For Common Core Inquirers, Columbus OH 4 9 2017

COMMON CORE’S REJECTION OF TRADITIONAL MATHEMATICS,

AND WHAT WE NEED INSTEAD

Dr. Stan Hartzler     HartzlerSJ@aol.com

www.classappcogpsych.com      Columbus, OH   4/09/2014

 

WHAT IS HAPPENING ON THE SURFACE?

I address first the Common Core mathematics assessments.  At the on-line PARCC site, I found examples so complex (and often so advanced) that they constitute a waste of time and money.

At Grade 4, the first sample item [handout] from CTB McGraw Hill shows an 11-by-8 grid, that supposedly models (or just represents) full bags of clams.  With effort, I realized that the squares on the grid actually represent the individual clams, not the bags.  The vertical columns, which share vertical borders with each other, represent the bags.  A better model would have the columns separated by at least a millimeter of space.  There are other issues with this example.

The second sample item asks the student to write three equations for which the sum is five-sixths.  Getting past the strange idea that an equation has a sum, a confusion of correct answers comes to mind, and will for any student successfully schooled in basics.

Item Three might be appropriate if Common Core had emphasized automation of arithmetic fact recall.  A useless horizontal line above the student’s answer space provides distraction.  An accompanying statement (page 26) asserts that each example shown aligns to a single Common Core Standard.  But the Item Three example aligns to two Common Core standards; this discrepancy is admitted to in the accompanying statement.

Other examples from other sources are likewise bad and often vague.

WHAT IS HAPPENING BEHIND THE CURTAIN?

From previous experience with testing and curriculum schemes, it is not hard to ascertain what Common Core people are doing.  They pretend to offer, at a price, access to the power of learning, but then withhold that learning and hoard the power.

They first create a national panic, with scary content jargon, with premature placement of difficult topics and exotic examples, and with reminders that we’re behind other countries. Never mind that our students fell behind because of previous worthless but expensive response to the last panic attack.

Second, with panic and jargon in place, Common Core people dumb down essential content in early grades, claiming to promote readiness and understanding.  I will return to the issue of content weakness shortly.

Third, the knowledge hoarders develop reassuring and foggy themes, such as real-world modernization and technological innovation.  The fog will help hide or excuse the dumbing down of basic curriculum content.

We see the basis of this garbage: insecure human nature.  Insecurity explains why people posing as caring saints want to hurt children.  Insecurity helps us see how we may end such schemes, if, Lord willing, we ever do.

The dumbing down of elementary mathematics content should be our greatest concern.  Stanford professor James Milgram has expressed valid concerns emphasizing high school content issues. But even if the final Common Core State Standards address Dr. Milgram’s concerns, students will come through elementary Common Core mathematics with inadequate arithmetic foundation, making upper-grade and high school experience difficult and sterile.

A proper elementary foundation begins with number, including counting forward and backward by ones, then by twos, threes, fours, and fives, and fluent recall of arithmetic facts.  Common Core people may claim that fluent arithmetic fact recall is what they intend by their vague language.  But without clear statements, the standards are open to abuse by publishers.

Then one of the most dangerous goals of the National Council of Teachers of Mathematics will be realized.  The original 1987 draft of NCTM’s Curriculum Standards proposed delay of fluent recall of easy addition facts until second grade.  (When I protested, the goal was improved.)

We know these things about fluent recall of arithmetic facts [handout]:

A) Fluent recall of arithmetic facts can be attained by simply reading a set of fact statements aloud each day, and in first grade, both for addition and multiplication.

B) Fluent recall of arithmetic facts enables strong understanding later.

C) Fluent recall of arithmetic facts makes higher mathematics easier to develop and master.

