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…

Developmental mathematics courses play a critical role in ensuring that students have the foundational mathematical skills necessary to succeed in higher educational mathematics coursework. With the introduction of the corequisite format in recent educational reforms, there has been a growing trend towards transferring developmental mathematics…

The topic of this research study is mastery learning, an educational theory that began with the work of John Carrol in 1963. The core principle of this theory is that all students can achieve uniform learning outcomes, but it will take some students longer than others to reach the same performance goals. The problem that this research study…

Using Coarsened Exact Matching (CEM), this analysis examined the impact of Zearn Math across 7,116 matched pairs of students in 31 Louisiana parishes. Students who completed an average of 3+ Zearn Math lessons per week during the 2021-2022 school year were compared to similarly matched peers who completed less than 1 lesson per week. Findings…

This study aimed to explore the effects of Mastery Learning Strategy (MLS) on senior school students' performance in Mathematics in Osogbo, Nigeria. The quasi-experimental study's goals were to investigate how MLS affected mathematics students' performance according to their gender and score levels. A purposive sampling technique was used to…

The understanding of the relationships between pattern recognition and mathematical abilities is important for students in their learning of mathematics and mathematics teachers in the design of their teaching pedagogies. This study examines the connections between pattern recognition and mathematical abilities of students from four Singapore…

This article explores the development of 'mastery mathematics' -- a significant development in mathematics in England -- and opens up some questions about the intended and unintended consequences of the promotion of this approach by the government.

This article provides conceptual ideas, data, and exercises, for integrating original sources of recent, state of the art, world-class life science research in the undergraduate mathematics curriculum and classroom. To this end, this article shows how one of the main goals of calculus in the life sciences, fitting parameters to data and assessing…

Mastery of mathematics depends on the people's ability to manipulate and abstract values such as negative numbers. Knowledge of arithmetic principles does not necessarily generalize from positive number arithmetic to arithmetic involving negative numbers (Prather & Alibali, 2008, https://doi-org.bibliotheek.ehb.be/10.1080/03640210701864147). In this study, we…

In response to a shift to high-stakes assessments, teachers are changing their instruction and approaches away from research-based formal training on best practices teaching in response to the stress and pressure this shift has created (Avalos et al., 2020; Gonzalez et al., 2017; Musoleno & White, 2010). More research is needed on teachers who…

In "School Rethink 2.0," editors Frederick M. Hess, Michael B. Horn, and Juliet Squire gather leaders immersed in the nuts-and-bolts work of educational reinvention to present ten promising education improvements and ways to implement them. Contributors, including acclaimed education pioneers Sal Khan, Beth Rabbitt, and Larry Berger,…

We present a system for math placement and intervention that pairs ALEKS PPL with an online, standards-based "bridge" course designed to prepare students interested in STEM for PreCalculus. To determine the efficacy of this system we studied ALEKS PPL placement scores, bridge course grades, ALEKS concept mastery percentages, and…

Mastery learning -- the process by which students must demonstrate proficiency with a single topic before moving on -- is well recognized as one of the best ways to learn, yet many teachers struggle or remain unsure about how to implement it into a classroom setting. This study leverages two field experiments to test the efficacy of a program…

In most mathematics textbooks, each lesson is followed by a set of homework problems in one of two ways -- blocked practice and mixed practice. Additionally, most mathematics textbooks rely on a common learning strategy called overlearning, that is, mastering a skill and continuing to practice this same skill. This study investigated the effects…

Learning experience designers consistently balance the trade-off between open and close-ended activities. The growth and scalability of Computer Based Learning Platforms (CBLPs) have only magnified the importance of these design trade-offs. CBLPs often utilize close-ended activities (i.e. Multiple-Choice Questions [MCQs]) due to feasibility…