Nicolas Senior shows how EMC3 's Launch-Explore-Summarise/Review model for mathematics lesson structuring sets the conditions to get the most out of both dialogic and direct instruction. He argues that this model will help teachers walk the balance between order and chaos.

Literature shows that the Nature of Mathematics Knowledge (NOMK) dates back to the era of Plato and Aristotle (Dossey, 1992). It suggests that mathematics teachers' beliefs, views, conceptions, and preferences about NOM influence the way in which they teach mathematics. It is important to understand how these conceptions are formed, which may…

Even though game elements can increase motivation and engagement, they also might distract learners and thereby decrease performance and learning outcomes. In the current study, we investigated the effects of intrinsically integrated game elements on performance and learning outcomes. In a pre-post training study, 85 adult participants were…

The Euclidean Discus Toss is an active and tactile learning activity that models the extended Euclidean algorithm with a frisbee relay. The extended Euclidean algorithm involves both iterative and recursive programming and is regularly taught throughout the mathematics and computer science curricula. The Euclidean Discus Toss invites students to…

Mathematical proofs play a paramount role in developing 21st-century skills, and the use of technology in mathematics learning has widely paved the way in the instruction of mathematical proofs. In mathematics education, GeoGebra has a significant role as a dynamic mathematics software in supporting students' learning process. This study aims to…

Most of the world's population believe in the idea of learning styles (Dekker et al., 2012; Howard-Jones, 2014; Macdonald et al., 2017; Torrijos-Muelas et al., 2021). The theory of learning styles conveys individuals learn best in a certain way (e.g., visual, auditory, or kinesthetic). An extension of this theory is the hypothesis that an…

A lack of student motivation in a higher-level high school mathematics class prompted the question: how does a teacher's belief in their ability to effectively teach content positively or negatively impact student motivation? The purpose of this phenomenological research study is to understand how teachers evaluate their self-efficacy and how that…

The algorithm for fraction multiplication is relatively easy to memorize and implement with accuracy. The simplicity of the algorithm masks the conceptual complexity involved in making sense of what fraction multiplication means in quantitative situations. One important interpretation of fraction multiplication involves fraction composition,…

Designing and implementing purposefully developed tasks have been linked to students' understanding of mathematical topics. We report on design principles and intentions that guided the development of "inquiry-oriented tasks." Through a qualitative analysis of the tasks, we identified seven themes that encapsulated these design…

This study examines how collaborative activity among students and the teacher to investigate disciplinary questions, which we term 'joint exploration', is established and maintained in a secondary mathematics classroom. Although collaborative and active learning is increasingly sought after in mathematics classrooms, studies of instances of joint…

Problem-based learning puts students in situations that suggest problems without providing instructions and available knowledge. Therefore, when using problem-based learning, students need to be flexible, self-disciplined, active and self-occupied with knowledge and turn the knowledge the teacher intends to impart into their knowledge. For locus…

Numerous studies (Anwar et al., 2016; Carpenter et al., 1980; Huang & Witz, 2013; Outhred & Mitchelmore, 1996; Machaba, 2016; Van de Walle, Karp & Bay-Williams, 2014; Winarti et al., 2012) have shown that students need help understanding the concept of area and perimeter. This study aimed to investigate what students know about finding…

We conducted a collective case study investigating two college algebra students' graph reasoning and selection on an online assessment. Students completed the assessment during individual, semi-structured interviews, as part of a broader validation study. The assessment contained six items; students selected Cartesian graphs to represent…

During the COVID-19 pandemic, many Texas students stayed home and learned virtually for portions or the entirety of the 2020-2021 school year. TEA (2021b) reports indicated virtual learners scored lower than students who returned face-to-face on many assessments. Research question one asked what are the perceived factors that affected 8th-grade…

Many approaches have been taken to study gender (in)equities in mathematics education, including studies of students' achievement on standardized tests, participation in postgraduate degrees and careers, participation in the classroom, and students and teachers' mathematics identities. In this dissertation, I used Baxter (2003b)'s Feminist…