Post-instrument covariates are often included as controls in instrumental variable (IV) analyses to address a violation of the exclusion restriction. However, we show that such analyses are subject to biases unless strong assumptions hold. Using linear constant-effects models, we present asymptotic bias formulas for three estimators (with and…

An important topic in the study of segregation are comparisons across space and time. This article extends current approaches in segregation measurement by presenting a five-term decomposition procedure that can be used to understand more clearly why segregation has changed or differs between two comparison points. Two of the five terms account…

Recently, Lima lamented on the 'time-consuming and tiresome' pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pencil-and-paper solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula.…

In multisite trials, learning about treatment effect variation across sites is critical for understanding where and for whom a program works. Unadjusted comparisons, however, capture "compositional" differences in the distributions of unit-level features as well as "contextual" differences in site-level features, including…

This work is part of an investigation conducted in Italy, which aims to explore the effects of instruction on secondary school students' combinatorial reasoning. We gave a questionnaire adapted from Navarro-Pelayo's research to two groups of students with and without instruction on combinatorics in order to analyse the students' performances and…

Background: The ability to translate concrete manipulatives into abstract mathematical formulas can aid in the solving of mathematical word problems among students, and metacognitive prompts play a significant role in enhancing this process. Aims: Based on the concept of semantic congruence, we explored the effects of metacognitive prompts and…

STACK is an online testing system that can automatically assess mathematical formulae. When working with STACK on a smartphone, inputting mathematical formulae is time-consuming; therefore, to solve this problem a mathematical formula input interface for smartphones has been developed based on the flick operation. However, since the time of…

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…

In multisite trials, learning about treatment effect variation across sites is critical for understanding where and for whom a program works. Unadjusted comparisons, however, capture "compositional" differences in the distributions of unit-level features as well as "contextual" differences in site-level features, including…

The most influential books on geometry are those of Euclid called "Elements". In our century, in addition to classical learning, various interactive software are used in teaching geometry. Among them, we can mention GeoGebra. GeoGebra is an interactive math measurement program that consists of teaching and learning from elementary to…

The construct of "learning potential" has been proposed to capture differences between learner independent performance and performance during Dynamic Assessment (DA). This paper introduces a new LPS formula implemented in a DA study involving Pakistani learners of L2 Chinese. Learners were randomly assigned to a control or experimental…

Spreadsheets are a core computational tool for practicing engineers and engineering students. While Microsoft Excel, Google Sheets, and other spreadsheet tools have some differences, numerous formulas, functions, and other tasks are common across versions and platforms. Building upon learning science frameworks showing that interactive activities…

This paper discusses a proposal for exploration and verification of numerical and algebraic behavior correspondingly to Generalized Fibonacci model. Thus, it develops a special attention to the class of Fibonacci quaternions and Fibonacci octonions and with this assumption, the work indicates an investigative and epistemological route, with…

This article deals with the problem of calculating the additional real-power losses in double-wound supply transformers with voltage class 6 (10)/0,4 kV, caused by unbalanced active inductive load connected in a star connection with an insulated neutral. When solving the problem, authors used the theory of electric circuits, method of balanced…

A relevant aim of research in education is to find and study the reasoning lines that students deploy when dealing with problematic situations. This can be done through an analysis of the answers students give to a questionnaire. In this paper, we discuss some methodological aspects involved in the quantitative analysis of a questionnaire by means…