A Fair and Balanced Approach to the Mean

  • A Fair and Balanced Approach to the Mean

    Susan A. Peters, Victoria Miller Bennett, Mandy Young, and Jonathan D. Watkins
    A sequence of five activities, progressing from concrete to abstract, can help students develop deep understandings of the mean.
    If a Jeopardy answer were, “Add ’em up and divide,” the question might be, “What is the mean?” But this is not what the mean is; it is the algorithm for calculating the mean. The mean can be interpreted as a fair-share value and as a balance point. Standards documents, including Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), suggest focusing on both interpretations. We propose a sequence of five activities to help students develop these understandings of the mean, and we offer insights for implementing the activities. We include extensive use of representations, from concrete to abstract (Bruner 1966), to scaffold students’ experiences and sequence discussions.