Calculating a love of math

The order of operations for engaging students in STEM begins with high-school math class

June 12, 2017

Do you like math? People tend to feel strongly one way or another, and likely your decision rides on your experiences in the classroom.

“Mathematics itself is fairly neutral,” said Jim Middleton, a professor of aerospace and mechanical engineering at Arizona State University’s Ira A. Fulton Schools of Engineering. “There is no reason to either love or hate mathematics outside the experiences we have in and out of school along with the cultural attitudes.” Chalkboard with math equations Download Full Image

When students’ enjoyment and understanding of math falters, so do the possibilities of STEM courses and career paths that require higher math in those student’s futures.

To keep math and STEM careers a possibility for all students, Middleton and Amanda Jansen, a professor of mathematics education in the School of Education at the University of Delaware, are studying what contributes to positive student engagement and therefore effective learning.

“These dynamics are not well understood, and as a consequence, mathematics curriculum and instruction in the U.S. is not serving the majority of students well,” Middleton said.

This ASU-UD team is the first to research moment-to-moment experiences of high school students studying mathematics over time as part of their three-year, $1.3 million National Science Foundation-funded study, “Secondary Mathematics, in-the-moment, Longitudinal Engagement Study.”

“We recognized a lack of research that could address, methodologically, how to investigate students’ experiences in the moment to understand the nature of their engagement with mathematics in a way that could reveal more general trends,” Jansen said.

By understanding these processes, they plan to help teachers to encourage more students to engage deeply, work hard, persist and become more mathematically capable.

Portrait of
Jim Middleton

Engagement = interactions + strategies + tools + organization

“The need for mathematics competencies is so dire, research needs to focus on areas that show the most promise of making positive change in students’ lives,” Middleton said.

Engagement-related variables, such as interest and usefulness, are the strongest predictors of learning, and the most effective place to make a positive change is in the classroom.

“If students are disengaging from mathematics in school, it is likely because school is turning them off from mathematics,” Jansen said.

Figuring out what turns students off of or on to math comes down to the classroom climate. Each classroom has a unique personality based on its students, curricula, strategies for thinking about difficult problems, and cultural attitudes that create a set of constraints on what’s possible for students.

“The big problem is we do not know what teaching strategies and classroom organization patterns impact learners in ways that encourage long-term, positive engagement,” Middleton said.

Middleton and Jansen plan to take into account the different classroom climates and their differences in engagement and mathematical performance to create effective professional development for teachers.

“It is entirely likely that there are many good ways to teach,” Middleton says, “but that some of those ways may be optimally effective in limited contexts.”

Gathering data to learn what best engages students

Portrait of
Amanda Jansen

“Our work has a ‘rubber hits the road’ practicality in that we are focusing on understanding and then changing the learning experiences of students to be more effective, inclusive and personally satisfying,” Middleton said. “This must be done in real classrooms with real teachers and real students so that the dynamics of teaching, learning, feedback and assessment can all be coordinated to contribute to positive outcomes.”

This is the first time secondary math classrooms will be studied so continuously at scale.

“The methodological contribution of this project is an app in which students will be signaled to report what they are currently doing in class and their reactions to this experience,” Jansen said.

Beginning in August, Middleton and Jansen will “mine” real experiences and interactions of more than 5,000 high school freshmen and sophomores in Arizona and Delaware, which together represent the cultural, linguistic and socioeconomic diversity of the United States.

The first two years of high school are a critical time to focus on engagement, Middleton said.

“This two-year period is a tremendous gatekeeper,” Middleton says. “Student struggles are a reflection of the learning experiences they have in the courses they take.”

The rules of math change dramatically from middle school to freshman algebra and again in sophomore geometry. Students often fall behind as they struggle with the content changes from algebra’s rules and computations to geometry’s visualization and proofs.

Middleton and Jansen will look at data collected over two years to see what makes for a successful classroom engagement experience.

“It will be most exciting to find the classrooms where students are more engaged, to understand those classrooms better, so more students have opportunities to learn and love mathematics while in high school,” Jansen said.

