**Standard Algorithms Should Be A High Priority!**

*Despite that, they are not emphasized in reform math classrooms.*

**Starting in the 1st grade, the standard algorithms and the supporting single-digit math facts should be a high priority through 3rd-grade core arithmetic.**The standard algorithms should be taught first along with the place value system, but they are not in many classrooms. Also, the standard algorithms for multiplication and long division should be learned no later than 3rd grade.

*The learning requires memorization, drill-to-improve-skill, and regular review.*For decades, reform math has embraced alternative strategies, calculators, and minimal guidance methods, not standard algorithms and straightforward explicit teaching. The standard algorithms, along with fractions, place value, and other key math topics are the

**core arithmetic**needed to prepare for algebra.

**The result of the reform math approach has been a massive number of students placed in remedial math at community colleges**, even up to 88% (Data: Pima Community College 2014). Note: Common Core and state standards based on Common Core are often interpreted through the lens of reform math.

**Regarding reform math**, no one uses the area strategy to multiply or partial quotient strategy to do long division, yet these reform math procedures are taught in our elementary schools along with a hodgepodge of other cumbersome, alternative processes or procedures to do simple arithmetic.Traditional

**4th-Grade**Core Arithmetic 1877 (19 Century America - Arithmetic)**[Find the interest of $80 for 7 months, at 6 per cent.]***Ray's New Intellectural Arithmetic***1877**(3rd & 4th Grade) Note: Dr. Ray died in 1855, but his arithmetic textbooks, which were used extensively in the 19th Century, have lived on.**Calculators are "absolutely unnecessary."****W. Stephen Wilson**, a math and education professor at Johns Hopkins University, points out, “I have not yet encountered a mathematics concept that required technology to either teach it or assess it.**The concepts and skills we teach are so fundamental that technology is not needed to either elucidate them or enhance them.**There might be teachers who can figure out a way to enhance learning with the use of technology, but it’s absolutely unnecessary."**Fake Math --> Flat Learning**

1.

**We have spent an enormous amount of money on education just to tread water.**It's what reform math has done. The 2015 NAEP, TIMSS, PISA test results clearly show flat learning. For nearly two decades, our community colleges have been bursting at the seams with remedial math students who lack skills in basic arithmetic and algebra.

*Kids never master the standard algorithms and aren't learning the factual and procedural knowledge they need to know for algebra in middle school. Many students are*

**weak***in calculation skills--whole numbers, fractions, decimals, percentages, and ratio-proportions, which are core arithmetic. Furthermore, drill-to-improve-skill and memorization have fallen out of favor in "modern" elementary and middle schools for decades; consequently,*Kids must master the skills necessary to succeed in arithmetic and later in algebra. Most do not and have become dependent on calculators.

**math competency has declined**substantially.**Clifford Stoll**points out, "Practice--repeated drill--is out of favor today. Yet, it's the core of math competency. If we want students that can handle math, they've got to memorize the times tables [even though it is not much fun], do plenty of problem sets and master arithmetic and algebra."2.

**Th**e

**mainstream media often promotes fake news, and the math taught in our schools often promotes fake arithmetic (i.e., flat learning) via reform math.**

*The news is packed with disinformation, speculation, and myth. It is often opinion passed on as fact and correlation as causation. Likewise, math in the classroom is packed with untested notions, myths and evidence-lacking claims, incorrect mathematics, biased research, correlation as causation, unsupported pedagogical theories, and the*For example, Professor

__misuse of anecdotal "evidence" as proof__. Anecdotal "evidence" doesn't prove anything!**W. Stephen Wilson**, an MIT-trained mathematician, testified that

*Investigations*(5th Grade TERC), a very popular reform math program, is mostly

**pre-arithmetic**. (It's fake arithmetic!)

**He testified that kids never get to real arithmetic!**

__The multiple strategies of reform math to perform simple arithmetic overloads the curriculum with extras and increases cognitive load.__

*These*Kids are

__alternative strategies__displace, marginalize, or delay the standard algorithms and waste instructional time.**n**

**ovices**and should learn

**one-efficient-algorithm**(i.e., the standard algorithm) to do each of the four whole number operations by the end of 3rd grade starting with addition and subtraction in 1st-grade. But, the "

**one algorithm for each whole number operaton**" has been the exception, not the rule.

**3. "Math standards tend to shortchange arithmetic.**But, a mastery of arithmetic is just what students need to succeed in higher-level math,"

*writes*Without the multiplication table cemented in long-term memory, strudents can't do multiplication, long division, fractions, percents, proportions, or algebra. Even subtraction across zeros has been a stumbling block in upper elementary school. In short, students are up against a wall. They have been victims of reform math.

**W. S. Wilson**. Also, "Children who do not master the standard algorithm begin to have problems as early as Algebra I," write Wilson, Garelick, Milgram, Stotsky, Klein, et al. But, I think the problem starts in 1st grade with reform math. Later, kids walk into 4th grade without knowing the multiplication table or the standard multiplication and division algorithms.**4.**

**More kids are graduating without high school math skills.**

*Remedial math courses in Prealgebra, Elementary Algebra (high school Algebra-1), and Intermediate Algebra (high school Algebra-2) at community colleges and some other colleges have been booming for over a decade!*

**Moreover, many students are taking high school math for college credit at the university and don't know it, says**W. S. Wilson

**: I**

**t's called College Algebra, which is roughly equivalent to high school Algebra-2.**

*K-12 math reforms have been ineffective.*

*Frankly, I think nothing will change*

*as long as reform math people are in charge.*

*Furthermore, politicians should not be making education policy.*

****

**5.**

**Standard arithmetic primes a child's brain for higher level math.**Content knowledge in long-term memory, both factual and procedural, enables problem-solving and clear thinking in mathematics. Algebra is accessible to very young children through basic arithmetic.

*But, K-12 math, as it is has been taught (i.e., reform math), does not get students ready for college level math.*College Algebra is high school level math, not college level.

*Also, AP Calculus is high school level calculus, not university level calculus needed for STEM.*

**::::: Flat learning is a strong dose of reality: The 2015 NAEP, TIMSS, PISA test results clearly show flat learning.**

**Reform math crusaders**have marginalized traditional arithmetic content (factual and procedural knowledge), standard algorithms, memorization, drill-to-improve-skill, and regular review.

*It is a waste of time! It is curriculum overload and cognitive overload.*

**Note:****Regarding reform math**, no one uses the area strategy to multiply or partial quotient strategy to do long division, yet these reform math procedures are taught in our elementary schools along with a hodgepodge of other cumbersome, alternative, processes or procedures to do simple arithmetic.*Let me be blunt.*

**Reform math, which has de-emphasized standard (traditional) arithmetic, is fake math and has led to flat learning and a surge of remedial math courses in college.**It is the reason that thousands and thousands of students are placed in remedial high school math at community colleges and even universities.

**Reform math stresses multiple strategies over content knowledge and standard arithmetic. And, unfortunately for the students, it has been given new life through Common Core and state standards.**

Contrary to the

**reform math establishment**, which consists of teachers, the

**NCTM, U.S. and State Departments of Education, professors in schools of education, and other progressive defenders, memorization and practice are needed to cement factual and procedural knowledge in long-term memory for use in calculating and problem-solving. It is a fundamental idea in the**

**cognitive science of learning**. The notion that memorizing or practicing dents a student's curiosity and imagination is bogus.

*All the memorizing, drill, rhetoric (the craft of thought), and content knowledge learning in very strict schools didn't dent or harm the creativity, inventiveness, or curiosity of Einstein and other brilliant scientists, including Plank, Heisenberg, Schrodinger, Bohr, and countless others.*

**R**

**igid schooling can create great minds!**

**John Saxon**(Saxon Math) went to war against fake math when he wrote his Algebra-1 book in the 80s and later created his math series (Saxon Math). He battled against schools of education and the huge NCTM establishment. For decades, fake math has produced mediocrity in U.S. math programs. However, the

**consequences**of fake math can be seen incontrovertibly at the local level: the massive number of high school graduates who end up in the

**remedial math**at a community college.

*The reform math people have destroyed math education in America.*

**"It is difficult to find words to describe my outrage at a document which proposes that we implement a totally radical and untested change in math pedagogy."**No, the quote is not about Common Core, although it fits perfectly. John Saxon wrote it in

**1989**when he bashed the new NCTM standards document as dummy math.

**Red Flag: U.S. Bombs PISA**

**U.S. math test scores for 15-year-olds (10th Grade) bombed to the bottom half of the 72 participating nations and regions in the 2015 PISA international test given every three years.**

Read More on my

**CommonCore Page**.**Note: There was a time when one algorithm was taught for each of the four operations. The algorithms were called standard algorithms and were the centerpiece of traditional arithmetic.**Common Core can be interpreted as teaching the addition standard algorithm in 1st grade, then one algorithm for each operation after that,

**but it isn't**. Most of the math establishment interpreted Common Core state standards as reform math in which students learn 3 or 4 different ways (multiple strategies that are more complicated and cumbersome) to do each operation rather than

**ONE way**, the standard algorithm, which is often sidelined, delayed, or not taught. In my opinion, the multiple strategies are

**EXTRAS**that have jam-packed the curriculum and wasted instructional time. After all, who calculates using area strategies, partial quotient strategies, or a hodgepodge of other cumbersome, more complex strategies (procedures) to do simple arithmetic? [No One!] American students need to learn standard algorithms from the get-go!

**But, most do not!**Instead, they are taught a version of reform math that stresses multiple strategies over content knowledge and standard arithmetic. Consequently, kids know little basic arithmetic.

**Larry Cuban**(Stanford) points out in his blog (12-3-16),

**“**The research supporting “personalized” or “blended learning” (and the many definitions of each) is, at best

**thin**

**.**Then again, few innovators, past or present, seldom invoked research support for their initiatives.

**”**The same goes for multimedia (Clark & Feldon). Evidence does not seem to matter much to educators. It seems clear that the emphasis is on using tech to engage students rather than on learning content knowledge in long-term memory needed for critical thinking (i.e., problem-solving).

**Stagnant national and international test scores in math and other subjects demonstrate it! Notes:**Thoughts without content are empty. Engagement is not the same as learning. Using tech does not mean better achievement.

****

*Please excuse typos and other errors on this page.*

**December is the most wonderful time of the year.**

**Do Good Deeds every day.**

**East Asian countries dominate the 2015 TIMSS Math results. U.S. students not only lag behind, but they are also not in the same ballpark.**(The more "rote" East Asian learners, who memorize and drill-to-improve-skill, soared far above U.S. students not only in

**content**

**knowledge**and ability to perform mathematics correctly but also

**problem-solving**at the Advanced levels.)

The

**2015 TIMSS**mathematics results show that our

**4th graders**dropped since 2011 (scale scores: 541 to

**539**) and were barely

**treading water**if that, but our

**8th graders have improved**somewhat since 2011 to 2015 (

**509 to**

**518**). (

**Note:**But, the 8th-grade students dropped on the

**2015**

**NAEP Math, a national test,**from 285 in 2013 to 282 in 2015; the 4th grade-students scored 240, the same as in 2007. And, only 25% of 12th-grade students were proficient or above in NAEP math.

**Note: Trends in Math and Science Study or TIMSS is an important international test given every four years. The TIMSS scale center point is 500. Some of the 2015 results were announced at the end of November 2016. The NAEP is a national test given every two years. The National Assessment of Educational Progress is often called The Nation's Report Card).**

**We have spent an enormous amount of money to tread water (flat learning)!**

**4th-Grade TIMSS 2015**

Since 2011,

**Finland’s**4th-grade students dropped (545 to

**535**) and fell behind the U.S. (

**539**). The Finnish 8th-grade scores were not released.

**At the 4th-grade level, U.S. students were not in the same ballpark as the East Asian nations:**Singapore 618, Hong Kong SAR 615, S. Korea 608, Chinese Taipei 597, and Japan 593. The next were Northern Ireland 570 and the

**Russian Federation 564**. The gap between Singapore and the U.S. is 79 scale points.

**8th-Grade TIMSS 2015**

**U.S. 8th graders showed improvement since 2011**(509 to

**518**), but they were still far behind the high performing East Asian countries. Our 8th-grade students are over 100 points below Singapore. The Scale Scores were: Singapore

**621**, Korea 606, Chinese Taipei 599, Hong Kong SAR 594, Japan 586. The next were the Russian Federation 538 and Kazakhstan 528. The gap from Japan to the Russian Federation was 48 points. The gap between Japan and the U.S. is 68 scale points.

The

**argument**(aka excuse) has been that US kids had never scored well on international tests.

**Is it a sign that U.S. math learning is declining? No!**In fact, our students have made incremental improvements over the decades. The

**stagnant test scores**do indicate that our students haven't gotten much better while students in other nations have soared in math achievement. America is not economically competitive.

**The reality is that children in East Asia have been best at math for over a couple of decades.**

There are

**reasons**why U.S. students lag behind their Asian peers. The Common-Core-influenced math curriculum is

**below world class**! Many teachers implement

**inefficient minimal guidance instructional methods**(group work). The trend in U.S. education has been to eschew memorization and practice, which are needed for the automation of fundamentals of

**standard arithmetic**in long-term memory.

**Furthermore, most of our K-8 teachers have been**

**trained poorly**in both math and science in schools of education, yet, elementary school teachers are asked to teach all subjects. Teachers are unaware of the

**cognitive science of learning**.

*In other words, we have not done what is needed to improve math achievement significantly. We have been running in place.*

**In short, we teach math badly, starting in 1st grade.**Kids have not advanced like their Asian peers. We seem more interested in small class size,

**technology in the classroom**, and test-based reforms than in developing high-quality teachers. In contrast to American classrooms, which are filled with tech (tablets, laptops, computers, etc.), little tech is used in Asian classrooms. Also, different from Asian nations, our schools of education are not selective. Sadly, the teaching profession has been riddled with problems.

*11-30-16, 12-1-16, 12-2-16. 12-3-16*

Notes:

**More TIMSS data will be released in late January 2017. I am interested in the percentage of students who reached the Advanced Benchmarks, which, I think, is the best way to judge the effectiveness of math programs from various countries. In a U.S. national math test (NAEP) given every two years, the 4th-grade students went from 235 in 2011 to 240 in 2015, which is down from 242 in 2013, while the 8th-grade students went from 279 to 282, which is down from 285 in 2013.**

**Mathematical reasoning, logic, and problem-solving come from mathematical knowledge and skill automated in long-term memory, not thin air.**

*You can't learn to ride a bicycle without a bicycle.*

Likewise, you can't learn to do arithmetic without doing a lot of arithmetic.

