This study used an open-ended problem-solving approach to teaching and assessing middle school students' understanding of the concept of arithmetic average. Three main results of this study show evidence of positive instructional impact on students' understanding of the concept of average: (1) the number of students who gave correct answers increased from pretest to posttest; (2) on the posttest, more students used appropriate strategies to solve the average problems than on the pretest; and (3) more students used multiple representations on the posttest to explain their solutions than on the pretest. The findings of this study indicate that learning the concept of average is cognitively more complex than the computational algorithm suggests. However, with appropriate instruction, students can have an understanding of the concept beyond the computational algorithm. (Author)