Mathematical concepts have been a consensus goal for decades, yet there is little consensus on what is meant by the terms "mathematical concept" and "mathematical understanding." This article attempts to discuss these terms in a way that can be of practical use to teachers. Greater clarity on "mathematical concept"…

The increasing role of artificial intelligence (AI) in daily life has led to the emergence of numerous skill sets associated with AI. AI literacy, which is becoming an important citizenship competence, has become a skill that has gained importance in recent years. It is thought that the aim of social studies to prepare students as active citizens…

An educator's teaching styles are essential to the increase in student learning. Mosston's Spectrum of Teaching Styles features 11 teaching styles ranging from a completely teacher-centered approach to a completely student-centered approach. These teaching styles are effective in addressing various student needs. Especially when multiple styles…

Pre-service teachers (PSTs) often struggle to teach STEM (Science, Technology, Engineering, and Mathematics) content effectively due to lack of training on how to plan a STEM lesson in meaningful ways as well as which subjects to integrate. This dilemma often results in an avoidance of STEM methodology altogether. This paper describes a productive…

To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…

Student Uncertainty as Pedagogical Resource (SUPeR) is a teaching approach that science teachers can use to promote student scientific literacy, practice, and learning. SUPeR helps students navigate scientific uncertainty to improve understanding of scientific concepts and phenomena. The SUPeR approach consists of four phases: (1) problematize a…

Our middle school mathematics department used lesson study to investigate how to introduce fractions division to our sixth-grade students. We highlight our learnings during the Study and Plan phases, describe our observations during the lesson, and provide tips for educators interested in using lesson study to study their own content.

This article provides an example of how one sixth-grade classroom teacher and an instructional coach built a bridge for students in a grade 6 self-contained classroom to support their conceptual understanding and procedural fluency with dividing fractions. Baseline data showed that most of the students in this class had mastered only the…

As middle school teachers, the authors want their students to develop voice and agency because they want them to be able to make productive decisions about how to approach mathematics, communicate mathematics, and use mathematics to interpret and transform the world in which they live. They use this article to present two vignettes that examine…

We describe a new approach to the use of video-based technology for conducting controlled experiments in classroom contexts. Specifically, we describe a process for editing video recordings of live classroom lessons to create multiple versions, such that only one aspect of the lesson is systematically varied. Other aspects of the instruction are…

Is anything more refreshing than going for a nice, long swim? The math scenarios presented in this article will take the reader back to hot summer days and remind the reader what a cool dip in the water feels like. Solving these problems is enjoyable and encourages the solver to think of the many ways that math is all around--even in the middle of…

Cultures need to accurately record dates and times for various societal purposes, ranging from knowing when to plant crops to planning travel. In ancient times, the sun and moon were used as measurement devices because of the scientific understanding of the physical world at that time. Ancient timekeepers monitored celestial events and either used…

Our social studies classrooms are filled with students from many different backgrounds. This article aims to help middle grades (grades 6-8) social studies teachers consider how trade books that feature the global South can be paired with primary historical texts in order to help students develop perspective consciousness. Social studies educators…

Jaya Carrier's decision to focus on developing a more independent approach to learning in history at Key Stage 3 was prompted by concerns about her A-level students. In seeking to establish secure foundations for students' own historical research, Carrier first examined the assumptions of her colleagues and her students. She quickly recognised…

One of the challenges in learning fractions is understanding how and why a fraction can have multiple interpretations. As presented in one textbook, a fraction is "a symbol, such as 2/3, 5/1, or 8/5, used to name a part of a whole, a part of a set, a location on a number line, or a division of whole numbers" (Charles et al. 2012, p.…