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…

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…

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…

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.…

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…

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…

This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

The area concept may appear in a wide range of problem situations. The representations used (geometrical, numerical and algebraic) in such situations entail particular practices that condition the partial area meanings. Thus, this study aims to characterize the partial area meanings mobilized in the resolution of area tasks. Each of the area…

The literature reports that students have difficulties connecting different meanings, multiple representations of the derivative, and performing reversibility processes between representations of f and f'. The research goal is to analyze the mathematical connections that university students establish when solving tasks that involve the graphs of f…

This study identifies language specific errors made with transcoding tasks to inform possible future pedagogic decisions regarding the language used when teaching early number. We compared children aged 5-7 years from Kuwait and England. The spoken Arabic language of Kuwait gave the opportunity to compare not only languages where the tens and…

Much of physics involves the construction and interpretation of equations. Research on physics students' understanding and application of mathematics has employed Sherin's symbolic forms or Fauconnier and Turner's conceptual blending as analytical frameworks. However, previous symbolic forms analyses have commonly treated students' in-context…