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…

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…

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 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…

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…

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…

An assessment of the possible effect of mathematics symbol instruction on achievement in word problems was the main thrust of the study. Two null hypotheses were tested in the study. The non-equivalent group pre-testpost-test quasi-experimentalresearch design was adopted. The multistage sampling technique was used to select a sample of 387…

Over the last several centuries, mathematicians have developed sophisticated symbol systems to represent ideas often imperceptible to their five senses. Although conventional definitions exist for these notations, individuals attribute their personalized meanings to these symbols during their mathematical activities. In some instances, students…

Mathematical symbols, such as those embodying quantum concepts, are indispensable for conveying complex ideas and relationships in academic writing. However, some education researchers and students keep a distance from anything mathematical: algebraic equations, geometrical reasoning, or statistical symbols. How to lower the access threshold for…

Perceptual learning theory suggests that perceptual grouping in mathematical expressions can direct students' attention toward specific parts of problems, thus impacting their mathematical reasoning. Using in-lab eye tracking and a sample of 85 undergraduates from a STEM-focused university, we investigated how higher-order operator position (HOO;…

Understanding of the equal sign is associated with early algebraic competence in the elementary grades and equation-solving success in middle school. Thus, it is important to find ways to build foundational understanding of the equal sign as a relational symbol. Past work promoted a conception of the equal sign as meaning "the same as".…

The ability to efficiently compare number symbols, such as digits, is associated with mathematics competence across the lifespan. Performance on symbolic number comparison tasks differ across age groups; young students who are developing fluency with digits improve on symbolic number comparison, and performance is better in adults than children.…

Experimentally manipulating Approximate Number System (ANS) precision has been found to influence children's subsequent symbolic math performance. Here in three experiments (N = 160; 81 girls; 3-5 year old) we replicated this effect and examined its duration and developmental trajectory. We found that modulation of 5-year-olds' ANS precision…