In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

Efforts to implement high-quality communication instruction for students with autism spectrum disorder (ASD) and complex communication needs (CCN) may be difficult for some educators with limited time and resources. In this article, we offer guidance on implementing several economic strategies that can be easily embedded into existing classroom…

This article describes "Build It!--The Rectangle Game" task that uses the context of a game to develop mathematical generalizations based on strategy. The underlying mathematics in this game-based task is for students to discover factors and prime and composite numbers through 100. The playful use of "The Rectangle Game"…

This article identifies and describes several different approaches to using game-mediated language learning (GML2), drawing in particular on Reinhardt and Sykes' (2012; 2014) framework and related literature. The article concludes with a brief discussion of potential applications to adult literacy and basic education settings and learners.

Fragile understanding is where new learning begins. Students' understanding of new concepts is often shaky at first, when they have only had limited experiences with or single viewpoints on an idea. This is not inherently bad. Despite teachers' best efforts, students' tenuous grasp of mathematics concepts often falters with time or when presented…

This article is devoted to the study of the possibilities of educational environment design in the arrangement of the schoolwork with children from migrant families so that they could positively adapt to the conditions of school and integrate into the culture of the host country. Based on a generalization of the problems faced by migrant children,…

This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

Of all the tasks that special education teachers are charged with completing, managing classroom behaviors has been reported as one of the most challenging and one of the top reasons the teachers are leaving the field. The task of providing effective support in classroom management is also daunting for leadership personnel in school systems. This…

Functional communication training (FCT) is a strategy to address problem behavior for students with various disabilities that is supported by a broad evidence base. Despite this support, multiple factors continue to dissuade educators from utilizing FCT in their classrooms. This article outlines the process of developing and implementing FCT plans…

A great deal of research on second language (L2) input has provided useful linguistic evidence for the development of generalizations about and hypotheses on the usage-based nature of L2 knowledge. However, despite the fact that classrooms are one of the most ubiquitous sites of L2 learning, we still know very little about the linguistic quality…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…

Investigating symmetric dot patterns provides opportunities for foundational mathematical learning that is not restricted to multiplication alone. Students have opportunities to learn about the properties of symmetry, about the generalization of patterns, about writing and interpreting equations--all areas of study in grades 3-5. And symmetric dot…

Inherent in the Common Core's Standard for Mathematical Practice to "look for and express regularity in repeated reasoning" (SMP 8) is the idea that students engage in this practice by generalizing (NGA Center and CCSSO 2010). In mathematics, generalizing involves "lifting" and communicating about ideas at a level where 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…

Treatment intensity is an aspect of communication intervention that has received limited empirical attention. In this article, we discuss key parameters of treatment intensity related to individuals with complex communication needs who use augmentative and alternative communication. We advocate for an examination of treatment intensity along with…