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.…

Learning progressions detail the incremental steps that students take as they learn to master a skill. These progressions are based on developmental research about how students learn and how their thinking develops as a result of instruction. A typical progression not only describes the stages that students must master, but it also shows what…

In three experiments, I tested for the presence of the naming capability, the participants' drawing responses of the stimuli learned in the absence of the visual stimulus, and the participants' comprehension of texts with and without pictures present. In Experiment 1, I tested for the presence of naming and the drawing responses for the stimuli…

Design research studies provide significant opportunities to study new innovations and approaches and how they affect the forms of learning in complex classroom ecologies. This paper reports on a two-week long design research study with twelve 2nd through 4th graders using curricular materials and a tablet-based diagnostic assessment system, both…

"That was the day I decided I was bad at math." Countless times, preservice and in-service teachers make statements such as this after sharing vivid memories of learning multiplication facts. Timed tests; public competitive games, such as Around the World; and visible displays of who has and has not mastered groups of facts still…

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 representation of numerical and non-numerical ordered sequences was investigated in children from preschool to grade 3. The child's conception of how sequence items map onto a spatial scale was tested using the Number-to-Position task (Siegler & Opfer, 2003) and new variants of the task designed to probe the representation of the alphabet…

Adaptive learning techniques have typically scheduled practice using learners' accuracy and item presentation history. We describe an adaptive learning system (Adaptive Response Time Based Sequencing--ARTS) that uses both accuracy and response time (RT) as direct inputs into sequencing. Response times are used to assess learning strength and to…

This publication is designed to extend and strengthen the computational skills and mathematical understandings of children in Grades 2 and 3. It presents an overall scope and detailed sequence for implementation by teachers and supervisors, based on the modern program introduced in pre-kindergarten, kindergarten and first grade classes. The scope…

The purpose of this study was to investigate a proposed model for the acquisition of the concept of displacement volume and to compare two methods of conservation task presentation. A 12-stage hierarchical model for the acquisition of the concept was proposed, based on four primary assumptions: (1) concept attainment can be measured by…

A lexicon of approximately 9,000 words classified into levels from kindergarten to grade 3 was compiled as a base for studying the spelling-to-sound correspondences needed in beginning reading. The spelling-to-sound correspondences were established for 69 grapheme units, resulting in a total of 166 correspondences for the one- and Two-syllable…

Forty Canadian Indian children in grades three and four were divided into two groups and given a minimum and a maximum remediation program to improve their sequential learning processes. The maximum program resulted in significant improvement in sequential tasks such as auditory and visual memory and reading tests. (JC)

This material developed as a resource in Los Angeles, California, is designed to assist teachers in the planning of social studies programs for grades one, two, and three. The ideas and suggestions are related directly to the two State textbooks which were adopted in 1971--"The Social Sciences: Concepts and Values," and "Voices of Life." The…