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Low Achievers May Benefit from Interactive Mathematics

December 2006

Brian Bottge	Enrique Rueda

Students with special learning needs require alternative forms of assessment that allow them to express all they know and can do. Without these accommodations, teachers can’t accurately measure student learning.

In a recent study, low-achieving students in mathematics made slightly larger gains on a multimedia computer-based assessment than on a traditional pencil-and-paper assessment. This suggests that the multimedia test may have accommodated at least some special needs of these students.

Constructivist Approach. . . What is it?

The new wave of reform in mathematics education encourages teachers to provide more opportunities for students to enhance their computing and problem-solving skills in concept-rich contexts. One such reform is known as the constructivist approach.

The constructivist approach to teaching encourages students to construct and reconstruct their math understanding as they interpret new information in light of what they already know. Students deal with novel problems in a variety of settings so they can recognize the relationships among important mathematical ideas.

But how can educators modify the teaching practices used in special education and other remedial settings to align with current reform-oriented practices? Judging from current practice and research, it will not be easy to make the transition to more constructivist teaching practices with students needing remediation, says UW-Madison education professor Brian Bottge.

Enhanced Anchored Instruction (EAI) provides one avenue. EAI requires students to solve a problem in a multimedia format and then apply what they learn. In related hands-on problems they construct something meaningful to them, for example, a skateboard ramp or a working model hovercraft.

EAI research addresses the curricular and instructional needs of low performing students in reform-oriented math contexts. But here’s the catch: Little attention has focused on developing assessments that can adequately measure the problem-solving ability of students who learn with EAI.

UW-Madison education professor Brian Bottge and colleague Enrique Rueda developed and evaluated the effectiveness of a multimedia computer-based assessment in a recent study of 109 seventh-grade students and their two math teachers. Students in each of the six classes were randomly assigned to either a computer-based assessment or a paper-and-pencil assessment.

Bottge had developed a multimedia EAI problem called Fraction of the Cost, which had been integrated into the school’s math curriculum the year before. Bottge developed Fraction of the Cost to address the knowledge and concepts in the National Council of Teachers of Mathematics (NCTM) Standards recommended for students in grades 6-8.

Fraction of the Cost includes an 8-minute video presentation, or anchor. It stars three local middle school students. In the video, they visit a skateboard store and discuss how they can afford to buy materials for building a skateboard ramp. To solve the problem, students need to (a) calculate the percent of money in a savings account and sales tax on a purchase, (b) read a tape measure, (c) convert feet to inches, (d) decipher building plans, (e) construct a table of materials, (f) compute whole numbers and mixed fractions, (g) estimate and compute combinations, and (h) calculate total cost.

After students in the math class view this video they describe the mathematics problems involved, then work in small groups. The teacher then assesses the students’ learning either with the computer-based assessment (CBA) or the paper-and-pencil based assessment (PPA). Each assessment contains constructed-response items (see below) that measure the concepts in Faction of the Cost.

The CBA measures the same concepts as the PPA, with the additional benefit of providing students a level of interactivity similar to what they had experienced in the contextualized authentic-like problems in EAI. Bottge anticipated that the new test would especially benefit the low-achieving students: They could access information for solving the EAI problem on the test rather than having to recall the relevant information from the instructional period.

To identify differences in students’ problem-solving strategies, Bottge recorded and measured students’ search paths as they worked on the CBA. Bottge predicted that the CBA would eliminate some of the cognitive demands of problems for the low-achieving students and would thus enable them to more fully demonstrate their understanding of the math concepts they had learned.

That seems to have happened. The study showed that low achievers made slightly larger gains on the CBA than on the PPA. This research provides a first step in developing multimedia-based assessments that can match the contextualized nature of Enhanced Anchored Instruction. The accommodations provided by more flexible test formats may have the potential to more adequately assess deeper understandings of students with poor language skills.

In future work Bottge expects to merge interactive assessments as used in this study with interactive instructional tools to provide formative measures of student skills. The aim is to help teachers individualize instruction and to help them evaluate the effectiveness of curricular materials and instructional practices.

This research was funded by grant from U.S. Department of Education, Institute of Education Sciences.

Bottge, B.A., Heinrichs, M., Mehta, Z. D., Rueda, E., Hung, Y., & Danneker, J. (2004). Teaching mathematical problem solving to middle school students in math, technology education, and special education classrooms. Research in Middle Level Education On-line, 27(1).