Knowing functions and functional thinking have recently moved from just knowledge for older students to incorporating younger students, and functional thinking has been identified as one of the core competencies for algebra. Although it is significant for mathematical understanding, there is no unified view of functional thinking and how different…

When learning about scientific phenomena, students are expected to "mechanistically" explain how underlying interactions produce the observable phenomenon and "conceptually" connect the observed phenomenon to canonical scientific knowledge. This paper investigates how the integration of the complementary processes of designing…

In this article we analyze how students reason about linear combinations across multiple digital environments. We present the work of three groups of undergraduate students in the Southeast United States (US) who were considered ready to take linear algebra. The students played the game "Vector Unknown," reflected upon aspects of their…

Recent research in mathematics education shows that by exploring the properties of figures and making conjectures, especially through dynamic geometry software, students can better develop their understanding of concepts. Furthermore, comparing different geometric worlds and, within them, different representations enhances Euclidean knowledge. In…

Conjecture formulation is crucial to mathematics education. Therefore, this study aimed to evaluate challenges prospective mathematics teachers (PMTs) encounter when using GeoGebra to formulate geometrical conjecture. A qualitative case study was conducted with an exploratory strategy to provide a complete comprehension of the occurrence. Six…

Nowadays, mathematics teachers in K-12 strive to promote their students' mathematical knowledge and computational thinking (CT) skills. There is an increasing need for effective CT-embedded mathematics learning material and a better understanding of students' views toward them. In this work, we present the results of a research study, which…

Using simulation approaches when conducting randomization tests for comparing two groups in the context of experimental studies has been promoted as a beneficial approach for supporting student learning of statistical inference. Many researchers have suggested that the data production process in simulations for the randomization test intuitively…

A better understanding of differences in the nature of human computer interaction (HCI) relating to GIS software can help with learning spatial concepts and spatial thinking skills. This motivates our study, which aims to create a standard measure of interaction with GIS software that can be used individually or along with existing measurement…

Limited literature addresses how elementary preservice teachers (PSTs) can advance their thinking about hierarchical geometric relationships. Informed by a commognitive perspective, we investigated this phenomenon as a matter of discursive change, focusing on word use, visual mediators, and narratives. We report on a teaching experiment involving…

Interpreting and creating computational systems models is an important goal of science education. One aspect of computational systems modeling that is supported by modeling, systems thinking, and computational thinking literature is "testing, evaluating, and debugging models." Through testing and debugging, students can identify aspects…

We present a case of one teacher's engagement in project-based learning for algebra I students. This teacher was a member of a cohort of mathematics teachers and career technical educators who participated in a two-week intensive summer institute investigating autonomous vehicles. During the academic year, the follow up support for these educators…

In this paper, we introduce a technology-enhanced pedagogical sequence for supporting lower secondary school students' sense-making of the concept of volume in a non-procedural and non-formula-driven way. Specifically, we illustrate a novel approach of using dynamic geometric environment (DGE) to introduce the meaning of volume and then deriving…

Preservice secondary mathematics teachers (PSMTs) need exposure to noticing students' mathematical thinking when students are engaged with technological tasks. In this paper, we share results from a study in which PSMTs first watched videos of students engaged with a technological mathematical task focused on the concept of function and after…

Despite significant research exploring students' quantitative reasoning, few studies have explored the semiotic processes that mediate its development. In this report, we present a case study to show how one student constructed a semiotic chain for a quantity as he worked with a mathematical task. Importantly, we connect frameworks for…

In the Winter semester of 2020 during a multimedia design and production class for pre-service teachers, the students were introduced to basic computer coding concepts such as variables, conditional statements, various expressions, logic, and syntax. For their final project, the students were asked to create an interactive instructional app using…