Knowledge assessments in undergraduate STEM education commonly evaluate response correctness to determine learner proficiency. However, simultaneous evaluation of learner metacognition more accurately assesses the multiple dimensions of knowledge and has been shown to increase assessment validity and reliability. Motivation for researching these…

Increasing use of intelligent tutoring systems in education calls for analytic methods that can unravel students' learning behaviors. In this study, we explore a latent variable modeling approach for tracking learning flow during computer-interactive artificial tutoring. The study considers three models that give discrete profiles of a latent…

The use of online learning objects in teaching algebra is examined in this research, emphasizing its benefits, such as accessibility, flexibility, interactive involvement, differentiated instruction, quick feedback, and links to real-world situations. Strategies include conceptual comprehension, interactive practice, individualized learning,…

In this paper, we report the analysis of thought processes used by Pre-Service Teachers' (PSTs') through clinical interviews as they solved an algebra task involving a linear pattern. The PST's were asked about a mathematical model they had constructed to describe a pattern problem. Our analysis suggests that conflict factors arise due to…

Appropriate placement into courses at postsecondary institutions is critical for the success of students in terms of retention and graduation rates. To reduce the number of students who are misplaced, using multiple measures in placing students is encouraged. However, in practice most postsecondary schools utilize only a few measures to determine…

From the socio-critical perspective of mathematical modeling, reflexive discussions about the nature, criteria, and consequences of mathematical models are not a natural consequence of modeling in school. This report is part of a larger study focused on stimulating reflexive discussions in practice employing constructivist grounded theory as a…

Most physics courses begin with one-dimensional kinematics, which is usually restricted to the case of constant acceleration. Here we report a unique exercise for an introductory algebra-based physics course involving the running and non-constant acceleration of the theropod dinosaur "Dilophosaurus wetherilli" and the world-famous…

We explore the various Mathematica functions for performing Gaussian elimination, specifically when the linear system contains input parameters. On the one hand, we want the solution, perhaps heuristically found, to be in terms of the input parameters, and as general as possible. On the other hand, we must adhere to all necessary conditions and…

Algebraic identities, which are considered as one of the important subjects of mathematics and mathematics education, have important areas of use such as physics, chemistry, many branches of engineering, as well as calculating the distances among the earth, sun and stars and planning space travels. Algebraic identities play an important role in…

To improve college students' achievement and success rate in the College Algebra course, a new program called Link2Success (L2S) was implemented in several sections of the course at the study's university. The program required students to increase their class time to six hours. Three of those hours were spent with certified tutors who helped…

This manuscript contributes to research on how algebraic thinking about operations and properties can develop, and relevant forms of curricular activity. The key question asked is: how can students' early algebraic activity be fostered through focusing on relations involving operations and properties? We adopt Radford's three aspects of algebraic…

This qualitative study sought to understand middle school students' developing mathematical arguments in a linguistically and culturally supportive classroom that featured mathematical writing and oral conferencing. Writing tasks and conferencing focused on developing the core algebraic practice of justifying by emphasizing audience and revision.…

Background: Although the generation of errors has been thought, traditionally, to impair learning, recent studies indicate that, under particular feedback conditions, the commission of errors may have a beneficial effect. Aims: This study investigates the teaching strategies that facilitate learning from errors. Materials and Methods: This 2-year…

In this paper, we discuss our experience in collaborating with mathematicians to increase their use of active learning pedagogy in a proof-based linear algebra course. The mathematicians we worked with valued using active learning pedagogy to increase student engagement but were reluctant to use active learning pedagogy due to time constraints.…

We propose an alternative formula for solving the biquadratic equation x[superscript 4] + bx[superscript 2] + c = 0, which is more convenient than the classical one whenever c is a perfect square. The method is suitable to be introduced to high school students together with the standard approach of the substitution y = x[superscript 2]. A…