Analyzing Pre-Service Primary Teachers’ Fraction Knowledge Structures through Problem Posing

Abstract

In this study it was aimed to determine pre-service primary teachers' knowledge structures of fraction through problem posing activities. A total of 90 pre-service primary teachers participated in this study. A problem posing test consisting of two questions was used and the participants were asked to generate as many as problems based on the following conditions: i) using both 1 2 and 3 4 fractions, and ii) using either 1 2 or 3 4fractions. Data were analyzed using both semantic and constant comperative analysis techniques. The results of the study showed that there was substantial diversity in the problems posed by pre-service primary teachers. Moreover, participants preferred to pose story and symbolic equations in first task and story equation in second task. Furthermore, the participants faced some issues such as not realizing 1 2 + 3 4 situation is more than 1, missing data, choosing wrong number, using different fractions and posing non-fraction problem.

The Analysis of the Problems Posed by Pre-service Elementary Teachers for the Addition of Fractions

“…To be able to determine what the students know and what kind of errors made in their posed problems, teachers need to pose correct problems themselves. In spite of its importance, in-service and pre-service teachers have difficulties in problem posing activities related to the fractions (Isik & Kar, 2012;Isiksal, 2006;Kilic, 2015;Rizvi, 2004;Rizvi & Lawson, 2007;Tichá & Hošpesová, 2012). Specifically, Isik and Kar (2012) stated that pre-service teachers made different type of errors when they were asked to pose problems related to the division of fractions.…”

“…The Analysis of the Problems Posed by Pre-service Elementary … International Journal of Instruction, January 2019 • Vol.12, No.1 fractions such as 1/2 and 3/4 and were asked to pose problems, most of them posed problems related to the addition of fractions (Kilic, 2015). However, the appropriateness of these problems and the type of errors made in these problems were not considered.…”

Fraction Multiplication and Division Word Problems Posed by Different Years of Pre-Service Elementary Mathematics Teachers

“…In the first three grades of the school, students learn comparing and ordering fractions. When students in the fourth and fifth grades, they begin to learn addition, subtraction, and multiplication operations with fractions (Kilic, 2015). Students start to experience posing problems with natural numbers from first grade.…”

“…Analyzing pre-service teachers' knowledge of fractions by problem posing will help teacher educators to develop their knowledge about fractions. Doing that will help pre-service teachers to be equipped problem posing (Kilic, 2015).…”

“…The studies on problem posing indicate that pre-service teachers' level of success in demonstrating problem posing skills is generally low (Isik, 2011;Isik, Isik & Kar, 2011;Toluk-Ucar, 2009). For professional development of pre-service teachers' we have to develop their mathematical knowledge structures during their education, and it is possible to achieve this goal through teacher education programs (Kilic, 2015). In Turkey, pre-service elementary mathematics teachers learn how to teach mathematics in elementary mathematics teacher education programs through method courses such as Mathematics Methods I and Mathematics Methods II.…”