Likewise, you can't learn to do arithmetic without doing a lot of arithmetic.

**Who calculates using area strategies, partial quotient strategies, or a hodgepodge of other cumbersome, more complex strategies (procedures) to do simple arithmetic? [No One!] Students need to learn standard algorithms from the get-go! But, most do not! Instead, they are taught reform math that stresses strategies over content.**

If US educators continue to teach elementary school arithmetic as

**reform math**, which stresses multiple strategies more than standard algorithms, such as in Common Core and state standards, then math achievement will remain

**flat**. "Despite huge increases in federal involvement in education, student performance in the United

States has remained stuck at

**average levels**since the late 1960s and early 1970s, observes

**Vicki E. Alger**(

*Failure,*2016). Some of the most recent reforms promoted or funded by the federal government or government agencies--such as the massive U.S. Department of Education with a $70 billion budget--include Common Core, NCLB (now Every Student Succeeds Act), Race to the Top, mandated testing, reform math, use of technology, inclusion policies, and others.

**There are always strings attached to federal dollars.**

**Standard algorithms**depend on the instant recall of

**single-digit number facts**. K-5 students need to

**automate the fundamentals of arithmetic**(ideas, skills, and uses) through consistent practice and use. But, educators continue to

**waste valuable instructional time**on "strategies" that will never be used because they are cumbersome, inefficient, and nonessential. From the get-go, starting in the first marking period of 1st grade, students need to learn single-digit number facts, standard algorithms, and essential content knowledge to move forward like their peers in top-performing nations. We need to

**upgrade curriculum to world class**and apply instructional methods that are explicit, productive, and competent (i.e.,

**strong teacher guidance**).

*Common Core and state standards are not world class.*

Also, we have been on the wrong road for decades. We jump around from blended learning to personalized learning, project-based learning, group learning, and so on. But, students don't get much better! Recently, I read that students should read from books and screens. After all, we are told, it is the digital age and reading instruction should change. "It ["The Changing Face of Literacy"] finds that, while experts quibble over what it means to be digitally literate, they agree on one thing: even the youngest children should be learning literacy with a mix of print and digital texts."

**Really?**

**Well, maybe the so-called experts are wrong!**

**Boaler and Zoido**write, "Research shows that an emphasis on memorization, rote procedures, and speed impairs learning and achievement."

**What a ridiculous statement!**(It is typical of reform math ideologues like Boaler.)

**Research has not shown this.**

*In fact, memorization of single-digit number facts, becoming skilled in using standard algorithms, and learning arithmetic content (ideas, skills, and uses) in long-term memory boost achievement and enable problem-solving. To get better at arithmetic requires practice-practice-practice, which has fallen out of favor, along with memorization, in modern classrooms. Memorization is critical in learning and life.*

11-24-16

**Rick Hess**,

*Education Next*, writes that the current education reformers are “passionate, Great Society liberals who believe in closing achievement gaps and pursuing equity via charter schooling, teacher evaluation, the Common Core, and test-based accountability." They say, "[No] reasonable person can disagree” with this. Really? The belief is brazen and presumptuous because many believe that the Common Core and test-based accountability, for example, have been counterproductive, along with reform math.

The

**evidence**that the math reforms will close achievement gaps is

**scant**. It's utopian thinking promoted by progressive ideologues. But, we do not live in

**Lake Wobegon**where all children are above average in intelligence. There will always be gaps (inequalities) because

**good education increases differences**, says Nobel-prize winning Physicist

**Richard Feynman**. The well-meaning pursuit of inclusion and social justice in the classroom, which

**Thomas Sowell**calls "

**equalization crusades**," is not real equity and is often divisive.

**In the real world, abilities and attitudes vary widely.**Some kids are better at math than others. Some kids study more than others. Some kids become elite Olympic gymnasts, but most never come close. Unfortunately, too many kids struggle with basic arithmetic because of the way it has been taught and presented, i.e, as reform math. Average children can learn arithmetic and algebra. Even if resources and opportunities were the same,

**Sowell**explains,

**"Fairness as equal treatment does not produce fairness as equal outcomes."**Musical ability, artistic ability, writing ability, athletic ability, academic ability, and so on vary widely in a population. Abilities need to be trained.

__Understanding does not produce mastery;__

**practice does**!Many parents are not teaching their kids how to behave, succeed, and achieve in school or life.

*Teachers can't do it all.*If we want students to do higher-order thinking, then they need to start with lower-order content-rich knowledge (lower level thinking). There is no substitute for

**knowledge**in long-term memory and the practice that gets it there.

11-23-16

**Rigid Schooling Created Great Minds**

The great minds of the

**Scientific Revolution**such as Galileo, Brahe, Kepler, Copernicus, Bacon, Newton, and many others didn't happen by accident. They came out of the rigid "Renaissance pedagogy," says Professor Scott L. Newstok ("How to Think Like Shakespeare"). In a later era,

**Einstein**and a bunch of other brilliant scientists, including Plank, Heisenberg, Schrodinger, Bohr, and many others, came out of rigid school systems.

**Indeed, all the memorizing, drill, and rhetoric (the craft of thought) in very strict schools didn't dent their creativity, inventiveness, or curiosity.**

**Indeed, Professor Scott L. Newstok writes, "An apparently rigid educational system could, paradoxically, induce liberated thinking."**The Renaissance also produced the

**great artists**such as da Vinci, Botticelli, Michelangelo, and others, along with

**great writers**like Francesco Petrarca (founder of Humanism), William Shakespeare, Christopher Marlowe, John Donne, and many others.

**Newstok**thinks that today's American school system is the antithesis of the rigid schools that produced world-changing minds. American schools no longer stress the importance of content knowledge, memorization, the drill of fundamentals to learn and improve, and the

**craft of thought (rhetoric)**. These are old fashioned, reformers say, "This is the 21st Century; we have Google and smartphones."

**Really?**

*The 6th graders I have cannot read the cursive writing I put on the board, so I have to print as if they were 1st graders. Neither can they multiply 0.245 by 100 in their heads, a skill I used to teach to 4th graders.*

Today's students have a lot of gaps in arithmetic (fragmentation)

*.*

**They are taught strategies rather than a coherent hierarchy of key content.**

*Also, Googling isn't the same as learning content knowledge in long-term memory.*

**The humanities and arts have been sidelined in many schools. Furthermore, math, science, and reading are taught poorly.**Kids don't have vocabulary study (e.g.,

*Vocabulary Workshop*) and don't learn standard arithmetic well.

**Studying traditional arithmetic and algebra requires effort!**

**K-12 pedagogy**is to blame for the huge number of students who place in

**remedial math**at community colleges. In the Tucson region, which is served by nine school districts, the range is from

**74% to 88%**of high school graduates had placed in remedial math in 2014, according to a study done by

**Pima Community College**. A reform math curriculum, instructional methods, and grade inflation are at fault.

**Note.**Common Core and state standards are an extension of reform math and the so-called "mathematical practices."

**Students are weak in standard arithmetic because, for decades, it has been sidelined by reform math and its ideology.**

**In addition to learning algebra (math) and chemistry (science), students should also study the humanities and the arts.**

**In short, they need a liberal education.**

*At Yale, the two goals of a liberal education are "training the mind to think [rhetoric] and filling the mind with specific content [knowledge]."*

**Unfortunately, a liberal education has been out of favor for decades.**Modern education is typically skills-based learning defined by technology and globalization, says

**Fareed Zakaria**(

*In Defense of a Liberal Education*, 2015).

