- * ARTICLES, LETTERS, ANNOUNCEMENTS (NATIONAL FOCUS) *
- “The Math Meltdown“
- (a) “Math Teaching That Adds Up” (The Monitor’s View)
- (b) “How Reform Adds Up: Finding a Clear Path Through America’s Math Maze“
- (c) “If This is Math, Then We’re at War“ by Mark Clayton
- (d) “Lessons from Abroad: Plan Better and Delve Deeper“ by Marjorie Coeyman
- (e) “A Proof that Math Opens Doors“ [Interview] by Mark Clayton
- (f) “In Michigan, Talking Your Way to a Solution“ by Mark Clayton
- SAN JOAQUIN VALLEY ANNOUNCEMENTS
* ARTICLES, LETTERS, ANNOUNCEMENTS (NATIONAL FOCUS) *
The 16 May 2000 issue of the Christian Science Monitor has a series of articles pertaining to mathematics education. Excerpts from these articles are found below. Parts 2 and 3 are scheduled to be published on May 23 and May 30 in the CSM.
[From the Web site] DOES MATH MATTER? A growing number of observers say a math deficit among US students threatens economic vitality in a high-tech age. A three-part series on what’s afoot in US classrooms.
(a) “Math Teaching That Adds Up” (The Monitor’s View)
What’s the best way to teach a child math? This simple question doesn’t have a simple answer in an age when schools must teach more than “the basics” to students who face a 21st century that will demand higher levels of reasoning and computational skills.
A debate over math teaching has divided schools and upset parents. It is far more than just a question of using calculators in classrooms as a Monitor series, starting today, reveals.
Rather, the drive to introduce new ways of teaching math is impelled by a need to keep the United States competitive in a technology-driven global economy. It’s also spurred by new theories of how children learn and a desire to ensure that students in poor school districts aren’t short-changed on math skills.
Unlike the “new math” of the Sputnik-era 1960s, when the aim was to produce more scientists and engineers, today’s methods teach relevancy and reasoning. They try to equip students to cope with all the new ways that math comes into our lives, from tax accounting to software.
But one side of the debate warns that students aren’t being taught the simplest math – such as multiplication tables – because teachers stress mainly an understanding of math concepts in “real life” problems. This “experiment” in teaching, opponents warn, still lacks confirmation that it produces math-savvy adults. A delegation of top mathematicians publicly decried the drift away from the rigor of learning basic calculating skills.
One answer to this debate, of course, is to somehow mingle the old and the new ways. But that can be impractical for many teachers and schools, which have tended to adopt complete sets of teaching materials fully steeped in only the new methods.
The bigger issue is whether national educators who are pushing the new math are correct, and whether they must change their methods.
Many schools feel pressure to respond to parents’ concerns that students master the basics and internalize a core vocabulary of thinking in numbers. But they also want to instill an understanding of how math applies to daily life.
The National Council of Teachers of Mathematics moved at least a little way toward an amalgam of old math and new math when it recently revised its influential guidelines for instruction.
This group has long taken flak from critics who feel its latest guidelines (put out in 1989) sent the country spiraling toward “fuzzy math.”
The council, clearly, has heard the critics. The revised guidelines acknowledge the importance of laying an early groundwork in the basics. But will teachers, many of whom have been hewing to the new math for years, readily alter their courses?
The evidence is mounting that students who never master fundamental algorithms, or systematic methods of doing calculations, will lose out in the workplace later on. High school students who have had nothing but “new math” approaches, where answers are often reasoned out in words, are sometimes tripped up by the intense numerical demands in college math.
Consider what’s happened in the Los Angeles Unified School District. It has adhered to the new math for years, and its superintendent and many teachers believe that approach produces better results among the low-income, urban kids who are their main constituency. The state of California, however, is demanding a return to basics. For one thing, the state has moved to limits the use of calculators in classrooms.
The battle is hotly joined in Washington, too. Federal lawmakers have given speeches on how the new math is ruining our youth. The Department of Education drew sharp comment last year when it made math-instruction recommendations that favored the new, conceptual approaches. (The federal recommendations have been questioned because some of the people who helped shape them had professional or financial interests in the programs being evaluated.)
