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.
Highlights
On 25 September 2015, the General Assembly of the United Nations presented the2030 Agenda for Sustainable Development, in which one of the goals is [1] (p. 16) “Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all”
Comparing the Spanish curriculum with the principles and standards proposed by the National Council of Teachers of Mathematics (NCTM) for school Mathematics [5], we found similarities, since the NCTM proposes to develop the understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers for students from 8 to 10 years
Given the characteristics of our study, we focus on the knowledge of the topics (KoT), since the teacher must possess a deeper mathematical knowledge than the one the students have to achieve [27], that is, concepts, properties, procedures, phenomenology and representation systems linked to a mathematical content [28]
Summary
On 25 September 2015, the General Assembly of the United Nations presented the2030 Agenda for Sustainable Development, in which one of the goals is [1] (p. 16) “Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all”. The teaching and learning of fractions have been topics of interest due to the difficulties that Primary Education students have with this content [29,30,31,32]. Kieren [33] differentiated four meanings for the concept of fraction: measure, ratio, quotient and operator, expanding to five with the inclusion of the part–whole meaning [29,34,35,36] Authors such as Lamon [34] underlined the importance of establishing and differentiating the five fraction subconstructs and their interpretation as an essential element for the conceptual understanding of fractions [37,38] (see Table 1)
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