To help students acquire mathematics and science knowledge and competencies, educators typically use multiple external representations (MERs). There has been considerable interest in examining ways to present, sequence, and combine MERs. One prominent approach is the concreteness fading sequence, which posits that instruction should start with…

The importance of multiplicative thinking in supporting students' learning of key topics and success in further mathematics is widely and clearly stated in mathematics education literature. However, multiplicative thinking is not clearly stated in curriculum documents of many countries including Australia. In the "Australian Curriculum:…

Algebra problem solving is one of the most difficult areas in the mathematics curriculum for secondary students with learning disabilities (LD) due to the higher-order reasoning demands and strategic thinking required. The purpose of this review is to examine how effective algebra problem-solving interventions conceptualize the cognitive processes…

"Patterning" is a cognitive intervention that is unknown to psychologists, but has nevertheless been taught for half a century in nearly all kindergartens and many preschools in English-speaking countries. Patterning is the understanding that a certain rule governs the sequence of items in a series. At the simplest level, if the series…

Background/Context: Which ideas should be included in the K-12 curriculum, how they are learned, and how they should be taught have been debated for decades in multiple subjects. In this article, we offer mathematics as a case in point of how new standards-related policies may offer an opportunity for reassessment and clarification of such…

In this article, we obtain a genetic decomposition of students' progress in developing an understanding of the decimal 0.9 and its relation to 1. The genetic decomposition appears to be valid for a high percentage of the study participants and suggests the possibility of a new stage in APOS Theory that would be the first substantial change in…

Project-based learning may enhance students' cognitive skills and knowledge construction. Online discussion stimulates the social interactions of project-based learning, and appropriate cognitive tools (such as concept maps) facilitate the coordination, planning, and implementation of projects. Currently, related studies on project-based learning…

Proposes a teaching viewpoint on comprehension which removes some of the abstraction; the final product is a teaching sequence for comprehension skills that is parallel in form to the teaching sequences commonly used for word recognition. (JM)

This study looks at a specific application of Ainsworth's conceptual framework for learning with multiple representations in the context of using multiple sequential graphic organizers that are student-generated for a process-writing task. Process writing refers to writing that consists of multiple drafts. It may be a process of re-writing without…

Sequenced writing assignments--a series of related writing tasks--offer students frequent opportunities to write and to acquire writing skills through redundancy, progressively more complicated cognitive and rhetorical demands, and a diversity of learning activities. The most frequently identified goal of sequencing is to move students beyond…

This study investigates the effects of content sequence on student learning. The treatments, a spatial and conceptual instructional sequence each consisting of identical content elements, were administered to students in a two-year college Botany course. Hypotheses tested were that sequence would have an effect on student perceptions of the…

This first in a series of seven related teaching guides that together outline a public school district's English language arts curriculum for kindergarten through grade six focuses on a course of study for kindergarten. The guide explains the district's overall philosophy and teaching goals and the philosophy behind the development of the…

This second in a series of seven related teaching guides that together outline a public school district's English language arts curriculum for kindergarten through grade six focuses on a course of study for grade one. The guide explains the district's overall philosophy and teaching goals and the philosophy behind the development of a curriculum…

This third in a series of seven related teaching guides that together outline a public school district's English language arts curriculum for kindergarten through grade six focuses on a course of study for grade two. The guide explains the district's overall philosophy and teaching goals and the philosophy behind the development of a curriculum…

IN THE PAST DECADE, ENGLISH AS A SCHOOL SUBJECT HAS BEEN REASSESSED TO ESTABLISH PRIORITIES, SPECIFY THE TASKS OF THE ENGLISH TEACHER, AND CREATE EFFECTIVE SEQUENTIAL, INTEGRATED PROGRAMS WHICH BALANCE CONTENT AND SKILLS. THIS SUMMARY REPORT CONSIDERS EMERGING CONCEPTS IN THE TEACHING OF LANGUAGE, LITERATURE, AND COMPOSITION, AND THEIR APPLICATION…