We introduce the concept of the "sequence of the ratios of convex quadrilaterals," identify some properties of these sequences and use them to provide new characterizations for some classic quadrilateral families. The research involves aspects of geometry, arithmetic and mathematical analysis, which converge to produce the results.

Graphing is a complex and critical skill for behavior analysts. We evaluated the effects of conceptual training modules and feedback checklists on verbal behavior about graphing conventions and adherence to graphing conventions with graduate students in behavior analysis. In Experiment 1, conceptual training increased the accuracy of verbal…

Children often learn abstract mathematics concepts with concrete manipulatives. The current study compared different ways of using specific manipulatives -- base-ten blocks -- to support children's place value knowledge. Children (N = 112, M age = 6.88 years) engaged in place value learning activities in one of four randomly assigned conditions in…

Numerous studies illustrate the value of simulations or project-based learning approaches to enhance the learning of science. Simulations can help students connect across macroscopic, microscopic, and symbolic representations of scientific phenomena, while project-based learning can provide a meaningful narrative and activities for students to…

Spatial skills, which represent the ability to mentally manipulate objects (Schneider & McGrew, 2012; Atit et al., 2020) have been shown to be correlated with entrance, persistence and success in STEM (Shea et al., 2001; Wai et al., 2009). Specifically, these skills have been shown to be necessary to geologists and geoscientists (Hegarty,…

This study analyses the potential of a learning analytics (LA) based formative assessment to construct personalised teaching sequences in Mathematics for 5th-grade primary school students. A total of 127 students from Spanish public schools participated in the study. The quasi-experimental study was conducted over the course of six sessions, in…

Identifying contingencies between constructs in a multi-faceted learning progression (LP) is a challenging task. Often, there is not enough evidence in the literature to support connections, and once identified, they are difficult to empirically test. Here, we use causal model search to evaluate how connections between ideas in a genetics LP…

Examples are an essential part of mathematics teaching and learning, used on a daily basis to teach and practice content. Yet, selecting good examples for teaching is complex and challenging. This article presents ideas to consider when selecting examples, drawn from a research study with algebra 2 teachers.

We used a sequential synthesis problem to investigate novice teachers' conceptual difficulties in hydrodynamics. Twenty-one new secondary level physics teachers from various regions of China, who had been in service for no more than 2 years, participated in the study. Each participant completed a written hydrodynamics problem consisting of four…

Strengthening Learning Progression (LP) for students' reasoning abilities is important, especially learning about diseases in Indonesia. This study aimed to map the learning progression of disease in Indonesia, compare and analyze its similarities and differences with the LP designed by National Research Council (NRC). This qualitative research to…

Whether to engage student preconceptions to facilitate conceptual change is an area of debate among conceptual change theorists. Here, we evaluate the efficacy of a preconceptions-based instructional sequence about groundwater previously described by (Arthurs, 2019). To assess the impact this instructional sequence had on facilitating the…

The integer is a basic concept in studying arithmetic and algebra. However, students still frequently experience misconceptions, especially in negative integer, count operations. Traditional games are activities that are often carried out by students in coastal areas so that they are relevant to be used as a tool to construct learning trajectories…

"Instructional Sequence Matters, Grades 9-12" is the one-stop resource that will inspire you to reimagine your approach to high school physical science. The book discusses the 5E (Engage, Explore, Explain, Elaborate, and Evaluate) as a specific pathway for teaching and learning. It also shows how simple shifts in the way you arrange and…

The cyclic format of the undergraduate physics curriculum depends on students' ability to recall and utilize material covered in prior courses in order to reliably build on that knowledge in later courses. However, there is evidence to suggest that people often do not retain all, or even most, of what they learned previously. How much information…

We are pleased to bring you this follow-up to Mairéad Hourigan and Aisling Leavy's article [EJ1289314] that was published in issue 1 this year. In this contribution, they demonstrate that embedding mathematics within a rich context and learning sequence assists with the consolidation of student understanding and makes more effective use of teacher…