**"In education, you increase differences..."**

Richard Feynman

**6-26-17 Notice:**ThinkAlgebra is undergoing major changes. Some of the content in CommonCore, FirstGrade, Snaps, and the Main (Index) page has been deleted. Expect more content to disappear. Also deleted were these pages: TKA and CognitiveScience.

*Click*

**Memory & Learning**

"

**To learn something is to remember it.**" If you can't instantly recall 6 x 7 = 42, then you haven't learned it..

At odds with the champions of discovery learning and other minimal guidance instructional methods,

**active teacher guidance during instruction**, not group work, should be the primary approach in our classrooms; however, the curriculum taught explicitly via worked examples needs to be world-class and properly sequenced. Identify**30%**of traditional mathematics that will have a**70% impact on achievement**, then allocate 70% of class time on the practice and review of the 30% for mastery emphasizing that**learning is remembering**from long-term memory.*The 30% includes the memorization of single-digit number facts and learning the standard algorithms from the get go.***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% of incoming students (Data: Pima Community College 2014).

**Note1:**Common Core and state standards based on Common Core are often interpreted through the lens of reform math.

**Note2:**

**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."**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**.**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 achievement)!**

**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

**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.

**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.**

**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.

**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.*

*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*).

## 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: 6-26-17****© 2004-2017 LT, ThinkAlgebra**