PA Coalition for World Class Math

                                         Research, Articles, Links, and More

Links for math groups in the U.S. are here.

Click here to visit the website of our umbrella organization: U.S. Coalition for World Class Math

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                               More Research and Articles:

 Gabriel Sahlgren, of the UK Centre for the Study of Market Reform of Education, has a short book "Real Finnish Lessons" describing his study into the Finnish education system and his findings. PDF is here. Excerpts:
As an evaluator of a progressive school, Professor Scheinin has first-hand experience of this issue in Finland. In that school, children were set mathematics tasks at the beginning of the week, during which they were supposed to work independently or in groups before reporting solutions at the end of it. What were the results?

“Sure, the pupils did a lot of good things – they became very independent and so on”, said Professor Scheinin. “But they were awful at mathematics. I mean shockingly poor – pretty much the worst in the country. Since then, I’ve been cautious in saying ‘out with the old and in with the new’ in regard to pedagogical methods.” (p. 56)

However, as this monograph has highlighted, the story from Finland backs up the increasing amount of evidence, which suggests that pupil-led methods, and less structured schooling environments in general, are harmful for cognitive achievement. Finnish teachers were, for many decades, traditional in their approach, reinforcing a hierarchical educational culture. While difficult to entirely disentangle from the effects of societal changes in general, the move towards less structured methods and authoritative school practices is likely to have had a causal effect, in and of itself, on the recent Finnish decline.

It has been suggested elsewhere that post-industrialisation renders teacher-dominated pedagogy and other authoritative aspects of schooling irrelevant, because teaching methods and school organisation in general must follow the trajectory of society. Today’s society is less about authority and obedience – and more about freedom and independence. Therefore, the argument goes, we must adopt the latter in schools.

Yet as Hannah Arendt pointed out 60 years ago, this is a fallacy. Schools are not supposed to be microcosms of the outside world. They are meant to be institutions that prepare pupils for that world. Pupils are not grown-up citizens and they should not be treated as such. So while society is moving in a direction towards less authority and more independence, this does not mean that education must
follow suit.

Indeed, it could be argued that it becomes even more important that schools retain some authoritative structures to ensure that pupils
accept the institution of schooling. If this is the case, the shift in methods may actually have contributed to declining acceptance of authority in schools rather than vice versa. ...

Schools are fundamentally socialising institutions and teachers have historically acted as authorities laying down the rules for pupil
behaviour. But if teachers take a back seat, there is no authority to internalise – which should be reflected in more unruly behaviour and less acceptance of teachers’ traditional role. After all, if adults do not behave as authorities, why would children view them as such? (p. 64-65)

Elementary School Mathematics Priorities  

Excerpt: The February, 2006, U.S. Department of Education study, The Toolbox Revisited, tells us that 80% of the 1992 U.S. high school graduating class went on to college. Only about half of those students graduated with a bachelor’s degree. The others dropped out. Inadequate preparation for college mathematics was a major contributor to the drop out rate. The foundation for K-12 mathematics is laid in the early years of elementary school. To succeed in college, this foundation must be solid.

K-12 American Students  

Abstract. In September 1989, the United States’ Governors Conference in Charlottesville, Virginia set an ambitious goal by declaring that “By the year 2000, United States students will be first in the world in mathematics and science achievements”. However, recent results of the ‘Programme for International Student Achievement’ and ‘Trends in International Mathematics and Science Study’ indicate that the United States students’ achievements in mathematics are far below world class standards. This paper seeks to discuss issues in an international context  related to the goal of creating world-class high quality mathematics education for all K-12 American students. In particular, the author also shares his reflections and depicts lessons from Singapore’s success story in mathematics education.   

