In this theoretical paper, I consider reversibility as a defining characteristic of mathematics. Inverse pairs of formalized operations, such as multiplication and division, provide obvious examples of this reversibility. However, there are exceptions, such as multiplying by 0. If we are to follow Piaget's lead in defining mathematics as the…

In the domain of "Counting & Cardinality," Common Core State Standards indicate that by the time students leave kindergarten, they should know the names and sequence of number words up to 100, be able to count to determine the number of objects in a small set (up to 20), and make comparisons between small sets of objects (National…

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…

Many educators face the challenge of engaging students in science and mathematics, often struggling to bridge the gap between theoretical concepts taught in classrooms and their real-world applications. This disconnect can lead to disinterest and disengagement among students, hindering their learning outcomes. "Cases on Informal Learning for…

This study, a sub-study of a National Science Foundation (NSF) funded research project, applies a modified strategy of the U[superscript 2]MC for an eight-week afterschool robotics curriculum to promote upper elementary students' computational thinking in the second grade. Twenty-one students in second grade participated in a Life on Mars project…

This article proposes a latent variable regression four-level hierarchical model (LVR-HM4) that uses a fully Bayesian approach. Using multisite multiple-cohort longitudinal data, for example, annual assessment scores over grades for students who are nested within cohorts within schools, the LVR-HM4 attempts to simultaneously model two types of…

With the understanding of importance of pedagogical content knowledge, professional noticing has become one of the research subjects of the mathematics educators for the last 10 years. This qualitative study which explores secondary school students' solution processes regarding the concept of equation ,one of the main components of algebraic…

Children in developing countries often lack sufficient support for early learning skills prior to beginning school. This research evaluates an educational media intervention using an animated cartoon program, "Akili and Me." The program was originally created in Tanzania to teach early learning skills. This program was adapted in content…

The primary purpose of International Computer and Information Literacy Study (ICILS) 2018 is to assess systematically the capacities of students to use ICT productively for a range of different purposes, in ways that go beyond a basic use of ICT. ICILS 2018 includes authentic computer-based assessments that are administered to students in their…

Estimating the effect of campus math tutoring support, this study demonstrates the use of propensity score weighted and matched-data analysis and examines the correspondence with results from parametric regression analysis.

This article discusses estimation of multilevel/hierarchical linear models that include cluster-level random intercepts and random slopes. Viewing the models as structural, the random intercepts and slopes represent the effects of omitted cluster-level covariates that may be correlated with included covariates. The resulting correlations between…

The ability of regression discontinuity (RD) designs to provide an unbiased treatment effect while overcoming the ethical concerns plagued by Random Control Trials (RCTs) make it a valuable and useful approach in education evaluation. RD is the only explicitly recognized quasi-experimental approach identified by the Institute of Education…

The precision of estimates of treatment effects in multilevel experiments depends on the sample sizes chosen at each level. It is often desirable to choose sample sizes at each level to obtain the smallest variance for a fixed total cost, that is, to obtain optimal sample allocation. This article extends previous results on optimal allocation to…

Computing in some form touches nearly every aspect of day to day life and is reflected in the ubiquitous use of cell phones, the expansion of automation into many industries, and the vast amounts of data that are routinely gathered about people's health, education, and buying habits. Computing is now a part of nearly every occupation, not only…

This research study explored robotics as the catalyst for computational thinking (CT) by sixth-grade students as they are engaged in a science lesson. The interactions, understandings, and applications are discussed, along with the participants' connections and implementations of CT concepts (decomposition, abstraction, pattern recognition, and…