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In This Issue
Note from Bridge Editor in Chief Ronald M. Latanision
Innovations and Opportunities in Engineering Education
The Algebra Challenge
Undergraduate Engineering Curriculum: The Ultimate Design Challenge
Opportunities in Engineering Education: Pathways to Better-Prepared Students
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Summer issue of The Bridge on Undergraduate Engineering Education
June 12, 2013 Volume 43 Issue 2

The Algebra Challenge

Wednesday, June 12, 2013

Author: Enrique J. Lavernia and Jean S. VanderGheynst

On January 30, 2013, PBS’s NewsHour devoted a segment to American schools that have introduced real-world applications to science, technology, engineering, and mathematics (STEM) education while at the same time promoting students’ ability to “get the concepts” over the supposed “intelligence” demonstrated by raw scores on tests. The program featured 8th grade students at King Middle School in Portland, Maine, who are designing robots to gather “resources” (in this case, ping pong balls). It also showed students in a statistics class at New York City’s High School of Telecommunications Arts and Technology discussing datasets, debating the pros and cons of various polling techniques, and creating their own exit polls—their teacher intends her pupils to become producers of information, not just consumers.1

While we’re delighted by the mainstream media exposure granted to these pilot programs, we’re simultaneously dismayed by the editorial slant that, in the 21st century, still regards such efforts as unusual examples of progressive teaching. In this article we focus on the specific need for innovation in the teaching of algebra, which for many students is a “wall” too difficult to scale and stifles their interest in even thinking about further study in mathematics or other STEM areas.

The Need to Transform STEM Education

Many courses suffer from overly structured styles of instruction that have been the norm for half a century: styles that haven’t changed despite great technological advances that could—should—have prompted exciting new approaches to teaching. The need to transform traditional approaches to teaching STEM is well established, as is the awareness that such approaches, particularly in a “gatekeeper” course such as algebra, are failing miserably.

Anecdotal evidence abounds in middle schools from California to Maine, all of it supported by research and statistical documentation going back at least three decades (Tuma and Reif 1980). More recently, a 2000 study demonstrated that women and underrepresented minority students are particularly ill served by traditional teaching methods (Rech and Harrington 2000), and a 2008 study revealed that the pass rate for Algebra I students was a shockingly low 39 percent nationwide (Gates 2008). A fresh approach is especially critical for the teaching of algebra, which has been recognized as the make-or-break moment in students’ K–12 education (Gates 2008; Rech and Harrington 2000). American middle schools, in particular, require innovations that bridge classroom mathematics instruction with other STEM tools and activities, particularly computing (Collins and Halverson 2009; NSF 2008).

Our point: This is not fresh information, and yet nothing has been done at a national level. Politicians, school boards, and teachers’ unions remain committed to testing requirements, ignoring the increasingly obvious fact that a top-down realignment of STEM education—starting at the university level and working down to kindergarten—may be one of the country’s most crucial challenges.

The US Bureau of Labor Statistics reported that more than 800,000 professional information technology jobs would be added during the decade ending in 2016, an increase of about 24 percent (Wright 2009). Although many of these jobs will not require a four-year college degree, all will demand a solid background in computer science (Wright 2009). And in California a study by the Public Policy Institute indicates that by 2025 the state could face a shortage of up to a million college graduates to meet its skilled workforce demands (Johnson and Sengupta 2009).

Despite all of this compelling evidence, US education is actually trending in the wrong direction. Classes in computer science and computer programming—a powerful means to help solve the “algebra crisis”—either remain largely absent from many secondary schools or are declining. The portion of schools offering an introductory programming course dropped from 78 percent in 2005 to 65 percent in 2012, with a corresponding drop from 40 to 27 percent in Advanced Placement classes (Nagel 2009).

People aren’t listening. Or, to be more precise, the right people aren’t listening.