So why does Common Core call for delay?  Also, why are the elementary mathematics vocabulary lists so weak?  Also,

• Why no telling time on a clock face to the nearest minute in first grade?
• Why delay identifying coins and their values?
• Why delay learning of traditional arithmetic processes, all setting the stage for algebra?
• Why make arithmetic processes complicated and pointless?
• Is pencil-paper work expected? Or will schools cave to premature calculator use?
• Where do students learn to verify results without a calculator?
• Where does serious reading and writing numbers begin — thousands, millions, etc.?

Without these topical foundations, students are denied participation in daily use of arithmetic.

Remember the name: National Council of Teachers of Mathematics.  Those of you who once had the International Reading Association and the National Education Association on your radar, make room for another target.  The National Council of Teachers of Mathematics has long been subversively peddling junk philosophies and practices, and undermining effective strategies.

One of the worst of the junk has been the impossible quest for magic learning approaches that will cement an idea in a student’s mind right away.  Cognitive psychologists, who scientifically study how people learn, recall, and apply, know that each new lesson is but a first draft, and that this first draft is efficiently tidied up in subsequent days, after sleep has provided natural  digestion of learning.

 

WHAT SHOULD BE HAPPENING?

As to methodology, why is there no mention of ongoing review in Common Core?

ONGOING REVIEW:  Imagine your basketball coach saying, “OK, team, Monday night’s practice will be only dribbling.  Tuesday night’s practice will be only free throws — no dribbling.  Wednesday’s practice will be only three-point shots — no dribbling or free throws.  Thursday’s practice will be only in-bounds plays.  Then you’ll put it all together in Friday’s game.”

No successful coach of athletics or director of music or theater would do anything so ridiculous.  With good coaching, each day’s practice is mostly cumulative review, with some time set aside for moving some aspect to a new level.

Yet the ridiculous, fragmented approach is how most people in the United States learned mathematics, and, consequently, why we have such national illiteracy and phobia regarding mathematics.

In the Oklahoma City Public Schools in the early 1980’s, students given a daily exercise salad of one add, and one subtract, and one multiply, and one divide quickly climbed from well below to well above the national average on the California Achievement Test.  These were mostly ghetto minority students.  They weren’t given equality.  They were given solid opportunity, and confidence for conquering more mountains.

Why are such strategies ignored?  Who are these perpetrators who instead use panic to destroy opportunity?

 

WHO IS MAKING MALICIOUS MATHEMATICS?

Years of investigating the motives of phony reform have shown many motives, all born of human insecurity:

• Secular humanism, using schools K-college to hide the inspiring beauty of mathematics, helping prompt atheism.  For example, John Dewey.
• Racism.  When schools fail, children are left to depend on family, leaving those with weak backgrounds without bootstraps.  Jim Crow laws are gone, but the insecure prejudice behind those laws is sadly still there.
• Corrupt political power, maintaining a fearful welfare population, begging for more tax money while insuring waste.
• Social control, conditioning mobs to bend to popular culture, peer opinions, and group-think.  (Bill Ayres pushing the Stalinist Vygotsky.)
• Job status, pay, and security, as mathematicians, engineers, and statisticians limiting entry to their professions.
• Self-preservation, as the National Council of Teachers of Mathematics, in many ways influencing creation of Common Core and Texas CSCOPE.
• Profit, by marketing faddish, worthless lesson materials, sustaining need.
• Sedition, weakening national defense and invention-driven economy.
• Higher education tuition grubbers, through uncredited remedial courses.

 

WHAT IS HAPPENING WITH SECONDARY MATHEMATICS?

To the secondary issues listed by Professor Milgram, I will add the list found in the handout [p. 4], and also two critical themes in algebra and geometry missing in Common Core.

The missing algebra theme is inductive thinking from arithmetic.  For example, if common denominators are needed to add arithmetic fractions, common denominators are also needed in adding algebra fractions.

Algebra use of exponents and coefficients is usually confusing.  Well-grounded students handle such difficulties through inductive generalization.

The missing geometry theme is deductive structure.  Geometry structure moves from undefined terms to definitions, to postulates, with theorem proofs based on all of the above and on previously established theorems.

