Critical thinking skills and dispositions are significantly important factors that aid in one's ability to understand and solve complex problems. Within the field of higher education, critical thinking skills and dispositions are valued and encouraged but are not always fully developed at the completion of the undergraduate degree experience.…

The inductive effect is one of the very important concepts of electronic effects in organic chemistry. In traditional teaching methods, only the origin, transmission mode, and decay of the inductive effect are introduced briefly, which is not conducive to students' complete understanding of the inductive effect. This work developed a new method to…

"TechCheck" is an assessment of Computational Thinking (CT) for early elementary school children consisting of fifteen developmentally appropriate unplugged challenges that probe six CT domains. The first version of "TechCheck" showed good psychometric properties as well as ease of administration and scoring in a validation…

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.…

Instructors manage several tensions as they support students to engage in mathematical disciplinary practices such as defining, conjecturing, and proving. These tensions include honoring students' contributions while simultaneously apprenticing students to following mathematical norms. I present a case study of a teacher-researcher in a laboratory…

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…

Upon graduation from an undergraduate institution, engineering graduates are expected to have a baselevel skill in technical skills related to their discipline. Teaching technical skills comes naturally to engineering programs as the conceptual understanding of the material form the foundation of engineering ability. However, engineering graduates…

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…

When learning chemistry, students must learn to extract chemical information from mathematical expressions. However, chemistry students' exposure to mathematics often comes primarily from pure mathematics courses, which can lead to knowledge fragmentation and potentially hinder their ability to use mathematics in chemistry. This study examines how…

The development of higher-order thinking skills requires appropriate learning techniques. Project-based learning and integrated learning are learning models that can be used for this purpose. This study aimed to evaluate the contribution of project-based learning and integrated learning to the HOTS development of students in 6 private schools. The…

When we look at the theoretical relationships between the three types of geometry, we find that the most primitive type is topology and that both Euclidean and projective geometry are derived from this earlier type. Therefore, Piaget described the first stage or level of understanding geometry as topological understanding. In this study, the…

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…

The relevance of this article is due to the need to form and develop algorithmic thinking of higher education students as the main requirement of the information society following 21st century skills and competences for new millennium learners. The purpose of the article is to consider algorithmic thinking as a new dimension of learning in higher…

In order to promote geometric understanding, teachers frequently use hands-on activities. Such activities can be used to expound upon the declarative statements and theorems of geometry. Using a compass, straightedge, and protractor, students are able to actively build conceptions involving bisectors, midpoints, and perpendicular lines.…