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Algebra: When X + Y = Confusion

The United Nations, foreign aid and an empty graph are the elements perplexing a class of West Salem High School algebra students as they try to complete the word problem. Their teacher, Steve Rhine, approaches one particular student who is staring at his paper, wondering what to do.

"Use the information in the problem to figure out the rule first, and then apply the rule to the graph," Rhine tells the student, who is leaning on his hand, struggling to make sense of numbers at 7:45 a.m.

Around the room, students try to graph the problem together. "You start at zero and you just draw the line," one boy tells his partner. "Go up one and over two," says another, his pencil drawing a line on the paper.

Drawing graphs, manipulating letters instead of numbers, using complex and abstract equations -- generations of students have attempted these algebraic concepts. Many succeed. Others give up. Many ask the same question: Why is algebra so difficult? Rhine has asked and answered that question in his research as a School of Education professor at Willamette University.

When Letters Replace Numbers
For 11 years, Rhine taught mathematics in Los Angeles, and this spring, he brushed up on his skills with the class at West Salem High. Rhine calls algebra the "gatekeeper" math course that stands between students and the rest of their education, including college. Yet so many struggle to understand it.

Part of the problem is that with algebra, students start moving away from tangible questions where they can see with their eyes that 5 plus 4 equals 9. Rhine says that once students start using variables and tools such as the quadratic equation, the concepts become more abstract. The students start thinking equations work "magically" instead of trying to understand how or why they work.

Rhine is working on a solution, "The Teacher's Handbook of Algebraic Thinking and Misconceptions." He says there are many common misconceptions students have in class -- such as looking at a graph and thinking it represents one thing, when it actually represents another. "The more teachers know about the misconceptions, the more they can help students learn the concepts," Rhine says.

Using Technology
Math is just one of Rhine's areas of research. He also is interested in technology's impact on education and has acquired two separate million-dollar grants to improve the use of technology in Oregon classrooms. "The government has spent billions and billions of dollars for technology in schools, and we are always hearing stories of the items gathering dust," he says.

Rhine directed one grant from the U.S. Department of Education Preparing Tomorrow's Teachers to use Technology program, or PT3. The three-year grant funded the Oregon Technology in Education Network, or OTEN, a group of six Oregon universities working to help teachers successfully use technology in the classroom.

Through the grant, students at Willamette's School of Education can access a technology library at the University that allows them to take items such as laptops or wireless routers to the elementary and secondary schools where they are student-teaching. They also learn how to write grants to obtain the technology they want in their own classrooms when they become teachers. Rhine edited and wrote part of a book titled "Integrated Technologies, Innovative Learning: Insights from the PT3 Program," which highlights successful technology projects across the country.

The second grant -- through Teacher Quality Enhancement, from the U.S. Department of Education -- helps the OTEN colleges develop better placements of their students in schools that support and are comfortable with technology use.

More than Just PowerPoint
Rhine says multimedia presentations in classrooms fulfill an important need for students: having more ways to represent what they know. Technology can be a great way for students to communicate their understanding and learn ideas in non-traditional ways, Rhine says -- if it is used effectively, with a good educational basis.

Simply having students make flashy PowerPoint presentations isn't enough; the presentations need to focus on real, relevant content. Without it, "the students had fun, they're interested, they're more engaged, but they learn nothing," Rhine says.

Back in his West Salem algebra class, Rhine has limited his technology for the day to the old-style overhead projector. He actively works his way around the room, making sure each student is on task and trying to help any who appear confused. He knows the importance of this class for the students' academic future. "So many students give up on math because they say, 'It just doesn't make sense to me.' We have to help students understand things better and not mystify them."



07-15-2006