id: 02334580
dt: j
an: 2000d.02870
au: Watson, Jane M.; Moritz, Jonathan B.
ti: The longitudinal development of understanding of average.
so: Math. Think. Learn. 2, No. 1-2, 11-50 (2000).
py: 2000
pu: Taylor \& Francis (Routledge), Philadelphia, PA
la: EN
cc: K40
ut: 
ci: 
li: doi:10.1207/S15327833MTL0202_2
ab: The development of the understanding of average was explored through
    interviews with 94 students from Grades 3 to 9, follow-up interviews
    with 22 of these students after 3 years, and follow-up interviews with
    21 others after 4 years. Six levels of response were observed based on
    a hierarchical model of cognitive functioning. The first four levels
    described the development of the concept of average from colloquial
    ideas into procedural or conceptual desriptions to derive a central
    measure of a data set. The highest two levels represented transferring
    this understanding to one or more applications in problem-solving tasks
    to reverse the averaging process and to evaluate a weighted mean. Usage
    of ideas associated with the three standard measures of central
    tendency and with representation are documented, as are strategies for
    problem solving. Implications for mathematics educators are discussed.
rv: