Adults' conceptualizations of fractions

The purpose of this study was to compare the misconceptions of adults with respect to the basic fractional concepts of partitioning, comparison, and equivalence with those misconceptions that have been identified by researchers concerning children. These concepts were examined in various models (continuous part-whole, discrete part-whole, and measure), and in various modes of representation (concrete, pictorial, and symbolic).; The participants in this study were four adult freshmen students enrolled in a Pennsylvania state university remedial mathematics class, who were self-identified as having difficulties with fractions. The students worked in groups of two or individually to perform given tasks developed to fit a matrix of the aforementioned concepts. Data was collected from the initial interviews, tasks, and diary questions, which were audio and video taped and then transcribed.; The following misconceptions with respect to fractional concepts were found in this study: (1) Confusion over the use of the word “more” (greater, less). (2) “Reducing” makes a fraction “smaller”. (3) The denominator refers to the number of pieces, regardless of the unequal sizes of the pieces. (4) Parts must be congruent, i.e., “look alike” or “look like one-half”. (5) Number in denominator must match the number of parts in the whole. (6) The unit makes no difference. (7) Mixed number interpretation in partitioning. (8) Whole number ideas apply to fractions. (9) A rule or procedure can be applied indiscriminately. (10) The number in the denominator indicated how many items are in each group instead of the number of groups. (11) When interpreting what part of a figure is shaded, the numerator is the number of shaded parts and the denominator is the number of unshaded parts (or vice versa).; There appeared to be six themes underlying all of the misconceptions held by these adults. These were: (1) lack of connections between modes of representation; (2) difficulty with various physical models, especially the measure model; (3) whole number interferences; (4) additive thinking versus multiplicative thinking; (5) measurement versus partitive division; (6) lack of self reflection, metacognition, or sense making of answers.