This Perspectives on Practice manuscript focuses on an innovation associated with "Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task" [EJ1264816] from Volume 7, Issue 2 of "MTE." We built on Aguirre et al.'s (2019) integration of mathematical modeling and social…

Proof facilitates conceptual and meaningful learning in mathematics education rather than rote memorization. In this study, incorrect theorems and proofs are used to assess secondary school pre-service mathematics teachers' proof assessing skills. Using the case study method, the study is conducted on preservice mathematics teachers studying at…

In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to…

In this report, we present cases where students constructed new quantities through operating on quantities that does not fit the definitions of existing theories on quantitative operations. As a result, we identified five quantitative operators--operators that can be used on single qualities in order to transform the quantity to a new…

From the socio-critical perspective of mathematical modeling, reflexive discussions about the nature, criteria, and consequences of mathematical models are not a natural consequence of modeling in school. This report is part of a larger study focused on stimulating reflexive discussions in practice employing constructivist grounded theory as a…

This paper presents a didactic proposal designed through the active methodology of collaborative learning to analyse the effect of the use of numerical simulation of a mathematical model on the learning of differential equations in engineering students. A mathematical model of a vibrating string was used, and the Octave Online platform was used…

Mathematical modeling describes how events, concepts, and systems of interest behave in the world using mathematical concepts. This research approach can be applied to theory construction and testing by using empirical data to evaluate whether the specific theory can explain the empirical data or whether the theory fits the data available.…

The objective of this work is to show an educational path for combinatorics and graph theory that has the aim, on one hand, of helping students understand some discrete mathematics properties, and on the other, of developing modelling skills through a robust understanding. In particular, for the path proposed to middle-school students, we used a…

Although reasoning is a central concept in mathematics education research, the discipline is still in need of a coherent theoretical framework of mathematical reasoning. With respect to epistemological problems in the dominant discourses on proof, mathematical modelling, and post-truth politics in the discipline, and in accordance with trends in…

Post-instrument covariates are often included as controls in instrumental variable (IV) analyses to address a violation of the exclusion restriction. However, we show that such analyses are subject to biases unless strong assumptions hold. Using linear constant-effects models, we present asymptotic bias formulas for three estimators (with and…

Physics and mathematics represent closely intertwined fields, wherein physicists employ mathematical modeling to address intricate problems. A challenge encountered by physicists involves bridging conceptual understanding with mathematical equations, a task that educators can facilitate by supporting students in navigating these two realms of…

Social justice mathematical modeling is powerful in helping teachers build awareness of social issues, critique existing systems, and engage in rich mathematical reasoning. In this article, we document a task in which 28 preservice teachers (PSTs) explored if teacher pay is fair and how to define "fair" mathematically. Through…

Literature screening is the process of identifying all relevant records from a pool of candidate paper records in systematic review, meta-analysis, and other research synthesis tasks. This process is time consuming, expensive, and prone to human error. Screening prioritization methods attempt to help reviewers identify most relevant records while…

Among the problems identified at Technical and Vocational Education and Training (TVET) colleges, low achievement in mathematical subjects is the most prominent one. This paper documents a qualitative case study undertaken at TVET College in Gauteng with the purpose of exploring the National Certificate Vocational (NC(V)) Level 4 students' errors…

Modeling with mathematics (MP4) is a mathematical practice standard that can be used to engage students in mathematical content standards as well as additional mathematical practice standards. Research has shown the benefits of mathematical modeling (e.g., Aguirre et al., 2019; Cirillo et al., 2016a), but also the challenges teachers can face…