Comparison of algorithmic and multiple-representation integrated instruction for teaching fractions, decimals, and percent

ABSTRACT

This study examined the effects of two teaching treatments [multiple-representation instruction (MR) and traditional algorithmic instruction (TA)] on students’ performance on mathematics problems that integrated fractions, decimals, and percent. Using a 2 × 2 crossover design, the effect of the teaching treatments and their sequences on student performance were compared. Students in the MR/TA treatment sequence group received instruction in which multiple representations were integrated followed by traditional algorithmic instruction, and students in the TA/MR treatment sequence group received treatments in the reverse order. Participants included 89 seventh-grade students enrolled in a pre-algebra course in an urban middle school in the Midwestern United States. Results indicated gains in performance from both teaching treatments (MR and TA), however, statistically significant higher performance was found with the traditional algorithmic treatment. In terms of the order of teaching treatments, no significant performance difference was found.

KEYWORDS:

• Algorithms
• middle school mathematics
• multiple representations
• rational numbers
• symbolic representations