2008年1月1日 · Students develop an understanding of fractions as a measure when they are able simultaneously co-ordinate the referent unit, symbolic notation and pictorial representations of various...

designed to probe conceptual understanding of fractions. Analysis revealed the CJ assessment process yielded high internal consistency, inter-rater reliability and validity. We discuss the implications of the results for using CJ to measure mathematical understanding in a variety of domains and contexts.

The measure concept of fraction can be interpreted as numbers that can be ordered on a number line. This notion is important for adding and subtracting fractions. For example, if two fractions with unlike denominators are interpreted as a measure (i.e., as distances from

It is critical that students internalize such reasoning, rather than memorizing formulas for converting units, in order to understand fractions and measurement. If a segment does not have an integer length, we can attempt to measure it by cutting our measuring unit into smaller parts and using them as finer units.

The 'fraction as a measure' idea is best demonstrated using a linear model. The measure model supports the understanding that a fraction is a number, with a position on a number line.

When teaching fractions, we need to take into account that fractions can be interpreted in several different ways (Kieran, 1976, 1993). The interpretations are part-whole, ratio, operator, quotient, and measure. There is inevitable overlapping between the interpretations, but in Table 1 each interpretation is exemplified using the fraction ¾.

2018年6月27日 · Here, we describe a progression of four fraction schemes that involve such mental actions: the part-whole scheme (PWS), the measurement scheme for unit fractions (MSUF), the measurement scheme for proper fractions (MSPF), and the generalized measurement scheme for fractions (GMSF).

We conducted teaching experiments to study how students can develop a measurement concept of fractions and how task sequences can be developed to promote the necessary abstractions.

improving and understanding the development of fraction compe-tence for fourth graders at risk for poor outcomes. We assessed the efficacy of a 12-week intervention and examined the processes by which effects occurred to increase understanding about the devel-opment of competence with fractions. Only a handful of studies