The nature of prospective mathematics teachers' pedagogical content knowledge: the case of multiplication of fractions

The purpose of this study was to investigate prospective mathematics teachers' knowledge of common conceptions and misconceptions that sixth and seventh grade students had about multiplication of fractions. In addition, prospective teachers' knowledge of the sources of these misconceptions and strategies they knew to overcome these misconceptions was examined. Data were collected from 17 Turkish prospective teachers at the end of the spring semester of the 2004-2005 academic year. A case study design was used in which data were collected through the Multiplication of Fractions Questionnaire and semi-structured interviews. The prospective teachers suggested many difficulties that elementary grade level students may have and stated that these difficulties stemmed from students' lack of formal knowledge and rote memorization of the algorithms. In addition, the prospective teachers suggested many strategies that could be used to overcome these misconceptions or difficulties. These strategies could be grouped under three headings: strategies based on teaching methods, strategies based on formal knowledge of fractions, and strategies based on psychological constructs.


The effects of a mathematics teaching methods course on pre-service elementary mathematics teachers’ content knowledge for teaching mathematics
Seviş, Şerife; Koç, Yusuf; Department of Elementary Science and Mathematics Education (2008)
The purpose of this study is to examine the effects of a mathematics teaching methods course on pre-service elementary mathematics teachers’ content knowledge for teaching mathematics (CKTM). In order to accomplish this purpose, pre-service mathematics teachers’ understanding of basic concepts and procedures in school mathematics, use of mathematical definitions, presentation of mathematical content to students, identification of common errors, misconceptions and solution strategies and evaluation of unusua...
Mathematical Knowledge for Teaching the Function Concept and Student Learning Outcomes
Hatisaru, Vesife; Erbaş, Ayhan Kürşat (Springer Science and Business Media LLC, 2017-04-01)
The purpose of this study was to examine the potential interrelationships between teachers' mathematical knowledge for teaching (MKT) the function concept and their students' learning outcomes of this concept. Data were collected from two teachers teaching in a vocational high school and their students through a function concept test for teachers and students, follow-up interviews with teachers, and classroom observations. Findings indicated that teachers' MKT and students' learning outcomes were related to...
UBUZ, BEHİYE; Ubuz, Behiye (Springer Science and Business Media LLC, 2015-12-01)
Two studies were conducted for the development and validation of a multidimensional test to assess undergraduate students' mathematical thinking about derivative. The first study involved two phases: question generation and refinement of the Thinking-about-Derivative Test (TDT). The second study included four phases as follows: test administration, generalizability analysis, confirmatory factor analysis, and subgroup validity analysis. Findings suggested that the 30-item multiple-choice TDT, which comprises...
Growth in children's understanding of generalizing and representing mathematical structure and relationships
Blanton, Maria; İşler Baykal, Işıl; Stroud, Rena; Stephens, Ana; Knuth, Eric; Gardiner, Angela Murphy (Springer Science and Business Media LLC, 2019-10-01)
We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3-5. Analyses showed that, while there were no significant differences between experimental and control students on a grade 3 pre-assessment measuring students' capacity for generalizing and representing generalizations, experi...
The Relationship Among Mathematics Teaching Efficacy, Math Anxiety, and Mathematical Self-Concept: The Case of Turkish Pre-Service Elementary Teachers
Işıksal Bostan, Mine (Philippines Journals Online (PhilJOL), 2010-11-01)
The purpose of this study was to investigate the relationship among pre-service teachers' mathematics teaching efficacy belief, math anxiety, and mathematical self-concept scores. The analysis was based on 276 elementary pre-service teachers enrolled in teacher education programs in Turkey. The Mathematics Teaching Efficacy Belief Instrument, the Abbreviated Mathematics Anxiety Scale, and the Experience with Mathematics Questionnaire were used as the measuring instruments. Structural equation modeling was u...
Citation Formats
M. Işıksal Bostan and E. Çakıroğlu, “The nature of prospective mathematics teachers’ pedagogical content knowledge: the case of multiplication of fractions,” JOURNAL OF MATHEMATICS TEACHER EDUCATION, pp. 213–230, 2011, Accessed: 00, 2020. [Online]. Available: