Hybrid Courses for Preparing Elementary Mathematics Specialists: Challenges, Successes, and Lessons Learned

Hybrid Courses for Preparing Elementary Mathematics Specialists: Challenges, Successes, and Lessons Learned

Kathleen Pitvorec (Learning Sciences Research Institute, University of Illinois at Chicago, USA) and Mary Jo Tavormina (Learning Sciences Research Institute, University of Illinois at Chicago, USA)
DOI: 10.4018/978-1-7998-1476-4.ch006

Abstract

Post-secondary education has seen an explosion of interest in computer-supported collaborative learning as a pathway for teacher education. Hybrid courses potentially provide broader access to coursework while keeping costs manageable. In this chapter, the authors report on the iterated design and implementation of hybrid courses designed to prepare teachers to become elementary mathematics specialists. The authors describe a framework for building face-to-face and synchronous online sessions that complement each other, while attending to community building, the exploration of mathematical and pedagogical content, as well as the development of leadership skills and tools. They discuss how they have addressed the challenges of online coursework in their evolving course design. They present their successes and how they have capitalized on the opportunities these successes offer, and they conclude by synthesizing the lessons they have learned, the implications of our work, and the recommendations they have for moving forward.
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Introduction

For decades, researchers at the intersection of elementary education and mathematics instruction have called into question whether the general preparation elementary school teachers receive for teaching mathematics is sufficient for supporting students in developing deep and durable understandings of mathematics (Labaree, 2008; National Research Council, 1989). Some researchers have approached this question by unpacking the mathematical knowledge needed for teaching (Ball, 1993; Ball & Bass, 2002; Ball, Hill, & Bass, 2005; Ball, Thames, & Phelps, 2008; Hill et al., 2008; Hoover, Mosvold, Ball, & Lai, 2016; Stylianides & Ball, 2008). National organizations in the U.S. such as the Conference Board of the Mathematical Sciences (2001, 2012) and the Association of Mathematics Teacher Educators (AMTE, 2017) have addressed the issue by outlining comprehensive standards describing how elementary teachers should be prepared—that is, what they should know and be able to do—in order to teach mathematics.

Developing highly-qualified mathematics teachers is more challenging and more necessary today with the implementation of the Common Core State Standards (2010) in the U.S. Teachers who have been generally prepared to teach elementary school may be less well-prepared to teach mathematics than was previously the case. In addition to requiring teachers to learn and make sense of more demanding content standards, instructional materials aligned with the Common Core State Standards (CCSS) expect teachers to incorporate and attend to a set of mathematical practices that were not part of traditional textbooks (Sztajn, Marrongelle, Smith, & Melton, 2012). Furthermore, many teachers learned mathematics in contexts where they did not experience practices like those described in CCSS during their own mathematics education (Ball, Lubienski, & Mewborn, 2001; Lortie, 1975).

One recommendation, which has persisted through the years, for ensuring students have highly-qualified mathematics teachers is that elementary school mathematics classes could be structured such that teachers who are better prepared to teach mathematics would do all of the mathematics teaching—especially in grades 4 through 6. Becker and Gleason (1927) did an extensive survey to explore departmentalization. The survey results indicated some potentially powerful advantages. For example, the teachers teaching mathematics would be better prepared with a deeper understanding of mathematics, as well as how children learn mathematics. In addition, they would have more time to prepare for their subject. In all likelihood, these teachers would bring an enthusiasm to teaching mathematics that is not common to all elementary school teachers. Furthermore, students would not only benefit from the mathematics teacher’s expertise in the subject matter, but they might also benefit from having a second teacher who potentially has a different teaching style than the students’ homeroom teacher, providing some variety for the students. Their survey participants noted that there may also be some disadvantages to departmentalizing, including that teachers might feel isolated if they are the only ones teaching mathematics, they may see themselves teaching a subject rather than students, scheduling might be complicated, and students may be missing some of the “hominess” of a self-contained classroom. The advantages and disadvantages that Becker and Gleason’s (1927) survey exposed still exist today, and we continue to hear calls for specialized teaching assignments as a way of potentially improving student achievement (Kilpatrick, Swafford, & Findell, 2001; National Mathematics Advisory Panel, 2008; NCTM, 1989, 2000).

Key Terms in this Chapter

Learning Environments: Refers to a physical location and/or context in which learning occurs. In this chapter, we are specifically referring to a combination of more traditional classroom contexts as well as synchronous online learning contexts.

Teaching Presence: Describes actions the instructor takes in the context of online instruction. This generally includes the design and facilitation of online class sessions. For the present context, this also includes attention to how the instructor directs cognitive and social processes during the online sessions.

Social Presence: Relates to how individuals engage with the online community and the development of interpersonal relationships in that community.

Social Learning: Refers to learning that takes place when individuals are working in cooperative or collaborative settings.

Learning Community: Is similar to a community of practice in that the learning community shares common content and pedagogical goals as well as norms for ways of interacting. For our courses, the individuals in the community meet regularly to collaborate on the coursework in both face-to-face and online contexts.

Cognitive Presence: Refers to how individuals in the community co-construct personal meaning through reflection and confirm meaning through discourse with community members.

Community Of Inquiry: Individuals who come together to collaboratively participate in critical discourse and reflection. These individuals co-construct knowledge that has both personal meaning as well as a taken-as-shared quality in the community.

Hybrid Synchronous Learning: Learning that results from the courses designed as hybrid synchronous courses—where there is a combination of traditional face-to-face sessions and synchronous online class sessions.

Teacher Professional Development: Involves structured professional learning with the goal of influencing teaching practices to improve student learning outcomes. In this chapter, course sessions, readings, and assignments provide teacher professional development opportunities.

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