Indicator C.1.1. Know Relevant Mathematical Content
Well-prepared beginning teachers of mathematics have solid and flexible knowledge of core mathematical concepts and procedures they will teach, along with knowledge both beyond what they will teach and foundational to those core concepts and procedures. (Standards for Preparing Teachers of Mathematics [AMTE], 2017 p.8)
Mathematics content courses are typically required course work for PSTs seeking teaching licensure for K-8th grade classrooms in the U.S. (Conference Board of Mathematical Sciences [CBMS], 2012; National Research Council [NRC], 2001; AMTE, 2017). Importantly, mathematics content courses should help PSTs develop a deeper and more comprehensive view and understanding of the mathematics that they will teach in order to be well prepared beginning teachers. Over time, researchers have offered insights on the nature of learning opportunities that teacher educators should give PSTs in mathematics content courses for elementary teachers. (Castro Superfine & Wagreich,. 2010; Castro Superfine & Li, 2014a, b; Gichobi, 2018, 2019; Li & Castro Superfine, 2018; Masingila, Olanoff, & Kwaka, 2012; Thanheiser, 2015; Thanheiser, Browning, Moss, Watanabe & Garza-Kling, 2010). For example, the work done by Thantheiser and colleagues examined how teacher educators can use current understanding of mathematical knowledge for teaching to design mathematics content courses for elementary teachers. Similarly, Castro Superfine and colleagues have focused on articulating general design principles and models for designing mathematics content courses that can provide productive learning opportunities for PSTs. In addition, other studies (e.g. Gichobi, 2018, 2019) demonstrated that PSTs can critically think about multiple ways of solving mathematical problems when given the opportunity to learn.
Furthermore, other existing research studies have provided insights into what happens in the content courses from the perspective of textbooks used in the courses (McCrory and Stylianides, 2014) and from the perspective of learners who take such courses (Hart and Swars, 2009; Hart et al. 2013). In particular, Hart and colleagues indicated that PSTs who participated in the study reported that their mathematics content courses did not support their development of a positive attitude towards mathematics learning and/or teaching. Other researchers have explored the design of innovative mathematics content courses and their effect on PSTs learning (Laursen, Hassi & Hough, 2016; Philipp et al. 2007). Using an inquiry-based approach, Larsen et al. (2016) reported that PSTs viewed their learning gains as relevant to their future teaching work. However, although significant progress has been made in providing insights into the nature of learning environment in mathematics content course (e.g. Gichobi, 2018, 2019; Larsen et al. 2016; Li & Castro Superfine, 2018), as yet there is little research that has focused on the extent to which online mathematics content courses can provide opportunities for PSTs to strengthen subject-matter knowledge and pedagogical skills.
Furthermore, with the evolution of web-based technologies and technology-based instruction, online education has partially become an integral part of higher education teaching (Sonmez & Koc, 2018; Law, Ng, Goh, Tay, & Sek, 2012; O’Malley & McCraw, 1999) Specifically, prior research has shown students’ perceptions on online learning had significant advantages such as saving them more time, helping them to plan their schedules better and enabling them to take more courses (O’Malley & McCraw. 1999). Similarly, Sonmez and Koc (2018) investigated pre–service teachers’ lived experiences in taking courses through the Moodle learning management system (LMS). Most of the participants in the study indicated that Moodle was user–friendly, beneficial, and enhanced interaction with both instructor and course content. However, some participants in Sonmez and Koc study argued that Moodle could not provide face–to–face interaction like in the classrooms and thus it was not suitable for certain math and non–math courses requiring such interaction. Using the existing literature and data collected from PSTs enrolled in an online and face to face mathematics content course, this chapter explores the following research questions:
- 1.
What are PSTs’ perceptions of U-PACE mathematics content course designed to develop their mathematics content knowledge for teaching?
- 2.
How do PSTs learning experiences in the U-PACE course compare with a traditional face to face course?
There are two goals in this chapter. First, the chapter makes visible the design of the course through the eyes of the students who completed the course. The chapter describes the PSTs’ experiences, perceptions, affordances and constraints for developing the content knowledge as well as the standards for mathematical practices through the U-Pace instructional approach. Second, the chapter compares PSTs’ learning experiences in the U-Pace online mathematics content course versus face to face course. Furthermore, this chapter builds on prior studies that have focused on the effect of U-Pace instruction on undergraduate students’ learning. (Fleming, Barth, Weber, Pedrick, Kienzler & Reddy, 2018; Fleming, Stoiber, Pfeiffer, Kienzler, Fleming, Pedrick, . . . Reddy (2016). The chapter concludes by discussing implications of the design on teacher preparation.