Such structure is important to a student designing a persuasive speech or an argumentative essay for language arts or social science.  Citizens may use persuasive structure to write civic improvement grants, to win out over other equally qualified but less persuasive applicants.  (Pre-law)

A missing and helpful theme common to all mathematics and most other disciplines as well, is generalization and discrimination, employed for classification and relationship, very helpful for organizing the giant pile of geometry vocabulary.  Classification and hierarchical ordering are inborn impulses.  These and sequential thought need exercise in core subjects.  See www.classappcogpsych.com for examples.

The classic Tower of Hanoi puzzle help students develop sequential thinking while having fun.  No such opportunities are suggested in Common Core mathematics.

Much more is missing.  But equally disturbing is the presence of general sloppiness and wrong answers in example problems.

The vague wording of many Common Core Standards is alarming. Publishers may claim alignment, but supply weakness:   The student will  “work with”  “understand”  “reason with”  “gain familiarity” “develop understanding”  “investigate”  “know”  “rewrite”  “experiment with”  “interpret” (instead of identify).

 

WHAT DIFFERENCE DOES THIS MAKE?

      Life or death for students, for community economies, for the USA.

    “A NATION AT RISK” REPORTED IT RIGHT: “AN ACT OF WAR”    

Quality mathematics programs enhance student enjoyment of these:

• Freedom of opportunity in life after high school.
• Confidence, for creativity and invention, driving economy ever upward.
• Inspiration and awe concerning the origins of the fantastic order and beauty of mathematics, and of nature.
• Confidence for independent thought about faith, government, self, purpose, and relationships.
• Engagement in endless, inexpensive recreational opportunities.

On the other hand, poor programs intensify student insecurity, leading to:

• Discouragement: giving up on themselves, and giving in to math myths, peer pressure, and popular culture.
• Disruption: looking for creative ways to use their brains in class — disruption, bullying, annoying. (Self-propelled lawn mowers)
• Distraction: seeking destructive excitement outside of school in high-risk behavior (drugs, sex, gangs, crime, curfew violations)
• Dropping out of school.
• Despairing of any meaningful purpose for life. Life?  Or death?  I bitterly recall one manipulator telling a semi-literate young lady at a ghetto high school: “You’re only good for one thing!”

With the negatives forces and consequences in mind, we must ask Bill Gates and David Coleman and Bill Ayers, and many others, including the Department of Education, the POTUS, and the National Council of Teachers of Mathematics, why?  AN ACT OF WAR.  “Woe to the person through whom the stumbling blocks come…”

If these vague Common Core standards are the blueprints of our future,

• Our children will suffer.
• Publishers claiming alignment will produce shoddy materials.
• Our nation will weaken beyond repair
• We will see more of this pattern of panic, control, and extortion.

VII.  WHAT DO WE NEED?

1. Teacher Education scholarships for those of strong academic potential, to diminish the current crop of sheepish, go-along teachers.
2. Teacher certification exams reflecting good common-sense learning principles and influence of cognitive psychology, not theory. Not Piaget.
3. New national organization for mathematics education with funds for press agency
4. Pre-engineering content in secondary courses, with ongoing review.
5. Greater participation in interscholastic mathematics competitions
6. Resistance to clamor about changes in how children think, changing needs in the workplace for mathematics, or integration of technology for technology’s sake
7. Maximized local control and free-market curriculum
8. Children raised to be spiritually-secure leaders of tomorrow
9. Prayer for spiritual growth, security, salvation, and forgiveness for all mankind, especially for our fellow citizens, most especially for leaders.
10. Common sense:

• Knowledge is power.
• Sharing knowledge is sharing power and opportunity.
• Denial of learning opportunity is absolutely a Civil Rights issue, and a symptom of rampant personal insecurity in our society.

Those with spiritual security must share knowledge and its power.

