Promoting Mathematics Teachers’ Pedagogical Metacognition: A Theoretical-Practical Model and Case Study

Researchers agree that “metacognition” conceptualizes the kind of learning that fits our fast-changing, meta-modern world: an autonomous, lifelong learning which is adjustable to new learning tasks. Metacognitive active persons develop such learning because they are aware of their knowledge and, simultaneously, they can control and regulate further learning by activating strategies and evaluating its efficiency (Flavell. Am Psychol 34(10):906–911, 1979; Schraw. Contemp Educ Psychol 19:460–475, 1998). Over the years, metacognition has been linked to improved student outcomes (e.g., Veenman et al. Metacognition Learn 1(1):3–14, 2006). In the field of mathematics, research findings indicate that failure or success in mathematics, such as problem-solving, can be due to the use of metacognition (Kramarski, Mevarech. Am Educ Res J 40:281–310, 2003; Schoenfeld. Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In DA Grouws (ed) Handbook of research on mathematics teaching and learning. MacMillan, New York, pp 165–197, 1992; 2011). The role of metacognition in mathematics sets new goals for teachers, since teachers’ ability to cultivate learners with metacognition during learning is tied to teachers’ own metacognition. If teachers are incapable of activating metacognitive skills, it will be difficult for them to instill these skills in their students. Research indicates that metacognition is not attained spontaneously; it demands explicit scaffolding (Kramarski and Michalsky. Learn Instruct 20(5):434–447, 2010). The current study has three main goals: (a) building a theoretical-practical model of pedagogical metacognition designed for preservice mathematics teachers that focuses on self-regulation processes; (b) applying this model in a technological-pedagogical context, supported by reflection; and (c) examining the implementation of the model with a case study methodology analysis of two preservice mathematics teachers. The pedagogical metacognitive model is applied through microteaching, which is based on planning, performing, and reflective evaluation of a teaching experience performed by one of the preservice teachers to his peers who act as students and recorded in a video-digital laboratory. Support for applying the model is provided through a technological web-based environment to help the preservice teachers to direct reflection on their metacognitive self-regulation process. Case studies of two preservice teachers’ actual teaching are analyzed and compared: one who explicitly implemented the theoretical-practical model and the second who partially implemented the model. The case study analysis will demonstrate practically mathematical teaching episodes with emphasis on metacognitive self-regulation process in a pedagogical context. The study offers important theoretical, practical, and methodological contributions for training mathematics’ pre-/in-teachers in a web-based environment.