The author shares some examples from her Bulgarian project, "Mathematics Through Experience", which approaches mathematics from a practical, real-life perspective in order to develop creative thinking: just like science! What was most important to her was to motivate her students to study maths and science by giving them a taste of how…

In this study we investigated eighth grade students' informal justification for the circle area formula to expand accounts of the measurement knowledge for middle-school age students. Data were collected during three paired interviews of a three-year teaching experiment. Here we describe schemes students exhibited as they operated on measurement…

A long-term observation of students' usage of a dynamic geometry in a classroom at all grade levels has challenged to develop an approach for learning and understanding mathematics in an easier way for both students and teachers. The paper deals with the results of a study that investigates the process and outcomes of the implementation of…

This article focuses on the concept of belonging as an embodied practice that is expressed by adolescents in multimodal ways and that can be nurtured inside and also beyond schools, such as within afterschool programs. We explore belonging in an afterschool program designed for court-involved youth. Our research is theoretically framed by…

Despite Common Core State Standards for Mathematics (CCSSI 2010) recommendations, too often students' introduction to proof consists of the study of formal axiomatic systems--for example, triangle congruence proofs--typically in an introductory geometry course with no connection back to previous work in earlier algebra courses. Van Hiele…

The use of traditional string figures by the Dr. Schaffer and Mr. Stern Dance Ensemble led to experimentation with polyhedral string constructions. This article presents a series of polyhedra made with six loops of three colors which sequence through all the Platonic Solids.

While the path to mathematical discovery is often intuitive and not simply reducible to the application of a method, neither is it in most cases entirely haphazard. Certain kinds of questions and certain ways of looking at things tend to produce new and interesting results. To illustrate, this paper tells a story of how someone might discover…

The NCTM Algebra Standard suggests that students use technology to explore the effects of varying the parameters in y = ax2 + bx + c. This article discusses an extension of this task that incorporates dynamic geometry software to engage students in generating, testing, and proving mathematical conjectures.

In spring 2015 Mississippi began testing the college readiness of all grade 11 public high school students and found that approximately 18 percent were ready for college math, a percentage that had changed little by 2017/18. This study examined: (1) the sequences of math courses that Mississippi students took in grades 6-11; (2) the math…

It is a modern trend today when formulating the curriculum of a geometric course at the technical universities to start from a real-life problem originated in technical praxis and subsequently to define which geometric theories and which skills are necessary for its solving. Nowadays, interactive and dynamic geometry software plays a more and more…

Mairead Hourigan and Aisling Leavy describe a range of teaching and learning activities focusing on the identification and classification of 2-dimensional shapes. The activities described are useful in highlighting students' misconceptions regarding non-traditioanl and non-prototypical shapes.

The main goal of this research was to assess the effect of a dynamic environment on relationships between the three geneses (figural, instrumental, and discursive) of Spaces for Geometric Work. More specifically, it was to determine whether the interactive geometry program GeoGebra could play a specific role in the geometric work of future…

This study was conducted using a new hybrid method of research which combined qualitative and quantitative designs to investigate the viewpoints of primary school students' conceptual understanding in learning geometry from the aspect of shapes and spaces according to van Hiele theory. Q-methodology is used in this research to find out what…

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…

This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies…