Unpacking Referent Units in Fraction Operations

Philipp, Randolph A.; Hawthorne, Casey

doi:10.5951/teacchilmath.22.4.0240

Cited by 4 publications

(3 citation statements)

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“…This was seen when they interpreted the amount leftover in their representation as ¼ instead of as 1/3 of a group of ¾. It has been suggested that one of the major reasons students struggle with fractions is that it requires attending to the referent unit (Philipp & Hawthorne, 2015). It is important that teachers have a developed understanding of referent unit so that they can help students make the unit or whole explicit.…”

Section: Discussionmentioning

confidence: 99%

“…Our study extends this work by including a division sentence that does not have a whole number answer as well as requiring teachers to solve their invented problems with a pictorial representation. It has been suggested that one of the major reasons students struggle with fractions is that it requires attending to the referent unit (Philipp & Hawthorne, 2015). In order for teachers to develop this understanding in students it is important that they are able to make sense of the unit with fraction division (Cramer, Monson, Whitney, Leavitt, & Wyberg, 2010).…”

Section: Teachers' Understanding Of Fraction Divisionmentioning

confidence: 99%

“…In our study teachers needed to have a greater understanding of the referent unit to correctly use their pictorial representation to come to the correct solution. One of the major reasons students struggle with fractions is that it requires attending to the referent unit (Philipp & Hawthorne, 2015). It is important that teachers are able to make sense of the unit with fraction division to develop this understanding with their students (Cramer, Monson, Whitney, Leavitt, & Wyberg, 2010).…”

Section: Conceptual Knowledge Through Multiple Representationsmentioning

confidence: 99%

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Fourth to Sixth Grade Teachers’ Invented Real World Problems and Pictorial Representations for Fraction Division

Stohlmann

Yang

Huang

et al. 2019

INT ELECT J MATH ED

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Teaching fraction operations for conceptual understanding is a challenging task. For the topic of fraction division especially, teachers need support because teachers find this difficult to teach and elementary and middle school students struggle to learn this concept. Well-structured professional development can assist teachers in exploring their own understanding as well as how to incorporate multiple representations in their instruction. This naturalistic inquiry study investigated fourth to sixth grade teachers' invented real-world problems and pictorial representations for fraction division. The teachers completed a written assessment focused on conceptual understanding of fraction operations through multiple representations at the beginning and conclusion of a weeklong professional development experience. The questions on the assessment were taken or modified from prior research studies. The results in this paper focus specifically on a task in which the teachers had to develop a real world story problem for 2 1 2 ÷ 3 4 and solve the problem by drawing a pictorial representation. The teachers showed statistically significant improvement on developing appropriate real-world problems and using pictorial representations to solve their problems. Implications for teachers' usage of multiple representations are discussed along with needed structures for professional development targeted on fractions.

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Section: Discussionmentioning

confidence: 99%

Section: Teachers' Understanding Of Fraction Divisionmentioning

confidence: 99%

Section: Conceptual Knowledge Through Multiple Representationsmentioning

confidence: 99%

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