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…

The aim of this research is to characterize profiles of the teaching competence "noticing students' mathematical thinking" in the context of the pattern generalization. Prospective primary teachers were asked to describe and interpret the answers of three primary students to three linear pattern generalization problems. Five profiles for…

The current study compared the use of serial and concurrent methods to train multiple exemplars when teaching receptive language skills, providing a systematic replication of Wunderlich, Vollmer, Donaldson, and Phillips (2014). Five preschoolers diagnosed with developmental delays or autism spectrum disorders were taught to receptively identify…

Exploratory learning environments (ELEs) promote a view of learning that encourages students to construct and/or explore models and observe the effects of modifying their parameters. The freedom given to learners in this exploration context leads to a variety of learner approaches for constructing models and makes modelling of learner behavior a…

This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…

The work describes an analogy-based small oscillations analysis of a standard static equilibrium lab problem. In addition to force analysis, a potential energy function for the system is developed, and by drawing out mathematical similarities to the simple harmonic oscillator, we are able to describe (and experimentally verify) the period of small…

In their first years, infants acquire an incredible amount of information regarding the objects present in their environment. While often it is not clear what specific information should be prioritized in encoding from the many characteristics of an object, different types of object representations facilitate different types of generalizations. We…

This mixed methods study investigated undergraduate elementary grades pre-service teachers' (PSTs) mathematical reasoning. In the context of combinatorics, we examined two aspects of mathematical reasoning, namely, the processes of enumerating and generalizing, and sought to understand the relationship between them through analyses of 150 PSTs'…

Generalization is a critical aspect of doing mathematics, with policy makers recommending that it be a central component of mathematics instruction at all levels. This recommendation poses serious challenges, however, given researchers consistently identifying students' difficulties in creating and expressing normative mathematical…

More robust and rigorous psychometric models, such as multidimensional Item Response Theory models, have been advocated for survey applications. However, item responses may be influenced by construct-irrelevant variance factors such as preferences for extreme response options. Through empirical and simulation methods, this study evaluates the use…

Fluency-based strategies such as Say All Fast a Minute Each Day Shuffled (SAFMEDS) effectively promote fluent responding (i.e., high rate and accuracy). It is possible, however, that the stimulus control developed through these activities inhibits stimulus generalization. We investigated this concern in a two-part study with college students.…

School-based evaluations of interventions are increasingly common in education research. Ideally, the results of these evaluations are used to make evidence-based policy decisions for students. However, it is difficult to make generalizations from these evaluations because the types of schools included in the studies are typically not selected…

Traditional drill and practice (TDP) has been shown to be both effective and efficient for increasing word recognition. WordSheets (WS) is a novel drill procedure similar to TDP with two key differences: (a) WS increases opportunities to respond, which may increase efficiency and (b) WS present instructional stimuli in a context that more closely…

In this research, we examined cross-domain effects of achievement goals. In two experimental studies, we manipulated achievement goals and assessed social reactions towards a hypothetical (study 1) and a real (study 2) target. Measurement of social reactions included prosocial behaviours such as helping, sharing and cooperating with others.…

Social skills instruction (SSI) provides a promising avenue for teaching and promoting positive social interactions to students with high-incidence disabilities. Within SSI, a distinction can be made between social skills and social competence. Social skills are specific behaviors one must perform correctly within a specific social context or…