeptical whenever someone evokes "follow the science." What does that mean?  Real science requires the replication of results, which is no easy task. Also, the media fails to tell us what we should hear, but tells us what they think we want to hear, suggests Sherry Seethaler (Lies, Damed Lies, and Science). Seethaler points out that data analysis is rarely simple and straightforward. Thus, it may be possible to draw more than one conclusion. So, what does "follow the science" mean? Experts may give their opinions, but an opinion is not fact


Critical Race Theory has no place in our schools. It teaches racism and indoctrinates children. "Critical race theory is a Marxist experiment to remake society based on class struggle. It is not an educational tool and certainly should not be funded with taxpayer dollars," write Rick Esenberg & Daniel Lennington. It's not about equity, not when equity means the fallacy of fairness. 6-16-21

Critical Race Theory: Equalizing Outcomes

✍️ There is a lot of talk about critical race theory (CRT), which, I think, is an impractical idea, and who better to blast it out of the water than Thomas Sowell, a black scholar, who, in 2010, probably earlier, wrote in an essay that equalizing down by lowering those at the top is a fallacy of fairness and a crazy idea taught in schools of education controlled by far-left liberals. Cutting content and lowering expectations hurt all students. Attempts to close achievement gaps by teaching less content is a red flag that CRT (equalizing outcomes) has crept in. CRT didn't just pop up. It has been around for decades in divers forms and is gleefully supported by teacher unions, the media, and a political party--in the name of equity, of course. Gee, I wonder which political party? (Comment: "Divers" was my favorite word in high school.)

Iowa Gov. Kim Reynolds states, "Critical Race Theory is about labels and stereotypes, not education. It teaches kids that we should judge others based on race, gender, or sexual identity, rather than the content of someone's character." 6-9-21

Equalizing outcomes is a fallacy of fairness, points out Thomas Sowell

Unchallenged students learn little!

The Teaching

✍️ Cutting content to close achievement gaps is lousy education, so is grade inflation. Gap closing should not be an educational goal, observes Sandra Stotsky (The Roots of Low Achievement, 2019). Educators and policymakers link poverty to poor achievement, which is a correlation, not a cause. Unfortunately, poor math achievement has not been related to the teaching in the classroom where the curriculum is below world-class and instructional methods are ineffective (i.e., minimal guidance = minimal learning). Moreover, reducing class size and pumping more money into schools have failed, too. 

✓ The liberal agenda has been to dumb down our kids, e.g., cutting content, using substandard instructional methods, inflating grades, etc. Not all teachers have bought into this, but many have.  

Comments about my TKA algebra project:  Soon, from equations in two variables (y = mx + b), 1st and 2nd-grade students construct an (x-y) table of values and plot (x,y) points in Q-I. This is a step beyond Feynman. Also, by the 3rd or 4th grade, students learn regular equation-solving techniques. Again, the classrooms of students I worked with were from Title-1 schools.

Education leaders say that slowing down math by cutting back on content and eliminating acceleration will help all students gain a deeper understanding. Really? Reducing class sizes to 15, which requires more teachers, the goal of the teacher unions, does not help students learn more. The problem is that many teachers are average, even mediocre. Schools need good tutors, one-to-one, not more teachers for smaller classes.

Praising a student for no good reason is part of the popular feel-good, self-esteem movement and a subtle form of indoctrination. American kids feel good about themselves, but many can't read, write, or do arithmetic well enough, so how can that be? Often, students are discouraged from excelling by reducing content, lowering expectations, inflating grades, and delaying essential math. Test prep also limits the content taught in the classroom. Often, useful content is restricted or not taught because it is not on the State test. 

✓ A major problem has been low expectations for all students.

✍️ I don't believe in delaying content in the math curriculum (e.g., Common Core). I think we should accelerate it for almost all students and rise to world-class benchmarks. U.S. educators grossly underestimate the content young children can learn with good instruction. 

Common Core delays content (see chart below), especially standard algorithms, one of the five "building blocks of elementary school mathematics," explains mathematician W. Stephen Wilson. He writes, "Mathematics is not a collection of unrelated topics. Mathematics is hierarchical. ...Certain topics must be taught [and mastered] before others." 