How should all this add up?
A reemphasis on basics is needed. All students should have sound math fundamentals, whether they move on to trigonometry, calculus, and so on – or whether their later math needs are limited to balancing checkbooks and figuring tips.
Having every student go at least as far as high school algebra makes sense for the children and the economy they’ll have to participate in.
While strengthening the basics, however, schools should be flexible, adapting new-style math instruction that addresses students’ abilities and their future needs for math.
Glance at the US economy, and it’s easy to conclude that math skills have never been as crucial to the country’s success.
For many decades, it hasn’t seemed to matter. Americans have freely joked about math insecurities, confident that at least some people had the right stuff to save Apollo 13 or build Microsoft. But recent comparisons that show US students trailing the international competition have rattled confidence. …
“We’re coasting right now,” says Harold Stevenson, a professor of psychology at the University of Michigan in Ann Arbor and an expert in math education. But, “The next decades are going to be ones devoted to science and technology, and if we don’t have that, where are we going to be in 20 years?”
Well behind math powerhouses, critics say. Textbooks being held up as models aren’t from the US – they’re from Singapore. US companies are clamoring for more visas to admit more skilled workers from Asian and European countries…
Americans have long had a love-hate view of math. They are enthralled by math whizzes in movies like “Contact” and “Good Will Hunting,” and enshrine dotcom successes. But they dismiss the number-savvy as geeks, and concede legwork to attain such skill lacks glamour in a society where video games trim attention spans and Barbie chirps that “math is hard.”
Calls to reform math education have been around at least since the 1920s, when schools started to teach math in more broadly applicable ways. In the ’50s, Sputnik spurred alarm – and more change. The pendulum has continued to swing with a fury supporting Bertrand Russell’s observation that “mathematics may be defined as the subject in which we never know what we are talking about….”
The ’60s hosted “new math”; the ’70s swung to “basics.” The late ’80s and ’90s hustled back toward problem-solving.
To other countries, the swings are puzzling. To US parents, they’re infuriating, spurring more “wars” that pit “skills” against “problem-solving” approaches…
Ironically, some innovations under attack are standard parts of strong programs in countries like Japan. That highlights the need for teachers who deeply understand math – and teach it well…
…A grass-roots rebellion is building among parents from Texas to Virginia, upset that their children are scoring poorly on national tests and grabbing a calculator for even simple problems. They’re worried children will be shut out of higher-level math courses and related careers. And they lay the blame squarely with a spate of new math programs now being adopted by schools nationwide.
Both on the Web and in testimony before Congress, the pejorative patter of angry parents lashes out at “rainforest math” and “MTV math.” Some refer to “new-new math,” a twist on the 1960s “new math” that was heavy on concepts and low on computation, and eventually rejected. While there is some evidence the rebellion crosses class lines, the most intense battles are in districts with affluent, well-educated parents who track school work closely…
Ironically, some of the programs most loathed by parents were cited as “exemplary” or “promising” last fall by the United States Department of Education. Many of them were designed to be in sync with National Council of Teachers of Mathematics standards. Typically, they rely heavily on teachers to guide students, and use calculators frequently and as early as first grade. They emphasize exploring solutions to real-life problems in small-group discussions…
The new programs were developed in the 1990s with federal funds. The aim: to stop the slide in US student performance on international math tests with a smarter approach to teaching an oft-dreaded subject.
Some parents, of course, have been pleased with the shift. “I think the new math is a good bridge for my son between the basic skills of elementary school and the higher concepts of high school,” says Susan Prasad, whose sixth-grader attends Kinawa.
Many school officials and front-line educators are enthusiastic as well, arguing that for the first time, more kids are enjoying and understanding math. Instead of a heavy focus on rote learning and a teacher who plays the role of “sage on the stage,” the teacher in newer programs is a “guide on the side.” That means students are getting a deeper conceptual understanding of math, they say.
Barbara Hoevel, the principal at Kinawa, is proud that her middle school was an early adopter of one of the new programs, Connected Mathematics, about three years ago. “When I have veteran teachers tell me for the first time that children understand concepts they’ve never seen children that age understand, then I support them,” Ms. Hoevel says.
