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 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 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…

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 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…

The challenges experienced by schools as a result of the COVID-19 pandemic led to numerous changes and forced teachers to rethink the way teachers use technology, both to communicate with students and to support their mathematics learning. To illustrate these changes in curriculum, teaching, and assessment, the author uses the topic of rational…

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,…

Process-Driven Math is a fully audio method of mathematics instruction and assessment that was created at Auburn University at Montgomery, Alabama, to meet the needs of one particular student, Logan. He was blind, mobility impaired, and he could not speak above a whisper. Logan was not able to use traditional low vision tools like braille and…

The necessity to evaluate professional development has become more pressing for districts in a time of increased accountability. A number of empirical studies had shown that it was difficult to measure the effects of professional development, especially its effect on transferring practice and student achievement. The purpose of this study was to…

Mathematical Argumentation skills have historically been overlooked in assessment, but the inclusion of Mathematical Argumentation in the Common Core State Standards (CCSS) as one of the Standards of Mathematical Practice challenges assessment developers to assess this mathematical practice. Explanation and justification of one's own thinking to a…

In this innovative book, two experienced educators present a fresh and engaging approach to mathematics learning in the middle grades with the transition from arithmetic to algebra. The authors provide a collection of balanced, multi-dimensional assessment tasks designed to evaluate students' ability to work with mathematical objects and perform…

The purpose of this study was to investigate the pre-service teachers' conceptions about the limit of same partial functions given in the form of both graphical and symbolic, the misconception that the pre-service teachers have the concept of limit, and whether there were any differences between pre-service teachers' algebraic performance and…

This article presents the authors' response to Asha K. Jitendra's Response to Xin and Zhang ("The Journal of Educational Research," 2009, Vol. 102, No. 6). The claim of "factual errors, including inappropriate quotes, misrepresentation of information, and inadequate scholarship in Xin and Zhang's text" are not justified. In this rejoinder, the…