Despite the long-time call for change in mathematics instruction, there are several barriers to change, and instruction has remained stagnant overall, taking the form of traditional lecture. Instructional coaching has many of the attributes of effective professional development from the literature and could be a major support for instructional…

Mathematicians teaching at the university level have a deep understanding and appreciation for the mathematics that they teach. However, they rarely receive much formal training in teaching. Thus, university mathematicians must rely on their mathematical understandings and personally developed ideas of teaching to guide their decision-making.…

Seaford School District has allocated significant resources and launched multiple initiatives to increase the achievement of Seaford Middle School mathematics students. These included adopting high quality instructional materials, hiring a school-based mathematics coach, purchasing curriculum materials, ensuring collaborative grade level planning…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

Algebraic thinking is an essential component of the K-12 mathematics curriculum. Early algebra focuses on the overall numeric structure (Kaput, 2008; Kieran,2018; Kieran et al., 2016) which focuses on the noticing of arithmetic patterns leading to generalizations supported by justification, reasoning and justifications (Blanton, 2008; Blanton et…

An increasing number of high school students are enrolling in statistics courses. Hence, an increasing number of teachers are needed to plan and implement these courses. Yet, many teachers report feeling unprepared to teach statistics. When planning and implementing these courses, teachers draw upon their knowledge and beliefs when making…

Mathematics teachers at the local middle school located in a southeastern suburban community were struggling to implement differentiated instruction (DI) strategies in mathematics lessons as presented in professional development (PD) sessions and as directed by school administrators. The purpose of this study was to explore middle school…

Research suggests that math anxiety correlates directly with individuals' views of mathematics-related experiences. Research also suggests that math anxiety may begin in early elementary grades and remain into adulthood. This study examined how teachers' experiences, perceptions, and mathematics confidence levels influence mathematics instruction.…

Although there is consensus on the relevance of the feedback given to student teachers, few instances in the literature have addressed this topic. Even less is said about feedback to mathematics lesson plans and how to characterize it. Lesson plans are artifacts that help establish a link between theory and practice, relate to a broader sense of…

This research examined how three middle school mathematics teachers who were supported by their district to use the Teaching Through Problem Solving approach interpreted and implemented the Standards for Mathematical practices (SMPs) developed by the Common Core State Standards (2010) and the Mathematics Teaching Practices (MTPs) developed by the…

The objectives for this study were to develop a checklist specifically focused on evaluating preservice elementary teachers' mathematics lesson plans through the lens of Universal Design for Learning (UDL) and to analyze some mathematics lesson plans using the UDL-oriented checklist. Information on the principles, guidelines, and checkpoints of…

Task selection is a critical element of mathematics teaching because mathematical tasks differ in the mathematical opportunities made available to students. Thus, it is important to examine both the tasks that PSTs chose and why they were chosen. This study examines the task selection of 10 pre-service teachers (PSTs) in a middle grades…

Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…

Children and adult learners benefit from viewing hand gestures at instruction across domains (Cook, Duffy, & Fenn, 2013; Huang, Kim, & Christianson, 2019; Ping & Goldin-Meadow, 2008). Within the domain of mathematical learning, gesture at instruction has been shown to benefit children and adults in laboratory and classroom settings…

A recent review of research on virtual manipulatives (VMs), defined as technology-based interactive representations of mathematical ideas (Moyer-Packenham, & Bolyard, 2016), suggests strengths relative to other instructional tools in supporting student learning of mathematics (Moyer-Packenham & Westenskow, 2013). Researchers have…