The right team to study education

This isn’t the first time Middleton and Jansen have collaborated on studying motivation and engagement in math education.

They’ve each researched mathematics classrooms independently, and together wrote a book for teachers — "Motivation Matters and Interest Counts" — and conducted an extensive review of the literature on student engagement for an upcoming compendium about mathematics education research with Gerald Goldin, distinguished professor at the Rutgers University School of Education.

Middleton believes he is in the right place to be figuring out how to change math class for the better for all students, educators and the future of STEM professionals.

ASU is one of the unique places in the world of academia where a school of engineering, as one of its main research themes, focuses on education and education improvement,” Middleton said.

The Fulton Schools in particular take an innovative approach to studying STEM education. Researchers focus on what Middleton calls “education engineering,” in which they look to improve education through the design of teaching and learning tools, technologies, management systems and environments — rather than study “what is” in the field of education, they study “what could be” and how to apply it in real situations.

Monique Clement

Communications specialist, Ira A. Fulton Schools of Engineering


New book by ASU researcher explores cancer’s pervasive mysteries

June 13, 2017

Evolution is a propulsive force, working incessantly to reshape life on earth, from the lowliest single-celled organisms to the planet’s vast forests, insect and bird populations, oceanic life and diverse mammalian species.

Like all living things, cancer cells are also subject to the stringent dictates of evolution. Indeed, cancer has proven to be among the most adept players in nature’s ceaseless game. Evolution is the reason humans and other life forms are vulnerable to cancer and why the disease has been so challenging to cure. Carlo Maley's research focuses on evolution and cancer biology. He is a researcher in the Biodesign Center for Personalized Diagnostics and an associate professor in the School of Life Sciences at ASU. Download Full Image

In a new book, "Frontiers in Cancer Research: Evolutionary Foundations, Revolutionary Directions," (Springer, 2017), Carlo Maley, a researcher at Arizona State University's Biodesign Institute, illuminates some of the central issues in current cancer study, from the vantage point of evolutionary and ecological theory. The book features chapters written by a range of researchers at the vanguard of the field. Their aim is to highlight some of the most intriguing unanswered questions in cancer research and to propose evolution-based strategies for addressing them.

Ignoring evolutionary transformation — cancer’s primary weapon of destruction — has limited progress toward the successful treatment and possible prevention of cancer. By the same token, the authors argue, the rules of evolution, if properly understood and applied, may help science to outwit cancer, either driving it to extinction or curtailing its lethality.

The book begins with a call to arms in the fight against cancer: “Nearly everyone working on cancer biology is actually working on evolutionary biology, even if they do not realize it,” Maley said. “Unfortunately, we suffer from a paucity of evolutionary biologists and ecologists who are studying cancer.” The following chapters deliver a rallying cry for other innovative researchers to enter the field and contribute their talents.

Historically, biology has been a largely experimental discipline. Charles Darwin, however, provided a theoretical framework for understanding living systems, a master narrative capable of accounting for the diversity of earthly life, through simple laws. Intriguingly, the twin forces of chance mutation and natural selection also provide cancer cells with their tenacious ability to carve out a hospitable niche, compete for resources and expand their reign at the expense of their host.

The wide-ranging text covers the genetics of cancer populations, genetic diversity within tumors (intra-tumor heterogeneity), the expansion of mutant clones, cancer stem cells in the dynamics of tumors, the evolution of metastasis, and techniques for improving cancer therapy through monitoring cancer’s evolutionary response to treatment.

Additional chapters address the patterns of human cancer susceptibility due to a mismatch between modern environments and those in which our species evolved, as well as the evolution of cancer suppression mechanisms that have emerged in different species; particularly the large long-lived animals like elephants and whales that are better at suppressing cancers than humans. Perhaps these adaptations can provide new sights relevant for human therapy and cancer prevention.