Trends in US STEM Performance and Ranking

The 2011 California STEM Summit, which took place October 10–11 at UC Davis, assembled more than 200 K–12, higher education, industry, and nonprofit leaders and policymakers from throughout the state. Participants were engaged and enthusiastic, and generated more than 350 concepts and suggestions to spark innovation in STEM education (CSLNet 2011).

Lurking behind the collaborative panel discussions that gave rise to these ideas, however, were the grim statistics that had prompted the summit. Although in the 1970s California was a national leader in K–12 and higher education, in 2011 it ranked 34th among all states in math and science proficiency in grades 4 and 8 (White and Cottle 2011). The “golden dream”—which once propelled young students to careers of excellence in industry, academia, and politics—had become a tarnished waking nightmare (Provasnik et al. 2012).

This disturbing news isn’t confined to California. The National Center for Education Statistics’ 2011 Trends in International Mathematics and Science Study (TIMSS), published in December 2012, revealed the problem’s international scope (Provasnik et al. 2012). The average math and science scores of US 4th grade students ranked them 11th and 7th, respectively, among the 57 countries and education systems that participated in the study. The situation is no better for US 8th grade students, whose math and science scores ranked them 9th and 10th, respectively.

But the rankings may actually obscure the extent of the achievement gap. Far more troubling is the fact that the average math score (509) of US 8th graders in 2011 showed no statistical improvement from the previous TIMSS, in 2007 (508), while countries such as the Republic of Korea, Singapore, and China/Taipei posted 2011 scores of 613, 611, and 609 (Gonzales et al. 2009; Killewald and Xie 2013).

With a mere one-point improvement over the course of four years—in the wake of No Child Left Behind—US students will never catch up. Indeed, they’ll never get close to catching up.

A Link Between Algebra and Dropout Rates

Children are dropping out of school because of algebra (Helfand 2006) at a time when they are needed for the nation’s economic security. A study from Education Week and the Editorial Projects in Education Research Center reported that 1.3 million high school students dropped out in 2010—roughly 7,200 per school day.2 And according to a report prepared by the Massachusetts Department of Elementary and Secondary Education,3

  • Dropping out of school impacts students’ self-esteem and psychological well-being as they discover that they lack the skills and knowledge to fulfill their desires;
  • Dropouts are 3.5 times more likely than high school graduates to be incarcerated during their lifetime; and
  • Earnings for students who quit school continue to decline: in 1971, male dropouts earned an estimated $37,087, which decreased by 35 percent to $23,902 in 2002.

Furthermore, a recent survey commissioned by Raytheon revealed that 89 percent of middle-school
students would rather do chores than math homework, and 33 percent would rather go to bed early!4 Since algebra is frequently taught in middle school, this finding may well apply to students’ attitudes about this specific class.

Yet classrooms across the nation continue to teach algebra the same way it was taught in the 1950s and ’60s. And since California legislators made algebra a statewide high school graduation requirement in 2004, more students are failing to graduate. A January 2006 Los Angeles Times article profiled one poor high school student who, over the course of six semesters, failed algebra six times. Midway through her senior year, she returned all her textbooks to the campus book room and left school for good (Helfand 2006).

“Repeated failure makes kids think they can’t do the work,” confirmed Andrew Porter, director of the Learning Sciences Institute at Nashville’s Vanderbilt University. “And when they can’t do the work, they say, ‘I’m out of here’” (Helfand 2006).

Why Is Algebra So Difficult?

Are the concepts of algebra truly harder than those explored in, say, fractions or percentages?

We believe the answer is yes.

Algebra isn’t like the math courses that come before it. It is abstract, with variables instead of integers. Once letters are inserted for numbers, students get lost. The information must be presented to them in some other fashion.

Math is like a foreign language. It comes naturally to some people; others require lots of time and help. Some people need to see it in a context that makes sense to them in order to grasp it. It usually requires lots of practice.

