Identifying Fractions on Number Lines

Abstract

This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. Two clinical teaching experiments and one large-group teaching experiment were conducted with fourth and fifth graders (N = 5, 8, and 30) The instruction primarily concerned representing fractions and ordering fractions on number lines. Tests and videotaped interviews indicated that unpartitioning, in particular, is difficult for students, although the instruction seemed to help. Associating symbols with representations also seems difficult and may depend on an understanding of the unpartitioning process.

İlköğretim 4-7. Sınıf Öğrencilerinin Denk Kesirlerin Sembolik ve Grafiksel Temsillerini İlişkilendirme Becerilerinin İncelenmesi

“…Similarly, the difference between the part-whole and measurement interpretations could be since the part-whole interpretation is the first one child learns about fractions. On the other hand, another reason for this could be that, as Bright et al (1988) and Toluk (2002) pointed out, the constant use of the part-whole Sakarya University Journal of Education interpretation promotes the belief that fractions are part of a whole rather than referring to a number. It may also be because, as Contreras and Martinez-Cruz (2000), Park et al (2013) have highlighted, teachers who have been taught predominantly using the part-whole interpretation throughout their education do not spend much time in their classrooms for interpretations other than the part-whole interpretation of fractions.…”

“…For instance, the reason why the mean score of the regional area representation is greater than the other representations, in general, may be because it is the most used representation by teachers as it supports the part-whole interpretation when introducing fractions (Armstrong & Larson, 1995;Baykul, 2005;Hull, 2005). However, the fact that the number line representation has the lowest mean score in all research settings can be explained by the fact that the number line representation corresponds to the measurement interpretation, which is difficult to learn, that the number line representation has two separate references points when specifying fractions, and so on (Bright et al, 1988). Moreover, students have problems dividing the whole into equal parts and, accordingly, breaking down points between 0 and 1 either into more or fewer parts than the required parts, which can also be listed as the reasons why students have difficulty representing a number line (Aliustaoğlu, Tuna, & Biber, 2018;Pesen, 2008;Wong & Evans, 2011).…”

“…The number line representation gives meaning to the concept of fractions as an abstract real number. Because of this property, the number line representation is the most important representation pointing to the measurement interpretation of fractions (Bright, Behr, Post & Wachsmuth, 1988;Clarke, Roche, & Mitchell, 2008;Sidney et al, 2019). That is why the representation of number lines is more difficult to understand than other representations.…”

Student Understanding of Linear Scale in Mathematics: Exploring What Year 7 and 8 Students Know

“…Research indicates that students have difficulty with using the number line to represent fractions (Baturo & Cooper, 1999;Behr et al, 1983;Bright, Behr, Post, & Wachsmuth, 1988;Larson, cited in Ni, 2000;Novilllis, cited in Ni, 2000). Hart (1989), in talking of the Concepts in Secondary Mathematics and Science (CSMS) study, indicated that scrutiny of all the easy CSMS items "suggested many secondary-aged children worked entirely within the set of whole numbers" (p. 46).…”

“…or or Bright et al (1988) report three teaching experiments, including a follow up to the work on visual distractors. They identify that the number line is different from other fraction representations.…”