The aim of this study was to show that some of the errors made by students when responding to mathematics assessment items can indicate progress in the development of conceptual understanding. By granting partial credit for specific incorrect responses by early secondary students, estimates of the difficulty of demonstrating full and partial…

Although trigonometry is an important section in secondary school mathematics curricula, many teachers find it challenging to teach as a result of insufficient pedagogical content knowledge (PCK). Therefore, the aim of this article was to report on how PCK on trigonometry manifests itself in teachers' practice. This exploratory case study was…

Teacher knowledge needed for teaching is widely studied to characterize its key categories. We report findings from a study on teachers' knowledge for mathematics in the Montessori schools. In Montessori accredited schools, teachers learn to teach mathematics in ways different from the teachers themselves experienced in non-Montessori schools. We…

Teacher professional learning occurs across various contexts. Previous studies on teacher learning and changes in practice have focused on either classroom contexts or learning communities outside of school, but have rarely investigated teacher learning across multiple contexts. Investigating teacher learning across the double contexts of…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…

This study examines how joint exploration is established and maintained among students and the teacher in secondary mathematics classrooms. We use the theoretical perspective of positioning to conceptualize joint exploration as involving the negotiation and coordination among participants to position students with epistemic agency and authority.…

In this article the authors provide an overview of the Interdisciplinary Mathematics and Science project conducted in Grades 1 to 6 in four Australian schools. The project teachers implemented an enquiry-based pedagogical model through 12 interrelated topics. This paper details how a range of mathematics and science concepts can be effectively…

The Common Core State Standards for Mathematics emphasize the importance of developing students' conceptual understanding, mathematical reasoning, and problem solving skills. This is a shift from the traditional approach to teaching mathematics and many teachers rely on curriculum resources to help them meet these new standards and expectations.…

Learning mathematics content is often portrayed as being irrelevant and not useful in secondary students' lives. The literature suggests that making mathematics content relevant to students' lives, their community, and society plays a vital role in their academic motivation, attitudes toward mathematics, engagement, academic achievement, and…

For years, the Air Force Research Laboratory (AFRL) in New Mexico has led an outreach effort called "Mission to Mars" to engage fifth grade students in applying science and mathematics concepts related to building a colony on Mars. Many organizations across the US canceled similar events due to the novel coronavirus (COVID-19) pandemic.…

The Philippines has undergone a fundamental overhaul of its educational system to highlight basic education and overcome its deficiencies. The educational reform prompts prospective teachers to connect the concepts taught to instill a more profound understanding. As such, the researchers explored the mathematical connections made by prospective…

In response to restrictions on visitors within school buildings during the COVID-19 pandemic, the evidence-based math fact fluency procedure known as the taped problems intervention was adapted for use in a virtual setting. The present study used a multiple-probe across participants design to evaluate the effects of the adapted intervention on the…

Interdisciplinary introduction to quantum information science (QIS) courses are proliferating at universities across the US, but the experiences of instructors in these courses have remained largely unexplored in the discipline-based education research (DBER) communities. Here, we address this gap by reporting on the findings of a survey of…

This memo includes results of data collection from the second cohort of Collaborative Partnership to Teach Mathematical Reasoning Through Computer Programming (CPR2) teachers from classroom implementation of CPR2 in fall 2021. Findings are included for the student pre-assessment, Student Computer Science Attitude Survey, and Learning Mathematics…

In this paper, we present a "route of activities" mainly addressed to first and second year engineering students attending the basic mathematics courses. These activities are intended to be a tool both for students and teachers. On the one hand, they should help the students to acquire a deeper understanding of the mathematical ideas and…