Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

Despite a large body of research demonstrating that generalization to novel stimuli can be produced by training sufficient exemplars, the methods by which exemplars can be trained remain unclear. The purpose of the current study was to evaluate 2 methods, serial and concurrent presentation of stimuli, to train sufficient exemplars. Five preschool…

The study of functions is a critical route into teaching and learning algebra in the elementary grades, yet important questions remain regarding the nature of young children's understanding of functions. This article reports an empirically developed learning trajectory in first-grade children's (6-year-olds') thinking about generalizing functional…

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 instructional design presented in this article discusses a procedure for arranging and sequencing examples and nonexamples for concept teaching in the classroom. Concepts are divided into two types: definition and observation. A definition concept is one in which the critical attributes are determined by the definition, e.g., war. Observation…

The effects of the Individualized Curriculum Sequencing (ICS) model on acquisition and generalization of skills by two severely handicapped preschoolers were evaluated. Results preliminarily supported the efficacy of the ICS model. Criterion performance and generalization across novel classroom activities and materials were evident for four of…

The content-process approach described in this k-12 teaching guide focuses upon knowledge as a basis for understanding and explaining that which is being investigated and, when practical, for predicting what may happen in the future as a result. A curriculum based upon this sequential interdisciplinary content process approach helps students to…