The National Assessment of Educational Progress (NAEP) program only reports state-level subgroup results if it samples at least 62 students identifying with the subgroup. Since some subgroups constitute small proportions of many states' general student populations, these minority subgroups are seldom sufficiently sampled to meet this sample size…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

We perform dynamic investigation of two surprising geometrical properties, each of which involves additional properties. In the first task the property belongs to two regular polygons with the same number of sides and with one common vertex. It is found that all the straight lines that connect corresponding vertices of the two polygons intersect…

Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students' generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support…

We propose a generalization of the classical Remainder Theorem for polynomials over commutative coefficient rings that allows calculating the remainder without using the long division method. As a consequence we obtain an extension of the classical Factor Theorem that provides a general divisibility criterion for polynomials. The arguments can be…

This study employed a multisite design to investigate the differential impact of deductive and guided inductive instruction for second language (L2) grammar development in ecologically valid classroom contexts. Students (n = 138) from eight intact third-year L2 Spanish classes in three public high schools in the United States received deductive…

Purpose: The present study aims to investigate the effects of a number of demographic and academic factors, such as gender, age, nationality (Emirati vs non-Emirati), high school major (arts vs science) and high school score, on the academic performance -- measured by overall grade point average -- of undergraduate students majoring in statistics…

This article examines the development of professional knowledge in pre-service mathematics teachers. From the discussion of a task associated with the multiplication of consecutive integer numbers, generalization is recognized as a process that allows to explore, to explain, and to validate mathematical results, and as an essential ability to…

This study shares two frameworks for analyzing teacher actions that support students in generalizing and examines how those frameworks align with teacher questioning. One classroom teaching episode focused on the mathematical activity of generalizing is shared to illustrate effective generalizing promoting practices. We found several patterns of…

Patterns and generalization are one of the most fundamental aspects of mathematics, which makes recent decades, mathematical tasks which include patterns, whether they are numerical or graphical, are mostly used, for example researching generalization. The aim of this paper is to investigate how a special kind of task concerning well-known…

We explore generalizability and fairness across sociodemographic groups for predicting on-time college graduation using a national dataset of 41,359 college applications. Our features include sociodemographics, institutional graduation rates, academic achievement, standardized test scores, engagement in extracurricular activities, and work…

Usage-based approaches to language acquisition explain language development as a gradual process of generalizing constructions through language experience. This study investigated second language learners' development of constructional knowledge from the perspective of usage-based language development. A total of 169 Korean EFL students at five…

We introduce the concept of "differential prediction generalization" in the context of college admissions testing. Specifically, we assess the extent to which predicted first-year college grade point average (GPA) based on high-school grade point average (HSGPA) and SAT scores depends on a student's ethnicity and gender and whether this…

The National Council of Teachers of Mathematics [NCTM] noted that middle and high school students are expected to be able to both explain inequalities by using mathematical symbols and understand meanings by interpreting the solutions of inequalities. Unfortunately, research has revealed that not only do middle and high school students hold…

This primer should provide the reader with a deeper understanding of the concept of test validity and will present the recent available validity evidence on the relationship between SAT® scores and important college outcomes. In addition, the content examined on the SAT will be discussed as well as the fundamental attention paid to the fairness of…