Research has identified some sources of student difficulty in understanding the horizontal translation of a function. The present study presents and focuses on another source for the difficulties: student conceptions of symbols involved in the horizontal translation of the graph of a function. We explored which student conceptions of the symbols…

We offer a new angle to explain the comprehension of mathematical infinity. We use Action-Process-Object-Schema (APOS) theory to explore the construction of different aspects of the cognitive Object related to this notion. We focus our attention on different ways of interacting with infinity, and how to act on infinite entities. Our aim is to shed…

Understanding the intricate quantifier relations in the formal definitions of both convergence and continuity is highly relevant for students to use these definitions for mathematical reasoning. However, there has been limited research about how students relearn previous school mathematics for understanding multiply quantified statements. This…

This study aims to examine the concept images of pre-service mathematics teachers for the concepts of single-variable and multivariable functions. In the present research, which was conducted with the case study method, a test consisting of three open-ended questions was used to obtain data about the definition of the concept of function and the…

In this article, we discuss the process of understanding continuity, which is one of the most fundamental concepts in mathematics. The continuity of mathematical functions is formally defined in terms of abstract symbols and operations. This representation of continuity is very abstract or dis-embodied. Therefore, it is difficult to acquire a…

This article reports on the understanding of the function concept by pre-service mathematics teachers from two countries (Germany and Croatia). We focused on investigating students' concept definition and concept image of the function in relation to their curriculum experiences. Data were collected using a questionnaire in the form of open-ended…

Given the vast experiences pre-service mathematics teachers (PSMTs) have with functions, one may assume that they have existing personal definitions and concept images. The purpose of this paper is to build an understanding of the variety of images that one might associate with a definition of function that includes 'for each input there is one…

STEM education is on demand more than ever as the workforce relies on 21st century skills and STEM disciplines. This paper presents a framework (IMS-TEAM) for integration of mathematics and science with the use of technology and modeling in an authentic context. The activity based on this framework is designed for and implemented with forty-four…

Pairing the mid-century work of Ada Dietz (1882-ca. 1970) with two compelling contemporary projects from Sonya Clark (1967- ), this article considers the ways in which normative mathematical ideas are remade through their engagement with weaving practice. Highlighting recent efforts to further ethnomathematics' original decolonial intentions, I…

This paper presents a new theoretical viewpoint blended from the perspectives that mathematical meaning is extracted (from objects falling under a particular concept) and that mathematical meaning is given (to objects that an individual interacts with). It is elaborated that neither uni-directional framing (whether involving extracting meaning or…

Global economic and societal shifts are causing movement from manufacturing economies to knowledge and information industries. As a result, learners must be equipped with the 21st century skills necessary for lifelong skill development and prosperity. Communication is identified as one of the essential 21st century skills for preparing students…

We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…

Studies on student learning of scientific concepts have shown that students often experience various difficulties in understanding basic physics concepts such as vector quantities, as a result of formal and informal learning. The purpose of the present study is to document Grade 11 students' difficulties in understanding vectors and their…

Science students should use mathematical and computational thinking to explain phenomena, but few examples of teachers engaging students in this important scientific practice have been found. This article describes a strategy for enhancing a lesson in which students use a mechanistic model to explain friction by adding mathematical and…

There is an ongoing discussion within the research field of mathematics education regarding the utilization of the history of mathematics within mathematics education. In this paper we consider problems that may emerge when the historical epistemology of mathematics is paralleled to students' conceptual developments in mathematics. We problematize…