Excerpt: The The single most important result of the Third International Mathematics and Science Study (TIMSS) is that we now know that student performance is directly related to the nature of the curricular expectations. I do not mean the instructional practices. I mean the nature of what it is that children are to learn within schools. (In the U.S., the curricular expectations are usually referred to as standards; in other countries they are known by various names.) After all, what is more central to schooling than those things we, as a society, have chosen to pass on to our children?
"A World Class K-7 Math Curriculum Verified by Outstanding Experimental Research,"  by William Hook  

Excerpt: "A variety of characteristics of participating countries and U.S. states were recorded during the 1995 tests. One of these characteristics was curriculum. A method to quantitatively describe curriculum was devised and applied to the A+ countries, and to participating U.S. states:  

 The U.S. curriculum was found to be, in comparison to the A+ countries:  

  • Not focused (far too many topics, particularly in the lower grades)
  • Highly repetitive (topics introduced too early, too little depth, endlessly repeated)
  • Incoherent (not presented in logical, step-by-step order)
  • Not very demanding (especially in middle school years)

 Curriculum was the only factor found to differ significantly between the A+ countries and the poor performing U.S. states. It was not teachers, not demographics, nor any other non-school factor.  


    Even top students show signs of decline in math - Steve Wilson, Johns Hopkins University

A Johns Hopkins mathematics professor reports that the mathematical prowess of JHU freshman in his Calculus I class has declined dramatically since 1989. Click here to read report.

                                              Wall Street Journal, May 2007

Rising to the Challenge

America’s Math and Science Curriculum Is Key to Future Competitiveness

by Joe Mullich

As America fights to regain its economic footing, there is a rising drumbeat for the country to raise its performance in science and math.

The indications of decline in these areas are widespread: Last year, the U.S. Patent & Trademark Office issued more patents to foreigners than Americans for the first time ever. The two primary sources for graduate students in science and technology at American universities are now China and South Korea. Science scores for fourth- and eighth-grade students in the U.S. have remained flat since 1995, while other countries have soared.

The United States National Academies, an influential advisory organization, issued a blue-ribbon report in 2005, called “Rising Above the Gathering Storm,” warning that America was losing critical ground in math and science skills — “the scientific and technical building blocks of our economy.”

The report traced America’s decline to “a recurring pattern of abundant short-term thinking and insufficient long-term investment.” The mosaic of culprits included: decades of declining or flat spending on research in most physical sciences, mathematics and engineering; dwindling education funding; and aggressive pushes by other countries to improve their math and science education.

Turning this situation around is “key to our future competitiveness,” says Dr. Francis Eberle, executive director of the National Science Teachers Association in Arlington, VA. “I don’t know that we’re going to have a ‘Sputnik moment.’ More likely, we will experience a growing awareness, where people will acknowledge the key role that science and technology has played in the lifestyle we enjoy today.”

Economic Implications

In the last half-decade, the campaign to improve science and math has seen both progress and stagnation. The Trends in International Mathematics and Science Study (TIMSS) 2007, an ongoing project to measure the skills of fourth- and eighth- graders in different countries, shows steady improvement in U.S. mathematics since 1995.

Still, America lags behind many other nations. And U.S. performance on the TIMSS science test has not improved in the past decade.

“Science has almost been eliminated from the K-sixth grade classrooms,” Eberle says. “The focus of the No Child Left Behind Act (which requires schools to administer annual math and language arts tests with the goal of steadily improving performance) has been on literacy and mathematics, and so we have a whole group of students not being adequately prepared for science careers.”

The decline in science and math may have directly affected the nation’s pocketbook. Last year, Eric Hanushek, a Stanford University professor, did a study in which he concluded that raising U.S. test scores in math and science would have a dramatic impact on America’s economy. Hanushek’s study was significant in that it measured quality (improvement in test scores) as opposed to quantity (years of schooling), which has usually been the focus of such studies in the past.

He concluded that raising U.S. test scores to levels of top countries would add two-thirds of a percentage point to the annual growth rate in gross domestic product. Because this applies to the total goods and services that America produces in a year, it has enormous implications for the country’s financial well-being. “The evidence on quality of education in math and science is starting to get people’s attention,” he says.

Other benchmarks are drawing notice as well. For example, the number of engineering degrees awarded in the U.S. has dropped 20 percent since its high point in 1985. China, for example, graduates some 400,000 engineers a year, compared to 70,000 in the U.S.

