Many existing methods of statistical inference and analysis rely heavily on the assumption that the data are normally distributed. However, the normality assumption is not fulfilled when dealing with data which does not contain negative values or are otherwise skewed--a common occurrence in diverse disciplines such as finance, economics, political…

Researchers have documented the importance of seeing a graph as an emergent trace of how two quantities' values vary simultaneously in order to reason about the graph in terms of quantitative relationships. If a student does not see a graph as a representation of how quantities change together then the student is limited to reasoning about…

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,…

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…

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…

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…

Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data…

The goal of this paper is to illustrate different ways that cardsorting activities (or "card stacks") can be implemented in the introductory physics classroom, along with various tips and resources for getting started. My first attempt at developing a card stack came about from simply wanting to try out a fun way to change student…

This paper addresses the need for empirical research on the processes by which students create algorithms. I analyse the collaborative work of three high-school students on a contextualised graph theory task, in which they created an algorithm for maximising the happiness score of a seating arrangement. The group found an optimal arrangement but…