Jordan canonical form (JCF) is one of the most important, and useful, concepts in linear algebra. Mathematics, physics, biology, science and engineering undergraduates often find the first application of real JCF in the discipline of differential equations (continuous models) to solving systems of differential equations. In this work, we apply…

Research demonstrates that when math-based gender stereotypes are activated (e.g., men are better at math than women), women display comparatively poorer math performance than men, a phenomenon referred to as stereotype threat. We evaluated the effectiveness of two forms of self-affirmation in reducing the effects of stereotype threat on women's…

Background/Context: In order to stimulate national and regional economic growth, policymakers and businesses have expressed great interest in growing the supply of workers with skills in science, technology, engineering, and math (STEM). At the same time, considerable efforts are being devoted to narrowing race and gender gaps in the STEM training…

While instructional coaching can support teacher improvement and student learning, their effectiveness and longevity in the role may be influenced by teachers' emotions, the quality of the teacher-coach relationship, as well as the cognitive and emotional climate of the school. In this study, we analyze the emotional experiences of a novice…

This paper is a part of a larger research study that we are conducting to develop a framework consisting of the data-driven best practices around teaching and learning algebra in K-12 classrooms. The purpose of this paper is to develop a usable definition for algebra interventions for the second stage of screening within the larger study, which…

Angularity is a persistent quantity throughout K-12+ school mathematics, and many studies have shown that individuals often conflate angularity with linear attributes (e.g., the length of an angle model's sides). However, few studies have examined the productive ways in which students might reason about angularity while attending to linear…

All children can develop high levels of math proficiency when they are given rigorous instructional tasks with appropriate teacher support. Preservice teachers (PSTs) must develop various instructional strategies tailored to the diverse learners in their classroom, including multilingual students. More research is needed on how PSTs can support…

Single case experimental designs are an important research design in behavioral and medical research. Although there are design standards prescribed by the What Works Clearinghouse for single case experimental designs, these standards do not include statistically derived power computations. Recently we derived the equations for computing power for…

Within this dissertation, I use design-based research along with discourse and interaction analysis to study classroom groups of mathematical learners to better understand and design for group structures and cultures that support students' learning mathematics and becoming mathematical communities. Specifically, I focus on the phenomenon of groups…

This study aims to investigate the primary school pupil's performance in answering Higher Order Thinking Skills (HOTS) and Lower Order Thinking Skills (LOTS) in mathematics questions according to gender and types of schools. A descriptive research design was employed in this study to collect quantitative data. Mathematics test questions were…

At the school level statistics begins with exploratory data analysis, or EDA. Statistical learning goes on to include statistical inference, which will be discussed in the second part of this article. In this article, the author will talk about EDA and CODAP. EDA can be thought of as looking for patterns in data using graphs and simple statistics…

Factor analysis is often used to model scales created to measure latent constructs, and internal structure validity evidence is commonly assessed with indices like SRMR, RMSEA, and CFI. These indices are essentially effect size measures and definitive benchmarks regarding which values connote reasonable fit have been elusive. Simulations from the…

The Mathematical Association of America's "Precalculus to Calculus: Insights and Innovations Conference" brought together representatives of mathematics departments from across the country with members of two national research projects to share and discuss both research findings and on-the-ground concerns of faculty. In this article, we…

Students in the elementary and secondary grades may use mathematics writing to express ideas and reasoning about mathematics. To understand current classroom practices related to the assessment and instruction of mathematics writing, we conducted a survey of kindergarten through Grade 12 educators across the United States who taught mathematics,…

The analysis of word problem types and schema-based diagrams are assumed useful for helping students and thus, important for preservice teachers to learn in their preparation programs. Drawing on pre-and post-assessments and videotaped demonstrations, this study analyzed elementary preservice teachers' understanding of addition and subtraction…