In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

Background: Many students face difficulties with algebra. At the same time, it has been observed that fraction understanding predicts achievements in algebra; hence, gaining a better understanding of how algebra understanding builds on fraction understanding is an important goal for research and educational practice. Objectives: However, a wide…

This study builds on the simulation framework of a recent paper by Stanley and Doucouliagos ("Research Synthesis Methods" 2023;14;515--519). S&D use simulations to make the argument that meta-analyses using partial correlation coefficients (PCCs) should employ a "suboptimal" estimator of the PCC standard error when…

In cluster randomized evaluations, a treatment or intervention is randomly assigned to a set of clusters each with constituent individual units of observations (e.g., student units that attend schools, which are assigned to treatment). One consideration of these designs is how many units are needed per cluster to achieve adequate statistical…

In cluster randomized evaluations, a treatment or intervention is randomly assigned to a set of clusters each with constituent individual units of observations (e.g., student units that attend schools, which are assigned to treatment). One consideration of these designs is how many units are needed per cluster to achieve adequate statistical…

Partial correlation coefficients are often used as effect sizes in the meta-analysis and systematic review of multiple regression analysis research results. There are two well-known formulas for the variance and thereby for the standard error (SE) of partial correlation coefficients (PCC). One is considered the "correct" variance in the…

Units Coordination and Covariational Reasoning are powerful frameworks for modeling students' mathematics in arithmetic reasoning and construction of relationships between changing quantities, respectively. This case study of an advanced stage 2, 8th-grade algebra student, Daniel, investigated connections between his units coordination and…

Purpose: Based on the general formula, which depends on the length and difficulty of the test, the number of respondents and the number of ability levels, this study aims to provide a closed formula for the adaptive tests with medium difficulty (probability of solution is p = 1/2) to determine the accuracy of the parameters for each item and in…

Staggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. Estimation remains challenging, however, and common regression methods can give misleading results. A promising alternative is the synthetic control method (SCM), which finds a weighted average of control units…

In this paper, we provide an elaboration of the notion of mathematical structure -- a term agreed upon as valuable but difficult to define. We pull apart the terminology surrounding the notion of structure in mathematics: relationship, generalising/generalisation and properties, and offer an architecture of structure that distinguishes and…

Recently, quantitative researchers have shown increased interest in two-step factor score regression (FSR) approaches to structural model estimation. A particularly promising approach proposed by Croon involves first extracting factor scores for each latent factor in a larger model, then correcting the variance-covariance matrix of the factor…

Studies that address preservice teachers' knowledge of area measurement emphasize their lack of knowledge and their tendency towards the use of formulas, without offering a body of knowledge that helps to address such difficulties. This study offers an approximation of the mathematical knowledge necessary for preservice teachers to solve area…

Correlation analysis has been used widely by researchers and analysts when analyzing large-scale assessment data. Limit research provided reliable methods to estimate various correlations and their standard errors with the complex sampling design and multiple plausible values taken into account. This report introduces the methodology used by the…

An introductory course in algebra may cover various types of polynomial manipulation, here we cover the background of these topics and a relatively unknown property of polynomials, namely Viete's relations. We define relevant operations and properties of polynomials over the real numbers as well as their algebraic forms, divisibility properties,…

The paper focuses on four upper secondary students' collaborative small-group mathematical reasoning (MR) with respect to a sinusoidal function. The students were collaboratively engaged in a process of MR regarding the relationships between mathematical theoretical descriptions of parameters in the algebraic expression of the sinusoidal function…