Common Core: Delay of Content, 2011 by LT

I found this out when I taught my algebra project (TKA) to typical urban 1st and 2nd-grade classes in 2011. I was told that it would not be possible to teach algebra to little kids, but I proved the critics wrong. In just 7 lessons, students learned the algebra content linked to standard arithmetic because the expectations were high and the teaching was there (i.e., explaining worked examples, practicing, and reviewing). Students learned the algebra content (equation-table-graph) because they were expected to. Classroom teachers were astounded. Educators need to implement high expectations and teach accordingly. 

✓  In my algebra lessons (TKA), new content was explained, linked to old content, and practiced. 

✍️ Many teachers barely know standard arithmetic, much less integrating it with algebra ideas. Mathematics has a dual role in conveying concepts and thinking, and I believe this duality is often lost in classroom teaching, especially the "thinking" aspect. Also, standard arithmetic is more demanding than other subjects because it is abstract and requires memorization and extensive practice to master. Moreover, one idea is based on or supported by prerequisite ideas. Thus, you can't skip around; the sequence is important. U.S. educators are not teaching the math content that children need to know and learn, starting with 1st-grade arithmetic. Reform math and minimal guidance group work do not cut it. 

✓  Minimal Guidance = Minimal Learning

✍️ Math Courses Matter! 

Students who take a rigorous course in precalculus in high school are much more likely to complete a 4-year bachelor's college degree than students who take only Algebra-2 (74% vs. 40%, respectively). 

✍️ In teaching mathematics, leaders never look at brain research. The starting point in arithmetic is numbers used as symbols, so the number 6 is the concept of 6, which is easily visualized on a number line. Add 1 to 5 to get 6, the next whole number (i.e., integer), and so on. To learn arithmetic, students must memorize basic facts. Repetition and drill are required so that fundamentals stick in long-term memory and are usable immediately for operational procedures, such as the standard algorithms, and for problem-solving. 

Start With the Number Line to Calculate Basic Facts.

The Number Line is Mathematics!  


Children are not asked to memorize without understanding. For example, asking students to memorize (automate) 7 + 5 = 12 is not without some level of understanding or knowledge of numbers, addition, magnitude, and place value, that 12 is 1ten+2ones, etc. The number line shows that 7 + 5 is 12. No other explanation is required. Children acquire a number-line understanding. The single-digit facts need to be automated in long-term memory, which involves drill-to-develop-skill. Memorizing factual knowledge and practicing standard algorithms are not obsolete. They are essential. 7 + x = 12. Find x.

Factual knowledge and procedural knowledge in long-term memory are needed to do arithmetic well. Problem-solving requires efficient calculating skills such as the standard algorithms. You don't learn arithmetic in group work (i.e., minimal guidance methods of instruction). You learn arithmetic through active, explicit instruction with flashcards, practice-practice-practice, and review.

Students, even in the 1st grade, should learn factual
and procedural knowledge
to master arithmetic,
which requires memorization and practice-practice-practice.

Comment: When I teach algebra to small children beginning in the 1st grade, I don't think of cultural relevancy or CRT, even though 90% of the students are minorities. They are expected to learn the content, which is often abstract, such as the number 6, the expression x + 2, or the equation y = x + x - 3. Algebra ideas are firmly rooted in standard arithmetic. "Math knows no races," writes David Hilbert. Yet, so-called experts say that a white teacher, such as myself, can't teach children of color. They are wrong!

✍️ Bright students covet advanced math!
Unchallenged students learn little. 

Credit: Kailey

7th-Grade Algebra-1
If I can teach typical 1st graders the equation-table-graph sequence in 7 lessons (TKA Project), certainly by 6th or 7th grade, even earlier, Algebra-1 can be taught to students who are prepared, but that's not how the K-12 education system works. As a result, U.S. math education has been a "catastrophic failure," according to Deift, Jitomirskaya, and Klainerman. 

Many K-8 teachers are not equipped to teach the prerequisites for algebra; consequently, their students are not ready for Algebra-1 in middle school. In addition, many teachers don't know enough arithmetic to teach it well.  

Below: 4th-Grade students at an urban Tucson K-8 public school with a diverse student population learn algebra fundamentals in my Teach Kids Algebra (TKA) Project, which I started in 2011. The students I teach have different backgrounds; however, they have similar opportunities to learn algebra. (Similar should not mean identical.) Algebra ideas are fused with traditional arithmetic. TKA, which is STEM math for elementary school students, can begin as early as 1st grade. Instead of dumbing down the math curriculum, TKA advances the U.S. curriculum to bring it up to and surpass international benchmarks.  
4th-Grade TKA Practice Sheet on Linear Functions

Educators grossly underestimate the content very young children can learn when appropriately taught and practiced for retention in long-term memory. Math fundamentals must be memorized and practiced for mastery, starting with standard arithmetic in 1st grade. Unfortunately, U.S. students are taught reform math, not traditional arithmetic. Consequently, many middle school students stumble over fractions, a 4th grade topic in international grade placement. 

Math is abstract and uses symbols to convey concepts. In addition to knowing basic math symbols and concepts, students also need proficient math skills to solve problems, starting with memorizing the single-digit math facts and practicing standard algorithms.

 Understanding does not produce mastery; practice does!
It's hard to do math without knowing math. 

Note: Equity has come to mean equal outcomes, which is an impossible task. To narrow achievement gaps in math, teachers inflate grades and "dumb down the curriculum so that everyone can pass, but no one can excel." It's a false narrative(Quote: Charles J. Sykes, Dumbing Down Our Kids) 

✍️ Failure: The K-12 system is not producing enough students who are prepared for "rigorous graduate-level work" needed for STEM careers. Deift, Jitomirskaya, and Klainerman ("America Is Flunking Math") point out that teacher education schools and courses are a significant part of the problem. They explain, "The vast majority of K-12 math teachers are graduates of teacher-preparation programs that teach very little substantive mathematics," but "are filled with courses such as social justice, identity politics, or, at best, methods courses with minimal math content." Moreover, teachers can't teach the content they don't know well. 

Why are some educators teaching children that math is racist? 
Crazy ideas like equalizing down or anti-racist mathematics, one of the latest fads that blends math with oppression, "threaten to further degrade the teaching of mathematics." Also, a student who majors in mathematics (not math education) or physics (not science education) should not have to go through a tedious, teacher-certification process to teach in public schools or any school. Even the late Richard Feynman, Nobel Prize winner in Physics, would not qualify to teach physics or math in our public schools. Who better than Feynman to explain complex ideas to children?  

Furthermore, the radical reformers want every student to take the same math no matter the student's level of achievement (one-track math). And, make sure to dumb it down enough (i.e., "equalizing down") so that all students or identities can pass. Kick Algebra-1 out of middle school and Calculus out of high school. For equity, no acceleration! It's sameness all the way, which is a drastic disservice to all students. Ill-advised, dumbed-down reforms often drive bright college students out of education and the classroom. (Note: "equalizing down, by lowering those at the top" is a "fallacy of fairness" is from an essay by Thomas Sowell, 2010.)

✍️ Some educators imagine that students have the same academic ability, which isn't true. Likewise, the same is true for athletic ability, artistic ability, or musical ability, etc.  Pretending that students are the same is a myth. Students do not have similar intellectual capacity, so "gap closing" should not be an educational goal, suggests Sandra Stotsky (The Roots of Low Achievement, 2019). Some kids are better at math than others. It's not going to change. The K-8 kids who are better at math need advanced content, but instead, they are given enrichment in so-called gifted programs, project-based stuff, or math for average students. Also, high-achieving math students are mixed with low-achieving students in the name of equity, a terrible idea. "Academic outcomes are not simply a function of money," writes Freddie deBoer. "Throwing money at our educational problems, while noble in intent, hasn't worked." Yet, we continue doing it. 5-22-21 

✓ Students are not equally creative or academically equal. 

✍️ Regression to Mediocrity
Our education system of mixed ability classrooms and minimal guidance methods in K-8 and even into high school is regression to mediocrity and a recipe for failureMoreover, looking at a screen--remote learning--is not proper schooling; it is "pretend" learning. Kids need active in-person teaching all day without screens. Teachers should stand in front of the class and explain how things work, especially in arithmetic and algebra. Also, popular project-based learning (i.e., group work) is not effective in mathematics. U.S. education has been littered with low expectations and failed fads.

We don't expect most students to take algebra in middle school or calculus in high school. Why not? Dumbing down starts early! We don't expect 1st-grade students to memorize the addition and related subtraction facts, learn the standard algorithms, grasp multiplication such as 3 x 4 as repeated addition: 4 + 4 + 4 = 12, find perimeters, and introduce algebra such as linear functions: equation-table-graph. Why not? In today's progressive classrooms, memorization and drill (practice-practice-practice) are branded as poor pedagogy. They are not. They are essential for learning. Lastly, Common Core and most state math standards are not world-class. 5-21-21

1st-Grade Algebra Lesson #7 (Point Plotting in Q-I and Finding Perimeters)
Urban K-8 School (Tucson, AZ)  Note: My Teach Kids Algebra (TKA) Project is STEM Math for elementary school children. It's a start.
1st Grade TKA
We grossly underestimate the content students 
can learn given proper instruction.

