Teaching Problem Solving Skills in Math and Science, Part 1
September 08, 2011
There has been a lot of discussion about the American education system in the news recently. It seems that everyone has a favorite approach they would like to implement. If I were to select an approach, it would be a problem solving approach. Present children with problems then teach them how to go about solving them and I think that you would find them flocking to math and science rather than fleeing from them. Apparently Sol Garfunkel, executive director of the Consortium for Mathematics and Its Applications, and David Mumford, an emeritus professor of mathematics at Brown, have similar feelings. They write, “It is through real-life applications that mathematics emerged in the past, has flourished for centuries and connects to our culture now.” [“How to Fix Our Math Education,” New York Times, 25 August 2011] They assert that the current educational approach “is based on the assumption that there is a single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers. This assumption is wrong.” They explain:
“The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact. Today, American high schools offer a sequence of algebra, geometry, more algebra, pre-calculus and calculus (or a ‘reform’ version in which these topics are interwoven). This has been codified by the Common Core State Standards, recently adopted by more than 40 states. This highly abstract curriculum is simply not the best way to prepare a vast majority of high school students for life. For instance, how often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a ‘group of transformations’ or a ‘complex number’? Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood. A math curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching ‘pure’ math, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations.”
For the so-called mathematically challenged, the world of math can be a scary place. Even students who aren’t challenged can find the subject too esoteric to be of much interest. Garfunkel and Mumford believe that by making the subject more relevant you can also make it more interesting; and, hence, you can draw many more students into math and science. They continue:
“Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers. Science and math were originally discovered together, and they are best learned together now. … We believe that studying applied math … provides both useable knowledge and abstract skills.”
Jim Simons, a mathematician and retired founder of Renaissance Technologies, reminds us that even if we get the curriculum correct, we still need talented instructors to teach it. “There is no substitute,” he writes, “for a gifted teacher who knows and loves his or her subject.” In the areas of math and science, however, he believes that the most gifted people don’t go into teaching but look for employment in areas where the remuneration is greater. As a result, he insists, “Short of repealing the law of supply and demand, the normal workings of our public education establishment cannot solve the problem.” Simons, however, hasn’t thrown up his hands in defeat. He writes, “Even with [facing today’s] formidable obstacles, there is a straightforward solution.” [“Drawing our best math and science minds into the classroom,” Washington Post, 8 November 2010] He explains:
“Six years ago a group of us established a pilot program to attract and retain highly qualified, subject-knowledgeable mathematics teachers for the New York public school system. By supplying scholarship aid where required, providing meaningful stipends to supplement salaries for new and experienced teachers, and convening professional seminars and workshops, Math for America has created more than 300 outstanding teachers in New York. … Affiliates are operating in Los Angeles, San Diego and the District, with Boston, San Francisco and Salt Lake City in the works. This initiative, financed primarily by private philanthropy, is a drop in the bucket compared with what is needed.”
In this day and age, when you start talking about money and government, there is no such thing as “a straightforward solution.” Simons, however, believes that federal assistance is absolutely essential to make the program work. He claims that “implemented intelligently and at sufficient scale” programs like the one in New York “could go a long way toward righting our debilitating national education imbalance.” He offers two specific recommendations:
“First is a scholarship program to encourage college students majoring in math, science and engineering to simultaneously prepare for careers teaching these subjects. Few of these bright folks even consider secondary school teaching. But entering the profession is one thing; staying in it is another. The second recommendation, a National Math/Science Master Teacher Corps, addresses the heart of the issue, the need to make the profession more attractive. … During their five-year renewable terms, members would receive annual federal stipends boosting their regular salaries roughly 25 percent, participate in corps activities, and act as leaders in their departments and schools. … These able, knowledgeable individuals would inspire students and colleagues, and at maximum size this transformational program would cost roughly $2 billion per year. America could make no better investment.”
If Simons really wants to see his program implemented, he should consider public/private partnerships that involve industrial sectors desperately seeking people with math and science skills. Visionary companies know that without the right curricula, the right teachers, and sufficient students, they will continue to suffer skill shortages far into the future. By investing in teachers, they would be investing in their own future success. Would companies be open to such partnerships? I can’t really say. I do know that earlier this year “a group of executives from major companies appealed directly to state governors, … urging them to set higher standards for student proficiency in science and mathematics.” [“Confronting the coming American worker shortage,” by Elizabeth G. Olson, CNNMoney, 20 May 2011] Olson continues:
“The group of executives, called Change the Equation, notes that only one fifth of today’s 8th graders are proficient or advanced in math, citing figures from national educational assessments. … The group gave each state a report card on its science, technology, engineering and math (STEM) education based on various factors including teacher licensing test results and student advanced placement test scores. If states do not set a meaningful bar for assessing these skills, the group warns, they risk contributing to the dilution of America’s global competitiveness.”
Olson agrees that “given current state and local budget squeezes, with teacher layoffs and the continued debate over whether education should be tightly tied to test results, it is doubtful that states will take any action.” She continues:
“For decades, companies have been sounding alarms by funding a plethora of projects, studies and surveys, and publicly advocating for more training and higher education standards for American workers. Millions of jobs that underpin the middle class ‘could go offshore’ if the shortage of highly educated and credentialed workers persists, adds [Anthony Carnevale, director of the Georgetown’s Center on Education and the Workforce].”
Instead of “sounding alarms,” companies should step up and partner with educators to implement some of the recommendations discussed above. To be fair, some companies have done more than whine. Olson reports, for example, that “Raytheon Co., a major defense contractor, has developed software to help state educators, lawmakers and others develop tailored plans to improve math and science education and workforce policies.” But not enough is being done. Olson explains:
“Recent research from the Forum shows that boosting the educational level of the workforce is a daunting pursuit. Only 16% of American students in their senior year of high school have both math proficiency and an interest in pursuing a career in the STEM disciplines, according to the research. And just under 60% of high school seniors are not proficient in math, so even if they are interested, their chances of landing a job in those fields are slim.”
Brian Fitzgerald, executive director of the Business Higher Education Forum, a group of executives and educators devoted to improving education in math, science and related areas, told Olson:
“We don’t understand the formation of interest in STEM disciplines. It’s been hard to move the needle. Is it that one teacher that makes a difference? What we know is that few 12th graders are interested in these disciplines, about 50% switch to other majors in college, only 19% graduate with a STEM degree, and only 10% of those go into STEM jobs.”
Olson asserts that this lack of interest is not from a lack of effort. “There are many corporate-sponsored programs,” she writes, “that aim to attract and help students interested in math and science, reaching back more than four decades to when the American Chemical Society started ‘Project Seed’ to encourage interest in the chemical sciences among minority students.” To learn more about what corporations are doing, read my post entitled Innovation and Child’s Play: Those Wild and Crazy Engineers. In another effort to get companies involved, Paul Otellini, president and chief executive of Intel Corp. and a member of the President’s Council on Jobs and Competitiveness, indicated that the Council “will be calling on U.S.-based firms to help sponsor mentoring programs, internships and permanent job commitments for students in engineering programs nationwide.” [“How the private sector can help curb our engineering shortage,” Washington Post, 4 August 2011] Those efforts, however, seem aimed at the higher education level. Student interest needs to get started much earlier.
Even though companies understand that they need to get involved in promoting math, science, and engineering education as a matter of self-interest, they also understand that education is not primarily their responsibility. As a result, Olson reports, “a group of major Business Roundtable companies warned top Congressional leaders in a letter they sent in March  that, ‘the private sector cannot replace’ federal support ‘for basic science and engineering research and math and science education that undergirds America’s national economic competitiveness.'” The fact is federal support is likely to be less successful than state and local support. Companies have offices and plants in specific areas and it is in those areas where they have need of skilled employees. Start working with children in elementary school and hold out the promise of a good job at the end of the educational tunnel for students who meet exacting standards (tailored to the business involved) and I think you would have a winning formula for the future. When parents see that education is preparing their children for real jobs by teaching them useful skills that can be applied in their daily lives, they are likely to be more involved in the children’s education. It might even encourage some them to go back to school knowing that their children can help them learn some of those same skills.
As a general rule, students aren’t staying away from math, science, engineering careers because of money. According to the Wall Street Journal, “Graduates with engineering degrees earned average starting pay of $56,000 in their first full-time jobs out of college, topping other majors. Communications and English majors only earned $34,000 in their first jobs.” [“Engineering, Computer-Science Pay More Than Liberal Arts,” by Joe Light, 25 October 2011] I believe that students pursue other majors because they didn’t become fascinated with math and science at an early enough age. Teach kids to solve problems and you gain life-long proponents because they will understand that math and science skills empower them. Solving problems also does wonders for a child’s self-esteem. Tomorrow I’ll discuss how Salman Khan, America’s best-known math teacher, has tried to excite kids about math.