Area should be experienced, not simply calculated. This task invites students to physically experience areas and the spatial relationships between them, as well as their own community.

This research study focuses on preservice teachers' (n=66) inspection of pedagogical connections between geography and geometrical reasoning. The aim of this study was to empirically investigate the use of mathematical analysis to enrich the social studies topics of the distortion of country sizes on the world map. The analysis of data collected…

In this article, we report on a video-based field study of an intergenerational family's enactment of a mathematical object (a torus) in the context of an immersive mathematics exhibition in a science center. To do this, we center interwoven, multi-party mobilities at multiple scales--walking, gesturing, touching, and postural adjustments -- as…

In order to promote geometric understanding, teachers frequently use hands-on activities. Such activities can be used to expound upon the declarative statements and theorems of geometry. Using a compass, straightedge, and protractor, students are able to actively build conceptions involving bisectors, midpoints, and perpendicular lines.…

Area models are an important strategy for representing and solving multiplication problems under the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010). The hands-on task presented in this article, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around…

Developing design concepts is crucial in architectural engineering education, yet helping students to develop these concepts is a challenging task. Despite previous research exploring design concepts, statistical analysis is scarce to evaluate their effectiveness. This study used the body movement methods from existing literature, combined with…

Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics…

Research reveals that many mathematics teachers find it difficult to stimulate learners' interest in learning geometry. One major reason suggested is that geometric concepts are not well conceptualised and comprehended by both learners and teachers. The study explored learners' views on how polygon pieces and dictionary mediate learning of…

These proceedings contain the papers of the 16th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2019), held during November 7-9, 2019, which has been organized by the International Association for Development of the Information Society (IADIS) and co-organised by University Degli Studi di Cagliari, Italy.…

According to the National Council of Teacher of Mathematics (NCTM) (2000), K-12 students should be given an opportunity to develop their spatial reasoning abilities. One of the topics that may allow students to develop their spatial skills is forming 3-dimensional objects using spinning and extrusion methods. Also, extrusion and spinning methods…

This study surveyed and analysed four secondary school students' writing about a square. Sfard's discursive approach to understanding mathematical discourse was used to analyse the responses collected from 214 Australian secondary school students. The results showed that geometric knowledge was developed experientially and not developmentally.…

The Commission on International Adult Education (CIAE) of the American Association for Adult and Continuing Education (AAACE) provides a forum for the discussion of international issues related to adult education in general, as well as adult education in various countries around the globe. The following purposes summarize the work of the…

This paper provides historical insights and educational background of Froebel's Gifts, hands-on materials developed in the early 19th century. Based on an explorative study with 54 German children (aged 5 to 10) in 2016, we first took steps to explore how these materials meet the demands for early mathematics learning of primary children. Starting…

Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…

The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…