**Starting with 1st graders, educators are training students for career readiness.**Why? Kids sit in groups to collaborate. Really? It is foolishness. When kids sit in groups facing each other, they tend to talk and are easily distracted. In short, students have difficulty paying attention in class.

**They learn not to pay attention.**

**David Geary**(

*Scientific American Mind*2011) explains, "Youngsters would rather pay attention to one another than to the blackboard." It happens when I meet two 4th-grade classes once a week. When I explain something on the board, many of the students are not watching.

**Attention**is a key to learning well.

**Without a spirited emphasis on the**

**humanities**, most kids won’t memorize the Preamble to the Constitution (We the people). They won't study poetry by Poe (“Once upon a midnight dreary, while I pondered weak and weary.”) or explore Shakespeare (“Be not afraid of greatness: some are born great, some achieve greatness, and some have greatness thrust upon them.”). And, most students probably will never read

**historical documents**like the

*Federalist*essays by Hamilton, Madison, and Jay or

**literature**like

*Silas Marner*by Eliot,

*Moby-Dick*by Melville, or

*The Turn of the Screw*by Henry James. Furthermore,

**Frederick Hess & Chester Finn**,

**Jr.**lament that "our schools do such a miserable job of imparting

**U.S. history and civics**to their pupils." Don't forget

**music, art, and languages like Latin or Classical Greek.**Many assert that "learning Mandarin is critical to the educational and economic success of American students." Really?

**Kids have trouble reading science textbooks, historical documents, and literature.**

**How did so many very young musicians get so good in such a short period?**Most of us can't begin to comprehend the amount of

**training and drills**that young violinists and pianists do to "perfect their craft" and skills, often starting at the age of 4 and evolving into soloists with orchestras at 10 or 11, even younger.

**Classical music, the old stuff, is not dead. The children are bringing it back.**

*Today, there are hundreds of excellent child pianists and violinists world wide rather than just a handful a few decades ago.*

**It's back to excellence.**There were over 300 entries to the

**2016 Menuhin Competition**, an international violin competition for young musicians who were born after 17 April 1994.

**Kids who excel are highly motivated to practice fundamentals. They also get outstanding instruction to optimize improvement and performance.**

*You don't get good at something unless you work at it. Learning is hard work.*Likewise, students don't get good at arithmetic unless they drill the fundamentals repeatedly.

*If you are satisfied with your math skills, then you will not get any better, and you will never be as good as you are right now without regular practice and learning.*

**The sad reality is that American kids are crawling instead of leaping in math.**

*Priorities and attitudes are misplaced.*Many American students whine about homework. The attitude is that school isn't that important, but kids can't live without social media! "I can google it," some say. Many students do just enough to get by in their school studies, even though they are years behind their peers from top-performing nations in math and science.

**Only 25% of high school seniors are proficient in math (2015 NAEP).**Often the humanities and arts are glossed over.

**Note.**

*We need to bring back art and music as core subjects to our schools. Test-based craziness, tight budgets, and bad decisions downsized or eliminated many the arts and subjects like history, literature, and geography.*

**Note.**American educators and parents--but not Asians and others--have bought into Piaget's developmental stages, which still influence American education practices. "Oh, that's developmentally inappropriate." No, it's not! Piaget's theory has been shown false again and again.

**What counts in learning isn't the child's age but the child's background knowledge. Does the child have the prerequisite math skills?**In my Teach Kids Algebra (TKA) program, I was able to fuse important algebra ideas to standard arithmetic skills, beginning in the 1st grade.

**We are not all equally creative.**Some believe that creativity comes out of thin air. It doesn't! Knowing stuff is essential to creativity. Knowledge matters!

**"You need to look back at the old things," the traditional stuff, to move forward. Einstein didn't toss Newton in the waste can; he built on Newton's incredible insights.**Indeed, we should

**imitate**the best from the past and "stand on the shoulders of giants." Tradition is not tossed out in highly creative cultures.

*Indeed, something new is not necessarily better.*In fact, most innovations in education flop because they were contrary to the cognitive science of learning and depended too much on

**anecdotal data**. Progressive reformers in education may have been well educated, but they often lacked wisdom and were too quick to toss out traditional arithmetic and instructional methods that had worked in the past. Their

**disruptive tactics**have been counterproductive in math education.

**Newstok**draws an extreme metaphor for today's "googling," i.e., finding information on the Internet with a search engine. He writes, "If you knew no words in a language, having a dictionary wouldn't help you in the least since every definition would simply list more words you don't know.

**Likewise, without an inventory of knowledge, it's frustratingly difficult for you to accumulate, much less create, more knowledge."**

*Knowing stuff counts.*

**Crowding**

It seems that educators are pretty good at addition.

**Over the past 50 years, a lot of stuff, some of it nonessential, has surged into the curriculum and classroom.**It includes the

**extras**in arithmetic and algebra (e.g., reform math, Common Core, so-called mathematical practices, state standards that are below world class, more complicated and multiple ways to do simple arithmetic). Intrusive, also, are government mandates and programs, disruptive evidence-lacking innovations, popular classroom practices that don't work, minimal guidance during instruction, etc.). But, I should also count the

**gadgets**in the classrooms, including computers, tablets, smartphones, graphing calculators, smart boards, Internet, online software and learning programs, etc. Furthermore, education is overflowing with

**failed theories and wrong ideas and reforms**, yet they still stick like glue. Test-based accountability has complicated curriculum and instruction and led to teaching to the test.

**In schooling, we are fixated on gadgets and test-based reform, but "tech and test" are not the solution; they, I believe, are part of the problem.**

*Gadgets have not transformed education and don't improve achievement.*

**"**

**Critical thinking does not exist as an independent skill."**(E. D. Hirsch, Jr.)

The Common Core math standards, now called state standards, were not benchmarked to the standards from top-performing nations. In fact, Common Core benchmarks were lower than the

**1997 California math content standards**, which were world class and emphasized the fast learning of

**standard arithmetic**, including the standard algorithms to operate on numbers, to prepare more students for Algebra-1 by middle school.

California rejected reform math based on standards from the National Council of Teachers of Mathematics (NCTM) because students could not do simple arithmetic. Contrary to the NCTM standards, the 1997 California math content standards were well written and stressed the fast learning of factual and procedural knowledge in long-term memory.

