Great article from SFGATE. I’ve posted the article here however I would strongly suggest following the link so you can read the tough love reader comments. Algebra It’s Everywhere on SFGATE.
I’ve come across many articles like this that infers that the U.S. is going to go Hel in a handbag if we don’t get more people to enter math and science careers to compete on the world market!
Algebra – it’s everywhere
Jill Tucker, Chronicle Staff Writer
Monday, August 25, 2008
The very word can twist the stomachs of otherwise well-adjusted adults, dredging up memories of nonsensical X’s and Y’s and a lifelong loathing of math.
For many, the math course was the educational equivalent of castor oil, forced down the throats of teenagers who questioned when they would ever encounter that train leaving Boston at 60 mph.
In July, the state Board of Education decided every eighth-grader must have a healthy dose of algebra – a decision critics attacked as failing to recognize the lack of qualified math teachers and the high failure rate for the middle school students already taking it.
Supporters, however, argued algebra improves critical thinking, is the gateway to college and puts all kids, regardless of income or ethnicity, on the path to a good career.
Lost in the debate was, well, algebra.
“I doubt if the politicians promoting this have any idea what they’re promoting,” said Keith Devlin, Stanford University researcher and mathematics professor, as well as the “Math Guy” on National Public Radio. “Few people know what algebra is.”
Algebra, says Devlin, is a language, a very precise language written in symbols, and it’s everywhere: in nearly all electronic devices, every statistic and each Internet search engine – and, indeed, in every train leaving Boston.
“You can store information using it. You can communicate information using it,” Devlin said. “Google has made billions capitalizing on algebra.”
Yet our schools don’t always do a very good job teaching it, Devlin said. Instead of showing students the possibilities and beauty algebra offers, they ultimately steer frustrated and bored students away from math and the 21st century careers that use it – the opposite of the intended result.
‘We’re turning kids off’
“Most of us who become mathematicians do so not because of our education but in spite of it,” Devlin said. “We’re turning kids off a subject that is useful and incredibly interesting and beautiful if taught correctly.”
Too often, algebra is taught as a set of rules and procedures – the equivalent of teaching a foreign language through vocabulary lists and repetitive conjugation of verbs, the students never understanding they could use the information to order a meal in Madrid or make a friend in China.
In short, the teacher matters. A lot. Just ask Alameda artist Alana Dill.
“I first took algebra in eighth grade from a bilious, creepy teacher who called all the girls ‘hon’ and all the boys ‘son,’ ” said Dill, 46, in an e-mail. “He talked like Foghorn Leghorn. I learned nothing.”
Devlin would like to see “mathematicians in residence” – in the tradition of artists in residence – at middle schools and high schools. They could visit schools, he suggested, and show students the cool side of math – like how an iPod uses algebra to play music.
“At any age, we will take the drudgery as long as we see a reason to do it,” Devlin said.
Algebra, by the dictionary’s definition, is essentially abstract arithmetic, letters and symbols representing relationships between groups, sets, matrices or fields. It’s a way to find a piece to a puzzle using the pieces you already have in place.
It comes in very handy for engineers, financial analysts and sociologists, not to mention World of Warcraft video game players, some of whom use algebraic formulas to decide which weapon is more effective under certain circumstances – perhaps another hook to lure unsuspecting teens into seeing the useful side of algebra.
“It takes the arithmetic you’ve learned and lets you answer questions, not just 5 + 4 = what. It lets you (change the unknown) to 5 + what = 20,” said Brett Wingeier, a biomedical engineer working on brain implants to treat epilepsy.
While that example is simple enough, algebra requires a mental leap from the solid ground of arithmetic into a shifting world of shapes and symbols.
Among the first folks to use algebraic ideas were the Babylonians, who created math puzzles – a 1600 B.C. sudoku, if you will.
Those ancient civilizations did algebra because it was fun.
Former UC Santa Cruz mathematician Paul Lockhart believes today’s schools have killed the fun part.
“In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done,” he wrote in a 2002 essay that traveled the digital world. “I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”
In schools, math is something students are supposed to be afraid of, something that’s supposed to be hard, Lockhart said in a telephone interview from the East Coast, where he now teaches at a private school in Brooklyn.
