This study examined a cohort of middle school pre-service mathematics teachers' understanding of the rate of change as they engaged in a model development sequence. By adopting a design-based research perspective, a model development sequence on the concept of rate of change has been designed and implemented as part of a mathematical modeling…

The aim of this study is to understand how students' mathematical thinking is activated and nurtured in solving a modeling problem, where the problem situation involves the design of a system. From a STEM integrated perspective, 9th grade students worked on a modeling task aiming to create an identification system based on hand biometrics. The…

This article proposes an interconnected framework, "Ways of thinking in STEM-based Problem Solving," which addresses cognitive processes that facilitate learning, problem solving, and interdisciplinary concept development. The framework comprises critical thinking, incorporating critical mathematical modelling and philosophical inquiry,…

As a first step toward automatic feedback based on students' strategies for solving histogram tasks we investigated how strategy recognition can be automated based on students' gazes. A previous study showed how students' task-specific strategies can be inferred from their gazes. The research question addressed in the present article is how data…

Programming is becoming increasingly common in mathematics degrees as it is a desirable skill for new graduates. However, research shows that its use is mostly restricted to computational or modelling tasks. This paper reports a study on students' perceptions of and difficulties with Lean, an interactive theorem prover introduced as part of a…

The manuscript describes a community-based mathematical modeling task that was implemented in a Calculus I classroom to engage students in mathematical modeling. Twenty-five undergraduate students engaged in this activity. These students selected a context that they found interesting, posed questions, developed constraints, came up with solution…

Connections among the mathematics, science, and engineering disciplines have been recognized and affirmed in national standards. For example, the application of mathematical ideas and skills within science has been highlighted in national science standards for over 20 years. More recently, the Next Generation Science Standards (NGSS; NGSS Lead…

The Coronavirus outbreak allows for a number of possible applications to classroom teaching (biology, computer science, Earth science, physics, statistics), as well as student research. A number of simple models reproduce fairly well the case numbers (total confirmed cases) of the Coronavirus pandemic in specific regions. These models may also be…

Worked examples support learning. However, if they introduce easy-to-confuse concepts or principles, specific ways of providing worked examples may influence their effectiveness. Multiple worked examples can be introduced blocked (i.e., several for the same principle) or interleaved (i.e., switching between principles), and can be sequentially or…

This article argues the importance of teaching students about the philosophical and mathematical underpinnings of Australia's superannuation system as an example of a real-world problem context. It also provides a rationale for teaching financial modelling and decision-making in ways that respect the diverse financial realities represented in…

The mathematics education community has routinely called for mathematics tasks to be connected to the real world. However, accomplishing this in ways that are relevant to students' lived experiences can be challenging. Meanwhile, mathematical modeling has gained traction as a way for students to learn mathematics through real-world connections. In…

Mathematics cannot be separated from everyday life. The use of mathematical concepts in cultural activities can be studied through the ethnomathematics program. However, ethnomathematics research may not be able to provide noticeable results, especially in constructing mathematical modelling for pedagogical purposes. Ethnomodelling later became…

In differential equations textbooks, the motion of a simple pendulum for small-amplitude oscillations is analyzed. This is due to the impossibility of expressing, in terms of simple elementary functions, the solutions of the nonlinear differential equation (NLDE) that models the pendulum, which is why the authors usually choose the linearized…

In the late 1800s and early 1900s, increases in metallurgic technology and better manufacturing methods made naval artillery a more powerful force. Guns could fire more powerful shells that could travel farther and hit a target with much greater accuracy. Torpedoes represented a major threat to even the most powerful of warships, forcing captains…

Transforming an observable phenomenon into a tractable model is a challenging process, from determining the appropriate modeling scale to making realistic simplifying assumptions. However, many modeling texts are anchored around problems that have already been synthesized into a digestible format, which inhibits an opportunity to engage students…