Chaitanya Jyothi Museum Opening, 2000

RAMANAM
In nomine Patris, et Filii, et Spiritus Sancti.  Amen.

Countrymen,

ORBIS NON SUFFICIT
SOLUS DEUS SUFFICIT

Thoughts responding to this article in the Seattle Times, which is reproduced following these thoughts:

The math approach changes with generations of teachers and administrators and their teachers in the schools of education. Basically, fads. Names change but the contents and motivations are the same. In the 70s, the conceptual method of today was called “New Math” and the computational method (which was in vogue during my primary and secondary education years) was called “Old Math.” Very imaginative nomenclature. 🙂

The oscillation, about every 30 years ( = every generation of teachers/administrators and their teachers), keeps up and probably always will. Usually takes a decade for the new iteration, with new name, of the previous style to be standardized. And then the cycle starts again toward the last style, etc, etc, and that just keeps going.

The driver is the desire to stay ahead of the rest of the world technologically. Always that is the driver. This generation says the conceptual approach is best. The next, thinking the computational approach is new and the best thing since sliced bread, gets it in their brain that the computational approach is best for achieving the constant goal of technological superiority.

Those are the only two approaches possible and so the oscillation is between only them, sometimes with “new” iterations but never anything that has not been done before by an earlier generation.

I did not care for the new math so much from what I saw and so we used old/computational math for homeschooling our offspring, with some new/conceptual math thrown in.

The classical name for new/conceptual math is — are you ready? — Algebra! In homeschooling I stressed Algebra, and rightly, because it makes one think and, in mathematical terms, factor.

The conceptual math mentioned in this article is factoring, a corner stone of Algebra and beyond.

The fact is that the goal of technological superiority has been maintained and even increased through the oscillations of styles of teaching math. That is because there are certain procedures that must be accomplished by mathematics and, regardless of the teaching style, those procedures must be learned and mastered.

The degree of learning and mastering aimed at, segregated by age group, the number and character of people intended to have a high degree of both, the earliest efficient moments to introduce the constellations of mathematical study and the overall purpose of mathematical learning are the significant questions, not the question of the style of teaching/learning math. Really any style is fine as is shown by the goal of technological superiority having been consistently achieved and even over-achieved.

Foreigners filling our universities are better at computation than our students are. But they are coming to our universities, not theirs or not theirs preferably. Why? Because here they are not or not so overtly put through schools as their first steps on the treadmills their governments, parents, villages, families and business corporations have planned for their lives.

The alarming phenomenon for governments, parents, and business corporations in the United States is the lowering of the degree of mathematical proficiency intended generally and the lowering of the intended number of highly proficient practitioners of the art specifically. That phenomenon, not the style of teaching math, drives the alarm now over conceptual math and earlier over computational math. The text books of both kinds always will be there, but the number of people who know about them, can use them and can benefit from them is diminishing.

That is the superficial worry. The depth worry is that on account of that phenomenon the goal of technological superiority cannot remain achievable. The thought of not being able to achieve that goal terrifies Americans. Americans are born and bred to nominalism and its pan-optic implementation as positivistic science.

Personally I expect the goal to be achieved overall but with a lot of Americanized immigrants forming the pool of those at the top of the degrees of mathematical proficiency.

Not a majority but a lot. It takes about four generations for immigrants to become Americanized to the point that they have intellectual freedom built into them. But it happens. And they want it to happen. Liberty is an irresistible force and sometimes intoxicant, which is not good, including for liberty.

The genuinely significant question is whether positivistic science can — leaving aside the question of whether it will — indefinitely sustain the technological superiority of a national sovereignty, the United States of America. I think not. It cannot — and by implication will not — sustain technological superiority because its genius is to particulate, to separate, to dis-tinguish.

A gestalt, an indivisible whole is required to support the activities of dissemblers. Therefore, if the United States of America continues to exist, the primary reason will be her spiritual creativity and the secondary reason her technological creativity. If she is merely technologically creative, she cannot resist the hammer blows of enemies, regardless of their moral condition, and she will not continue.

I expect the United States of America to continue, and for the reason just mentioned.

———

New-math curriculum stirs passions among Bellevue parents, teachers
By Rachel Tuinstra
Seattle Times Eastside bureau
12 July 2007

SIDE BAR:

Conceptual math

This is a fifth-grade math question from the textbook “Investigations,” which deals with number sense and getting students to look at different strategies to solve a problem. The teacher would guide students to think of “sensible” ways to approach this multiplication problem:
Choose any two of these as a first step to complete 14 x 9 =
A. Start by solving 10 x 9 =
B. Start by solving 7 x 9 =
C. Start by solving 14 x 10 =

Students are asked to break the question into numbers that are easier to multiply. For instance, they could solve 10 x 9 = 90, and 4 x 9 = 36. Then they would add both sums together: 90 2 36 = 126. (Alternatively, they could start with 7 x 9 and then multiply the answer by 2, or start with 14 x 10 and then subtract 14.)

