Incorporating open-ended real-world tasks enhances students' access to mathematical and real-life knowledge and maximizes learning experiences. This article examines how a secondary mathematics teacher used an open-ended problem on distributing pay raises to teach mathematical concepts and fairness to students. The teacher's actions exemplify…

Developing structure sense is an important part of learning algebra. We investigated learners' structure sense of algebraic expressions involving brackets. This led us to propose the constructs "surface structure" sense and "systemic structure" sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we…

In this article, we examine how 10th graders make use of different intertwined representations when solving algebraic word problems. It is structured in a quantitative phase, with 61 students and a subsequent follow-up case study with nine pairs of students. We found that drawings and tables, used as auxiliary representations within variants of…

The aim of this study is to examine the argumentation-based problem solving processes of 10th grade students in the context of quadratic equations. The study was carried out in a public high school in Istanbul. The study group consists of three male students selected by the method of "homogeneous sampling". In the research, special case…

Mathematically gifted students have a high potential for understanding and thinking through mathematical relations and connections between mathematical concepts. Currently, it is thought that generalizing patterns algebraically can serve to provide challenges and opportunities that match their potential. This article focuses on a mathematically…

The National Council of Teachers of Mathematics (NCTM, 2014) highlights that effective teaching practices promote students' reasoning and sense making through various problem-solving strategies. Rather than telling students what to do and how to solve problems, teachers are expected to engage learners in accessible real-life problem situations…

Students in upper secondary education encounter difficulties in applying mathematics in physics. To improve our understanding of these difficulties, we examined symbol sense behavior of six grade 10 physics students solving algebraic physic problems. Our data confirmed that students did indeed struggle to apply algebra to physics, mainly because…

Mathematics is of major importance in science subjects. Unfortunately, students struggle with applying mathematics in science subjects, especially physics. In this qualitative study we demonstrate that transfer of algebraic skills from mathematics in physics class can be improved by using pre-knowledge effectively. We designed shift-problems…

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

The ties between literacy and numeracy exist in the development of vocabulary and language for understanding mathematical concepts. Research indicates that explicit instruction in mathematics vocabulary supports success with mathematics problem solving (Biemiller 2009; Pierce and Fontaine 2009; Rubenstein and Thompson 2002) for native…

Textbook content has the ability to influence mathematical learning. This study compares how linear functions are presented in two textbooks, one of South African and the other of German origin. These two textbooks are used in different language-based streams in a school in Gauteng, South Africa. A qualitative content analysis on how the topic of…

This paper examines the process of instrumental genesis through which students develop their proficiency in making use of movable points and slider bars--two tools that dynamic mathematics software provides for working with variable coordinates and parameters in the field of functions. The paper analyses students' responses to task sequences…

The problem of taking a data set and separating it into subgroups, where the members of each subgroup are more similar to each other than they are to members outside the subgroup, has been extensively studied in science and mathematics education research. Student responses to written questions and multiple-choice tests have been characterised and…

Algebra is critical to high school graduation and college success, but student achievement in algebra frequently falls significantly below expected proficiency levels. While existing research emphasizes the importance of quality algebra instruction, there is little research about how to conduct problem analysis for struggling secondary students.…

The difficulty in observing, recording, and examining internal representations has been well documented (Goldin & Shteingold, 2001). However, the important role that these internal representations play in the learning and understanding of mathematical concepts has been noted (Yackel, 2000). This study sought to develop a framework for…