From art to artillery
Algebra is actually an art, a beautiful leap of the imagination that schools have turned into a field artillery manual, the mathematician said.
Lockhart favors self-discovery in math, letting students explore the hows and the whys themselves, unraveling problems like a fun puzzle rather than learning and solving equations for no apparent reason.
But his vision doesn’t always translate well to the high-stakes realm of standardized testing, which quite literally requires students to solve for X on the eighth-grade exam. That can create a conundrum for time-strapped teachers who must teach the straightforward math skills needed for the state’s multiple-choice test.
“I believe everybody can learn algebra,” said San Francisco schools Superintendent Carlos Garcia. “I’m just not sure everyone can teach algebra so that the kids understand it and make it fun.”
Garcia has some experience with this. While he personally didn’t like algebra as a kid, he aggressively enrolled eighth-graders in algebra when he was the superintendent in Clark County, Nevada. He acknowledges that many students failed it, but they were failing basic math anyway.
A local decision
But he disagreed with California’s mandate, saying it should be a local decision based on resources, including the number of qualified teachers.
The Santa Cruz-based Center for the Future of Teaching and Learning slapped a strongly worded warning label on the state’s new algebra requirement, saying the state doesn’t have nearly enough qualified teachers to do the job.
“Scant attention has been paid to this critical issue, and California’s approach to math instruction still doesn’t add up,” according to the center’s July report on the issue.
About a third of those teaching Algebra I in state middle schools do not have a credential in math, the center found.
That will get worse with the new requirement, said state Superintendent of Public Instruction Jack O’Connell.
“My fear is it’s going to turn kids off and contribute to the dropout rate,” warned O’Connell, who recently estimated that it will cost $3.1 billion to train and recruit teachers while boosting student proficiency in pre-algebra and arithmetic before the requirement goes into effect in 2011.
Many teachers say the middle-schoolers won’t be ready, either. Understanding algebra requires not only a solid foundation of arithmetic (fractions, division and decimals, for example), but also the maturity to focus on abstract concepts.
“Our plea is, ‘Algebra when ready,’ ” said Hank Kepner president of the National Council of Teachers of Mathematics. “We would not want to put an age level on it.”
Recently retired high school algebra teacher David Goldman called the state board’s decision “farcical.”
“Some kids are not ready for algebra in the eighth grade,” said Goldman, who taught at Redwood High School in Larkspur. “We’ve seen over the years if you try to accelerate that, it just doesn’t work. … At Redwood we saw a lot of kids that came in and then had to repeat it again in the ninth grade.”
Teach it over two years
He supports possibly starting algebra in eighth grade, but slowing it down to a two-year course for some.
Last year, 42 percent of the 250,000 eighth-graders – about half the class – who took algebra scored as proficient or above on the state test.
Business leader Jim Lanich, who applauds the state board’s decision, said schools should get students up to speed in the academic standards at each grade level.
Algebra is eighth-grade math, said Lanich, president of California Business for Education Excellence. It’s the job of teachers and state schools to get them there – without spending $3.1 billion on top of the $50 billion the state already spends on its schools.
“The kids are leaving fourth grade now that will be required systemwide to take the eighth-grade Algebra 1 test,” he said. “We have three years to get them to grade level.”
Laptop computer. The computer is just an implementation in electrical circuits of a special form of algebra (called Boolean algebra) invented in the 19th century. Ordinary algebra is used to design and manufacture computers, and is at the heart of how to program them.
Cell phone. A cell phone is a particular kind of computer. An important feature of cell phones is that your phone receives all the signals sent to every cell phone in the region, but only responds to signals sent to your phone. This is achieved by using signal coding systems built on algebra.
Parking cop. Today’s parking enforcement officers may carry equipment connecting them directly to a central vehicle database that registers your parking fine before you get back to the car and see the ticket on the windshield. Without algebra, such a system could not exist.
Hybrid car. Modern cars often come equipped with GPS, a highly sophisticated system that is designed using enormous amounts of mathematics that builds on algebra.
Delivery truck. Large retail chains use mathematical methods to determine the routing and scheduling of their delivery trucks; algebra is fundamental to those methods.
Stoplight. These days, stoplights are centrally controlled by computers, so there is even algebra involved in turning the light from red to green.