Students attempting to learn algebra confront many unique challenges (Rakes et al. 2010). First, algebra is often the first course where students engage in abstract reasoning and problem solving (Vogel 2008). Second, unlike basic mathematics—which deals solely with numbers—students must learn the language of mathematical symbols and the rules of arithmetic operations (Kilpatrick et al. 2001). Finally, algebra’s structural characteristics can be too subtle for students who cannot, for example, recognize the difference between the expression −x2 + 5x − 6 and the equation −x2 + 5x − 6 = 0 (Carraher and Schliemann 2007; Howe 2005; Kieran 1992).

The interaction of the three fundamental concepts of algebra—abstract reasoning, the language of mathematics, and mathematical structure—is a formidable impediment for many students trying to master algebra (Rakes et al. 2010).

Innovative Approaches to Teaching Algebra

Although the PBS NewsHour segment presented the use of robots at King Middle School as revolutionary, it’s by no means the only example of innovative teaching tools. Many schools around the country have used LEGO Mindstorms NXT to promote K–12 student learning of STEM (Crowley et al. 2003; Franz and Elmore 2009; Gale et al. 2007; Karp et al. 2010). The Los Angeles Unified School District has experimentally implemented a high school computer science curriculum with a full-year course that includes human-computer interaction, problem solving, Web design, robotics, computer applications, and an introduction to programming (Goode and Chapman 2009).

All of this comes as no surprise here at UC Davis, which is doing something quite similar . . . and it happened almost by accident.

Robotics

Dr. Harry H. Cheng came to UC Davis in 1992 as a robotics and computing researcher in the College of Engineering’s Department of Mechanical and Aerospace Engineering. Since then he has earned numerous honors and awards, he regularly publishes journal articles and book chapters, and he has chaired or served as a guest speaker at dozens of conferences in the United States and China. Cheng and former graduate student Graham Ryland recently invented an intelligent, reconfigurable modular robot—dubbed the “iMobot” (Figure 1)—that earned a National Science Foundation Innovation Award grant and was featured in newspapers, magazines, and on television5 (Anderson 2011).

Figure 1

The design of Cheng’s iMobot technology is affordable, anthropomorphic, and modular, so it has an immediate appeal to a wide range of learners and serves as a launch pad for their imagination and creativity. In various classrooms, iMobots have been configured and programmed to represent dance troupes, soldiers, felines, vehicles, and even a barista. One robotic “game” involves projectiles: if a ball is shot from a specific point and a robot must be programmed to catch it, students must deal with variables relating to where the robot will be sent, the force and arc of the projectile, and so forth.

Tailoring Teaching for Today’s Technology

Cheng has become most passionate about his outreach activities outside the lab. As director of the UC Davis K–14 Outreach Center for Integrated Computing and STEM Education (C-STEM), he has joined colleagues across the country in recognizing that the computing and robotics fields are ideal for engaging at-risk students in K–12 schools. His efforts initially highlighted robotics and computing, but he learned via teacher feedback that algebra was students’ biggest problem, since they need to complete that course before moving on to computing. He therefore shifted his focus to help K–12 teachers present algebra in a manner that resonates with their students.

Cheng has come away with some strong opinions. “This is the 21st century, but some of the teaching methodology hasn’t been updated with the times,” he notes. “Teaching skill sets learned 30 years ago won’t cut it; today’s kids are too tech savvy for that.”

The idea is to tailor the teaching curriculum for young students whose lives are consumed by smart phones, MP3 players, tablets, and all sorts of other technical gadgets. Cheng views his fields, computing and robotics, as a natural fit—a way to depart from rote pencil-and-paper exercises. And he’s quick to clarify a key point: He’s not talking about building new curricula, with more funding and fancy technology, solely for the benefit of top-tier students, most of whom arguably don’t need such help. He worries most about at-risk students, the ones who often get left behind. He wishes to better educate all students, not just those who plan to attend college.

