Existing studies have defined and assessed disciplinary literacy, mathematical literacy, and general academic language. However, there is a need to define and assess mathematics discipline-specific language (MDL), particularly for elementary school teachers. Therefore, the purpose of this study was to develop a research instrument to assess the…

Although many researchers theorize that primitive numerosity processing abilities may lay the foundation for whole number concepts, other classes of numbers, like fractions, are sometimes assumed to be inaccessible to primitive architectures. This research presents evidence that the automatic processing of nonsymbolic magnitudes affects processing…

The purpose of this research was to reveal how the construction process of symbolic representation and verbal representation made by students in problem solving. The construction process in this study referred to the problem-solving stage by Polya covering; 1) understanding the problem, 2) devising a plan, 3) carrying out the plan, and 4) looking…

This study is focused on the structure of equivalence problem to probe the evolution from operational to relational view of students' understanding of the equals sign. We propose a modified construct map which incorporates the intermediate levels in such a transition which were previously ignored. Our findings suggest that the structure of number…

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of…

Mathematical conjectures and theorems are most often of the form P(x) ? Q(x), meaning ?x,P(x) ? Q(x). The hidden quantifier ?x is crucial in understanding the implication as a statement with a truth value. Here P(x) and Q(x) alone are only predicates, without truth values, since they contain unquantified variables. But standard textbook…

This study looks at the various verbal and non-verbal representations used in a process of modelling the number of annual plants over time. Analysis focuses on how various representations such as words, diagrams, letters and mathematical equations evolve in the mathematization process of the modelling context. Our results show that (1) visual…

Elementary school children (ages 7-11) struggle to understand mathematical equivalence, a foundational prealgebraic concept. Some manipulations to the learning environment, including well-structured nontraditional arithmetic practice alone, have been shown to improve children's understanding; however, improvements have been modest. The goal of…

The aim of this study is to investigate relationships between note-taking and the orchestrating of math-talk in whole-class teaching. A lesson on (average) velocity in a Swedish Grade 6 has been observed. Taking an inferentialist stance on human understanding, the study conceptualizes teaching and learning from the perspective of how students come…

Numerical and symbolic representations are used extensively in physics problems. However, relatively little is understood about how students respond to these two representational formats when they are solving problems. This study examined the effect of the representational format (numeric vs symbolic) on the problem-solving performance,…

Higher-level mathematics requires a connection between literal symbols (e.g., "x") and their mental representations. The current study probes the nature of mental representations for literal symbols using both the priming distance effect, in which ease of comparing a target number to a fixed standard is a function of prime-target…

This paper explores how a group of pre-service elementary school teachers training to become mathematics teachers for elementary schools arrived at generalizations based on patterns. Two representative problems were investigated with these preservice teachers. The focus of this study was how these preservice teachers analyze and symbolize…

The Merriam-Webster dictionary defines "transition" as: (a) the passage from one state, stage, subject, or place to another: change; or (b) a movement, development, or evolution from one form, stage, or style to another. The word transition can refer to an active shift of the person in space and time or status, for example; it can also…

This study investigated features of instructors' classroom discourse on the derivative with the commognitive lens. The analysis focused on how three calculus instructors addressed the derivative as a point-specific value and as a function in the beginning lessons about the derivative. The results show that (a) the instructors frequently used…

This paper examines the chronotopic nature of physics discourse and instructional practices that are mediated through the integration of disciplinary spatial repertoires and mathematical symbolic systems. The paper addresses how meanings are constructed during instruction between bilingual international teaching assistants (ITAs) and undergraduate…