IPod. This is a math device in your hand. The iPod stores music using sophisticated mathematics built on algebra. And the iPod shuffle mechanism uses regular school algebra to order your songs randomly.
“Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.” Fran Lebowitz
“Algebra … the intensive study of the last three letters of the alphabet.”
“The fact is that there is nothing as dreamy and poetic, nothing as radical, subversive and psychedelic, as mathematics.” Paul Lockhart, mathematician
“I don’t know anybody who uses algebra. But I’m not hanging out with architects and engineers.” Carlos Garcia, San Francisco Unified School District superintendent
“Algebra was my three best years of high school.” State Superintendent of Public Instruction Jack O’Connell, joking
“Algebra is the gateway to critical thinking, pivotal for success in science, engineering and technology.” Gov. Arnold Schwarzenegger in a July letter to state school board President Theodore Mitchell
In school “I was more interested in solving the mystery of the Maidenform bra than I was in alge-bra, but the teachers got through to me.” Chandler White, 62, insurance claims adjuster, San Francisco
“Algebra definitely set me on a path to study the humanities . … Literature and philosophy hold many complex concepts that lead to better critical thinking.” John Koetzner, 53, community college instructor, Healdsburg
“At the risk of perpetuating the stereotype of librarians … I’d be glad to state, on the record, that algebra is uniquely useless in life, and that the only good number is a call number.” Nadine Walas, 39, librarian, Pacific Heights
“I am 77 years old, a retired priest of the Episcopal Church. I nearly died trying to do algebra in 1946.”
Robert Warren Cromey, San Francisco
“What is always to be hoped is that the instructor will reach the kids’ natural curiosity. Math is actually fun, and it is easy.”
Camden McConnell, 66, senior structural engineer, Oakland
Solve for X
Here are some sample questions from the state’s Algebra I standardized test:
1 Two airplanes left the same airport traveling in opposite directions. If one airplane averages 400 miles per hour and the other airplane averages 250 miles per hour, in how many hours will the distance between the two planes be 1,625 miles?
2 What is the solution for this equation?
|2x-3| = 5
A. x = -4 or x = 4
B. x = -4 or x = 3
C. x = -1 or x = 4
D. x = -1 or x = 3
3 What are the solutions for the quadratic equation x² + 6x = 16?
A. -2, -8
B. -2, 8
C. 2, -8
4 Which quadratic function, when graphed, has x-intercepts of 4 and -3?
Answers: 1-A; 2-C; 3-C; 4-B
Source: California Department of Education
Once upon a time … For more than 4,000 years, people have been using algebra to understand time and the heavens, and to build civilizations. Ever-more-complex technology is the result.
ca. 2000 B.C.
Ancient Babylonians first use algebra in building and astronomy. They construct an accurate calendar and are able to predict eclipses of the sun and moon. They discover what later becomes known as the Pythagorean theorem, and apparently form a knotted rope into a 3,4,5 right triangle to measure out right angles when constructing buildings.
800 B.C.-A.D. 200
The Greeks, Indians and Chinese all independently develop elementary algebra, apparently viewing it more as an intellectual pursuit than something with practical application. Like the Babylonians, however, they do use it in building and astronomy.
The Indians develop the subject further, along with the decimal number system we use today.
Leonardo of Pisa writes a book, “Liber abaci,” describing how the algebraic methods developed in India can be used in business, commerce and trade, for buying and selling, distributing profits, exchanging currencies and the like.
Galileo and others show how to use algebra to understand the world we live in. This is the birth of modern science, and soon thereafter of technology.
It all starts with the basics
From then on, there is a steadily increasing use of algebra – or, more precisely, the sophisticated systems that build on it (calculus, scheduling, inventory control, network theory) to design technologies and create greater efficiencies in business and commerce.
For almost all the applications from the 17th century onward, the mathematics used is more advanced than algebra. But the work builds directly on the algebra learned in school – and, to an outsider, even looks much the same as school algebra, with x’s and y’s, equations and the like.
Just as the child who learns to pick out “Three Blind Mice” on a piano with one finger can build on that to become a great pianist, so too a child who learns algebra can go on and master more complicated, algebra-based math to do all kinds of cool things. In both cases, it’s just a matter of learning how to do more complicated versions of the same thing.