**[**

**1997**

**CALIFORNIA 3rd-grade (World Class) MATH Standards**:

**2.4**Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 x 3 = __).

**2.5**Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 ÷ 5 = __).

**]**

It is unfortunate that California ignored the

**National Math**

**Panel**and scrapped the straightforward, 1997 world-class content standards for inferior Common Core math standards in 2010. (Note. The explicit teaching of standard arithmetic to prepare students for Algebra-1 in middle school had been the principal recommendation of the National Mathematics Advisory

**Panel**of 2008.)

**Nearly 140 years ago, American 2nd-grade students learned multiplication and division in the public schools.**

*The young students memorized single-digit number facts and drilled to improve skill and performance using both abstract questions and word problems.*

**I observed that most of the abstract questions and word problems involved two or more operations (multi-step)**.*The arithmetic content taught today is meager compared to Ray's 1st/2nd-grade 94-page textbook (1877).*

**1. 2nd-Grade Abstract Questions**

*How many are 6 and 5, less 4, multiplied by 7?*

How many are 2 and 5, less 3, multiplied by 9, divided by 6?

How many are 6 x 8 - 4?

How many are 2 and 5, less 3, multiplied by 9, divided by 6?

How many are 6 x 8 - 4?

**2. 2nd-Grade Word Problems**

*:: James bought 3 lemons, at 2 cents each, and paid for them with oranges, at 3 cents each: how many oranges did it take?*

:: What will 63 marbles cost, if 14 marbles cost 2 cents?

:: I bought 2 yards of cloth, at 4 dollars a yard, and 3 yards, at 2 dollars a yard: how much did all cost?

:: What will 63 marbles cost, if 14 marbles cost 2 cents?

:: I bought 2 yards of cloth, at 4 dollars a yard, and 3 yards, at 2 dollars a yard: how much did all cost?

******Source:**

*Ray's New Primary Arithmetic*1877. The text was 4.5 x 7 inches, 94 pages long, and covered all of the 1st and 2nd-grade arithmetic. What a novel idea:

**two grade levels in one tiny book**--no color, graphics, etc., just pure arithmetic! In stark contrast, Pearson's

*enVision Math*2nd-grade paperback (2011) is huge, approximately 11 by 16 inches, and 644 pages long.

For the latest, click

The next great debacle in education is already here. It is NCTM

Note. Wayne Bishop's quote was found in a column he wrote for the San Gabriel Valley Tribune, 9-2-16

**.**__CommonCore__The next great debacle in education is already here. It is NCTM

**reform math**repackaged via Common Core and state standards, in which alternative, nonstandard algorithms have replaced standard algorithms, and traditional arithmetic has been tossed aside for reform math. [Note. Reform math in Common Core (e.g., Eureka Math = EngageNY) and Common-Core-influenced state standards tend to stress real-world problems, group work, discovery learning, tech, and nonstandard algorithms, often at the expense of mastering fundamental content; i.e., mathematical ideas, skills, and applications. The consequence has been**flat learning**.*Simply, our kids are not learning nearly as much arithmetic and algebra as kids in many other nations.*Mathematician,**Wayne Bishop**writes, "The Common Core math standards, and the**misguided philosophy of mathematics education**behind them [e.g., Mathematical Practices (reform math), Piaget's theory, minimal guidance during instruction, inclusion, etc.], are the heart of the problem."**Surprise! Common Core benchmarks are not world class and "less rigorous than the 1997 California standards," says Dr. Bishop.***In California, Common Core is a downgrade, not an upgrade.***In contrast to Common Core, the 1997 California math standards were composed by mathematicians and matched the best in the world. The idea was to get more kids into Algebra-1 by middle school, which was also the recommendation of the****National Mathematics Advisory Panel**(*Foundations for Success*, 2008). Like the old California standards, the Panel's presumption had been to prepare many more students--not just the best students--for algebra starting with the 1st grade. Also, Common Core claims the “so-called” real-world problems allegedly demonstrate problem-solving skills.**Really?**In contrast, children should learn**routine problems**and their variants and learn pattern recognition to evolve into better math students. In short, children need to know (in long-term memory) the fundamental ideas, skills, and applications of mathematical content before they can do mathematics well, think clearly, and solve problems in mathematics. They also need straightforward instruction using worked examples and plenty of practice (drill-to-improve-skill). The early memorization of basic facts and practice of standard algorithms are essential.Note. Wayne Bishop's quote was found in a column he wrote for the San Gabriel Valley Tribune, 9-2-16

**To The No Child Left Behind - Google Generation**

Scott Newstok,an English professor at Rhodes College, wrote an essay from a convocation he gave to the Class of 2020. (The Chronicle of Higher Education). Here are a couple highlights from his essay:

Scott Newstok,

Class of 2020, welcome to college.

**The most momentous event in your intellectual formation was the 2001 No Child Left Behind Act, which ushered in our disastrous fixation on testing.**Your generation is the first to have gone through primary and secondary school knowing no alternative to a national regimen of assessment.

**Neoliberal reformers — the ones who have been assessing you for the past dozen years — act as if cognitive “skills” can somehow be taught in the abstract, independent of content.**[They can't.]

**But knowledge matters.**Cumulatively, it provides the scaffolding for your further inquiry. In the most extreme example, if you knew no words in a language, having a dictionary wouldn’t help you in the least, since every definition would simply list more words you didn’t know.

**Likewise, without an inventory of knowledge, it’s frustratingly difficult for you to accumulate, much less create, more knowledge.**As the Italian novelist Elena Ferrante said, “There is no work … that is not the fruit of tradition.”

**End**

**1. College Trajectory (High Skills)-->4-Year University**

Some charter and many independent schools require all their students to take Algebra-1 in 7th or 8th grade. It is the college trajectory, and it has worked very well. Most public middle schools had an Algebra-1 course for the best students.

**I don't advocate college-for-all.**Some kids need a trajectory that leads to calculus in high school, and Common Core isn't it.

**It is hard to judge which students should follow this trajectory.**

*Kids who take advanced math courses (Algebra-2 with trig, precalculus, and calculus) and core science courses in middle school (physical science) and high school (chemistry and physics) go on to earn a bachelor's degree.*Also, a

**student does not need to be gifted or a genius to learn Algebra-1 in middle school, AP Calculus in high school, or grasp some algebra fundamentals in 1st grade.**Average kids can do these things when they are

__taught well__and

__work hard__to achieve.

**2. Community College (Middle Skills)-->2-Year College**

Learning

**m**

**iddle skills**are valuable for many students. They are learned through

**community college programs,**and, sometimes, through limited apprenticeships. To enter community college, a student needs to be good at math, which has been a

**stumbling block**. Students are often sidetracked to the

**remedial math**

**rut**. It is clear that K-12 schools must do a better job teaching kids math, and Common Core is not it. Our high schools should offer a

**vocational alternate to college for all**.

I recommend that students should pass an

**arithmetic and**

**Algebra-1 achievement test**to enter a community college, and, if the student needs more math, then it would be taken as part of a 2-year associate's degree or certificate.

**What is clear is that most future jobs will require some college, but how much college?**

**Note.**Earning

**a bachelor's (4-year) degree at the university "is not the right answer for everyone." Many students would be far better off "by robust technical training [community college] that will lead them to middle-skill jobs," observe**Newman & Winston

**(**

*Re skilling America*

**, 2016).**Tn short, there are good jobs available for those who have the

**right middle skills**via an associate's degree or certificated program.

*These jobs do not require a 4-year bachelor's degree.*

**3. High School Diploma or GED (Low Skills)**

****ToBeContinued 7-13-16

**1. This is reform math, not standard arithmetic.**

**2. It's inefficient and wastes instructional time.**

*The arithmetic taught should be useful and efficient. The “many ways” of nonstandard, more complex, alternative algorithms of reform math to calculate simple arithmetic problems are not efficient.*

**In short, reform math has screwed up the learning of standard arithmetic, which is essential.**

**Why would anyone suggest that this is a good way to teach novices subtraction?**Still, it is typical of

**reform math**.

*Making Number Talks Matter*(Humphreys & Parker, 2015) shows five different ways to subtract, including Decomposing the Subtrahend (shown above), but

**not**the standard algorithm. The book focuses on contentious mathematical practices (Common Core) and implies that standard arithmetic (old school) "destroys a child's intellect, and, to some extent, his integrity."