Programs for Teachers

Cheng’s passion and innovative methodology have drawn the attention of the National Science Foundation, which in September 2012 awarded a pair of grants. The first, a two-year grant in the amount of $300,000, will help Cheng study collaborative mathematics learning—specifically algebra—with robots. The second provides $950,000 over three years to study how the use of robotics programs in schools can change students’ attitudes toward STEM subjects. For his research in both these areas, Cheng and his co-investigators have recruited teachers from Sacramento-area schools, from grades 6 and up, and provided them with robots, teaching resources, and training.

The grants have allowed Cheng to expand programs he had already put in place. The Computing Research Experiences for STEM Teachers (CREST) project, inaugurated in 2011, was designed to create an enduring partnership between UC Davis faculty members and local secondary school STEM teachers, to help the latter guide their students toward further C-STEM studies and related careers. The program is supporting 45 computer science and STEM teachers—15 per year, for three years: 11 in-service teachers and 4 preservice teachers each year—as CREST Fellows. These individuals join Cheng for six-week summer programs, augmented by follow-up seminars and discussions that continue through the participating teachers’ academic year. As a result, more than 30 schools from 20 districts in the greater Sacramento region have adopted the C-STEM research-based algebra and computing curricula, and roughly 1,500 K–12 students have benefited.

Clay Dagler, one of the participating instructors, has taught algebra at Sacramento’s Luther Burbank High School since 1999. Now into his first revised academic year, Dagler already sees the results. “My kids are jazzed by the robots,” he says, “which demonstrate how math is used, and where it goes in the future. The computer programming is engaging for them, because they can ‘see’ math in action. This isn’t merely solving an equation on a page; students actually work the problem.”

Competition

Ancillary “marquee events” include activities such as Robotics Academy competitions and the annual UC Davis C-STEM Day (Figure 2). At the C-STEM Day on May 5, 2012, middle and high school students showcased their skills in robotics and problem solving, while teachers, educators, and policymakers discussed how best to use computing, technology, engineering, and robotics in K–14 education. The third annual C-STEM Day, on May 4, 2013, featured two major activities: a RoboPlay Challenge Competition and a Math Programming Competition. The day concluded with an awards ceremony honoring achievement and excellence, along with scholarships for graduating students.

Figure 2

There are many such events across the United States: the FIRST Robotics Competition for high school students, the FIRST LEGO League Competition for students ages 9–14, the Junior FIRST LEGO League for students in grades K–3,6 the VEX Competition for high school students,7 and the Botball competition for middle and high school students.8

A Brandeis University evaluation of the FIRST Robotics Competition showed that participating students are more likely than the national average to attend a four-year university and major in engineering or computer science (Melchior et al. 2005). A workshop presentation on the Botball competition showed that participating girls became “significantly” more interested in robotics and STEM fields (Weinberg et al. 2007). Such studies clearly indicate that participation in robotics activities and competitions increases students’ interest in STEM postsecondary study and careers.

Collaboration

Interactive programs offer a supplementary benefit: They expose children to the advantages of a shared, collaborative method of “working the problem,” stimulating curiosity and facilitating long-term retention of the concepts. This is the desired result known as “deep learning,” which actively engages students, often collaboratively, in a search for relevance in their schoolwork. Deep learning promotes a level of long-term retention generally absent from traditional methods that are more apt to focus on memorization (Halpern and Hakal 2002; Millis 2010).

Additionally, collaborative learning tasks are effective because they encourage—even necessitate—contributions from each member (Cohen 1994), compelling participants to engage with the task and each other (Barron 2000, 2003). In other words, circumstances both require and allow for students to function effectively as a group, and thus more accurately mirror how STEM careers actually function in industry.

The Importance of Incentive

Incentive is another variable in the equation. Even now, in too many schools, passing algebra means only one thing: being “allowed” to take geometry. And passing geometry grants entry to Algebra II. That’s not much of a carrot; children must be captivated by tempting goals.

But even with hands-on relevance in the presence of robotics, algebra remains a wall to be climbed. Students must be encouraged to understand the exciting goals that await on the far side of that wall, which means opening a dialogue about future careers at a much earlier age.

