Classification is a complex process that involves scientific concepts and higher-order mental processes such as abstraction, generalization, and pattern recognition. Even though it is an important competence for understanding the world, dealing with data and information, and solving complex problems, the education system embeds just its simplest…

Emergent graphical shape thinking (EGST) entails conceiving a graph as being dynamically generated via the trace of a moving point constrained by two changing quantities. As such, Paoletti et al. (2023) argue that meanings for quantities within a situation and meanings for graphical representations must be connected, or bridged, to engage in EGST.…

Recently, abstracted quantitative structures (AQS), a construct from quantitative reasoning, has been offered as a means to conceptualize and study mathematization during mathematical modeling. Extending this theoretical work, we provide empirical evidence that an intervention targeting participants' AQS can assist in aligning modelers' models…

Building Thinking Classrooms (Liljedahl, 2021) provides teachers with a new method of designing and sequencing tasks called "thin slicing," which emerged from variation theory. The results of the present study indicate that an analysis of the dimensions and ranges of variation within such a task offers insights into learning…

The study discussed here aims to describe students' understandings of the definition of a mathematical function, which was achieved through a pilot case study of clinical interviews with four participants -- two ninth graders and two twelfth graders. The participants were recruited from the same urban public high school in the northeast of the…

In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

Learning to teach mathematics content courses designed for prospective elementary teachers (PTs) is challenging. Mathematics content instructors must be prepared to not only teach mathematics content, but engage PTs in understanding children's mathematical thinking strategies, learning trajectories, and misconceptions (Carpenter et al., 1996;…

The ability to interpret mathematical symbols and understand how they capture contextual relationships is a critical element of algebraic thinking. More often than not, students see algebra as merely a list of rules for manipulating abstract symbols, with limited to no meaning. Instead, for students to see algebra as a powerful tool and rich way…

Creative thinking in mathematics is an essential 21st Century skill that can be developed and encouraged through an exploration of mathematical concepts. In the context of the new "Australian Curriculum: Mathematics," this article explores the possibilities that are unlocked when students engage with tasks creatively in mathematics. By…

Many students lack the ability to maintain positive perceptions of their mathematical self-belief, resulting in undesirable social, emotional, and academic outcomes. The purpose of this study was to investigate the impact of a cognitive reframing strategy on third and fourth grade math intervention students' perceptions of their mathematical…

This study tested the mediating role of self-directed learning skills (SDL) between students' conceptions of mathematics and their achievement in mathematics using a structural equation model. Data were collected using the "Conceptions of Mathematics Questionnaire" and the "Self-Rating Scale of Self-Directed Learning", together…

Problem posing has an important place in mathematics education curriculum in many countries. There are a few studies in the literature that reveal students' problem posing processes. The purpose of this research is to examine the problem posing processes of middle school students in geometry. The Research was carried out with 160 students who are…

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…

Combinatorial proof is an important topic both for combinatorics education and proof education researchers, but relatively little has been studied about the teaching and learning of combinatorial proof. In this paper, we focus on one specific phenomenon that emerged during interviews with mathematicians and students who were experienced provers as…

In this meta-analysis of 40 studies with 55 independent samples and 7,988 participants, we examined the relation between mathematics vocabulary (MV) and mathematics performance, and we investigated the mechanism underlying this relation. Our findings suggest that MV was moderately related to mathematics performance. Higher-order mathematics tasks…