This study examined students' ability to learn mathematics in a self-directed teaching environment. One of the main goals of the educational system is to nurture independent learners who can grow up to be inquisitive, critical, creative, and capable of piloting their own learning. This implies making a change in the way the role of the mathematics…

This study looks at how students embody their ideas about geometry conjectures and how those ideas travel within and between student groups. In one classroom of a Title 1 high school, students participated in a three-part program in which they: (1) played "The Hidden Village," a motion-capture video game where they assess the veracity of…

The achievement gap that exists in K-12 education between Latino student students and other races is not only evident but profound. To bridge this gap, underlying factors needed to be explored. One such factor that has affected overall student performance is math anxiety. Researchers have determined that math anxiety has had a tremendous impact on…

This classroom study immersed high school geometry students in the creative and intellectually challenging design task of developing unique logos using mathematics and technology. The students applied and deepened their knowledge of transformations while using dynamic geometry software. One of the main aims of the task was to elevate student…

The surface area of a sphere as a function of radius, "r," is a derivative of the volume of the sphere, and a few other families of solids with this property are known. Sometimes, the derivative relationship can be reached with a tricky choice of size parameter "r." This paper presents an activity for students that discovers…

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

Educators in mathematics have long been concerned about students' motivation, anxiety, and other affective characteristics. Typically, research into affect focuses on one theoretical construct (e.g., emotion, motivation, beliefs, or interest). However, we introduce the term affective field to account for a person's various affective factors…

Powerful learning environments (PLEs) are based on a social constructivist theory of learning, providing a stimulating, resource-rich and inquiry-supportive environment for student self-regulated learning. Fidelity of implementation (FOI) for such PLEs is dependent on several factors, the most critical factor being the teacher's belief system,…

One important aspect of teaching is reviewing tasks in preparation for instruction. The goal of the multicase study of four secondary teachers was to examine the interplay between their mathematical knowledge for teaching [MKT] and what they attend to when reviewing a mathematics task. We engaged secondary mathematics teachers in a…

Offering secondary math educators an innovative holistic and process-orientated approach for implementing nonroutine problems into their curriculum, this book defines and establishes practical strategies to develop students' problem-solving skills. The text focuses on the process skills necessary to solve nonroutine problems in mathematics and…

In this paper, the authors discuss their experiences with ungrading at a small public university in the U.S. and a large public university in Germany. The courses described are Calculus 1 and a content course for pre-service secondary teachers of mathematics. The professors teach differently: one with lecture, the other with inquiry-based…

This study used traditional and holographic video, along with eye-tracking technology, to examine how preservice teachers' physical act of looking is associated with how they attend to and assess students' fraction reasoning. Findings revealed that, although viewing of holograms may have influenced more focus on students' work area, there was…

This study presents the lived experiences of eight African American male recent high school graduates in their mathematics classes. These young men are currently attending various colleges across the United States in pursuit of obtaining a college degree. A few of the young African American men who were interviewed faced challenges during their…

The purpose of this quantitative comparative study was to determine the differences in literacy and mathematics pass rates between AY 2021-2022 and AY 2022-2023, whether a 21st CCLC Program contributed to score differences and whether there is an interaction between them in a southeastern state. A two-way mixed ANOVA was used to answer the…

When examining students' participation in these mathematics discussions, the focus is on their verbal contributions. However, students' nonverbal contributions--such as pointing, drawings, and models-- can be crucial resources for advancing the mathematical thinking and the collective activity of a classroom community (Johnson et al., 2023; Webb…