Everyone has to start as a beginner. School algebra is the “Three Blind Mice” of modern science and technology and of many business techniques.
In real life Experts in science, computers, sports – even marijuana – use algebra in everyday work
Brett Wingeier, San Francisco, 34
Biomedical engineer working on brain implants for epilepsy
Uses algebra and geometry to calculate the size of the hole to put in a skull to accommodate an electrode.
Patrick Paulitz, Orangevale, 43
Converts blocks to megabytes, calculates percent increase or decrease in disk space usage.
Chris Conrad, El Cerrito, 55
Court-qualified cannabis expert
Calculates area, mass, bulk, weights, yields and dosages and compares against police findings.
Marcia Benjamin, San Leandro, 51
Calculates a swimmer’s lap pace to swim, for example, a 200-meter freestyle race in 2:28.
Jim Hahn, San Jose, 47
Corporate trainer, quilter
Resizes quilt patterns.
E-mail Jill Tucker at firstname.lastname@example.org.
I’m reposting here in case that site is EVER dismantled. You have no idea how much I cry over all the lost art history and philosophy sites I used for my graduate work.
This stuff is too good to disappear!
I’m a Visual/ Spatial-Naturalistic. Mathematical/Logical fades in and out. Very frustrating!
More than one type of Intelligence
Well developed language ability. Likes to read, write, and speaks with confidence. Verbal strengths often linked with Interpersonal skills
Thinks logically, enjoys puzzles, patterns and intellectual challenges. Tends to be precise and can be uncomfortable with lack of organisation. Often links with Visual/Spacial abilities
Thinks in images, and pictures. likes to paint and draw, can be a day dreamer. Good at reading maps and charts. Sometimes links with Mathematical/Logical
Likes physical movement, touching and acting out. Finds it difficult to sit still. Enjoys hands-on experiences and sports and are skilled at expressing themselves through movement. Often associated with Musical/Rhythmic
Tuned in to sounds and rhythms in the environment, Enjoys music. Likely to play an instrument. Quickly become bored and will create musical distractions (e.g. hums, whistle, taps). Can link with Bodily Kinesthetic
Likes social interaction, and team participation and capable of interpreting moods and temperaments. Easy to get along with. Links strongly with Verbal/Linguistic
Understanding of internal strengths and weakness. Comfortable with being alone. Strong willed, and self-directed, needs time to think and reflect Can link with any other intelligence.
Skilled at recognising and classifying. Connected with the environment. Notices differences and similarities. Can link with any other intelligence
I’m on a math quest for the G.R.E. I always struggled with math, however I’ve stumbled upon a great math site that features different learning styles for teachers to use called Making Sense of Maths.
Here’s a sample of the site:
Different Learning Styles
Making connections between different learning styles can enhance learning by capitalising on the students’ preferred sensory modes.
I am going to use the A.V.K. model as an example,
but other models such as Multiple Intelligences, Myers Briggs, and Bloom’s and Williams’ taxonomies are also useful, and connections can be made between them.
What is A.V.K.?
This model will be a familiar one to most teachers.
Auditory learners make up around 20% of students, and learn best through listening;
Visual learners (40%) learn best through visual representations, and
Kinesthetic learners (40%) learn best through physically touching and doing.
The students’ preferred modes can be recognised through observation, and may be revealed in their speech, for example, “I hear you”, “Oh, I see now”, and “That feels about right”.
Why is this model important?
Traditional teaching methods have over-catered for auditory learners, with teacher talk the most common form of teaching. Students who have a primary preference for visual or kinesthetic learning may not receive concepts in a form they can understand and use.
With the cummulative nature of the mathematics spiral curriculum, students must be helped to make links between learnings, or more knowledge may not necessarily mean more understanding.
Some students are better able to build upon learning received in a form different from the traditional teacher talk.
I was so inspired by the site that I drew a comic of my favorite math teacher who had a different way of teaching math to artists. His name is Russ Bettencourt. If anyone knows where Russ is, please forward this comic to him:)
I picked up a Wonder Woman graphic novel the other day and when I flipped through it, I found a element with a shocking resemblance to my own story in In Between Days.
This issue of my comic was web published in 2007 and featured on Animation Nation