Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems

Abstract

The preservice primary school mathematics teacher needs training that focuses on school mathematics and its didactics. Research has shown the importance of developing mathematical content knowledge as well as adequate didactic knowledge. Teacher education programs must address both to provide an effective teaching-learning process. The present research aims to assess the mathematical content knowledge of 194 prospective teachers about fraction word problems faced by students at the Primary Education stage, based on the Mathematics Teachers′ Specialized Knowledge (MTSK) model. By means of the preservice teachers’ written answers, we explored their knowledge and identified the associated error to fraction word problems (one-step and multistep) in which the fraction has a meaning as an operator. Preservice teachers showed some difficulties when working with this content, difficulties that were intensified when they solved multistep problems. The most common error founded in both types of problems is related to the meaning of fraction as operator. The results show a weak prior mathematical content knowledge and as a consequence, it is necessary to establish preventive actions in the training degrees since an insufficient mathematical content knowledge prevents them having a proper didactic knowledge.

Portraying mathematics teachers’ knowledge for teaching the addition of fractions through representations

“…This matches the original ideas of Ball et al (2008), as they considered teachers' ability to "evaluate the instructional advantages and disadvantages of representations used to teach a specific idea and identify what different methods and procedures afford instructionally" (p. 401) part of their KCT. It is also consistent with López-Martín, Aguayo-Arriagada, and García López's (2022) description of KCT in the case of fractions as knowing "the different ways of representing a fraction (discrete models and continuous models)" (p.3).…”

“…In this question, knowledge of teaching and content does an amalgam, which defines teachers' KCT. That is, KCT, in this study, outlines teachers' ways of representations while teaching the addition of fractions (Ball et al, 2008;López-Martín et al, 2022), and representations indicate visual models such as circles, squares, triangles, number lines, etc.…”