✍️ Input ≠ Output 
The Educational Opportunity Project at Stanford University inferred that "Racial, socioeconomic, and gender disparities in academic performance and educational attainment are stubborn features of the U.S. educational system." Are these disparities the cause of low achievement? I think they are correlations or assumptions, if that. 

✓ Correlation is not causation. 

"Statistics are not facts," explains Daniel J. Levitin (A Field Guide to Lies, 2016). "They are interpretations. And your interpretation may be just as good as, or better than, that of the person reporting them to you." The data may suggest correlations, but correlations are not facts. (I can link big feet to spelling, but big feet do not cause good spelling. Similarly, good spelling does not cause big feet.) 

The problem is that the blame for the gaps should mostly fall on schools of education, the NCTM standards, Common Core, and teachers who, for decades, have been using ineffective curricula and flawed instructional methods. It's called reform math couched in minimal guidance methods (e.g., discovery, project, etc.). In short, group work. It has been a train wreck. 

Thomas Sowell (Discrimination and Disparities, 2019) states that equal input does not result in equal output. I'm not even sure that similar inputs (e.g., equal opportunities) can exist. Sowell warns not to confuse correlation and causation. Alsoprojecting beyond the actual data (extrapolation) is a flawed methodology, an idea I used to stress elementary school students in Science--A Proces Approach (1967). Statistics is not science, and inferences are not facts. 

Our kids are at least two years behind their Asian peers by the 4th or 5th grade in math. Why? Our students have not been taught the math that students in high-performing nations learn, a conclusion from The National Math Advisory Panel (2008).

It is that simple! Students aren't taught!

  It behooves us to be aware that critical race theory (CRT) and Marxism have crept into our schools. Almost everything in education seems to be race-based or equity-based, which is inexcusable. Education is no longer about teaching kids to read, write, and do arithmetic. It's about equity, diversity, inclusion, identity, and culturally relevant lessons, even in arithmetic. The more stress put on equity by lowering standards, the less focus on academics, an inverse relationship. Mixing high-achieving students with low achieving students, inflating grades, and reducing the curriculum criterion to level the playing field result in a low-quality, low-expectation, mediocre education. Teaching less math content is a reckless, ill-advised strategy that hurts most kids. "It's crazy."

Lowering standards dumbs down the curriculum and our kids. All students get the same math without regard to achievement or prerequisites, which had been the equity strategy of Common Core (CC) and state standards primarily based on CC. It's another stupid idea.

✍️ Teaching Less Content Is Not Equity. It's irresponsible and a

"Fallacy of Fairness," says Thomas Sowell

Experts tell us that kids are far behind in math due to at-home learning via remote or online. But they were far behind their Asian peers before the schools were closed. Some expert educators say that kids learn math, not at home but in the classroom where deep learning takes place--"it's how children learn best, which is often project base or done in groups," reports Valerie CavazosReally? The experts are wrong about learning, which has been insufficient for several decades before the virus because the dumbed-down curriculum was taught using minimal guidance methods. Now, with remote lessons, it is worse. 

The goal of "so-called" deep learning is often used "to justify teaching less content," writes Sandra Stotsky (The Roots of Low Achievement, 2019). The strategy of gap-closing is to teach less math content--by lowering those at the top. Stotsky explains that gap closing should not be an education goal. Kids were already two-grade levels behind Asian kids by the 4th or 5th grade with regular classroom teaching before the virus. Group work and project-based learning are reform math and inferior to explicit teaching via worked examples and practice. (Kirschner, Sweller, & Clark: "Why Minimal Guidance During Instruction Does Not Work," 2006)

✓ Minimal Guidance = Minimal Learning

✍️ Barbara Oakley, an engineering professor at Oakland University in Rochester, Mich, says the key to mathematics expertise is practice, not conceptual understanding as some common-core proponents would have educators believe." There will always be achievement gaps because good education creates inequalities, explains the late Richard Feynman.

