We describe 24 third (8-9 years old) and 24 fifth (10-11 years old) graders' generalization working with the same problem involving a function. Generalizing and representing functional relationships are considered key elements in a functional approach to early algebra. Focusing on functional relationships can provide insights into how students…

Functional thinking is an established route into algebra. However, the learning mechanisms that support the transition from arithmetic to functional thinking remain unclear. In the current study we explored children's pre-instructional intuitive reactions to functional thinking content, relying on a conceptual change perspective and using mixed…

Little-to-no research examines the provision of targeted mathematical interventions to students struggling with mathematics in a virtual environment. And yet, the global pandemic of 2020--extending into 2021--found schools in such a scenario. This article reports two studies in which researchers explored the intervention package of explicit…

We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3--5. Analyses showed that, while there were no significant…

An open mind--the willingness to consider experiences, beliefs, values, perspectives, etc. that differ from one's own--allows the learner to explore how diverse people across the world think and act. Open-mindedness creates opportunities to rethink assumptions, identify misinformation, and consider alternative ways to make decisions.…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…

The purpose of this study was to determine if a typical third-grade boy and fifth-grade girl and a boy with learning disabilities could benefit from the combined use of Direct Instruction (DI) flashcard and math racetrack procedures in an after-school program. The dependent variable was accuracy and fluency of saying basic multiplication facts. A…

Although brief experimental analysis (BEA) procedures have been effective for aiding instructional decision making in the area of reading, there is a paucity of research extending this technology to mathematics. This study extends the literature on mathematics BEA by using an abridged data series that compares skill- and performance-based…

This study examined the degree to which teacher behaviors established as predictors of achievement generalize to Hispanic students. Participants included 995 students (68% Hispanic) across Grades 3 through 5 and their teachers (N = 46) in an urban school district in the Midwest. Classroom dynamics were measured using the Classroom Assessment…

This study investigated the effects of repeated readings on the reading abilities of 4, third-, fourth-, and fifth-grade English language learners (ELLs) with specific learning disabilities (SLD). A multiple baseline probe design across subjects was used to explore the effects of repeated readings on four dependent variables: reading fluency…

This paper reports results from two studies aimed at examining whether perception of social acceptance and actual social acceptance differ according to the presence of an illusion of scholastic incompetence. Results of both studies conducted in Belgium and in Quebec (respectively 179 and 543 participants) show that children's illusion of…

This guide presents information and clinical tools to implement the Anger Coping Program, an empirically supported intervention for students in grades 3-6. Practitioners are taken step by step through setting up treatment groups, teaching vital skills for reducing aggression and disruptive behavior, and building strong partnerships with teachers…

Generalization is the key to effective autism intervention--when children can apply new skills across settings, they'll make broad, long-term improvements in behavior and social communication. The first how-to guide to generalization is finally here! Practical and reader-friendly, this is the book that helps professionals take today's most popular…

This study examined the effects of providing explicit metacognitive instruction prior to cognitive strategy instruction on students' with learning disabilities ability to generalize a vocabulary strategy learned in a special education setting to a general education setting. The subjects were eight elementary school students with learning…