The purpose of this study was to examine relationships between students' semiotic representational transformations and students' mathematics performance outcomes in digital math games. The study employed a convergent parallel mixed methods design. Students in Grades 4, 5, and 6 (ages 9-12) played nine digital math games. Researchers administered…

Mathematics anxiety hinders students' mathematical achievement already in primary school, but research on its effects beyond whole number knowledge is limited. The main aim of the current study is to examine how state and trait mathematics anxiety relate to performance across five tasks that are relevant for the development of mathematics in…

In the last two decades, studying the possible relations between the history of mathematics and mathematics education has revealed the importance of certain foundational issues concerning the nature, relevance and validity of historical knowledge vis-à-vis problems of teaching and learning, which call for deeper exploration. Reviewing aspects of…

Rational number knowledge is critical in both current and future mathematical success. Despite its importance, there is a gap in understanding regarding how children process quantitative information from discretized non-symbolic fractions when salient surface features interfere with this process. This study examines five research questions aimed…

Mathematics plays a significant role in many study programs. However, several studies show deficiencies and a decline in beginning undergraduates' skills in mathematics in many content domains. However, it remains unclear whether they have improved in so-called process competencies like modeling, mathematical reasoning, or using different…

Purpose: This comparative study sought to identify best practices concerning symbolic mathematical communication between primary school teachers and students in Japanese, Laotian, and Thai classrooms. Method: The target groups were 18 teachers and 671 students in Grade 1 to Grade 6 mathematics classrooms in Japan, Lao PDR, and Thailand. A total of…

Symbolic and situational mathematics are the two major representations of mathematical knowledge. Although previous literature has studied the relationship between the two from the perspective of teaching practice, learning effectiveness and behavioural performance, there is still a lack of empirical psychological research on cognitive mechanisms…

A long-standing debate in the field of numerical cognition concerns the degree to which symbolic and non-symbolic processing are related over the course of development. Of particular interest is the possibility that this link depends on the range of quantities in question. Behavioral and neuroimaging research with adults suggests that symbolic and…

Research over the past 20 years has suggested that our intuitive sense of number--the Approximate Number System (ANS)--is associated with individual differences in symbolic math performance. The mechanism supporting this relationship, however, remains unknown. Here, we test whether the ANS contributes to how well adult observers judge the…

This study is focused on the relational thinking of first-grade students following their first 3 months of instruction from the Measure Up (MU) curriculum, an adaptation of the El'konin-Davydov curriculum. Following Davydov's outline of instructional material, the MU first-grade materials were designed to have students identify the quantitative…

Mathematical competence in middle childhood predicts socioeconomic status in adulthood. Therefore, it is important to understand the components that constitute mathematical competence from kindergarten to sixth grade. Using an analytical approach, in this article, I identify three components: understanding numbers, understanding mathematical…

Many people find that solving story problems is challenging. A key source of the difficulty is symbolizing problem situations. In two experiments, we tested whether diagrams promoted successful symbolization of two-operator story problems, and we tested whether diagrams that depicted the integration of operations were more beneficial than diagrams…

Children's spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a separate construct from spontaneous focusing on numerosity (SFON) and examined whether it is uniquely related to numerical abilities and mathematics…

Given the importance of the ability to use variables flexibly in Calculus and students' difficulties related to various uses of variables, this study examined how variables are treated in calculus class. Data for this study came from graduate teaching assistants' (TAs') classroom teaching, which plays a crucial role in undergraduate students'…

Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific…