Developing Technological Pedagogical Content Knowledge of Pre-Service Math Teachers

Omar Hernández-Rodríguez
University of Puerto Rico

Need – Several researchers have found a gap between the methods courses taught at universities and the field experiences that prospective teachers perform in schools (Darling-Hammond et al., 2005). To close this gap, we modified the course on the use of manipulatives and technology in teaching mathematics at the secondary level. We report how the activities combined with clinical experiences help strengthen the prospective mathematics teachers’ (PMT) professional observation. We define professional observation as the capacity to describe, explain and predict the consequences of teaching moves. In this investigation, describe is the ability to identify, differentiate and classify the components of the teaching and learning process; explain is the ability to relate classroom observations to specific didactic concepts; and predict is the ability to forecast the consequences of classroom activities with student learning (Blomberg et al., 2011; Seidel & Stürmer, 2014; Zaragoza, 2021).Guiding Questions – We ask, how can professional observing be scaffolded in methods courses? Specifically, we focus on answering: What activities promote the development of professional observing? How do PMTs connect theoretical knowledge with the teachers’ practice they observe?Participants (N=16), mathematics PMTs, were exposed to theoretical aspects about the development of mathematical proficiency in students and, in addition, were asked to observe the classes of their cooperating teachers (CT). They used three instruments to report how CT developed the students’ mathematical proficiency (FKilpatrick et al., 2001). To prepare the instruments, we use models presented in the literature (Gleason et al., 2015; Jackson et al., 2011; Mathews et al., 2009; Sawada et al., 2002).PMTs’ reports of their observations (n=48) were used as a source of information for this research. These observations correspond to the first three components of mathematical proficiency (conceptual understanding, procedural fluency, and strategic competence). Four researchers created the codebook, discussed it, and performed pilot test coding in pairs until achieving a Kappa coefficient greater than 0.75. Subsequently, they coded individually and held regular discussion meetings to calibrate the coding. The purpose of coding was to determine the development of PMTs’ professional observations. Outcomes – Preliminary analyses indicate that PMTs are more likely to describe predominant class events. They can identify, relate, and differentiate the actions of the CT and the students in the class; however, they barely abound in their explanations. The PMTs hardly reported the observations of the mathematics classes they saw with the didactic concepts studied in the methods course. Nor do they were abundant in their predictions. They barely anticipate the consequences of classroom activities with student learning.Broader impacts – The findings allow us to propose alternatives to teacher training programs and bring professional knowledge closer to practice. First, we highlight the aspects to consider in the observation instruments used by the PMT. Second, we describe the relevant classroom events for the PMT. Finally, we recommend tasks to promote PMT’s ability to explain and predict, for example, to conduct discussions with peers about observations, using a specific set of questions that encourage explanation and prediction.


Wanda Villafañe-Cepeda, University of Puerto Rico; Juliette Moreno-Concepción, University of Puerto Rico; Yency Choque-Dextre, University of Puerto Rico