Abstract
Teacher educators have a responsibility to help prospective teachers in their professional growth. It is important that teacher educators not only teach prospective teachers about benefits of active learning in student learning, but that they also prepare future teachers in using pedagogical methods aligned with active learning principles. This manuscript provides examples of how mathematics teacher educators can promote prospective teachers' active learning and professional growth by bringing together the Flipped Classroom method with video content on teaching and learning as well as workplace learning opportunities in a pedagogy course. The professional learning of prospective teachers is framed according to the components of the Pedagogical Content Knowledge (Park & Olive, 2008; Shulman, 1986). Implications for future trends in teacher education are provided.
TopLiterature Review
Active Learning and Nature of Mathematics
Recent research in learning recommends use of several different approaches in learning such as problem-based learning, cooperative learning, project-based learning, etc. (Bell, 2010; Donnelly & Fitzmaurice, 2005). One common aspect of such different approaches is the active role of the learners and their involvement in the inquiry process. Although benefits and challenges of implementing active learning have been frequently discussed in engineering education, there is room for research and dissemination of best practices on active learning in teacher education practices.
Before focusing on practices of teacher education, it is important to explore the nature of mathematics and how it fits the active learning recommendations. In the Standards for Mathematical Practices (Common Core State Standards Initiative, 2010), it is suggested that mathematically proficient students make sense of problems, engage in reasoning, analyze different situations and construct meaningful arguments, model by using mathematical language, use tools in a strategic manner, pay attention to details as well as regularities and patterns in the process of problem solving. In their influential publication about habits of minds, Cuoco, Goldenberg, and Mark (1996) described general habits of mind which will not only serve in learning mathematics but also help become members of a learning society in the following way: being pattern snifters, describers, thinkerers, inventors, visualizers, conjecturers and guessers. It is apparent that such demanding practices and habits of mind will not be improved by traditional lecture where learners are the passive recipients of information. In contrast, learners are called to develop new ways of thinking rather than being consumers of information. A recent pedagogical method that has a potential to bring different aspects of active learning to come together and have an influence greater than the sum of their individual impact is the Flipped Classroom pedagogy that will be presented in this chapter for the particular use in mathematics teacher education.
Key Terms in this Chapter
Flipped Classroom Method: Inverting in class and out of class activities such that there is more allocated time for active learning and teacher facilitation of meaningful discussion during class time. Homework is in general in the form of viewing video materials (which maybe supported by audio materials and readings) and becoming familiar with the foundations of the content before coming to the class.
Professional Vision: Using specialized professional knowledge to attend to and interpret events related to one’s profession ( Goodwin, 1994 ).
Professional Noticing: Learning to notice important aspects of classroom instruction is considered an important area of expertise for teachers. van Es and Sherin (2002) describe three significant aspects of noticing that constitute a basis for the conception of professional teacher noticing: 1. Identifying what is important or noteworthy about a classroom situation; 2. Making connections between the specifics of classroom interactions and the broader principles of teaching and learning they represent; and 3. Using one’s context to reason about noteworthy events (p. 573).
The TIMSS Video Study: “The TIMSS 1999 Video Study was a study of eighth-grade mathematics and science teaching in seven countries. The study involved videotaping and analyzing teaching practices in more than one thousand classrooms. Goals of TIMSS 1999 Video Study: investigate mathematics and science teaching practices in U.S. classrooms, compare U.S. teaching practices with those found in high-achieving countries, discover new ideas about teaching mathematics and science, develop new teaching research methods and tools for teacher professional development, create a digital library of images of teaching to inform U.S. educational policy, stimulate and focus discussion of teaching practices among educators, policymakers, and the public” (TIMSS Study, http://www.timssvideo.com/about-site AU37: URL Validation failed the service http://www.timssvideo.com/about-site is temporary unavailable. ).
Clinical Interview: One-to-one interviews conducted with students in order to gauge their understanding, which could be used both for assessment and research ( Ginsburg, 1997 ).