In our mathematics methods courses for elementary preservice teachers, we work to uncover and confront students' understandings as well as misconceptions about important mathematical topics. Karp and colleagues' ("Teaching Children Mathematics", 21(1), 18-25) "13 Rules That Expire" article has been a useful resource for us to…

Even though the "Next Generation Science Standards" (NGSS) were released over a decade ago, science is still infrequently taught in early childhood and elementary classrooms. A lack of teacher confidence due to inadequate content knowledge may be a contributing factor, making access to high-quality elementary science methods courses even…

This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. Results show that both lessons and the textbook introduce important cognitive resources briefly and focus on other units of knowledge. Implications to these results are also discussed.

This study sought to explore math and science teacher educators' use of various media to represent practice within methods courses. There is little understanding of why certain media is used over other representations and the rationale for these choices. Specifically, the study focused on the prevalence and familiarity of teacher educators with…

The purpose of this study was to examine mathematics preservice teacher (PST) learning to notice for equity as they participated in an experimental, practice-based methods course. Activities intended to support PST learning included the use of equity-based lenses in video analysis, live lesson observations, and case study analysis. We analyzed…

When we look at the theoretical relationships between the three types of geometry, we find that the most primitive type is topology and that both Euclidean and projective geometry are derived from this earlier type. Therefore, Piaget described the first stage or level of understanding geometry as topological understanding. In this study, the…

The goals of science education include providing students with real-world learning experiences that connect directly to learning objectives and deepen student interest in science. Learning experiences that occur outside of the science classroom can help science educators respond to these goals. To encourage the use of learning environments beyond…

Mathematics education researchers suggest that it is important for teachers to select mathematics tasks that align with their goals for students; however, this can be challenging as there are many facets of alignment to consider. In this article, I present a rubric that details the alignment between tasks and learning goals. This rubric was…

Several observation protocols in different theoretical frameworks and components have been designed and validated by teacher trainers and professional development providers to capture and categorize observational data on the characteristics and level of inquiry in science practices. However, certain constraints limit their wide use, such as the…

Despite problem posing's prominence in mathematics education research, its implementation in classrooms is limited. Therefore, teacher educators should incorporate problem posing tasks into preparation programs to help prospective teachers gain confidence in their abilities. One approach to teaching problem posing includes providing examples. The…

Research has revealed that a small percentage of weekly instructional time in the elementary grades is dedicated to teaching science. Additionally, elementary educators receive limited preparation to teach science concepts compared to math or literacy skills. Therefore, this study examined if utilizing poetry to teach science concepts had a…

The Association of Mathematics Teacher Educators recommends that well-prepared beginning mathematics teachers apply their understanding of mathematics, curriculum, pedagogy, student learners, and social constructions to facilitate mathematics learning for all students. Using the context of a secondary methods course, where prospective mathematics…

Science, technology, engineering, and mathematics (STEM) integration is a desired outcome according to Next Generation Science Standards. However, learning to teach integrated STEM content has been challenging for teachers. Consequently, the purpose of this qualitative study was to describe how 16 preservice teachers enrolled in a mathematics…

Mathematics teacher educators have suggested preservice mathematics teachers' (PMTs') practices provide evidence of their mathematical knowledge for teaching (MKT). PMTs engage in approximations of practice to rehearse teaching. To explore connections between MKT and PMTs' practices, we operationalized six MKT subdomains in terms of approximations…

Because of their brief nature, vignettes are a strategic way to highlight or explore complex instructional practices. Using a qualitative approach, we examined how the use of vignettes in a Vignette Activity Sequence contributed to secondary mathematics preservice teachers' understanding of the Mathematical Practices and the Mathematics Teaching…