In the same chapter of his book "Opera Geometrica," Torricelli published two discoveries: 1) initial velocity of a jet from a container increases with the square root of the depth of the hole; 2) he drew the pattern of jets from three openings at the wall of a container filled with water to constant level "H" and determined the…

In this study, based on the analysis of a teaching experiment with middle school students, we propose a framework for describing meanings of a point represented on a plane in terms of multiplicative objects in the context of graphing. We classify those meanings as representing: (1) non-multiplicative objects; (2) quantitative multiplicative…

Middle school students (n=144) worked with an applet specially designed to introduce the concept of function without using algebraic representations. The purpose of the study was to examine whether the applet would help students to understand function as a relationship between a set of inputs and a set of outputs and to begin to develop a…

The authors question how hermetic texts in mathematics, history, and philosophy of mathematics, specifically those referring to abstract algebra, can be open to the understanding of researchers, teachers and students who are intentionally willing to understand them. This discussion suggests that the openness may happen through hermeneutic…

In this research, a new test for understanding simple fractions has been developed for students at the beginning of lower secondary education. In many countries, mathematics education in Grade 5 builds on elementary students' developing concepts of fractions. Understanding fractions causes many difficulties for students, and research on mental…

Interpreting statistical graphs and making inferences based on the graphs are a precursor for formal statistical inferences. To support student inferences, both teachers and future teachers should have adequate knowledge regarding students' thinking on graphs as well as their potential misinterpretations and difficulties in interpreting graphs. In…

The methods and techniques used by teachers have an important place on the basis of many students' negative perspectives and failures towards mathematics. Integrating technology into mathematics learning environments is inevitable since it is of great importance to create rich learning environments to increase students' interest and understanding…

The concrete-representational-abstract (CRA) sequence of instruction is an explicit methodology for teaching mathematics using multiple representations of concepts. Learning concepts through multiple representations fosters conceptual understanding and mathematical thinking. This article describes how a special education teacher used explicit CRA…

Problem solving has been the focus of the Common Core State Standards for Mathematical Practice. Helping students acquire critical-thinking and problem-solving skills has become the primary goal of mathematics education across all grade levels. However, research has found that many students struggle with word problems because of poor text…

Computational thinking (CT) has acquired the status of a necessary 21st-century skill and is currently being introduced in school curricula around the world, despite a lack of consensus about what it entails. The aims of this review are to provide an overview of the existing literature on CT activities in primary mathematics education, and to…

When mathematics educators work towards making mathematics more relevant, they often think about including more real-world applications into mathematics lessons. But what happens when a lesson is devoid of real-world contexts? In what ways can students find it relevant? This study explores how high school students perceived relevance when they…

This paper describes the authors' journey in designing a linear representation that aligns mathematics and music to support fractional reasoning. The three authors, guided by the theoretical framing of realistic mathematics education, engaged in a task design process over a 12-month period to develop integrated resources. Data were collected in…

This qualitative case study aimed to investigate prospective middle school mathematics teachers' instructional responses based on the students' correct and incorrect functional thinking within the context of pattern generalization. The data were collected from thirty-two prospective teachers through a written task and semi-structured interviews…

This study explored the mathematics teacher identity (MTI) of three purposefully selected grade 6 non-specialist primary school mathematics teachers. The participants' subject matter knowledge and didactical skills were explored by means of semi-structured interviews, lesson observations, and document analysis of lesson plans. The data were…

Studies have found that problems exist with respect to elementary school teachers' understanding of proportions and their knowledge of the appropriate methods for teaching the concept. This study aims to help aspiring elementary school teachers form a healthy mathematical identity and deepen their understanding of mathematics. This quantitative…