This article presents a curricular reasoning model developed based on research conducted with middle grades teachers as they planned, taught, and reflected on a geometric transformations unit. Teachers can use the model to become aware of their own curricular reasoning to make key mathematical decisions as they plan and teach their lessons. While…

Digital task design is an important issue when integrating technology into mathematics education. However, existing frameworks often are not fine-grained enough for supporting teachers in designing tasks or they only focus on geometric topics. In this paper, we share a case study as the first cycle of our design-based research study that aims to…

This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

Relying on the students' cultural background to teach mathematics may be a strong incitement for the learning process. This background can include artistic creations, items from the news, among others. Because of the strong presence of space related news (in particular the almost simultaneous launching of three spacecrafts towards Mars), we…

This article presents a reflection on a teaching experience involving the use of the Brügner tangram, an interesting but little-known manipulative material. It details an activity conducted as part of an undergraduate mathematics education course for prospective primary school teachers. The main objective of this paper is to present the…

This paper aims to describe the design and inspection of the quality of a digital learning platform to diagnose mathematical ability levels of seventh-grade students with regard to the topics of Measurement and Geometry. A total of 517 seventh-grade students from 23 schools in four regions, namely north, northeast, central, and south of Thailand…

Learning curves are an important tool in cognitive diagnostics modeling to help assess how well students acquire new skills, and to refine and improve knowledge component models. Learning curves are typically obtained from a model estimated on real data obtained from a finite, and usually limited, sample of students. As a consequence, there is…

In the seventeenth century, Guarino Guarini, mathematician and architect, affirmed that architecture, a discipline that primarily deals with measures, relies on geometry: therefore, the architect needs to know at least its basic principles. On behalf of Guarini's words, we designed a set of interdisciplinary teaching experiences, between…

The recent increase in the number of mathematics museums has given rise to a need for tools with which to design and assess mathematics educational proposals in this non-formal context. This study proposes the use of the van Hiele model, a benchmark in mathematics instruction, for the design of interactive museum models focusing on mathematics…

In this paper, I discuss the potential transformations to teach K-12 geometry topics with the technology of 3D Pens, which enabled 3D models to be created instantly via one's moving hands. I draw on an example of using constructionist learning activities with 3D Pens to teach young children, 'how tall is the triangle?'

The Three Little Pigs launched a lesson in which kindergarten students were challenged with designing a house out of materials such as marshmallows and toothpicks that could withstand the Big Bad Wolf. Students engaged in the engineering design process and geometry standards while building and testing their models.

The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…

Studies that address preservice teachers' knowledge of area measurement emphasize their lack of knowledge and their tendency towards the use of formulas, without offering a body of knowledge that helps to address such difficulties. This study offers an approximation of the mathematical knowledge necessary for preservice teachers to solve area…

The narrative permeating higher education institutions globally is the intention to advance the quality of preservice mathematics teachers to gain better performance than mathematics school learners. In this article we report on a qualitative case study which explored the pedagogical content knowledge (PCK) of preservice teachers (PST) (n = 20) at…

The document presents a set of categories for the analysis of the conceptualization of the congruence of polygons--a central theme in school mathematics--and details the application of the analytical tools used, derived from Grounded Theory, in this construction. This set of categories is called 'Interpretive Model of the Conceptualization of…