Chapter 7 How to Stimulate In-Service Teachers’ Didactic Analysis Competence by Means of Problem Posing Uldarico Malaspina, Carlos Torres, and Norma Rubio 7.1 Introduction Recently, researchers in mathematics education are becoming more interested in problem posing (Felmer, Pehkonen, & Kilpatrick, 2016; Malaspina, Mallart, & Font, 2015; Singer, Ellerton, & Cai, 2015; Torres & Malaspina, 2018). These scholars claim that it is very important for teachers to develop problem posing skill by both modifying given problems as well as posing them from concrete situations. Evidently, in a problem posing activity, the person’s mathematical knowledge is brought into play, but if the problem posed is aimed at contributing to the student’s knowledge—or more specifically, to understanding and solving other more complex problems—then the teacher’s didactic-mathematical knowledge must also intervene. This aspect is closely related to the teachers’ didactic analysis competence, which has been broadly studied within the onto-semiotic approach of cognition and mathematics instruction (OSA) (Breda, Pino-Fan, & Font, 2017; Rubio, 2012). In our study, we focus on analyzing what representations, strategies, and resources teachers showed while dealing with tasks that involve problem posing activities (Font, Planas, & Godino, 2010; Torres & Malaspina, 2018). Thus, we adopt the lines of research that use problem posing as a window of oppor- tunities for students and teachers to understand mathematics, as well as the studies of specific strategies for problem posing (Kontorovich & Koichu, 2009; Malaspina et al., 2015; Milinkovié, 2015; Mallart, & Font, 2015). The work shown by 15 in-service high school mathematics teachers on problem posing is analyzed, and evidences of the close link between the didactic analysis competence and the problem posing skill that facilitate learning are discussed. U. Malaspina (B ) · C. Torres, · N. Rubio Pontificia Universidad Católica del Perú, Lima, Peru e-mail: umalasp@pucp.edu.pe © Springer Nature Switzerland AG 2019 P. Liljedahl and M. Santos-Trigo (eds.), Mathematical Problem Solving, ICME-13 Monographs, https://doi.org/10.1007/978-3-030-10472-6_7 133