**What nonsense!**The reason kids are poor at basic arithmetic ("fragile skills") is that they do not practice enough, or it hasn't been taught well.

**The idea of drill-for-skill to automate essential fundamentals in long-term memory has fallen out of favor for decades due to reform math and progressive ideology.**

**[**

*Number Talks*cites a so-called

__common mistake in middle school math__: 1/3 + 1/3 = 2/6 = 1/3. How can this be a common mistake in middle school?

*Even my 1st graders did not make this kind of error.*

**If middle school kids are making this mistake, then it shows how badly arithmetic had been taught in elementary school. Their reasoning is wrong!**]

The reason kids have “fragile skills and shallow understanding” is that basic arithmetic skills have been taught poorly, especially via reform math and its methods.

**College professors lament that students can’t do simple arithmetic without reaching for a calculator (e.g., 0.256 x 100), which is directly linked to 25 years of reform math.**

**Kids can't calculate!**Standard arithmetic can be taught poorly, too, but, under the

**reform-math regime**, math achievement has been static because the intent was not stellar achievement; it was equal outcomes, says

**Thomas Sowell**, and socialization via group work.

*Consequently, reform math has not prepared more students for Algebra-1 in middle school.*

**The "one-size-fits-all" C**

**ommon Core state standards embrace reform math and the nonstandard, inefficient algorithms--more of the same.**

**Math Matters (More Than You Think)!**

Kids who take advanced math courses(Algebra-2 with trig, precalculus, and calculus) and

Kids who take advanced math courses

**core science courses**in middle school (physical science) and high school (chemistry and physics) go on to earn a bachelor's degree. (Note. These courses are not integrated science or conceptual courses.) Solid 8th grade physical science and high school chemistry and physics courses require a

**good math background**. Indeed, the math courses taken in middle and high school affect the probability of obtaining a college degree and the student's future earnings. Math matters, but not all math courses are equal. (Note. Not all courses labeled as college prep are college prep. Many pre-algebra courses are labeled as algebra.) Students need to take

**advanced**math courses.

**This is contrary to Common Core's doubtful rhetoric (guess) about college and career readiness and the Next Generation science standards.**A college degree (associate's, bachelor's, or master's) is your best bet for the future job market, especially in the managerial and professional fields, not just a high school diploma.

According to the

__, "Those with at least some college education have captured 11.5 million of the 11.6 million jobs created during the recovery. While jobs are back, they are not the same jobs lost during the recession.__

**Georgetown University report****The Great Recession decimated low-skill blue-collar and clerical jobs, whereas the recovery [January 2010 to January 2016] added primarily high-skill managerial and professional jobs."**

If your degree is in an

**overloaded field**(e.g., some STEM fields) or the wrong field, then you will be lucky to find a job. Many students follow their dream and end up living at home with a worthless degree, large student-loan debt, and no real job prospects. Kids need to be practical and major in a field that will put food on the table.

**A student does not need to be gifted or a genius to learn Algebra-1 in middle school, AP Calculus in high school, or grasp some algebra fundamentals in 1st grade.**Average kids can do these things when they are

__taught well__and

__work hard__to achieve.

**Note.**Parts of this page have been removed. If you would like a pdf of the original, please email ThinkAlgebra@cox.net. I will continue to shorten content. 6-1-16

Starting in the

Also, teaching many different thinking strategies, along with confusing, complex, nonstandard calculation procedures to do simple arithmetic, such as those found in

-----

**1st grade**, I believe it is essential to establish a solid foundation of**standard arithmetic**in long-term memory, and then start applying the arithmetic students have learned through**routine problems**with increasing levels of difficulty. A**hierarchically sequenced****curriculum**requires a**sharp focus on achievement**, the rapid mastery of**factual and efficient procedural knowledge,**instructional methods based the**science of learning**, and strong teacher guidance, which means**the teacher should be the academic leader, not a facilitator as taught in ed school. "****Minimal guidance in mathematics leads to minimal learning**," write**Sweller, Clark, and Kirschner**. Indeed, minimal learning has been the narrative for decades.Also, teaching many different thinking strategies, along with confusing, complex, nonstandard calculation procedures to do simple arithmetic, such as those found in

**reform math**via Common Core or state standards, instead of**straightforward**knowledge and skills in**standard****arithmetic**, has been a colossal waste of valuable instructional time.**Kids are novices and need background knowledge. They need to drill-for-skill, so essential factual and procedural knowledge sticks in long-term memory.**

In grades 1 to 4, the automation of standard arithmetic and the learning of algebra fused to arithmetic often boil down to hard work and persistence.In grades 1 to 4, the automation of standard arithmetic and the learning of algebra fused to arithmetic often boil down to hard work and persistence.

-----

**The latest K-12 fad is****personalized learning**, which would require the complete computerization of schools. In a few decades, maybe half the teachers would be cut. The downsized teaching staff would "remake schooling" as an "adjunct faculty" and would supervise or facilitate the personalized learning, suggests**Mark Naison**, a college professor at Fordham University.**I think it is a truly bad idea from special interests**(aka corporate-based reform), and I doubt it would happen on a wide scale, but suppose I am wrong? Suppose schools districts across the US adopted personalized learning, thinking it would be the future in education?**-----**

Note.Topics are presented randomly. Please excuse typos, errors, andNote.

**redundancies.**

**Notes.**

(1) We need to get disruptive kids out of the classroom, stop playing good behavior games, stop testing for so-called "soft skills" that are hard to define and measure, just as "understanding" and "creativity" are almost impossible to measure.

(2) K-5 kids don't need group work and discovery or collaborative activities. They need academic achievement in basic reading, math, and writing.

(3) College readiness and career readiness are

(4) Kids need a liberal education, which includes math and science, along with the humanities and the arts. In addition to math and science instruction, make sure K-5 students have music, art, PE, library, recess, English grammar, spelling, history, and geography.

(5) To get to algebra-one in middle school, elementary school students should automate standard arithmetic first, not reform math. By the end of 3rd grade, students should be proficient in all four whole number operations (aka standard algorithms, place value, and single-digit math facts, and the rules of arithmetic).

(6) Students are not the same, so the one-size-fits-all ideology in Common Core or state standards is nonsense.

(7) Equalizing downward is an illusion of fairness and a nutty idea taught in schools of education.

(8) Teachers should implement the

(1) We need to get disruptive kids out of the classroom, stop playing good behavior games, stop testing for so-called "soft skills" that are hard to define and measure, just as "understanding" and "creativity" are almost impossible to measure.

(2) K-5 kids don't need group work and discovery or collaborative activities. They need academic achievement in basic reading, math, and writing.

