Using the SAMR and UDL Models to Differentiate Online Instruction

The purpose of this chapter is to discuss two frameworks that are useful for integrating and differentiating technology within online learning environments for students with disabilities: Universal Design for Learning (UDL) and the Substitution, Augmentation, Modification, Redefinition Model (SAMR). Following a review of the literature of each framework, the interactive software program, Desmos®, will be used to demonstrate how to integrate these two models. Finally, the authors make recommendations that will support all students to benefit from an online environment and engage in inclusive learning experiences.

Supporting Mathematics Teaching Practices in Online Teacher Education

In this chapter, the author provides an example of an integrated and collaborative activity for in-service mathematics teachers that was implemented synchronously online. While prior research details how this lesson developed middle and secondary teachers' mathematics content knowledge of logarithms and teachers' science content knowledge concept of pH, this chapter focuses on how the lesson was converted from a face-to-face format to the online format while supporting research-based essential teaching skills, specifically NCTM's Mathematics Teaching Practices (MTPs). Evidence is provided for how three MTPs were upheld using the online platform Blackboard Collaborate, followed by recommendations for other teacher educators wishing to engage teachers in online learning that supports mathematics education goals of integrated STEM education through mathematical discourse, conceptual understanding, and reasoning about mathematical representations.

Formative Assessment Online via Flipped Interactive Screencasts

With the rise in online learning accompanying the ever-increasing technology era, flipped classroom models have become increasingly popular. The flipped classroom model offers the benefit of maximizing class time for more interactive and collaborative activities, as the screencast introduces new material at home as students' initial contact with novel content. However, screencasts by nature are homework assignments not completed live, so formative assessment must be purposefully implemented with face-to-face mathematical classroom interactions. This study follows websites that allow teachers to embed questions within the screencast that requires student responses throughout the video that provide teachers data and accountability to at-home screencast assignments that inform the teachers of student understanding, which in turn guide teachers' development of the following day's instruction. Thus, the study's results provide implications and conclusions for practical application of flipped interactive screencasts.

Facilitating Mathematical Discourse in Online Learning Environments

Facilitating meaningful mathematical discourse in an online setting can be a challenge for instructors. The purpose of this chapter is to analyze an instructor's discourse interventions to encourage mathematical discourse in online asynchronous discussions in an analysis course for secondary mathematics teachers (SMTs). The SMTs were required to participate in the discussions and encouraged to ask/answer questions, share/compare their ideas, and explain their thinking/answers. Instructor responses were analyzed using both Mazzolini and Maddison's four categories of response the respect to instructor intervention—(1) question, (2) answer, (3) mix of answer and question, and (4) other—and Simonsen and Banfield's five recurring categories—(1) resolve, (2) validate, (3) redirect, (4) expand, and (5) withhold. With respect to instructor intervention, the author suggests mainly withholding from responding and to use expand, redirect, question, or mix if necessary to encourage mathematical discourse.

Learning to Teach Mathematics Online

Online learning has become an important vehicle for student learning. The number of students choosing the online learning option to earn their degrees has grown over the recent years. Many universities across the US already offer web-based learning and are placing more courses online. This trend is motivated by several issues among which is new pedagogical opportunities web-based learning provides, advancement on research in online education, increasing student numbers, reaching diverse audiences, and meeting students at their own time and place. Even so, there is little research on its effectiveness especially in the context of mathematics teaching to strengthen preservice teachers' subject-matter knowledge and pedagogical skills. This chapter presents an investigation into how online learning can meet the goals of teaching mathematics in a way that is consistent with mathematics education reform goals of developing mathematical understanding.

Online Mathematics Teacher Professional Development

The purpose of this chapter is to describe an online learning environment that has been used for professional development with mathematics teachers and can be used for pre-service teacher education. The description of the Blackboard Learn and Blackboard Collaborate combination for the mathematics teacher education enables teachers to collaboratively engage in inquiry, reasoning and justification, and technology integration as participants. In addition, teachers can have opportunities to discuss various ways to incorporate these ideas more fully into their instructional practices.

Engaging Mathematically in Synchronous Platforms

In a qualitative self-study, two teacher educators introduce the notion of engaging mathematically to study synchronous interactions in two of their online courses for K-8 teachers. By studying the interactions between themselves and their teachers, the teacher educators are able to describe novel opportunities, negotiations, struggles, and insights involved in engaging mathematically in online platforms. Their mathematical and pedagogical illustrations convey new possibilities for synchronous online interactions during mathematics lessons. These descriptions address a gap in the research on online teaching about how mathematics can be negotiated within these platforms, as well as concerns about the meaningfulness of interactions in online settings. Implications to teacher education practitioners and researchers, and developers of learning management systems suggest the importance of the teacher education community taking a lead role in ensuring that online teaching has a purposeful part to play in the field of mathematics teacher education.

Preservice Teacher Perceptions on the Design of a U-Pace Online Course Compared to a Conventional Face-to-Face Mathematics Content Course

This chapter examines preservice teachers' (PSTs) perceptions on the design of both an online and face-to-face mathematics content course for elementary and middle school preservice teachers. The chapter describes the instructor's design goals, considerations, and describes PSTs' experiences in the process of completing the course. Further, the chapter describes the features of the course that provided productive learning opportunities for PSTs. Drawing from PSTs' reflection after completing an online course and face-to-face course, the chapter compares PSTs' experiences and learning outcomes from the online course compared to a traditional face-to-face course. Finally, the authors explicate the affordances and constraints encountered by both the instructor and the students as they completed the online course.

Strategies and Tools for Promoting Discourse During Mathematics Problem-Solving in Online Settings

Inquiry-based mathematics instruction with collaborative reasoning and problem-solving necessitates opportunities for rich discourse as students make and test conjectures, explain their reasoning, and critique the reasoning of others. This discourse occurs in an environment where participants feel safe to try out ideas and learn from mistakes. Research in mathematics education includes many frameworks and strategies for encouraging discourse in face-to-face settings. Orchestrating such discourse presents a unique challenge in online settings where discourse usually takes the form of discussions about shared readings or experiences rather than collaborative problem-solving of a mathematical task. Examples of strategies and tools for orchestrating discourse during mathematics problem-solving in a graduate program for K-5 teachers that meets in both synchronous and asynchronous environments are shared. This is followed by a discussion of the affordances and constraints of supporting discourse in online settings. Finally, recommendations for instruction and directions for future research are suggested.

Synchronous Online Model for Mathematics Teachers' Professional Development

In this chapter, the authors present the design rationale for and empirical results from a predominantly synchronous three-part online model for the professional development of mathematics teachers in rural contexts. They describe how the design of the components are complementary and are intended to support teachers to develop challenging instructional practices, even when the teachers are geographically remote and dispersed. The three parts include an online course, online video coaching, and online demonstration lessons. They describe how they used conjecture mapping to enhance collaboration within the project team and to inform iterations of the model. They then present empirical results related to each of the components of the model and draw conclusions based upon what they have learned.