Opening the Gateway: Interventions Aim for Algebra Success

This article was first published in WestEd's R&D Alert, Vol. 9, No. 1, 2008.

Middle and high school students struggling to master algebra require instruction that addresses reasons for their lack of success. Targeted instruction needs to fill the gaps in their mathematical knowledge and emphasize deep understanding of key algebraic concepts.

Providing such targeted instruction is the goal behind Aim for Algebra^TM, an intervention curriculum created by WestEd to boost achievement in algebra for all students, particularly those for whom algebra has been especially challenging.

"Typically, students who struggle are put in one algebra class after another and repeat the same lessons over and over," says Steve Schneider, Director of WestEd's Mathematics, Science, & Technology Program. "We've taken a step back and asked, 'What do these kids need to be successful?'"

That's an important question, given that algebra is widely considered the "gatekeeper" course that determines whether students will have access to higher education. More and more states and school districts are mandating algebra as a condition for high school graduation.

"As we look at data from urban school districts especially, we find a fairly high proportion of kids not passing algebra, which means that in a large number of cases, they won't graduate from high school," says Schneider. "Our intent is to change that by developing a curriculum to replace the materials currently being used that aren't working."

He says the Aim for Algebra program is "not business as usual" but builds on research-based learning theory. "Its purposeful sequencing and scaffolding of tasks allow students to bridge the conceptual gaps created by traditional algebra curricula."

The first six modules in the Aim for Algebra curriculum (formerly known as Algebraic Interventions for Measured Achievement) were developed with funds from the U.S. Department of Education's Institute of Education Sciences (IES). The materials were field-tested during the 2005-06 school year throughout California, where they were used with more than 1,000 students in grades 7 through 10.

The field tests found that students exposed to the Aim for Algebra modules exhibited statistically significant increases in performance on module-specific assessments. Researchers determined that each module led to increased student achievement, that the increases were substantial, and that the data showed no ceiling effect, meaning that continued student improvement could be expected.

In addition, teachers involved in the field testing rated the Aim for Algebra materials better at engaging students and helping them understand algebraic concepts than curriculum materials they had used in the past.

A second IES grant, awarded on the basis of those positive findings, is supporting the development of five more modules, a move that expands the scope of the materials to that of a full-year curriculum. Meanwhile, researchers continue to evaluate data from a randomized, controlled trial study of Aim for Algebra's effectiveness that was conducted during the 2006-07 school year.

WestEd Senior Program Manager Kimberly Viviani, who coordinates production of the Aim for Algebra curriculum materials, says the content is based on cognitive research on how students learn. As a result, activities are designed to help students understand underlying algebraic concepts in a deep way, organize their thinking, work with multiple representations, and learn incrementally.

Aim for Algebra also incorporates the wisdom of experienced math teachers and mathematicians. "We talked with a group of them about where most students encountered difficulty with algebra, and we then developed modules based on what they had to say," says Schneider. "The consensus was amazing. Everyone agreed on which topics gave students the most trouble." As a result, the six modules developed to date cover: signed number operations, variables and expressions, ratio and proportion, patterns, the coordinate plane, and inequalities.

A typical Aim for Algebra lesson begins with the teacher introducing a new concept by connecting it to previous work and building on students' prior knowledge. After engaging in tasks that introduce and expand the focus of the lesson, students complete a series of activities that might ask them to represent a situation mathematically or use manipulatives to model a concept. Teachers guide students through the tasks, first with very structured instruction, then leading students to perform the tasks independently.

Schneider says these conceptual tasks are far more valuable than lessons that simply teach students to use algorithms, or procedures. "The students memorize the algorithms, but they don't understand why they work," he says. "And without that knowledge, their ability to transfer their skills to new situations is very limited."

By contrast, the opportunities for multiple representations and alternative solutions in Aim for Algebra lessons mean that students "engage topics in a deep, conceptual way that ultimately helps them be successful in algebra," says Viviani.

Woven throughout the modules is an emphasis on algebraic reasoning and problem solving. In other words, students are encouraged to move beyond "numerical thinking," which focuses on numbers and numerical answers, to considering mathematical relationships.

Viviani says Aim for Algebra was designed to be flexible. Depending on students' needs, teachers can reinforce concepts that students already have learned; refresh knowledge students may have learned, but since forgotten; or re-teach concepts that students misunderstood or never learned.

Aim for Algebra modules, which include all manipulatives necessary for implementation, can replace or supplement the math curriculum already in use. Each module has multiple lessons, and each lesson is accompanied by a teaching guide. The modules can be used in a regular classroom or in an intervention program to support students struggling with algebra. They can be used with an entire class or in small group situations. Each module also has a pretest and posttest, helping teachers differentiate and individualize instruction.

Teachers learn to use Aim for Algebra at a two-day professional development seminar, followed by a one-day follow-up session later in the year.

Aim for Algebra is most unique, Viviani says, in the way it sequences and scaffolds specific lessons. "Each module flows from beginning to end, building on itself," she says. She is especially gratified by the enthusiasm teachers are showing for the program. "They say it's very valuable, and different from the materials available in the past," Viviani says.

So different, in fact, that in at least one class, when the bell rang at the end of the period, students did not get up to leave.

For more information on Aim for Algebra, contact Steve Schneider at 650.381.6410 or sschnei@WestEd.org, or Kimberly Viviani at 650.381.6429 or kvivian@WestEd.org.

Contact Information

Kimberly Viviani
650.381.6429
kviviani@wested.org