This paper investigates the connection between the spiral teaching method and mathematical rigor in K-12 education. Defining rigor as a balanced integration of conceptual understanding, application, and procedural fluency (contrasting it with rote learning), the paper posits that the spiral approach cultivates this rigor. By revisiting…

Algebra is critical in shaping future mathematics success and is integral to the K-12 curriculum. Despite its inclusion, a common challenge arises as students' progress to higher grades without a solid foundation, resulting in challenging learning experiences. This action research study focuses on the algebraic learning experience of a Grade 7…

Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…

This research study presents the PGBE model for teaching and learning percentages with students of Grade 7 when their cognitive development enables the conceptual understanding of percentages as proportional statements, and offers the possibility for more effective matching of them with fractions and decimal numbers. The abbreviation PGBE presents…

Schools seem firmly rooted in the emphasis on computational mastery, and seldom seem to have time to develop other areas of mathematical thinking, such as real-world problem solving and the application of mathematical concepts. All too often, children seem to do well in math in the early grades because they easily memorize the facts and the…

This study gives insights into how Logo-like microworlds can affect cognitive development related to mathematics education of students with math learning difficulties. In particular, we analyse the case of a 15-year-old student with dyslexia and severe dyscalculia. Among the various cognitive aspects involved, here we delve into the development of…

A test of the effectiveness of patterning instruction was conducted with 140 first-graders. First, 383 first-graders from 20 classes were screened on a patterning test. The eight in each class who scored worst were given individual 15-minute lessons on patterning or reading or mathematics or social studies three times weekly for a period of 6 1/2…

Young children must develop basic concepts of numeracy--one being that numbers have magnitudes that increase linearly--before they are able to succeed in mathematics. Children from low-income families have been found to be at a greater disadvantage in the development of numeracy, but this disadvantage can be overcome through the use of a simple…

Developing critical numeracy is important in a society where mathematics plays a particular and significant role. One way of helping learners to develop the level of numeracy required to participate in society is by exploring ideas embedded in rich, accessible tasks. These can be linked to contexts that have relevance in their lives. One…

This article describes some aspects of Piaget's Theory of Cognitive Development. It highlights the importance of giving young children specific access to explore conservation in measurement, which will give students invaluable experiences in measurement that in years to come will be regarded as their prior knowledge of the concept. This is…

Algebra is a gateway to expanded opportunities, but it often poses difficulty for students with learning disabilities. Consequently, it is essential to identify evidence-based instructional strategies for these students. The authors begin by identifying three areas of algebra difficulty experienced by students with disabilities: cognitive…

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…

Children's thinking follows natural developmental paths in learning math. When teachers understand those paths and offer activities based on children's progress along them, they build developmentally appropriate math environments. The authors explain math learning trajectories and why teaching math using the trajectories approach is effective. A…

Investigated the pedagogical quality of physical space by adapting a classroom to create a material "educational field" and testing children's performance on a "go to the front and right of the tower" activity. Found that the educational field made it possible for children to put into relation two spatial reference systems and…

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…