Learning to compute with fractions is a major challenge for many students and especially for students with disabilities (SWD). Phase 1 of this study employed a randomized pretest-posttest comparison design to test the effects of two versions of formative assessment combined with an instructional program called Fractions at Work. In one condition,…

Since the seminal introduction of the propensity score (PS) by Rosenbaum and Rubin, PS-based methods have been widely used for drawing causal inferences in the behavioral and social sciences. However, the PS approach depends on the ignorability assumption: there are no unobserved confounders once observed covariates are taken into account. For…

Recent government moves in many countries have seen coding included in school curricula, or promoted as part of computing, mathematics or science programmes. While these moves have generally been associated with a need to engage more young people in technology study, research has hinted at possible benefits from learning to program including…

This paper argues neoliberal programs of government in education are equipping parents for calculativeness. Regimes of testing and the publication of these results and other organizational data are contributing to a public economy of numbers that increasingly oblige citizens to calculate. Using the notions of calculative and market devices, this…

Surprisingly few empirical studies address how computational thinking works "in the wild" or how games and simulations can support developing computational thinking skills. In this article, the authors report results from a study of computational thinking (CT) as evinced through player discussions around the collaborative board game…

In this paper, we present a third-grade ecology learning environment that integrates two forms of modeling--embodied modeling and agent-based modeling (ABMs)--through the generation of mathematical representations that are common to both forms of modeling. The term "agent" in the context of ABMs indicates individual computational objects…

A laboratory project for the upper-division physical chemistry laboratory is described, and it combines IR and Raman spectroscopies with Gaussian electronic structure calculations to determine the structure of the oxalate anion in solid alkali oxalates and in aqueous solution. The oxalate anion has two limiting structures whose vibrational spectra…

A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation…

A first-grade teacher has students use their hands and fingers to engage in and develop understanding of counting, to combine groups to facilitate counting by fives and tens, and to describe their findings using words and equations.

The impact of misspecifying covariance matrices at the second and third levels of the three-level model is evaluated. Results indicate that ignoring existing covariance has no effect on the treatment effect estimate. In addition, the between-case variance estimates are unbiased when covariance is either modeled or ignored. If the research interest…

There is a renewed debate about whether educated adults solve simple addition problems (e.g., 2 + 3) by direct fact retrieval or by fast, automatic counting-based procedures. Recent research testing adults' simple addition and multiplication showed that a 150-ms preview of the operator (+ or ×) facilitated addition, but not multiplication,…

To further understand student thinking in the context of combinatorial enumeration, we examine student work on a problem involving set partitions. In this context, we note some key features of the multiplication principle that were often not attended to by students. We also share a productive way of thinking that emerged for several students who…

What happens to memories as we forget? They might gradually lose fidelity, lose their associations (and thus be retrieved in response to the incorrect cues), or be completely lost. Typical long-term memory studies assess memory as a binary outcome (correct/incorrect), and cannot distinguish these different kinds of forgetting. Here we assess…

The relevance of the problem studied in the article is caused by the fact that now the process of reforming the housing and utilities sector in the Republic of Tatarstan continues. Its purpose is to increase the quality of service for public and to protect their legitimate rights and interests. That is why it is one of the aspects of social and…

This work aims to demonstrate the use of Excel spreadsheets for solving L-L extraction problems. The key to solving the problems successfully is to be able to determine a tie line on the ternary diagram where the calculation must be carried out. This enables the reader to analyze the extraction process starting with a simple operation, the…