This article describes "Verse Chronograms" in the Cabrera Portrait (1750) of Sor Juana. The author explains the meaning of three hard-to-see sets of verses inscribed on the canvas, that are a kind of text known as a chronogram, a literary puzzle in which the numerical values of letters that correspond to Roman numerals are added up so…

Math performance is negatively related to math anxiety (MA), though MA may impact certain math skills more than others. We investigated whether the relation between MA and math performance is affected by task features, such as number type (e.g., fractions, whole numbers, percentages), number format (symbolic vs. nonsymbolic), and ratio component…

Background/purpose. One of the current problems facing mathematics students, graduates in mathematics, and engineering is the disconnection between the meanings, symbolic representations, and graphics of derivatives when solving problems, which hinders their understanding. This article analyzes engineering students' understanding activated by…

This study aimed to describe students' semantic representation obstacles in solving geometric problems. There are three types of obstacles, that are ontogeny, epistemology, and didactics obstacles. This study was carried out on three subjects with different obstacles and focused on math semantic representations in solving geometry problems. The…

Across multiple age groups and academic disciplines, research has shown that incorporating multimodal signs into instruction can enhance student learning. For instance, gesture might be synchronized with speech or written signs. The present study reports on the semiotic resources used by a teacher-researcher to support kindergarten students'…

Here we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners' conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several…

The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

This article reports on an empirical study that investigates the way students' performance in solving arithmetical tasks may be related to their performance in solving algebraic tasks. The sample consisted of 203 Grade 6 students. The arithmetical tasks involved arithmetical expressions with known quantities, whereas the algebraic tasks involved…

Symbolic numeracy first emerges as children learn the meanings of number words and how to use them to precisely count sets of objects. This development starts before children enter school and forms a foundation for lifelong mathematics achievement. Despite its importance, exactly how children acquire this basic knowledge is unclear. Here we test…

It is important for students to develop a relational understanding of the equal sign, but students often have simultaneous operational and relational conceptions (i.e., SOR conceptions). This case study carefully explored how a student's conception of the equal sign changed during a classroom teaching experiment and analyzed the possibilities and…

This study explores opportunities to learn definite integrals in three widely used textbooks in the U.S. Definitions, worked examples, and exercise problems were coded using research-based cognitive resources in definite integrals. The results show that limited opportunities for students to explore multiplicative relationship between two…

Teacher perception is one of the most important factors determining classroom teaching practices. Multiple representations are used extensively in mathematics classrooms, especially in developing conceptual understanding. The data in this study, which aims to compare Turkish and US middle school mathematics teachers' perceptions of multiple…

When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (co-vary). How much a change in one variable or parameter is associated with a change in another depends on how they…

This dissertation is on the topic of sameness of representation of mathematical entities from a mathematics education perspective. In mathematics, people frequently work with different representations of the same thing. This is especially evident when considering the prevalence of the equals sign (=). I am adopting the three-paper dissertation…

The link between a student's math fluency and their success in general chemistry has been thoroughly documented in the literature. One diagnostic instrument that can be used to assess a student's arithmetic skills is the Math-Up Skills Test (MUST), a 20-question, free-response math test completed in 15 min. The MUST instrument assesses the…