Research on mathematics teachers’ knowledge has generally focused more on mathematics concepts than mathematical processes. This paper addresses the latter with a focus on mathematical problem solving (PS). It reports on a study that investigated the pedagogical knowledge for PS of prospective elementary school teachers of mathematics (PTs). Participants were 149 PTs at a university in Spain. They were at the end of their teacher education program. Data sources consisted of a questionnaire on knowledge of learning PS and a questionnaire on knowledge of teaching PS. Findings indicated that the PTs held combination of different levels of knowledge of PS learning and teaching. Many of them demonstrated appropriate knowledge of many characteristics for (1) PS learning consisting of student as a problem-solver, PS as a worthwhile task, non-cognitive factor related to PS, and (2) PS teaching consisting of PS teaching approaches, discourse in PS, intervention during stuck state in PS, PS assessment, and PS resources. However, there were also contradictions and limitations to their knowledge with implications for teacher education. These combination of appropriate and inappropriate knowledge resulted in some conflicts that are related to teaching actions and would limit student’ learning of PS.

La importancia que presenta la resolución de problemas en la enseñanza y aprendizaje de la matemática es una premisa aceptada en la comunidad de educadores matemáticos. No obstante, los marcos que describen o caracterizan el conocimiento de los profesores sobre las matemáticas escolares han dado poca relevancia a este proceso. Partiendo de revisiones curriculares y teóricas, presentamos una organización del conocimiento del profesor de educación primaria sobre la resolución de problemas de matemáticas. En ella diferenciamos un conocimiento sobre la resolución de problemas del que emergen los componentes relativos al concepto de problema, proceso de resolución y disposición para afrontar un problema; y un conocimiento pedagógico sobre la resolución de problemas en el que distinguimos un componente referido al aprendizaje y otro a la enseñanza. Nuestra reflexión ratifica la idea que la naturaleza distinta de un proceso como la resolución de problemas provoca un conocimiento que los modelos han omitido.Teacher knowledge components for teaching problem solving in primary educationProblem solving is central in teaching and learning of mathematics, an accepted premise in the community of mathematics educators. However, the frameworks that describe or characterize teachers' knowledge have given little relevance to this process. Starting from curricular and theoretical revisions, we present a proposal of organization for the knowledge of primary teacher about problem solving. We differentiate a knowledge of the process from which the components related to the concept of problem, resolution process and disposition to face a problem emerge; and a pedagogical knowledge where we distinguish a component referring to learning and another to the teaching of problem solving. Our reflection confirms the idea that the different nature of a process such as problem solving, causes a knowledge that the models have omitted.doi: 10.30827/pna.v13i2.7876Scopus record and citations

Mathematics teacher candidates enter teacher education with knowledge that could support or limit their learning. It is therefore important to gain insights of this knowledge to inform teacher education. This paper offers such insights for prospective mathematics teachers’ initial knowledge of problem solving (PS) for teaching at the beginning of their teacher education programme. It reports on a study that investigated three categories of problem-solving knowledge for teaching: problem characterization, the PS process, and PS disposition. Participants were 109 prospective primary teachers at a university in Spain. Data sources were questionnaires designed for the study to explore the initial knowledge held by the participants for three categories of problem-solving knowledge. Findings indicated that the participants’ knowledge was stronger regarding the PS process and disposition than for problem characterization but had limitations that needed to be addressed in their teacher preparation programme.

In this paper, we studied the knowledge on didactic contents reflected by future elementary teachers when answering questions related to teaching and learning fractions. Following a qualitative methodology, specifically a case study, 9 senior pre-service elementary teachers were interviewed using a structured approach. The topic was presented to the subjects using a narrative they had previously written on how to initiate the concept of fractions with school children. After reading it, they were asked questions regarding task design, learning objectives, and mistakes and difficulties. Results identified two trends in the participants’ knowledge: a procedural or technical trend in which the stated knowledge emphasizes procedures, processes, or action modes, and a conceptual or cognitive trend in which the stated knowledge emphasizes the functional understanding of fractions and their relationships. As a conclusion, it is essential that initial teacher training emphasizes mathematical as well as didactic contents.