Such dialogue is particularly crucial in populations where parents didn’t attend college, or where there is an absence of a supportive environment at home. Having such conversations early is important, because these students aren’t exposed to college—it’s not discussed in their homes, and they may not have relatives who went to college. Children need to be told about the possibility of additional, specialized education after high school and the benefits of pursuing such an education.

And yet such conversations aren’t integrated into today’s K–12 curriculum. Unless a good relationship exists between a local college and a school, students may not get that message.

Moving Forward

Although the feedback from Cheng’s middle and high school teacher-collaborators is encouraging, the results thus far are anecdotal, lacking the authoritative stamp of carefully tabulated results over time. For that reason, Cheng is working closely with research associates at the WestEd STEM Education Group to gather the hard data that will be necessary to build his local program into something larger. “If pilot programs are to be respected in the long term, and have a genuine impact,” says WestEd’s Jennifer Mullin, “you must have a good research agenda and plenty of data.”

But that takes time. The 854,000 new professional information technology jobs reported by the Bureau of Labor Statistics need to be filled now, and the number increases each year. Potential candidates for those jobs are already in middle or high school.

And yet the innovative, breakthrough—and successful—teaching methods being used at a few forward-thinking schools from Maine to California are still regarded as little more than pilot programs and novelties. They need to expand; they need to become national programs.

We at the university level—professors, department chairs, and deans—must become much more aggressive, much more vocal, in our demand that hidebound instructional techniques be replaced. We must insist on better preparation of students to fill college and university classrooms with engaged and resourceful undergraduates and postgraduates, who in turn will stimulate American tech industries that are desperate for inventive minds.

The few dozen K–12 teachers involved in such programs need to be given a stage from which they can share their results, so that instructors in classrooms across the country can experience the miracle of a once-failing algebra student who looks up one day and excitedly says, “I get this now!”

References

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 FOOTNOTES

 1 PBS NewsHour. Teachers Embrace “Deep Learning,” Translating Lessons into Practical Skills (January 30, 2013). Available online at www.pbs.org/newshour/bb/education/jan-june13/charter_01- 30.html.

 2 “Progress on Graduation Rate Stalls; 1.3 Million Students Fail to Earn Diplomas.” Education Week/Editorial Projects in Education Research Center, June 20, 2010. Available online at www.edweek.org/media/ew/dc/2010/DC10_PressKit_final.pdf.

3 The report, Dropout Reduction: Prevention, Intervention, and Recovery (updated Dec. 6, 2011), is available online from the Massachusetts Department of Elementary and Secondary Education (www.doe.mass.edu/dropout/); these statistics are from the Overview section on Consequences of Dropping Out.

 4 “Raytheon Inspires Students with New Virtual World of Math Via MathMovesU.com” (January 2008). Available online at www.prnewswire.com/news-releases/raytheon-inspires-students- with-new-virtual-world-of-math-via-mathmovesucom-57528972. html.

 5 “Transforming Robots Not Just Science Fiction,” ABC-TV Channel 7, San Francisco (May 12, 2011). Available online at http://abclocal.go.com/kgo/video?id=8130456.

6 FIRST (For Inspiration and Recognition of Science and Technology) is a national nonprofit program “founded in 1989 to inspire young people’s interest and participation in science and technology” (www.usfirst.org).

7 The VEX Robotics Competition is sponsored by the Robotics Education & Competition Foundation, which “seeks to increase student interest and involvement in STEM by engaging students in…robotics engineering programs across the US and internationally.” Information about the robotics competition is available at www.roboticseducation.org/vex-robotics-competitionvrc/ .

8 “The Botball Educational Robotics Program engages middle and high school aged students in a team-oriented robotics competition” (www.botball.org).

About the Author:Enrique J. Lavernia is dean and Distinguished Professor in the Department of Chemical Engineering and Materials Science and Jean S. VanderGheynst is associate dean and professor in the Department of Biological and Agricultural Engineering, both at the University of California–Davis College of Engineering.