Ms. Prasad agrees. “My son is so excited about math, and I see him drawing on his math skills and translating them into the real world,” she says.
But other parents and educators are skeptical that the chosen methods work – or that there was scientific evidence to support their adoption by the DOE or the local school districts. In Okemos, parents have primarily targeted two new programs: “Investigations in Number, Data, and Space” at the elementary level and “Connected Mathematics” at the middle schools.
“I used to be a math teacher,” says Patricia Hagan, mother of three grade-schoolers in Okemos. “My husband and I have done our own research and feel much of what is out there is based on unproven theories. We’d just like to have some unbiased scientific research to back up what’s being taught…
One key problem with Connected Mathematics and other reform programs, many parents say, is that they are too dependent on the teacher. Being “discovery based,” textbooks rarely give examples of how to work out a problem, they complain. Unless the student can recall the teacher’s instruction or took great notes, he or she might not have a clue what to do on a homework problem – and neither might a parent, they say…
For educators, the results of the Third International Mathematics and Science Study were the equivalent of the shot heard ’round the world. While for some countries – particularly top-scoring Singapore, Korea, and Japan – the test results released in 1997 were an affirmation. To the US, the scores were an alarming reminder that much was wrong…
There are no easy answers. In fact, if anything, the TIMSS research has served to debunk a number of facile assumptions about where the US may be stumbling in comparison with others. For instance, TIMSS-sponsored studies show that US math teachers on the average have considerably higher levels of education and work longer hours in the classroom than those in many countries that outperform us.
Math teachers in Japan and Germany generally assign less homework than US math teachers. And Japanese eighth-graders – whose scores soar above those of US eighth-graders – watch on the average about the same amount of TV as do their American peers.
So if toughening teacher requirements, assigning more homework, and turning off the TV are not the main lessons the US needs to learn from abroad, what are they? The US can learn from others in many areas, say math educators, but most point to some key aspects:
Curriculum and lesson development-Compared with those of most other TIMSS nations, US math curricula are often described as “a mile wide and an inch deep”…
Another weak point of US curricula appears to be too much focus on arithmetic over too long a period of time…
Textbooks-…The Singapore texts… are inexpensive and lightweight, with simple illustrations. Their size encourages kids to keep them in their backpacks and tote them home. That’s a virtue not confined to the Singapore texts: While the typical US math textbook is about 700 pages, in most of the other TIMSS nations, math texts were no more than 200 pages.
Insufficient teacher planning time-American teachers spend far more time in the classroom than their counterparts in countries like Japan, China, and Russia, all of which provide more planning periods and time for teachers to improve their knowledge of subject matter. American teachers also have little if any opportunity to collaborate to develop lessons – a common practice in Asian countries.
Expectations-Parents and teachers in the US often don’t expect all children to perform well in math. Many believe that children won’t like the subject – perhaps because that mirrors their own experience. But in Asia and France, that’s not the case
Calculators-Students in US math classes make much more use of calculators than students in most better-performing nations…
Through studying other countries, a fresh perspective is … gained, says Mr. Hiebert, professor of education at the University of Delaware and co-author of the “Teaching Gap.”
“It’s like holding up a mirror and noticing things about yourself that you didn’t notice before. And then you realize, they’re just practices, they’re not written in stone. You can change them.”
(e) “A Proof that Math Opens Doors“ [Interview] by Mark Clayton
Don’t tell Evelyn Boyd Granville that math lovers are nerds. This child of the Great Depression and daughter of a janitor has a mission: neutralize the belief among today’s students that being good at math makes you a social misfit.
“There’s a lot of peer pressure to be cool, to be like the rest of the crowd – and this whole word they’ve invented, ‘nerd,’ didn’t exist in my day, thank goodness,” says Ms. Granville, the first black woman in America to earn a PhD in mathematics, from Yale University in 1949. “You could be great at music at a young age, and nobody looks upon you as weird … do they? We must get beyond this for mathematics. And I think we can”…
Granville, who has taught math for decades to students from college to grade school, is being hailed as a mathematical beacon to a new generation of US students. Last year, she was honored by the National Academy of Sciences. Dow Chemical Co. sent her on a national tour of grade schools to help inspire future mathematicians.