Computational math

This is a fifth-grade math problem from a Singapore Math textbook:
Solve: 492 x 98 =

The Singapore curriculum introduces multiplication problems in the second grade. The materials teach different strategies for doing these problems, such as memorizing multiplication tables and breaking problems down into smaller numbers. By fifth grade, the materials would assume students have mastered these skills, and would be able to multiply complex numbers.

ARTICLE:

Summer weekdays start with a reading and math exercise at the Killeen household in the Bellevue School District.

Kira, 8, and Nate, 10, work through multiplication problems in a textbook filled with pages of equations that they solve using conventional computations. It’s the kind of math study most school districts have steadily moved away from. Sheila Killeen and other parents say that shift is a mistake.

Deb Carmichael, a mother of three children who attend nearby Lake Washington schools, sees her children learning math in a whole different way — and enjoying and understanding it better than she ever did. This kind of math, which has taken hold in most Eastside classrooms, focuses more on understanding the problems and less on rote memorization of formulas or algorithms.

Educators and parents say it’s a debate between conceptual vs. computational math.

It’s a battle centered around curriculum, teaching materials and textbooks with the question on everyone’s mind: What is the best way for students to learn math?

The debate has spurred Eastside parents to sign petitions and lobby district officials for changes; some even have decided to run for school board.

What most students are learning in Eastside classrooms and across the nation is known as “conceptual” math, sometimes called new math, or what Killeen and other parents call “fuzzy” math.

In elementary grades, it focuses more on the “why,” not just the “how.” Students are asked to explain what the numbers mean, not just what the correct answer is. They are shown different ways to do the same problem and are encouraged to find their own methods.

But some parents say this method is shortchanging children, leaving them without a solid foundation in basic math concepts.

Parents statewide have banded together in a group called “Where’s the Math?” that advocates a more straightforward or traditional math curriculum — often called “computational” math.

Computational math focuses on how to do a math problem correctly and efficiently, and may include more practice and drills for basic math facts.

The group regularly e-mails a newsletter to about 1,600 parents and teachers, said Julie Wright, co-founder of “Where’s the Math?”

Three Eastside parents are seeking school-board seats as a way to better advocate a switch to computational math. In the Bellevue district, Killeen and Michael Murphy, a financial analyst for Boeing, are both running for the Bellevue School Board on a “Where’s the Math?” platform.

And in the Lake Washington School District, Chris Carlson decided to run for the School Board after watching his son struggle through the conceptual-math curriculum.

In Lake Washington, a group of “Where’s the Math?” parents submitted a petition with more than 200 signatures to the district’s new superintendent, Chip Kimball, asking him to replace the district’s math curriculum.

In the Northshore School District, parents met with district officials in April about concerns about how their children were learning math. Starting in the fall, Northshore plans to offer workshops so parents can better understand the curriculum and help their children with homework, said Susan Stoltzfus, district spokeswoman.

Conflicting reports

So far, the math battle has proved to be emotional and contentious.

Some teachers and parents who endured endless flash cards and drills to memorize math facts say the conceptual curriculum is more balanced and interesting. Parents say their children are doing math problems in elementary school that they couldn’t tackle until junior high or high school. Teachers say their students are excelling in math.

“It makes higher math more accessible to them,” said Zandria Hopper, a fifth-grade teacher at Elizabeth Blackwell Elementary School in Sammamish. “They are pressed to justify and reason from kindergarten on.”

But other parents tell a different story. They talk of their children coming home with math workbooks that include lots of word problems asking students to explain different ways to solve them, but very little math. They say their children aren’t learning the basic building blocks of math.

A nationwide problem

Math curriculum is also on the minds of State Board of Education members. The board is in the beginning stages of a major math renovation. The math panel, along with a consultant, is expected to recommend changes by the end of August.

“Washington is not alone in this problem,” said Thomas Shapely, spokesman for the state Office of Superintendent of Public Instruction. “Math is a problem nationwide. No one is doing super-well in math.”

Seattle schools opted for a compromise. It recently approved a new math curriculum, using “Everyday Math” as its primary curriculum and “Singapore Math” — which takes a more computational approach — for supplemental teaching material.

Issaquah School District also recently approved the use of Everyday Math for its elementary classrooms.

The materials look very different on the surface, said Rosalind Wise, K-12 mathematics-program manager for Seattle Public Schools. “Everyday Math” is aligned to current state standards, and Wise believes it encourages both conceptual thinking and algorithmic problem solving. The district is using “Singapore Math” materials to give students a different approach to math, Wise said.

” ‘Singapore’ starts off procedurally: ‘Follow the rule,’ ” Wise said. “But it leads kids to a deeper understanding of mathematics. Both styles approach math differently, but they both get at the same procedural knowledge.”

There is more common ground between the two sides of the math wars than people want to admit, said Gini Stimpson, longtime educator and adjunct faculty for the University of Washington.

“We need to have both conceptual understanding and computational fluency,” said Wright. “There’s probably more that both sides agree on than we disagree on.”

Rachel Tuinstra: 206-515-5637 or rtuinstra@seattletimes.com
Copyright © 2007 The Seattle Times Company

Update 1: Updates to Department of Education and Department of Justice Guidance on Title VI

AUM NAMAH SHIVAYA