Among the most easily ignored common-sense principles of learning are these:

•           Time causes forgetting, or extinction.  Even though I taught Simon & Garfunkel’s song, “Sounds of Silence”, over several years in the 1970’s, I struggle now to recall those lyrics.  Time causes forgetting.
•           Further learning causes confusion, or interference.  Learning the next Simon and Garfunkel song meant more practice on the “Sounds of Silence”; else, I would get the songs confused.  Further learning causes confusion.
•           Ongoing review (such as in the athletic coaches’ practices & Saxon) turns forgetting into recall power, and turns confusion into conceptual understanding.  And while vouchers are good, significant gains have been made in public schools with patient use of common-sense ongoing review.

WHERE MAY WE FIND INSPIRATION?

•           In finding for the plaintiffs in Brown vs. Board of Education, the Supreme Court of the United States stated that “Education in public schools is a right which must be made available to all on equal terms.”
•           As with Brown vs. Board of Education, we are faced with civil rights and human rights violations, the core education issue of life, liberty, and the pursuit of happiness, a core issue of generating income for supporting churches and missions, and principled political candidates.
•           Only look at North Dallas High School in the 1980’s and 1990’s to see what can be accomplished with these simple, common-sense principles applied in mathematics classes of disadvantaged students.  The story of the school board’s removal of the Saxon mathematics books, over teacher protests, was covered by 60 Minutes.  A year later, Newsweek told how the teachers were still using the Saxon material secretly.  Nikki Hayes’ biography of John Saxon tells the whole story.
•             I have only wrath for such destructive politics, forcing students into victim situations and attitudes.  We are faced with a complex mess demanding decisive action by true leaders.  At North Dallas High School and elsewhere, disadvantaged students were given more than empty hope and negative change.  Until the Dallas ISD administration took it away, North Dallas High school students saw empty hope and negative change replaced by learning, confidence, and scholarship opportunities, the education envisioned by the majority opinion in Brown vs. Board of Education. 

Unlike deprived Common Core students, and most other students over recent generations, whose frustration is still my daytime and nighttime pain, the North Dallas students could sail though algebra homework, with a song from their ancestors’ time ringing from the same skies that gave Brown the victory over the Board of Education:

    Oh, Freedom – –  Oh, Freedom  – –  Oh, Freedom over me      And before I’d be a slave, I’ll be buried in my grave              And go home to my Lord, and be free. 

Mathematics learning issues are issues of Judeo-Christian faith — naked, and you clothed me; hungry, and you fed me; discouraged, and you gave me a way out.  “Inasmuch as ye have done it unto the least of these, my brethren, ye have done it unto Me.”

These issues are civil rights issues as well.  The degrading Jim Crow laws once told some people that they were inferior.  These laws are gone, but the human insecurity prompting such degradation is not.

Jim Crow laws have been replaced by mathematics classes devoid of clear direct instruction, empty of the efficient Saxon exercise structure, and bereft of helpful assessments.  This time, the targets for degradation are children of every race, faith, and background short of extreme privilege.

Mathematics classes taught per the recommendations of Common Core and [handout] the National Council of Teachers of Mathematics will bind the minds and spirits of today’s children more firmly and destructively than the coal-mine company store bound the incomes of the immigrant miners, binding more firmly and destructively than the iron chains bound the hands and feet of the slaves of early America.

A NATION AT RISK, AN ACT OF WAR.

•           Where are the civil rights leaders?  Many are cashing in on white guilt and ongoing victim politics, which would disappear with programs enjoyed by students in Oklahoma City and North Dallas High School.  Without the National Council of Teachers of Mathematics and Common Core to perpetuate victim populations, such so-called leaders would be forced to consider the spiritual motivation and the productive and unifying principles eloquently expressed by  Dr. King and his contemporaries.
•           We may never be free at last, free at last, from the insecurity that drives degrading curriculum.  We can take steps to diminish the power of those who hoard learning.  Let us ask for God’s help, to seek the Lord’s will, to know the Lord’s will, to do the Lord’s will, humbly working for His honor and glory.