I explore some facts about the area, position, etc. of the Steiner ellipse using GeoGebra and numerical analysis. Students can use these for mathematical inquiry.

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

Mathematical inquiry involving hands-on activities has received increasing attention in mathematics education. Besides various customized physical teaching aids, subject-specific information technology, such as Dynamic Geometry System (DGS), finds extensive use in mathematical inquiry activities. However, effects of DGS and physical manipulatives…

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…

In the disciplines of dance and mathematics, binary identities commonly split individuals into either (non)dance and/or (non)math people. However, these shorthand assessments become dangerous because they constrain disciplinary knowledge, and limiting one's identity and capabilities remains antithetical to broad education goals. Capitalizing on…

One goal of inquiry-oriented instruction is student engagement with others' mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others' ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the…

This study reports the classroom mathematical practices proposed in an instructional sequence grounding on the principles of inquiry-based learning (IBL) through the use of the dynamic geometry software (DGS) in learning to teach geometric transformations. A 5-week instructional sequence consisting of IBL activities that were guided by the…

A digital wall is a tool for students to structure and register their online work on mathematical problem-solving activities that involve the coordinated use of digital technologies. How could students use such digital wall to understand mathematical concepts and to develop problem-solving competencies? The aim of this study is to analyze and…

As three-dimensional (3D) printing technology is fast becoming more affordable and accessible, calculus instructors can now consider using 3D printing and 3D printed models to actively engage students in core concepts relating to objects in R[superscript 3]. This article describes three lessons for a multivariable calculus class in which students…

The study investigated the effects of a technology-integrated guided inquiry-based approach on pre-service mathematics teachers' conceptual understanding of geometry when compared to a guided inquiry approach and a traditional teacher-centered approach. A non-equivalent pretest-posttest control group quasi-experimental design was used. A…

Justification skills should be fostered in teaching mathematics as they are highly related to effectiveness in problem solving. However, pre-service mathematics teachers do not always have the necessary skills in using mathematically convincing language and justifying their solutions. Thus, they should be introduced to a variety of instructional…

In this paper we present the results of a study which was carried out in an inquiry-based teaching and learning environment with the use of 'what if not' methodology coupled with the integration of dynamic geometry software. The vast majority of the students reported that they perceived themselves as participants rather than spectators. Most of…

As mathematics educators we want our students to develop a natural curiosity that will lead them on the path toward solving problems in a changing world, in fields that perhaps do not even exist today. Here we present student projects, adaptable for several mid- and upper-level mathematics courses, that require students to formulate their own…

The central roles that modelling plays in the processes of scientific enquiry and that models play as the outcomes of that enquiry are well established (Gilbert & Boulter, 1998). Besides, there are considerable similarities between the processes and outcomes of science and technology (Cinar, 2016). In this study, we discuss how the use of…

This article presents four inquiry-based learning activities developed for a liberal arts math course. The activities cover four topics: the Pythagorean theorem, interest theory, optimization, and the Monty Hall problem. Each activity consists of a dialogue, with a theme and characters related to the topic, and a manipulative, that allow students…