Sandra Stotsky points out that closing gaps should not be an educational goal. Students who study more, practice more, pay better attention in class, are more industrious, delay gratification, and have an optimistic attitude create inequalities. 

✓ Understanding does not produce mastery; practice does!

✍️ Today, education seems more about equity, diversity, inclusion, identity, and culturally relevant lessons than excellence, achievement, and teaching kids to read, write, and do arithmetic. Critical Race Theory (CRT), for example, teaches hate for America and its foundation and promotes bias and discord. Thankfully, some teachers don't buy into the "critical race theory" and its ramifications. Children are not and should not be indoctrinated as little activists; they are students. Parents, teachers, state legislatures, school boards, and leaders must block radical Critical Race Theory (CRT) from schools. 
✍️ Fairness Policies Downgrade Individual Excellence
There is a war on achievement and excellence!
Equity no longer means fairness!
Arithmetic is no longer just arithmetic.

Unfortunately, the reform math people have dominated mathematics education in our schools for decades and believed that their ideas (pedagogy, ideology, & philosophy) are superior regardless of evidence. Their "fairness" policies are flawed because they downgrade excellence and individual achievement. The reformers think that "equalizing downward by lowering those at the top" is a good policy (1), but I believe it has been a destructive, biased policy. The "fairness crusades" have marginalized individual achievement, hard work, and excellence in our schools.
(1) The quote is from Thomas Sowell (Dismantling America).

✍️ The proposed California math framework* cancels gifted programs, homogenous ability grouping, Algebra-1 in 8th grade, and high school Calculus, all in the name of equity. In short, no student should get ahead. That's equity? No, it isn't. It's a "fallacy of fairness," says Thomas Sowell, and an overt bias against bright students who study more and work harder to achieve. In my opinion, the new math framework is directed against high-achieving students, usually Asian students. I hope the CA Department of Education does not approve it. (*Some information in this post is from Steve Miller's Twitter.)

I need calculus for STEM. It's gone!

Angry parents (Virginia) are raging against equity math in which everyone gets the same math--no remedial classes to help weak students, no accelerative courses for advanced students. But, it appears that Virginia is backing away from equity math and the anti-tracking movement, according to Jay MathewsI hope parents in California, Arizona, Oklahoma, and elsewhere do the same.

Equity math is a fallacy of fairness and originates from Critical Race Theory (CRT), which has been around for most of this century and before. CRT is far-left radicalism and should not guide the curriculum, but it has crept in. CRT teaches racism. It is anti-white, anti-grouping, anti-achievement, and anti-bright students who work hard to achieve. If you disagree with CRT, you are attacked and called a racist.

Robbie Soave at Reason, reporting on the CA math framework, writes, 
  • "In fact, the framework concludes that calculus is overvalued, even for gifted students." [Really?]
  • "The framework's overriding perspective is that teaching the tough stuff is college's problem: The K-12 system should concern itself with making every kid fall in love with math."  [Really?]
  • "Broadly speaking, this entails making math as easy and un-math-like as possible. Math is really about language and culture and social justice, and no one is naturally better at it than anyone else, according to the framework." [Really?]
  • "The entire second chapter of the framework is about connecting math to social justice concepts like bias and racism." [It's true! It's Critical Race Theory.]
✍️ The CA math framework wants to dumb down arithmetic and algebra so that all children can learn the same math. After all, according to the framework writers, everyone is just as good at math as everyone else. But, unfortunately, the assertions and assumptions made by radicals in the math framework demonstrate how deep Critical Race Theory has penetrated education and how bent the thinking of many education leaders, and teachers has become. And, it is coming to a public school near you.

✍️ The amalgamation of strategies, mixed classrooms, and minimal guidance methods to learn basic arithmetic has been a recipe for poor achievement. Yet, in my opinion, the new California math framework advocates more of the same with a twist of culturally relevant lessons. Really? Critical Race Theory (CRT) has crept into the curriculum, even in math.

✍️ "Almost all of us improve with good teaching and plenty of practice, whatever the activity. That's why education is worth the effort." (Ian Stewart, Significant Figures 2017)

✍️ To find talented kids, in contrast to enrichment-centered programs at many schools, the Center for Talented Youth (CTY) at Johns Hopkins requires elementary school students to take the School and College Ability Test or SCAT (verbal + quantitative) at least two grade levels ahead and score at the CTY level. Thus, a 3rd grader would take a test designed for 5th graders, and so on. In the 7th grade, middle school kids need very high scores on the College Board SAT to qualify. In addition, all summer and online courses for admitted students are academically accelerated. As a result, eligibility for CTY classes is not easy. "Johns Hopkins Center for Talented Youth (CTY) is the world leader in gifted and talented education, serving the world's brightest students." Also, visit Bright Now.

