In this study, we investigated how secondary students interpret algebraic expressions that contain literal symbols to stand for variables. We hypothesized that the natural number bias (i.e., the tendency to over-rely on knowledge and experiences based on natural numbers) would affect students to think that the literal symbols stand for natural…

We conducted a descriptive exploratory study in which we analyzed 313 sixth to eighth grade students' answers to a word problem, accompanied by diagrams, involving generalization in an algebraic functional context. In this research, we jointly addressed two objectives: (a) to determine the strategies deployed by students to generalize and (b) to…

Tasks involving real-world contexts offer opportunities for teachers to engage students in mathematical practices (Standards for Mathematical Practice; NGA Center and CCSSO 2010). The practice of reasoning abstractly and quantitatively requires students to decontextualize and contextualize a task. Decontextualizing a task involves representing it…

This paper investigates and considers factors that affect success in solving a stand-alone geometrical problem by 182 students of the 7th and 8th grades of elementary school. The starting point for consideration is a geometrical task from the National Secondary School Leaving Exam in Croatia (State Matura), utilising elementary-level geometry…

The purpose of this study was to investigate how the 8th graders interpreted the equal sign in the pan balance activities they created on Scratch. Five eighth graders (4 girls and 1 boy) in Turkey participated in this study. Case study was employed as a qualitative research method. Data was gathered through the Scratch files created by the…

The present study investigates the understanding of the equals sign among middle school students. The study data were gathered from a total of 433 middle school students (111 in the fifth grade, 106 in the sixth grade, 95 in the seventh grade and 121 in the eighth grade) using a ten-item equals sign test developed by the researcher. The study…

The equal symbol has been used in diverse mathematical frameworks, such as arithmetic, algebra, trigonometry, set theory, and so on. In mathematical terms, the equal sign has been used in fixed command of standings. The study reports on the students meaning and interpretations of the equal sign. The study involved Grade 6, 7, and 8 students in a…

Creative thinking is the cognitive activities that process the received information to produce new representations. Therefore, it is necessary to develop creative thinking and represent a problem. This study aims to investigate the students' creative thinking processes based on representation in solving mathematical problems reviewed from…

One of the attributes of rational numbers that make them different from integers are the different symbolic modes (fraction, decimal and percentage) to which an identical number can be attributed (e.g. 1/4, 0.25 and 25%). Some research has identified students' difficulty in mental calculations with rational numbers as has also the switching to…

This study, firstly, aimed at investigating the various types of the multiple math representations and transitions among them in the 8th grade math textbook, and secondly, teachers' use of these representations in teaching. The current study employed the content analysis approach to investigate the multiple mathematical representations and…

All mathematics is comprised of three elements: symbols, nominalizations, and images, and the combination of these three elements determine the mathematical meaning. However, adolescents may not be aware of these three elements. When asked to describe mathematical language, they will often name equations and images, two of the three elements. Over…

There is an ongoing need to support students' learning of linear functions, and the study of slope makes up a foundational component of this learning. We applied techniques from systemic functional linguistics to document the meanings that were established through spoken interaction between a student and her tutors during discussions of slope. We…

With the understanding of importance of pedagogical content knowledge, professional noticing has become one of the research subjects of the mathematics educators for the last 10 years. This qualitative study which explores secondary school students' solution processes regarding the concept of equation ,one of the main components of algebraic…

Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby…

Mathematical problem solving typically involves manipulating visual symbols (e.g., equations), and prior research suggests that those symbols serve as diagrammatic representations (e.g., Landy & Goldstone, 2010). The present work examines the ways that instructional design of student engagement with these diagrammatic representations may…