She believes in the need to make math meaningful to students, recommending, for instance, that grade-schoolers be taught the history of math’s impact on society. But her campaign is an uphill battle: Most US students don’t have the math skills of children in other countries…
In 1967, she accepted a professorship at California State University in Los Angeles, where she taught math to teachers.
Today, with “math wars” in full swing, her philosophy doesn’t fit neatly with professional mathematicians – or math educators’ constructivist, or discovery-oriented, approach. Instead, she blends tradition and progress in a way not easily categorized. Granville, for instance, is a product of rigorous, traditional math training. Yet she taught and wrote a book on “new math” – part of a short-lived 1960s movement to diverge from rote learning and teach deeper concepts.
She advocates letting students explore multiple ways of problem solving – emphasizing clever techniques not in the books. She is similarly adamant that math must not be taught as a “series of disconnected, meaningless technical procedures from dull and empty textbooks”…Granville isn’t ready to let current reform off the hook. Calculators in elementary classes should be rare, she says. Even in high school, their regular use can “cripple” the ability to manipulate equations and understand deep interrelationships in math, she says. …She adds that basic addition and multiplication tables must be memorized early. Inability to automatically do “basic algorithms,” make algebra and higher math exceedingly difficult for students, she says…
She and her kids use a textbook from the Connected Mathematics Project, a math-reform program developed at Michigan State University in nearby East Lansing. It emphasizes learning in groups, using calculators, and real-life problems….State test scores seem to back up her faith in the program.
“I love this class,” she says. “The focus is much more on the teacher. It’s critical for them to listen to each other. People misinterpret these classes. They’re not about algorithms, they’re about understanding fractions.”
If you live in Central California, you may want to take advantage of the following opportunities (either as an adjunct instructor or participant). Contact Lori Hamada, Mathematics Coordinator for the Fresno County Office of Education, by June 1 for more information: firstname.lastname@example.org
The three institutes listed below will be held at the UC Center, Shaw Avenue, Fresno. If you do not live close to Fresno, contact Susie Hakansson, Executive Director of the California Mathematics Project, for institutes in your area: 310-825-8814 or email@example.com
= Algebra Institute: 160 hours and $1500 stipend
June 19-30 (8 a.m.-5 p.m.) + 5 follow-up Saturdays throughout the school year
= Mathematical Models with Algebra Applications I/II: 120 hours and $1000 stipend
June 19-30 (8:30-12:30 and/or 1:30-5:30) + 5 follow-up Saturdays throughout the school year for each course
AB 1331 (9 Fresno County districts; to be held at the UC Center, Fresno)
= Cohort I: July 24-27, October 27-28, January 30, February 27
= Cohort II: July 31-August 3, November 3-4, February 6, March 6
(AB 1331 professional development program) Trainer of Trainers workshops (both will be held on 12-16 June 2000; 9 a.m. – 4 p.m.):
= Grades 4-7 (will be held at the Tulare County Office of Education)
= Algebra (will be held at the Fresno County Office of Education)
Sessions will be held at the Fresno County Office of Education
= Course I, Course II, Algebra I: July 25-27 + 5-6 follow-up days throughout the year
= Geometry, Algebra II, Math Analysis: August 1-3 + 5 follow-up days throughout the year
(Note: CPM Course I and II cover the California Mathematics Content Standards for grades 6 and 7. Teachers whose schools have adopted other textbook series will find the workshops useful in providing ideas for teaching middle/high school mathematics concepts. Student teachers may attend free of charge.)
Applications for mathematics tutors (12:30 – 2:30 daily, June-July) are being accepted now.
COMET is an online newsletter that seeks to provide timely information in a digest format about state (California) and national news, articles, events, opportunities, and web resources related to mathematics education. Information from a variety of print and online sources is compiled and distributed via COMET approximately once a week during the academic year. The target audience includes California PreK-12 teachers of mathematics and school/district administrators, as well as university faculty throughout the nation who are interested in issues related to mathematics education (with a focus on California news). Because COMET is based at California State University, Fresno, mathematics education opportunities in Central California are also included.