Rigorous Standards Yield Results

While some people feel outsourcing could resolve some of the shortfall, Don Giddens, dean of engineering at the Georgia Institute of Technology, disputes that notion. “The U.S. advantage is the innovative, free-thinking engineers we produce,” he says. “Some countries emphasize a ‘crank and grind’ engineering education. That’s all right for commodity engineering, but R&D requires a broader thinking that we need to keep at home.”

There are clear indications that improvement can be had. Two states, Minnesota and Massachusetts, have seen huge leaps in science and mathematics performance by putting a rigorous focus on standards and teaching. In 2007, as a result, Massachusetts’ eighth-grade TIMMS science score zoomed to 556, well above the U.S. average of 520. If Massachusetts were a country, it would have had the third best science performance in the world, trailing only Singapore and Chinese Taipei. The United States as a whole ranked only eleventh.

In the same testing, “Minnesota had more than three times the gain than the United States as a whole,” says William Schmidt, a Michigan State University professor who worked on the state’s standards effort. “They have left the U.S. behind.”

Corporate America Steps Up

Many feel it’s imperative for the rest of the U.S. to catch up. “Corporate America can play a powerful role in this,” Schmidt adds. “The public was worried about climate change for a long time, but the green movement didn’t get on the front burner until the business world became involved.”

Indeed, companies are stepping up and wielding a tremendous influence, moving beyond the bully pulpit and going into the trenches. They are running TV commercials designed to raise the standing of science and math careers. They are having their scientists visit classrooms and sponsoring student trips to laboratories. They are funding — and developing — programs to fill gaps in the mathematical education of elementary and middle school teachers.

Last October, for example, Intel committed $120 million over the next decade to stimulate more interest among young people in math and science. The company already runs a host of programs, including the nation’s oldest pre-college science competition, Intel Science Talent Search, whose finalists have gone on to win seven Nobel Prizes.

“It’s essential we do this because math and science form the foundation for innovation,” says Julie Dunkle, U.S. education project manager for Intel. “Fluency in math is needed to understand science, and science creates the innovations that will help solve the challenges we face, such as Swine Flu and global warming. As an innovation company, it makes sense for Intel to get involved and it’s critical to our country’s ability to create a deeper talent pool that the country needs to compete and thrive globally.”

Joe Mullich has received more than two dozen awards for writing about education, technology and other topics for publications including the Los Angeles Times, The Scientist, Men’s Health, and Reader’s Digest.

                                        Calculators and mathematics achievement

Although the National Council of Teachers of Mathematics (NCTM) recommends the integration of calculators into the school mathematics program at all grade levels (NCTM 1989), research on the effect of calculator use on achievement is not definitive. Some studies have concluded that calculator use does not undermine basic skills (Hembree and Dessart 1986, Suydam 1979) and that calculator use has a positive effect on achievement in early grades (B. Smith 1996, Hembree and Dessart 1986.) Critics, however, have pointed to deficiencies in the majority of studies supporting calculator use. Many of these studies were of short duration, lasting only a few weeks, and lacked sufficient controls to equate comparable groups or to screen out other influences on student outcomes (Loveless and Diperna 2000.)

A recent Brookings Institution study (Loveless and Diperna 2000) examining test results from both the National Assessment of Educational Progress (NAEP) and the Third International Mathematics and Science Study (TIMSS) raises additional questions about the influence of calculator use on achievement. For example, in both NAEP and TIMSS, students were asked how often they use calculators in class. On both tests, calculator use is correlated with lower math scores. On the 1996 National NAEP Mathematics Assessment, 4th graders who reported that they used calculators in class every day had the lowest NAEP scores of any response category. Students who reported using calculators only once or twice per month had the highest scores. A similar pattern was evident on 4th-grade TIMSS. Frequent calculator use is negatively correlated with math achievement in several countries. A vast majority of 4th-grade students in the highest scoring nations (Japan, Singapore, and South Korea) report that they never use calculators in math class.

Although Loveless and Diperna acknowledge that these results do not necessarily imply that calculator use results in lower academic achievement (low math skills may actually push individual students to rely on calculators more), their findings suggest that additional, high-quality research on the use of calculators at the elementary level is warranted, particularly because of the equity issues involved. In 1996, black and Hispanic students were about twice as likely as white students to report that they use calculators every day (Loveless and Diperna 2000.)

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