In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Using multiple representations (MR) such as graphs, symbols, diagrams, and text, is central to teaching and learning in physics classrooms. While different studies have provided evidence of the positive impact of the use of MR on physics learning, a comprehensive overview of existing literature on the use of MR in physics education, especially at…

The purpose of this study was to explore how students with high- and low-prior-knowledge employed multiple representations in argumentation evaluation and generation tasks. The argumentation performance and eye-movement behaviors of 96 college students in these tasks were investigated. The number of participants who proposed complex argumentation…

The aim of this study is to examine the graphic reading and interpretation skills of teacher candidates with problem situations prepared in the context of the COVID-19 pandemic, which is a socio-scientific situation. The study is conducted with case study of qualitative research methods. The participants of the study consisted of 52 elementary…

The understanding of graphs and extraction of relevant information from graphs plays a major role in physics education and is also important in several related fields. Recently, Susac "et al." [Phys. Rev. Phys. Educ. Res. 14, 020109 (2018)] compared physics and psychology students' understanding of graphs in the contexts of physics and…

One challenge associated with introducing systems thinking in chemistry classrooms is the increase in content complexity that students face when they engage in this type of approach. Placing core chemical ideas within larger systems has promise, as long as students are not overwhelmed by the added complexity. Although there are many potential…

We design, validate, and administer a 24-item test to study student understanding of linear functions in 1D kinematics [x(t)] and mathematics [y(x)] in the 9th grade. The items assess identification and comparison of initial position and velocity in 1D kinematics and of the y intercept and slope in mathematics using a graph or an algebraic…

In this article, the authors introduce the Into Math Graph tool, which helps teachers learn about their students' mathematics-related experiences and mathematical engagement by inviting students to define and graph their engagement over time. This tool documents and allows teachers to understand how and why students' engagement increases,…

The food industry is an important constituent of a country's economy, which provides the population with food. The development of the food industry and the supply of food products to the entire population requires improving food-manufacturing technologies, such as the process for production of extruded poly-cereal food products using…

While education increasingly relies on social media technologies to provide richer learning experiences, the rigid and course-centric design of curricula still imposes a challenge for students to construct meaningful connections between social media and formal learning. Building on the knowledge graphs' potential to establish semantic links among…

There is a lack of research examining the use of curriculum-based measurements (CBMs) with special populations, particularly English Language Learners (ELLs). The current study used an alternating treatments single-case design with five Latinx ELL students to examine scores across three math fluency CBM modalities. One-minute probes using either…

Accuracy is widely recognized as one of the main dimensions in evaluating task-based oral performance. Indicators of accuracy vary in the literature of the effects of pre-task planning on the oral production. Enlightened by previous studies in pre-task planning and third-person singular "-s," this article intends to find out whether the…

For the least-squares analysis of data having multiple uncertain variables, the generally accepted best solution comes from minimizing the sum of weighted squared residuals over all uncertain variables, with, for example, weights in x[subscript i] taken as inversely proportional to the variance [delta][subscript xi][superscript 2]. A complication…

This paper describes two classes of advanced data mining methods that can obtain actionable insight from cooperative education data: text mining of job descriptions and graph mining of job interview data. While these methods are not new in general, they have not been widely used in co-operative education research. A technical overview of each…

This paper proposes a novel application of knowledge space theory for identifying discrepancies between the knowledge structure that experts expect students to have and the real knowledge structure that students demonstrate on tests. The proposed approach combines two methods of constructing knowledge spaces. The expected knowledge space is…