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…

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…

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…

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…

While some tertiary mathematics educators approximated the familiar invigilated, closed-book assessment regime in the online environment forced upon us all by a pandemic, others either by choice or necessity needed to devise a new way to assess their students' learning. This Classroom Note both synthesizes advice from the literature about what…

This study examined secondary mathematics teachers' content knowledge for teaching the concept of function. Content knowledge, for the purpose of this study, includes the common content knowledge and specialized content knowledge domains of Ball and her colleagues' Mathematical Knowledge for Teaching (MKT) framework. Data were collected through a…

Mastery-grading techniques such as mastery-based grading, specifications grading, and standards-based grading are assessment techniques professors are implementing in order to support a growth mindset of learning, decrease test anxiety, and help students develop a deeper understanding of course objectives. In this paper, we provide an analysis of…

Standards-based grading (SBG) is an assessment/grading system that attaches scores to the mastery level of specific learning objectives. This methodology is gaining momentum in the K-12 environment but has been largely overlooked at the post-secondary level. In this paper, I will discuss the implementation of this practice in a College Algebra…

Purpose: The main purpose of this study was to examine mathematics teachers' abilities in developing formative assessments when teaching algebraic reasoning after utilizing two innovations: lesson study and open approach. Methodology: A single group quasi-experimental research design was employed in two mathematics classes in a school in…

The central purpose of this dissertation was to examine the difference in achievement levels between one- and two-way feedback between the student and teacher and the impact it has on achievement levels in a northeastern Texas school district. Effective feedback from the teacher had shown to improve student outcomes in mathematics on a regular…

Specifications grading is a version of mastery grading distinguished by giving students clear specifications that their work must meet, and grading most things pass/fail based on those specifications. Mastery grading systems can get quite elaborate, with hierarchies of objectives and various systems for rewriting and retesting. In this article I…

A common challenge among mathematics professors is to structure a course so that students are motivated to complete enough work to master the material without creating an unmanageable grading workload. We will discuss a strategy that the author devised to successfully confront this challenge (after many other failed attempts): using online surveys…

The purpose of this study is to determine whether the Mississippi Academic Assessment Program (MAAP) English II and Algebra I scores correlate with American College Testing (ACT) English and Mathematics scores, to examine the methods teachers use to prepare students for the MAAP test, and to determine whether these methods enhance…

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…