Studies Find Payoff in 'Personalizing' Algebra
While "personalization" has become a buzzword in education, it can be hard to determine what really makes a subject relevant to individual children in the classroom. An ongoing series of studies at Southern Methodist University suggests learning students' interests upfront and incorporating them into lessons can get struggling students to try harder and substantially improve their performance in algebra.
"You don't think the words, the little details of context, will make a difference when you are solving a math problem, but it really does," said Candace A. Walkington, an assistant professor of teaching and learning at Southern Methodist in Dallas and the lead researcher for the reports. The most recent of them is expected to be published later this year in a special issue of the Journal of Educational Psychology on advanced learning technologies.
The studies, which were discussed at a recent meeting here at Carnegie Mellon University, highlight one way to boost learning in algebraic expression, a concept considered critical in the Common Core State Standards but which educators say is perennially challenging to students. The study found that personalized math problems not only made it easier for students to understand what was being asked, but also helped boost the confidence of students who may have been intimidated by the subject.
Word problems at any level can be challenging, but Michael Shaughnessy, a mathematics and statistics professor at Portland State University in Oregon and the immediate past president of the National Council of Teachers of Mathematics, said it is particularly difficult for students to make the switch from looking at a concrete arithmetic problem—the cost of a sweater on sale for 20 percent off, say—to the generalized arithmetic in algebra, such as an equation for finding the cost of any item in a storewide 20 percent-off sale.
One method for estimating the cost of new home construction is based on the proposed square footage of the home. Locally, the average cost per square foot is estimated to be $46.50.
You are working at the ticket office for a college football team. Each ticket to the first home football game costs $46.50.
You are helping to organize a concert where some local R&B artists will be performing. Each ticket to the concert costs $46.50.
You have been working for the school yearbook, taking pictures and designing pages, and now it’s time for the school to sell the yearbooks for $46.50 each.
You work for a Best Buy store that is selling the newest Rock Band game for $46.50.
"That process is one of the harder things in the algebra trajectory to do," Mr. Shaughnessy said.
Steven Ritter, the founder and chief scientist at Carnegie Learning Inc., a Pittsburgh-based publisher of math curricula, had seen similar problems while designing his company's Cognitive Tutor software. Administrators found students who had learned how to identify an equation using a positive slope in one word problem showed no transfer of skills to identify a problem using a negative slope. Small changes to contextual details completely threw them.
In one high-poverty Texas school using the software, Ms. Walkington thought she saw a reason why students weren't making those logical connections. Many didn't relate to the question scenarios, which were often about harvesting grain or building greenhouses.
"If [a student is] already pretty fluent in math and has a high level of interest in math," Ms. Walkington said, "it doesn't really matter how you dress up the problem, they see it as what it is: a math problem, linear equation in this case."
Struggling learners, by contrast, often had little self-confidence in math. They weren't sure how to approach problems and often wouldn't even attempt them, even if they had just completed similar problems in class.
Results for Students
Ms. Walkington surveyed 145 9th graders who were using the software about their interests in areas such as sports, music, and movies. Then she randomly assigned them to take the linear-equation unit either receiving standard word problems or one of four variations tailored to their interests.
The students who received personalized word problems solved them faster and more accurately than students who received the standard questions, particularly when it came to translating the story scenarios into symbolic equations.
Moreover, the strongest effects occurred for students who were struggling the most before personalization.
"Problems that required a relatively high reading level and more-challenging knowledge components, those were the steps of the problem that were particularly affected by the personalization," Mr. Ritter noted during the Sept. 12 discussion at Carnegie Mellon.
"It kind of makes sense if you think [about it], if you're a big sports fan … you are probably better able to read things about sports because you understand the vocabulary, you understand the situations, and for you, the readability is better," he said.
Ms. Walkington, who did not attend the Pittsburgh event, thinks the personalization did more than just make it easier to understand the problems; it gave students a reason to try.
The tutoring software includes hints, and invariably some students will try to game the system by clicking through multiple hints to get the answer. But students were significantly less likely to game the system for personalized problems, according to the researchers.
"If we gave [struggling learners] a nonpersonalized problem, often they wouldn't even attempt it, but if it was a personalized problem, they were more likely to try it and often succeed," Ms. Walkington said.
That's encouraging, Mr. Shaughnessy said. "The whole thing with algebra for kids is they say, 'This isn't relevant to me.' Making it relevant in any way is a good thing," he said.
Moreover, the improvement continued for students two months later, when all students had moved on to a new unit—a finding that surprised Carnegie's Mr. Ritter.
"Somehow they got interested enough that it carried over even when the problems didn't correspond anymore to the personalization," he said.
The findings build on Ms. Walkington's previous pilot of the math personalization, which found similar results with only 24 students, and a study of a similar approach to reading personalization by researchers at Carnegie Mellon. The reading study also found benefits to incorporating student interests in texts.
"A lot of the previous work on personalization used a method where they just inserted words—a favorite food or a pet's name," Ms. Walkington said. "We tried to make more authentic connections as to how they might use numbers in connection to following their own interests."
Next fall, Ms. Walkington is expanding the computer personalization to 200 students, and also exploring whether a teacher could use surveys or informal interviews early in the school year to personalize face-to-face lessons in the classroom.
"I don't see a reason it shouldn't work besides the logistics" of developing different versions of problems, which she said took about five to 10 minutes each during the pilots. "It's just a matter of the teacher knowing students' interests enough to formulate the questions," she said.
At the same time, Carnegie Learning has already incorporated the personalization format into the MATHia software it released this year for grades 6-8; the company is evaluating whether the personalization improves performance in a wider student population.
Vol. 32, Issue 05, Pages 1,14-15
Get more stories and free e-newsletters!
- Superintendent, Lexington Public Schools
- Lexington Public Schools, Lexington, MA
- Fort Worth Independent School District, Forth Worth, TX
- Director II-Sudent Support Services
- Deer Valley Unified School District, Phoenix, AZ
- International Schools First Ever iFair
- International Schools Services, Multiple Locations
- Superintendent, South Orange & Maplewood
- The School District of South Orange & Maplewood, Maplewood, NJ