✍️ Tangents in 4th Grade

Trig Ratios in 4th Grade Math, An Extension of Ratios and Proportions
The equal sign should be an "approximately equal" sign. 

✍️ If I want to find out if something works in the classroom, I test it and learn from my mistakes, which is the approach that the late Siegfried Engelmann had used. Try it first; see what happens. For example, I decided to teach kids trig ratios in the 4th grade (the late 1990s) as an extension to ratio and proportion lessons. The trig lessons worked better than expected via worked examples, explicit teaching, and practice. No calculators! No group work. No minimal guidance methods. Even though the "trig ratio" lessons functioned well in my 4th-grade classroom, it is not proof they will succeed in other elementary school classrooms. It depends on the students' prerequisite knowledge and the teachers' math background.

✍️ On the other hand, what schools usually do is implement without knowing if something works, which is a stupid approach to education. School decisions often rely on testimonials, so-called studies or research, flashy, colorful materials or textbooks, and impressive "too good to be true" sales pitches. Some teachers might actually page through a textbook, but they don't read it. Colorful Graphics in textbooks and on classroom walls often distract children from the task at hand.

Schools buy expensive programs without testing them. "It's all in the implementation," educators are told. "If you do it right, kids will learn." Also, "We will train your teachers ($$$$$)." But kids don't learn much--little bang for the buck. The software or videos often lack credible instructional value. Why? The classroom teacher isn't giving the lesson. There is little follow-up to the video. Teachers can't ask probing questions, give a different explanation, or answer student questions. 

Reformers: "If we only had more funding and more time." 
Good intentions are not good enough! 
District: "We bought all these computers and software, so use them!" 
Your evaluation depends on it.

✍️ Marxist radicals have taken over education at the local, state, and federal levels. The only way to close gaps, they say, is to lower content standards and eliminate excellence. No child gets ahead. The radicals have redefined achievement as "privilege," says Thomas SowellThese are terrible ideas! "Equalizing down, by lowering those at the top," is a crazy idea, a "fallacy of fairness," not equity, explains Sowell in his book of essays and his latest book below. 

Credit: EmB

✍️ When education cowers to activism, racism, and radicalism, you are no longer talking about education. You're talking about indoctrination! Today, much of education is not about teaching kids to read, write, do arithmetic or about achievement, merit, and excellence. Government schools advocate equity, diversity, identity, and inclusion. They are strongly supported by teacher unions, schools of education, federal and state departments of education, school boards, and others, including the media. I believe education has gone down the rabbit hole, an abyss. Commonly, there seems to be an inverse relationship between excellent academics and equity. The "equity" reformers have been dumbing down the curriculum for decades. 

✍️ Einstein based his theories of relativity on two impossibilities
1. "It’s impossible to exceed the speed of light."
2. "It’s impossible to tell the difference between gravity and acceleration." 
If either of these assertions were not true, the laws of physics would change radically, even fall apart. Physics is the most fundamental science, yet it is downplayed in the NextGen science standards in favor of issues-based science. Also, K-12 teachers are weak in chemistry, physics, and math. Science textbooks cannot be trusted and often imply a correlation, even a theory, as a fact

I am thinking about impossibilities in learning theory. Perhaps one is that it is impossible to have an empty slate. You were born as a learning machine with innate intelligence, abilities, and genetic differences that can widely vary from person to person, group to group, or even within children from the same family, etc. DNA determines who we are. (Quote: QuantaMagazine, 2021; DNA from Robert Plomin blueprint, 2018 MIT)

Think On These Things

"Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good report; if there be any virtue, and if there be any praise, think on these things." (St. Paul's Epistle to the Phillippians, KJV)

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How I teach elementary school students algebra: Teach Kids Algebra.

Note: I was not able to sign in to make changes on this page on the afternoon of 
6-8-21 for unknown reasons. Now, I am able to sign in to make changes or additions to this page. 

This page is too long, so I am thinking of starting a new page, perhaps Cogitatus4 or some other name. "Do you want to build a snowman?"