An interaction in a fixed effects (FE) regression is usually specified by demeaning the product term. However, algebraic transformations reveal that this strategy does not yield a within-unit estimator. Instead, the standard FE interaction estimator reflects unit-level differences of the interacted variables. This property allows interactions of a…

When analyzing instructional quality in mathematics, observational measures can consider domain-specific instructional approaches (e.g., effective teaching of mathematics) and content-focused practices (e.g., effective teaching of a specific mathematical topic). In this study, we analyze lesson videos from secondary algebra classrooms using two…

Algebra is critical in shaping future mathematics success and is integral to the K-12 curriculum. Despite its inclusion, a common challenge arises as students' progress to higher grades without a solid foundation, resulting in challenging learning experiences. This action research study focuses on the algebraic learning experience of a Grade 7…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…

This study addresses a significant gap in educational research by employing statistical methods to measure the sequencing of different components and content topics in textbooks. It is well-documented that the structure and sequencing features of textbooks play a crucial role in enhancing students' learning. However, existing literature has…

The School of Engineering of the Polytechnic of Porto (ISEP) has embraced the DrIVE-MATH project, since September 2017. Active-learning (AL) techniques were implemented in several Math courses, namely Linear Algebra and Analytic Geometry, Probability and Statistics, Statistical Models, Computational Mathematics, and Differential and Integral…

This paper describes a study that used a novel method to investigate conceptual difficulties with mathematical induction among two groups of undergraduate students: students who had received university-level instruction in formal mathematical induction, and students who had not been exposed to formal mathematical induction at the university level.…

The National Council of Teachers of Mathematics (NCTM, 2014) highlights that effective teaching practices promote students' reasoning and sense making through various problem-solving strategies. Rather than telling students what to do and how to solve problems, teachers are expected to engage learners in accessible real-life problem situations…

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…

For the first time in 32 years, the national average scale score in mathematics dropped by seven points across the country in grades four and eight, according to the latest results of the National Assessment on Educational Progress (NAEP). The 2022 results in mathematics were staggering, in which "math performance fell for the first time in…

We describe here lessons learned in designing an early algebra curriculum to measure early algebra's impact on children's algebra readiness for middle grades. The curriculum was developed to supplement regular mathematics instruction in Grades K-5. Lessons learned centered around the importance of several key factors, including using conceptual…

Knowledge assessments in undergraduate mathematics 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. Research into…

For the first time in 32 years, the national average scale score in mathematics dropped by seven points across the country in grades four and eight, according to the latest results of the National Assessment on Educational Progress (NAEP). The 2022 results in mathematics were staggering, in which "math performance fell for the first time in…

One of the challenges of understanding the complexity of so-called reform mathematics instruction lies in the observational tools used to capture it. This article introduces a unique tool, drawing from commognitive theory, for describing classroom discussions. The Realization Tree Assessment tool provides an image of a classroom discussion,…

The mode of assessment is one of the most important factors influencing learning. E-assessment usually includes only checking the final answer, thus limiting teacher's ability to check the complete solution, and it does not allow inclusion of math proofs problems that constitute an important part of math content. The e-assessment module of Halomda…