(3) College readiness and career readiness are

*not*equivalents.(4) Kids need a liberal education, which includes math and science, along with the humanities and the arts. In addition to math and science instruction, make sure K-5 students have music, art, PE, library, recess, English grammar, spelling, history, and geography.

(5) To get to algebra-one in middle school, elementary school students should automate standard arithmetic first, not reform math. By the end of 3rd grade, students should be proficient in all four whole number operations (aka standard algorithms, place value, and single-digit math facts, and the rules of arithmetic).

(6) Students are not the same, so the one-size-fits-all ideology in Common Core or state standards is nonsense.

(7) Equalizing downward is an illusion of fairness and a nutty idea taught in schools of education.

(8) Teachers should implement the

__cognitive science of learning__, not ideology.

College Ready = Career Ready (Really?)

*Achieve --> Common Core***College ready and career ready are not equivalents, yet the one-size-fits-all ideology behind the idea of "sameness" thrives in American classrooms.**What does all this have to do with Common Core? In 2008,**Achieve**laid the foundation for what is called Common Core, including the one-size-fits-all ideology and the advanced mathematics keystone.**Put simply,****Common Core formulates college readiness as being equivalent to career readiness, which is a stupid idea.**The one-size-fits-all ideology does not fit reality.*The*__same curriculum__is taught to**all students**without regard to individual achievement, ability, and goal; i.e.**,**those who plan to attend a 4-year university, a 2-year community college, a vocational school, or those who plan to enter the workforce without postsecondary education.**Common Core explicitly states that it is not for STEM students.***Apparently, its so-called "advanced math" cornerstone does not extend much beyond elementary algebra.***The Common Core ideology makes no sense. It caters to the narrow,**skewed vision**of special interests and elites that advocated "advanced math for all students."***But, what is advanced math in Common Core? Presumedly, it boils down to the mantra***Algebra for All**,*but, in my view, first-year Algebra isn't advanced math.*(**Confusion**: Do the Common Core reformers rebrand statistics and probability as advanced math? These topics are found in pre-Common Core Algebra 2 textbooks, along with trig and other topics.)**Advanced math is a STEM sequence: Algebra 2, trig, precalculus, and calculus.***In the real world, s**ome students don't need advanced mathematics (e.g., Algebra 2), and it should not be a requirement for a high school diploma; however, it should be a requirement for STEM studies at the community college and university levels.**More information is found in Math Notes:***Click Here****.****(Aside.***David Hume***wrote, "A wise man proportions his belief to the**evidence.")****It is 2016! The same old problems persist. Kids are crawling instead of leaping in math. Achievement has been stalled.**

**Good grief, t**

**he N**

**AEP math test scores in 2015 for 4th and 8th-grade students are lower than in 2013.**

**There is a war on excellence.**Indeed, reform math via Common Core or its rebranded configuration (aka state standards) promotes mediocrity, not excellence, in learning. Reform math methods ignore the cognitive science of learning and suggest that learning standard math well is not that important. Reform math focuses on nonstandard, complicated ways to do simple arithmetic, pushing the standard algorithms to the back burner.

**Put simply, reform math obstructs the fast learning of core standard arithmetic.**

**Reform math via Common Core or Common Core rebranded as state standards**, which is the case in almost all states, confuses beginners and overloads their working memory.

__Students are novices, not little mathematicians.__

*Put simply, reform math makes simple arithmetic excessively complicated.*

*Many students are held back academically because they get the same curriculum, which is the mantra of Common Core reform math progressives.*Also, in reform math via Common Core, the

**standard algorithm**is merely one of the many ways--often

__not__the preferred way, the reformists say--to calculate.

**I**

**ndeed, reform math via Common Core or state standards often supersedes simple, old-school arithmetic with complicated procedures (models, strategies).**

For decades,

**fractions and long division**have been sidelined and taught poorly in elementary schools. The widespread practice has hindered a child's numerical development and ability to do algebra and higher math. It is a primary reason that U.S. students are not prepared for algebra by 8th grade. In short, most US students are not taught enough math content. Students in other nations routinely do algebra in middle school, but our students don't.

**Standard arithmetic has been marginalized by Common Core's version of reform math.**

**The early mastery of standard arithmetic--not reform math--is required to prepare for algebra. Certainly, the "mantra that one-size-fits-all model [cannot] possibly do justice to the diversity of academic subjects," says**

**Gerald Graff [1].**Also, another problem is the dissimilarity of knowledge, achievement, and academic abilities or skills of students. Therefore, the students who walk through the school door often vary widely in academic ability, so a one-size-fits-all formula is a poor fit.

**The one-size-fits-all Common Core doesn't fit low ability kids (two much content) or high ability kids (too little content) in math.**Even

**average kids**don't master enough standard arithmetic when it is taught through the lens of reform math. In short, there should be different levels of

**instructional objectives**to (better) match students, but that's not the "one size" Common Core way.

Even though reasoning abilities have increased on the

**Weschler Intelligence Scale for Children or WISC**since 1950, students have

*not improved much*in several key WISC subtests:

**Information**(basic knowledge),

**Arithmetic**, and

**Vocabulary,**says

**Mark Bauerlein**

**[2]**

**.**He writes,

**"The lesser subtest outcomes [Information, Arithmetic, & Vocabulary] explain why academics have stalled for U.S.**

*For example, in 2015, "both the 4th- and 8th-grade students score lower in NAEP mathematics than in 2013."*

**John Dewey still lives on ...**

**Progressives believe that utopia is possible in education: everything is relative.**"For them, science is just another opinion..., so their

**core issues are fairness and equality, not excellence**," observe

**Berezow & Campbell**(

*Science Left Behind*)

**[3]**.

*It is the same problem we have with progressive education today:*Berezow & Campbell explain, "But rather than keep what worked and improved what did not, Dewey set out to reshape education from the ground up...

**skewed priorities**.**It was not set up to improve learning**; it was actually designed for social acclimation reasons on the latest pop psychology." John Dewey lives today. Is it any wonder that the education reforms are bizarre and don't work well?

**Learning is stalled.**

**Footnotes**

[1] The quote from

**Gerald Graff**is from his chapter on the new anti-intellectualism found in

*The State of the American Mind*, edited by Bauerlein & Bellow, 2015.

**[2]**The quote from

**Mark Bauerlein**is from his chapter on the new anti-intellectualism found in

*The State of the American Mind*, edited by Bauerlein & Bellow, 2015.

**Bauerlein makes an excellent point that helps explain the reason that academics have stalled in the US.**

**[3]**

**Berezow & Campbell**writes, "This is the crux of science [and math] education as an issue in American life. It is not a matter of promoting excellence; it is a matter of pursuing political priorities. To progressives, the focus is not on providing a quality science [or math] education for students... There is a war on excellence."

**The progressives dominate education policies and ignore the cognitive science of learning because it doesn't fit their framework or agenda**.

