In the target article, Xing and colleagues (2021) claimed that 6- to 8-year-olds who spontaneously referenced the midpoint of 0-100 number lines made more accurate magnitude estimates and scored higher on a standardized math achievement test than other children. Unlike previous studies, however, the authors found no relation between accuracy on…

The purpose of this study was to examine teachers' perceptions of the Illustrative Mathematics (IM) using data from teacher interviews from year 1 and year 3 of their implementation of IM. In year 1, 22 Algebra 1 teachers were interviewed; in year 3, 13 teachers participated. Interviews were conducted using a semi-structured protocol that included…

Background: Base-ten thinking (BTT) -- children's ability to reason in tens and ones is a crucial measure of Foundation Phase learners' mathematical performance in South Africa. Aim: The study looks at the six learners using BTT to solve additive tasks through two different assessments. Setting: Six purposely selected Grade 3 learners in…

Background: An efficacy study based on a randomized controlled trial (RCT) was designed to evaluate the impact of ASSISTments on math learning among middle school students, including those from high-needs rural schools. Despite extensive recruitment efforts in 2021 (during the pandemic), only a few schools and their teachers agreed to participate,…

This is a technical report detailing the analytic methods used to assess the effects of a virtual professional learning community (vPLC)-enhanced ASSISTments intervention. The report uses a quasi-experimental design and partially nested regression model to account for clustering and reveals that while overall effects were positive but not…

This report is a companion to the "Scaling Teachers' Professional Development for ASSISTments: Evaluation Final Report" and presents an in-depth look at how the integration of the ASSISTments platform with a virtual professional learning community (vPLC) supported middle school math teachers in improving instruction, fostering student…

Competency-based learning (CBL) is a grading strategy that emphasizes the mastery of content. At Middle Technical College (MTC), success rates in the college algebra class have decreased. This study will answer two questions: how will a CBL approach to learning affect student perceptions of their success and what are student perceptions of after…

U.S. students have lost significant learning in mathematics and other subjects since the start of the coronavirus disease 2019 (COVID-19) pandemic in early 2020. The 2022 National Assessment of Educational Progress mathematics scores for students in grades 4 and 8 reflected record declines; the largest decreases were for students experiencing…

In this paper, we examine mathematicians' views on the value of advanced mathematics for secondary mathematics teachers. The data comprise semi-structured interviews with 24 mathematicians from 10 universities. The findings indicate that the value of advanced mathematics courses for prospective secondary mathematics teachers lies in their…

The purpose of this study is to explore the relation between the teaching of Mathematics and the teaching of Statistics at high school level in the South African Context. The study also examines and analyses examples of statistical teaching situations from both a mathematical and a statistical perspective with view to reveal the links between the…

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…

Algebraic identities, which are considered as one of the important subjects of mathematics and mathematics education, have important areas of use such as physics, chemistry, many branches of engineering, as well as calculating the distances among the earth, sun and stars and planning space travels. Algebraic identities play an important role in…

This is the third article in the "On the Shoulders of Giants" series that takes an outstanding mathematician, tells something of their life and work, and provides an item or two based on their achievements that can be used in a primary class. This article focuses on the work of Cheryl Praeger, with an activity based upon her work with…

All differential equations students have encountered eigenvectors and eigenvalues in their study of systems of linear differential equations. The eigenvectors and phase plane solutions are displayed in a Cartesian plane, yet a geometric understanding can be enhanced, and is arguably better, if the system is represented in polar coordinates. A…

The purpose of this article is to describe and illustrate learning trajectories (LTs) and introduce a new, comprehensive set of resources that support teaching meaningfully and joyfully. An LT for a topic has three parts: (1) a mathematical goal; (2) a developmental progression of levels of thinking; and (3) teaching practices (environments,…