Although previous research has demonstrated that the acquisition of mathematical skills requires support from multiple cognitive abilities, the associations between cognitive precursors in different domains and mathematics at different hierarchical levels among primary school children are not well understood. This study explores the cognitive…

Researchers have demonstrated a much-needed shift in pedagogical practices to incorporate literacy strategies. This dissertation provides additional empirical evidence to expand the body of research by utilizing a comparative readability analysis that examines the academic language of a popular calculus textbook. A sample from the published…

Research in the area of equivalence and the equal sign dates back decades, demonstrating students often possess misconceptions concerning the meaning of equivalence and the equal sign. Students often understand the equal sign to mean the answer comes next (i.e., an operational definition) instead of the same as (i.e., a relational definition).…

One typical challenge in algebra education is that many students justify the equivalence of expressions only by referring to transformation rules that they perceive as arbitrary without being able to justify these rules. A good algebraic understanding involves connecting the transformation rules to other characterizations of equivalence of…

A language is a system of communication, consisting of a set of sounds or written symbols that enable people to communicate. In chemistry, a particular language is required in order to represent the phenomenological world by means of symbols. Choosing the right words and knowing the precise definitions for chemical concepts is needed for avoiding…

This study investigated how students reason about the partial derivative and the directional derivative of a multivariable function at a given point, using different graphical representations for the function in the problem statement. Questions were formulated to be as isomorphic as possible in both mathematics and physics contexts and were given…

Previous research suggests that the Approximate Number System (ANS) allows people to approximate the cardinality of a set. This ability to discern numerical quantities may explain how meaning becomes associated with number symbols. However, recently it has been argued that ANS representations are not directly numerical, but rather are formed by…

Theoretical yield and extent of reaction (degree of completion) are important concepts in stoichiometry and in chemical kinetics. We provide expressions describing theoretical yield (Y) and maximum extent of reaction (fractional yield, f[subscript max]) for five examples of commonly encountered reversible chemical reactions: A [equilibrium sign]…

Reading comprehension and arithmetic skills are essential abilities for children, particularly at the early career. Examine the link between language proficiency and numeral information process amongst primary school children. This study examines numeral comprehension in 600 Chinese primary second graders with different levels of decoding and…

In this article, we discuss the process of understanding continuity, which is one of the most fundamental concepts in mathematics. The continuity of mathematical functions is formally defined in terms of abstract symbols and operations. This representation of continuity is very abstract or dis-embodied. Therefore, it is difficult to acquire a…

The concept of integration appears in many different scientific fields, and students' understanding of and ability to use the definite integral in applications is important to success in their STEM (science, technology, engineering, and mathematics) classes. One of the first types of application problems that students encounter is finding the…

In mathematics education, students are repeatedly confronted with the tasks of interpreting and relating different representations. In particular, switching between equations and diagrams plays a major role in learning mathematical procedures and solving mathematical problems. In this article, we investigate a rather unexplored topic with…

In this article we investigate the transparency of language in learning place value in either a Southern African indigenous language (isiXhosa, Setswana, Oshiwambo or Emakhuwa) or a European-based language (Afrikaans, English, German or Portuguese). Since language is a key mediator in developing place value understanding, it is important to…

Symbols are a cornerstone of the written language of mathematics and mathematical sciences. However, variations in their use pose a constant challenge to students. This paper reports data from first year undergraduate students studying mathematics, statistics and/or physics collected using surveys and interviews. It became clear that multiple uses…

The authors assessed a battery of number skills in a sample of over 500 preschoolers, including both monolingual and bilingual/ multilingual learners from households at a range of socio-economic levels. Receptive vocabulary was measured in English for all children, and also in Spanish for those who spoke it. The first goal of the study was to…