We present an instructional approach to teaching causal inference using Bayesian networks and "do"-Calculus, which requires less prerequisite knowledge of statistics than existing approaches and can be consistently implemented in beginner to advanced levels courses. Moreover, this approach aims to address the central question in causal…

A Trigonometric function is one of the challenging materials for not only high school students but also pre-service teachers and teachers. On the other hand, An understanding of trigonometric function is an initial stage in understanding calculus derived from it such as limit, derivative, and integral. Thus, the competency in trigonometric…

This article is a presentation of a three-day sequence of lessons that engaged fifth-grade students in an exploration following the activities of scientists. From asking questions and analyzing data, to engaging in scientific modeling, to defending their theories to the scientific (classroom) community, these fifth graders were mirroring how…

Although modeling is an integral process in applied mathematics, students rarely encounter modeling opportunities in their calculus courses. We introduce a laboratory experience as a starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients…

Using multiple representations (MR) such as graphs, symbols, diagrams, and text, is central to teaching and learning in physics classrooms. While different studies have provided evidence of the positive impact of the use of MR on physics learning, a comprehensive overview of existing literature on the use of MR in physics education, especially at…

The aim of this study is to examine the graphic reading and interpretation skills of teacher candidates with problem situations prepared in the context of the COVID-19 pandemic, which is a socio-scientific situation. The study is conducted with case study of qualitative research methods. The participants of the study consisted of 52 elementary…

This article analyzes an episode of classroom mathematics activity mediated by graphing technology from 3 different theoretical perspectives. An important line of research in the learning sciences focuses on graphs as "inscriptions", foregrounding learners' interactions with and around the material properties of graphical displays.…

Systems of equations are an important topic in school mathematics. However, there is limited research examining productive ways of supporting students' understandings of systems of equations. In this paper, we first present a conceptual analysis of potential ways students may leverage their quantitative and covariational reasoning to graph systems…

Traditional school laboratory exercises on a system of moving objects connected by strings involve deriving expressions for the system acceleration, a = (?F)/m, and sketching a graph of acceleration vs. force. While being in the form of rational functions, these expressions present great opportunities for broadening the scope of the analysis by…

The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…

In this article, the authors introduce the Into Math Graph tool, which helps teachers learn about their students' mathematics-related experiences and mathematical engagement by inviting students to define and graph their engagement over time. This tool documents and allows teachers to understand how and why students' engagement increases,…

While education increasingly relies on social media technologies to provide richer learning experiences, the rigid and course-centric design of curricula still imposes a challenge for students to construct meaningful connections between social media and formal learning. Building on the knowledge graphs' potential to establish semantic links among…

One challenge associated with introducing systems thinking in chemistry classrooms is the increase in content complexity that students face when they engage in this type of approach. Placing core chemical ideas within larger systems has promise, as long as students are not overwhelmed by the added complexity. Although there are many potential…

To learn with data, students need "data" to explore. This can be deceptive--data-rich experiences typically involve much more than a straightforward science lab. Solving real problems with data means identifying authentic questions that are meaningful to students and provide a foundation for deep inquiry. Such situations often lend…

Results in Mathematics Education, from different theoretical perspectives, highlight students' difficulties with graphs, both in interpreting given ones and in producing their own graphs. In this paper, we take an affective lens to understand both a student's relationship with mathematical graphs and a teacher's role when a task with a graph is…