'STEM'ming the hate; teaching algebra in a new way
Too many people don’t “get” algebra. A failing algebra grade keeps more students from graduating high school than any other subject. As many as 40 percent who do pass and go on to four-year colleges find themselves in remedial math because they fail placement tests.
The problem is so severe that some people advocate removing the requirement for high school and college graduation.
Arnulfo Pérez, assistant professor of mathematics education, is taking another approach: Make algebra so engaging — by introducing real-world applications such as engineering circuitry and computer programming — that students are drawn to it, and may even pursue STEM or computing careers.
Pérez and his Ohio State team received a $1.2 million National Science Foundation (NSF) grant in November to do just that. Kathy Malone, assistant professor of science education, and Christopher Stewart, associate professor of computer science, are co-PIs.
Taking a computational approach to teaching algebra
Their project, “Assessing the Impact of Computer Modeling and Programing in Secondary Algebra,” figures that virtually every American student takes algebra, either in middle or high school. Those classrooms present a perfect laboratory for introducing computational thinking: solving problems — including those onerous, multistep algebra calculations — using concepts fundamental to computer science.
The NSF’s STEM+Computing Partnership program, which is funding the project, seeks to innovatively integrate computing into other STEM disciplines. For Pérez, the idea is to break from the traditional approach of teachers demonstrating an algebra problem and students regurgitating the example.
“How do we teach our students to get better at algebra if we’re just doing the same thing? We cannot just say it louder, or say it clearer,” Pérez said. “We need to look at how we’re teaching algebra to make sure they get it.”
So Pérez and his colleagues developed a project-based unit for teaching linear functions that borrows from physics, engineering and computer science. Twenty algebra teachers from South-Western City Schools near Columbus will pilot the unit next year. The district was chosen because its racial makeup closely matches the national norm, as determined by the National Assessment of Educational Progress.
Ohm's Law = a linear equation
Students use a model, called a breadboard, to lace red and green wires between AA batteries and a tiny LED bulb. They flip a switch and the bulb glows faintly; the more batteries they use, the brighter it becomes. They take measurements with a multimeter and log the results into tables on a web portal designed by Ohio State graduate students.
Using their data, the computer plots a graph and generates an equation:
V (voltage) = I (current) x R (resistance)
Ohm’s Law. Not only is it a law of physics, it’s a linear equation. Suddenly, algebra becomes a lot more tangible, and more interesting.
Sliding a toggle on the website, students see what happens to voltage if they increase resistance or current if they decrease voltage — without having to physically test it.
“Now we can make predictions,” Pérez said. “Students see the graph, table, equation. All three have a connection. Any time they move the table, or equation, it changes all of them at once. So there’s this dynamic interaction.
“As a researcher, this gives us an opportunity to see how students work all three representations of the function. At the end we want them to be comfortable with all three,” he said.
Under-represented students get introduction to coding
As students toy with the slider, a split screen reveals the coding used to design the portal. They can adjust arrays within the coding to change the graph and table.
“We call it the Trojan horse approach to computer programming,” Pérez said. “We’re introducing computational thinking concepts for computer science into an algebra classroom.”
To get that introduction to computer science, a student typically must attend an after-school program, summer camp or specialized STEM school. Students underrepresented in STEM fields — women, low-income students and minorities — are particularly at risk of getting left behind because they have less access to these opportunities.
“Everybody takes algebra, therefore we throw a wider net to draw more students into experiences that make computational thinking relevant,” Pérez said.
That’s the push the National Science Foundation is looking for. Computational thinking applies to a multitude of subjects because it provides a creative framework for solving anything: engineering problems, understanding human behavior or winning sports games. The concept is transferable to other areas because it encourages persistence in the face of challenge, tolerance for ambiguity and flexible thinking.
“It’s a transcendent approach,” Pérez said.
Giving teachers the tools to teach differently
Yet promoting computational thinking across curricula is not easy. Rare is the teacher who is proficient in programming, algebra, electrical engineering and physics.
“The real challenge for teachers,” said Michael Cox, curriculum coordinator for South-Western City Schools, “becomes having a knowledge base or being willing to explore the areas where students can develop the thinking to solve real problems.”
“How does more than one teacher do that: How do you get 20 people, the whole school, the whole district to do that? That’s the challenge we’re facing,” he said. “But 20 teachers have 600 students that they can affect.”
Pérez remembers getting up at 4:30 a.m. to prepare algebra lessons as a new teacher in Houston. Creating well-designed teaching units that incorporate computational concepts is key to getting teachers to implement the approach, he said.
“If we can develop these units in a way that makes them accessible for the teacher, then they have resources available to them so they don’t rely heavily on the textbook,” he said.
The researchers introduced teachers to the unit in June. It will be presented to students in spring. After the data from the study is assessed, Pérez believes the correlation will be clear: All students can be engaged in a way that demystifies algebra, makes it relevant to them and opens a path to STEM and computer science fields.