In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

This study investigated the effect a computer intervention program has on student proficiency in the Algebra 1 End of Course (EOC) examination. This study utilized the intervention math program IXL Math, a computerized program that targets individual students' skill practice and supports students' need to accelerate mastery of Algebra 1 skills in…

Despite repeated discussions and practice, algebra students continue to make variable errors, in many ways, year after year. This same problem appeared thirty years ago in a list of common errors that math teachers today would immediately recognize, many involving exponents and distribution (Marquis 1988). Similar complaints even appeared in the…

This case study highlights a high school math teacher's successful journey of taking the steps needed to move away from traditional teaching methods to innovative pedagogies supporting mastery-based teaching and learning. Mastery-based learning (also called competency-based learning) is a shift away from traditional, one-size-fits-all teaching.…

In the context of a generic harmonic oscillator, we investigated students' accuracy in determining the period, frequency, and angular frequency from mathematical and graphical representations. In a series of studies including interviews, free response tests, and multiple-choice tests developed in an iterative process, we assessed students in both…

Homework in introductory physics represents an important part of a student's learning experience; therefore, choosing the manner in which homework is presented merits investigation. We performed three rounds of clinical trials comparing the effects of mastery-style homework vs. traditional-style homework with students in both algebra-based and…

This study examined the effectiveness of the iPad app Mathspace on high school students' algebra computation and skill maintenance. The participants in this study were four ninth grade students enrolled in beginning algebra at a large, urban high school. All four students were struggling to obtain grade-level algebra skills and were reported by…

Background: This study investigated learning outcomes and user perceptions from interactions with a hybrid intelligent tutoring system created by combining the AutoTutor conversational tutoring system with the Assessment and Learning in Knowledge Spaces (ALEKS) adaptive learning system for mathematics. This hybrid intelligent tutoring system (ITS)…

This article examines the effectiveness of a technology-based algebra curriculum in a wide variety of middle schools and high schools in seven states. Participating schools were matched into similar pairs and randomly assigned to either continue with the current algebra curriculum for 2 years or to adopt Cognitive Tutor Algebra I (CTAI), which…

Peer-led Team Learning (PLTL) is an instructional method reported to increase student learning in STEM courses. As mathematics is a significant hurdle for many freshmen engineering students, a PLTL program was implemented for students to attempt to improve their course performance. Here, an analysis of PLTL for freshmen engineering students in…

The math emporium model was first developed by Virginia Tech in 1999. In the emporium model students use computer-based learning resources, engage in active learning, and work toward mastery of concepts. This approach to teaching and learning mathematics was piloted in a rural STEM high school. The purpose of this experimental study was to compare…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

This study utilized an explanatory mixed-methods research design to investigate the effect of learning environment on student mathematics achievement, and mathematics self-efficacy, and student learning style in a ninth grade Algebra I classroom. The study also explored the lived experiences of the teachers and students in the three different…

Over the past 2 years, almost 45% of the students attending a local suburban high school failed Algebra 2. The purpose of this study was to compare the impact of a cooperative instructional technique (student teams-achievement divisions [STAD]) to traditional instructional methods on performance in high school algebra. Motivational and cognitive…

In 2001, Black Hills State University (BHSU) redesigned college algebra to use the computer-based mastery learning program, Assessment and Learning in Knowledge Spaces [1], historical development of concepts modules, whole class discussions, cooperative activities, relevant applications problems, and many fewer lectures. This resulted in a 21%…