In this design experiment study, we investigated the problem: What conditions might foster students' discernment of a critical aspect--variation in unidirectional change (e.g., discerning a "decreasing" increase)? At a public middle school in a large US city, we led a sequence of three days of whole class lessons, followed by task-based,…

Humans possess a remarkable ability to recognise both simple patterns such as shapes and handwriting and very complex patterns such as faces and landscapes. To investigate one small aspect of human pattern recognition, in this study participants position lines of "best fit" to two-dimensional scatter plots of data. The study investigates…

This study aims to examine prospective elementary mathematics teachers' conceptual knowledge level for congruence and similarity in triangles subject and to examine their ability to represent the knowledge, to associate the knowledge with daily life, and to justify and solve the geometry problems about this subject. The study is designed in a…

This monograph provides in-depth mathematical logic as the foundational rationale for the novel and innovative online instructional methodology called the 4A Metric Algorithm. The 4A Metric has been designed to address and meet the meta-competency-based education challenges faced by 21st century students who must now adapt to and learn in a…

In the present study we aimed to develop a multidimensional test assessing high school students' knowledge about triangles, and then to determine the validity evidence for it based on the internal structure and relations to another variable and its reliability. The test developed was administered to 557 tenth grade students. To assess the validity…

This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic…

By considering the example of proving the triangle postulate, this study aimed to explore Hong Kong preservice and novice teachers' knowledge competencies and their beliefs about preformal and formal proofs. The findings revealed that such teachers are not proficient in using preformal proofs and do not realize that preformal proofs are a useful…

The origins and development of our geometric intuitions have been debated for millennia. The present study links children's developing intuitions about the properties of planar triangles to their developing abilities to read purely geometric maps. Six-year-old children are limited when navigating by maps that depict only the sides of a triangle in…

In this report, we discuss the findings from 2 pilot studies investigating the effects of interventions designed to provide students in Grades 3-5 with opportunities to work with dynamic and static models of angles in a dynamic geometry environment. We discuss the effects of the interventions on the children's development of quantitative reasoning…

The purpose of this research is to compare the level of competence in stereometry of the university students taught using the authors' ICT oriented learning method based on the Van Hiele model for stereometry concepts, as opposed to traditional teaching methodology. The study deals with second year undergraduate students form the Department of…

Some mathematics concepts, especially geometry, have not been understood well by students. The current curriculum in Indonesia strongly recommends the use of manipulatives in mathematics learning. However, the presence of manipulatives only cannot guarantee the students could construct their knowledge of concepts. This research aims to find out…

The important role that geometry plays in the mathematics curriculum has been extensively documented. However, the reduction of geometry in school mathematics, and the focus on basic computation and procedures, raises the question of the competencies students acquire and the classroom atmosphere in geometry lessons. The goal of this multiple case…

Many aspects of the geometry of linear statistical models and least squares estimation are well known. Discussions of the geometry may be found in many sources. Some aspects of the geometry relating to the partitioning of variation that can be explained using a little-known theorem of Pappus and have not been discussed previously are the topic of…

During the last reform, Slovakia has reduced geometry in curriculum in primary mathematics education. Pre-school education schools devote more time to geometry in curriculum, but this is not mandatory for all the children. In the primary schools, teachers devote very little lessons time to this problem. These lessons are mainly focused on…

We asked: "What are the similarities and differences in mathematical processing associated with solving learning-based and insight-based problems?" To answer this question, the ERP research procedure was employed with 69 male adolescent subjects who solved specially designed insight-based and learning-based tests. Solutions of…