The topic of cancer heterogeneity is a central theme of the book. The existence of a wide variety of mutant cells — usually present in the patient before initial diagnosis — presents the most formidable challenge to effective treatment. The authors propose that such diversity is so ubiquitous that it may be applied as a universal biomarker — an early warning beacon indicating the propensity for cancer development or the severity of the particular cancer diagnosis. Diversity may therefore provide a common denominator, useful for tracking and characterizing cancers through all their bewildering subtypes.

In addition to disease diagnosis, measures of cancer cell diversity may also help guide the course of therapy. Here, the authors stress a central misconception in conventional cancer treatment — one which persists in spite of evolutionary theory. Efforts to eradicate all cancerous cells in a diverse population effectively select for those cells resistant to treatment. Eliminating evolutionary competition between varying cell types allows resistant post-treatment cells to expand without limit, forming a sort of super-charged cancer, less susceptible to management.

The authors trace the history of the current impasse in cancer treatment, attributing it in part to the revolution in molecular biology, which may have unwittingly acted to sideline evolutionary approaches. Clinical methods that met with enormous success in treating viral and bacterial infections have proven largely impotent against the protean nature of cancer, which, unlike a foreign pathogen, is a moving target comprised of the host’s own cells.

As John W. Pepper of the National Cancer Institute writes in the book: “ ... cancer cells are genetically heterogeneous but fundamentally human, as opposed to infectious cellular diseases that are homogeneous and fundamentally non-human.” Clearly, a reevaluation of reductionist tactics will be critical in breaking the treatment stalemate. Magic-bullet approaches to cancer, the authors argue, have dominated clinical thinking but have largely amounted to dead ends.

The dynamic nature of evolution poses particular challenges for cancer research and treatment. Cancers are often diagnosed at a single time point, with one sample per tumor, an approach that masks the subtle evolutionary processes driving cancer progression. A transition to multiple sampling to yield a more representative, time-sensitive picture of tumor evolution is encouraged, though at present, this is often cost- and time-prohibitive.

A popular theory declares that not all cancer cells are created equal. Even cells that are genetically identical may behave differently. In this view, so-called cancer stem cells, which are distinct from neighboring cancer cells in that they are self-restoring, act to drive the progression of the disease, with surrounding cells acting merely as bystanders.  From the standpoint of treatment, cancer stem cells are of central concern and a failure to eradicate them will inevitably lead to regrowth of the tumor.

Chapter 8 is devoted to cancer’s most lethal attribute, its ability to spread from the region of primary malignancy to other areas of the body, a phenomenon known as metastasis. Indeed, most cancer fatalities are the result of metastasis. Here again, research has only scratched the surface in terms of understanding the subtle particulars driving this aspect of cancer. What seems clear is that metastasizing cells often display greater aggressiveness and adaptability compared with their primary tumor counterparts. Thwarting metastasis is therefore among the primary objectives of ongoing research, with evolutionary models paving the way for new insights.

Given the selective pressure exerted by anti-cancer drugs, which cause Darwinian dynamics to select for treatment-resistant cells, what alternatives exist? One of the most exiting clinical innovations resulting from an evolutionary re-thinking of cancer is described by Robert Gatenby, a pioneer in what is known as “adaptive therapy.”

The basic idea is to maintain cells in the tumor that remain sensitive to the therapy so that they can out-compete resistance cells. The goal is to maintain the tumor at a stable size. So, when the tumor shrinks in response to therapy, the oncologist lowers the dose, but when it grows, she raises the dose. The aim is to stabilize the tumor by insuring active intra-tumor competition, rather than attempt to kill a maximum number of cells via conventional chemotherapy or radiation.  The method is likened by Gatenby to the predator-prey arms race often seen in adaptive landscapes of differing species.

How can we deal with the evolutionary resilience of cancer? The sobering conclusion of the book stresses cancer’s virtually limitless capacity to reemerge in new, resistant guises due to compulsive evolution, a fact that may continue to sabotage our best efforts to shut it down. Prevention and the earliest possible interventions — when heterogeneity may still be limited — offer the best chances in the near term for beating this implacable illness. Time is the enemy. 

Richard Harth

Science writer, Biodesign Institute at ASU