Panel or grouped data are often used to allow for unobserved individual heterogeneity in econometric models via fixed effects. In this paper, we discuss identification of a panel data model in which the unobserved heterogeneity both enters additively and interacts with treatment variables. We present identification and estimation methods for…

This research aims to develop a combining game-based learning with design thinking using block-based programming to enhance computational thinking and creative games for primary students and will be referred to as game-based learning from now on. The purpose of this research is to 1) develop a model for game-based learning, 2) develop the system…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

Inappropriate treatment of missing data may introduce bias into the value-added estimation. We consider a commonly used value-added model (VAM), which includes the past student test score as a covariate. We formulate a joint model of student achievement and missing data, in which the probability of observing a test score depends on observing the…

Student growth percentiles (SGPs) are currently used by several states and school districts to provide information about individual students as well as to evaluate teachers, schools, and school districts. For SGPs to be defensible for these purposes, they should be reliable. In this study, we examine the amount of systematic and random error in…

Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive…

Sources of longitudinal achievement data are increasing thanks partially to the expansion of available interim assessments. These tests are often used to monitor the progress of students, classrooms, and schools within and across school years. Yet, few statistical models equipped to approximate the distinctly seasonal patterns in the data exist,…

This article explains the process behind estimating a National Education Cost Model (NECM) and generating from that model projections of per-pupil costs to achieve 2016 national average outcomes (reading and math grades 3 to 8) across all districts in the United States, from 2019-20 to 2020-21. This article is a follow-up to a preliminary report…

The development of international surveys on children's learning like PISA, PIRLS and TIMSS--delivering comparable achievement measures across educational systems--has revealed large cross-country variability in average performance and in the degree of inequality across social groups. A key question is whether and how institutional differences…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

Computer science (CS) and computational thinking (a problem-solving process used by computer scientists) teach students design, logical reasoning, and problem solving--skills that are valuable in life and in any career. Computational thinking (CT) concepts such as decomposition teach students how to break down and tackle a large complex problem.…

An aggregation strategy is proposed to potentially address practical limitation related to computing resources for two-level multidimensional item response theory (MIRT) models with large data sets. The aggregate model is derived by integration of the normal ogive model, and an adaptation of the stochastic approximation expectation maximization…

Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

Public schools with impressive records of serving lower-performing students are often overlooked because their average test scores, even when students are growing quickly, are lower than scores in schools that serve higher-performing students. Schools may appear to be doing poorly either because baseline achievement is not easily accounted for or…