Many learners have difficulties moving from whole number understandings to rational number understandings. These conceptual understandings and misunderstandings often become visible as students represent that understanding in pictorial and symbolic representations of the rational number. Pictorial representations of rational numbers can include area models, linear models, and set models among others. When the representation is a part/whole area or measurement model in which the total number of equal size pieces in the whole matches the denominator and the shaded part of the whole equals the numerator, this is referred to as a “simple representation” of the fraction. When the pictorial representation has a whole where the number of equal parts is a multiplicative factor of the denominator of the fraction in symbolic form then this is considered an “equivalent representation” (Wong and Evans, 2007). One of the critical attributes of a simple or equivalent representation when partitioning a whole is that the size of each of the parts needs to be an equal size region although they do not necessarily need to be of the same shape. O<en during instruction students work with models that are already the same size and shape (Van de Walle, Karp & Bay-Williams, 2010). This sometimes leads to students thinking that the pieces must be the same shape while others do not even consider size as an attribute at all.

These assessments are designed to elicit misunderstandings, over-generalizations, and/or misconceptions associated with simple representations of a fraction.

Representing Fractions I is designed to elicit misconception 1 where students consistently associate the number of pieces shaded with the numerator and the total number of pieces for the en1re figure with the denominator but do not pay aLen1on to the size of the pieces (or region).

Representing Fractions II is designed to elicit misconception 2 where students associate the number of pieces shaded with the numerator and the total number of pieces for the entire figure with the denominator and do pay attention to equal shape pieces but do not consider different shape/equal size pieces or equivalent representations.

Funded by IES Award #R305A110306-12 See project description at http://ies.ed.gov/funding/grantsearch/details.asp?ID=1083

For more informations about this project contact Cheryl Tobey: ctobey@edc.org