**Excellence is not necessary.**

------------------------------------------

**Do not confuse low-income kids with low-ability kids.**

*I have found many low-income kids who learn math faster and better than their peers; however, their academic growth in math is often stymied by a range of factors, such as the following:*

*(1) the slow pace of instruction;*

*(2) being asked to "teach" other kids (group work);*

*(3) topical redundancy (spiraling curriculum);*

*(4) the idea that every child gets the same;*

*(5) "equalizing downward by lowering those at the top" in the name of fairness;*

*(6) teaching reform math; and*

*(7) teaching to the test.*

**[Aside. The**

**inference**

**that Common Core reform math and its standardized testing will jump-start stalled achievement so that all students will become college- and career-ready without remediation is untested,**

**unproven**,

**and far-fetched**.

**The inference is pure speculation--a guess--and not supported by valid evidence.**

*We already know that progressive reform math (NCTM) failed in the past and that standardized testing, with implied consequences, and teaching-to-the-test do little to improve actual achievement in math.*

**Standard arithmetic**has been marginalized by Common Core's version of reform math. Contrary to Common Core, the early mastery of standard arithmetic--not reform math--is required to prepare for algebra. American educators don't get this, but Singaporean teachers do.

**]**

## Kids Must Memorize Times Tables & Master Fractions!

Fraction Magnitudes - 2nd Grade, LT

**Fractions and long division are key building blocks in a young child's numerical development. For decades, our math programs have marginalized their importance, but research has shown that this was an epic mistake. Kids must memorize times tables to do long division, fractions, and algebra.**

*A violist won't get to Carnegie Hall without memorization and years of practice, and kids won't master arithmetic or algebra without memorization and years of practice. Indeed, you won't get good at anything without memorization and practice, lots of it, whether it be violin, mathematics, gymnastics, Latin, piano, Physics, and so on.*

**Our kids**

**may not be the next Mozart, Newton, or Murdock, but, "through effort, [they] can develop passable skills in music, math, and writing"**(Breznitz & Hemingway,

*Maximum Brainpower*, p. 192).

For decades, fractions and long division have been sidelined and taught poorly in elementary schools. The practice has hindered a child's numerical development and ability to do algebra. It is a primary reason that U.S. students are not prepared for algebra by 8th grade. Students in other nations routinely do algebra in middle school.

## Kids can learn algebra

*Algebra grows out of arithmetic.*

First grader in my algebra class

**The following has been my**

*core premise*for decades: "We begin with the hypothesis that any subject [e.g., arithmetic, algebra, calculus] can be taught effectively in some intellectually honest form to any child at any stage of development." - Jerome Bruner*(The Process of Education, 1960)*

*The implication is that children, even in 1st graders, can learn fundamentals of algebra. As a guest teacher, I teach little kids algebra*(

**)**

__Teach Kids Algebra__*And, yes, 1st graders can learn some fundamentals of algebra, such as*

*(1) numerical relationships (functions),*

*(2) equality (an equation is like a balance),*

*(3) true/false math statements (left=right),*

*(4) the rule for substitution,*

*(5) function rules (x,y),*

*(6) table building,*

*(7) equation writing and solving, and*

*(8) graphing in Q-I; e.g., y = x + x + 2.*

In Teach Kids Algebra,

**algebra is fused to arithmetic**, which makes algebra accessible to very young children. Algebra grows out of arithmetic, so

__good arithmetic skills__are essential and reinforced in TKA. Algebra is a tool for reasoning and requires clear thinking and arithmetic knowledge.

The structure and method of mathematics are that

__one idea builds on another and that everything fits together logically__.

__, which should start in 1st grade, is necessary for reasoning and problem solving. Indeed,__

**Automaticity of fundamentals**__strong math skills through practice__are key to the process.

__Chains of reasoning__connect ideas to each other as complexity builds over time. Understanding, at first, is functional and grows slowly.

**When taught well, math teaches kids to think; it makes them smarter.**

## Automate fundamentals Through Practice

*To move forward, kids need to master [automate] fundamentals through practice. *

US kids need to practice to automaticity.

**Math takes lots of practice and a certain amount of memorization. There are no short cuts. Kids get good at arithmetic or algebra only through practice. Fundamentals must be in long-term memory for instant use in problem-solving.**

**There is no substitute for automaticity of factual and procedural background knowledge in arithmetic.**

*Learn skills all the way to automaticity!*National and international tests show our students lag behind. US kids are weak in both factual and procedural knowledge in mathematics.

**Common Core and state standards based on Common Core are below the Asian level.**

In Common Core, the concentration on strategies to do arithmetic reduces the importance of systematic learning and automation of number facts and efficient math procedures, both of which are critical for

**(1)**

**higher-level thinking**(

__Willingham__: long-term memory learning)

**,**

**(2)**

**creativity**(

__Lemov__: practice to automaticity)

**,**and

**(3)**

**Problem-solving**(

__Polya__: prior knowledge).

__Willingham, Lemov, and Polya say the same thing__

**Note**.**:**

__the automaticity of__

__knowledge (factual, procedural, and conceptual) in long-term memory__is needed for higher-order thinking in mathematics.

**Daniel Willingham**, a cognitive scientist, explains, "If you know that

**9 x 7 = 63**, you need not use valuable

__mental space__[working memory] to do that calculation as part of a more complex problem.

**Knowledge of math facts [automaticity] is known to be an important component of competence in algebra and beyond.**" It is important to tax working memory [exercise it].

Furthermore, Willingham says,

**"Students must have both content knowledge and practice using it."**Indeed,

**thinking well**requires knowing facts and procedures stored in long-term memory. It is important for students to make "

**connections across pieces of information**," writes

**Art Markman**(

*Smart Thinking*).

**Financial Knowledge Gap**

Notes:

Notes:

**There is a solid link between income and financial literacy.**

**Today's kids don't know**

**personal finance.**It's not taught in school, but it should be. Financial literacy used to be taught as early as the 4th grade in 1887 when math skills were highly praised and practiced for mastery. "In the absence of basic math skills, financial responsibility is a hollow concept," writes

**William Poundstone**(

*Head in the Cloud: Why Knowing Things Still Matters*). The link is one reason I teach simple and

**compound interest**in prealgebra. One 6th-grade student remarked that she could not save enough money at today's interest rates (savings and checking accounts) to buy a house.

**(Note:**You can have $2,000 in a checking account that earns only

__3 cents interest per month__. Investment alternatives are real estate, the stock market, and others. Concepts such as risk-reward, diversification, and debt need to be taught to increase financial literacy.

**)**After paper-pencil calculations to learn the

**iteration**

**concept of compounding**, the students used scientific calculators and

*guess and check*to find how many years it would take for $20,000 compound annually at 9% to reach $370,395 (convergence). The students refused to give up until they found the solution. "The most powerful force in the universe is compound interest." (Einstein, Gates) "Wealth flows to whoever uses compounding to his or her advantage," writes

**Poundstone**.

*Personal finance should be taught in schools, which is difficult when kids don't know basic arithmetic and algebra or the difference between linear and exponential growth.*

20000(1.09)^x = 370395 The students use guess and check to solve an exponential equation. Incidentally, the exponent x is 33.87 years: $370395.311679229308546010783955...

## Contact ThinkAlgebra

3rd graders in Teach Kids Algebra.

This website is undergoing many changes in Please excuse typos, errors, redundancies, etc.

*LarryT, Founder:**ThinkAlgebra & Teach Kids Algebra**Model Credits:**Hannah, Remi, & kids in my algebra classes***Email LarryT at**__ThinkAlgebra@cox.net__.**Last update: 1-5-16, 3-11-16, 6-1-16, 12-24-16****© 2004-2017 LT, ThinkAlgebra**