In this study, we aim to investigate activities using models in a design project in three technology classrooms. Activities that use models are important for students' development of knowledge and skills connected to the design process. Nevertheless, few empirical studies have thus far examined how models and modelling are used in a classroom…

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…

Based on the instructional interaction principles outlined by Chen and Wang (2016) in third-generation distance learning, this study employs a recursive logical perspective on the evolution of the theory of interaction in distance education. It constructs a structural equation model to measure the mediating utility path of the learner's proactive…

Background: In professional contexts, engineers use engineering judgment to create mathematical models. Despite the importance of judgment in professional practice, the development and enactment of engineering judgment by engineering students are understudied. To better prepare students for engineering careers, there is a need to recognize and…

Problem-solving skills are advantageous when resolving complicated and multidimensional challenges. Problem-solving skills can be developed through active learning models that engage students in the learning process. One active learning model is RICOSRE. The main focus of RICOSRE is problem-solving activities in (1) reading; (2) identifying the…

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…

Complementary to existing "normative" models, in this paper we suggest a descriptive phase model of problem solving. Real, not ideal, problem-solving processes contain errors, detours, and cycles, and they do not follow a predetermined sequence, as is presumed in normative models. To represent and emphasize the non-linearity of empirical…

Mastery of mathematical literacy is essential for developing life skills in the 21st century. Mathematical literacy is even more critical in elementary schools as it forms the basis for mastery at the junior and senior high school levels. Elementary school students differ in their characteristics from students at the higher education level. They,…

Current approaches used by educational institutions to address the problem of student cheating are not working. This is because the discourse of academic integrity that currently dominates is, on its own, inadequate for addressing the problem. We propose that in order for higher education institutions to challenge cheating effectively, they need…

Self-explanation prompts in example-based learning are usually directed backwards: Learners are required to self-explain problem-solving steps just presented ("retrospective" prompts). However, it might also help to self-explain upcoming steps ("anticipatory" prompts). The effects of the prompt type may differ for learners with…

To make sense of our interconnected and algorithm driven world, students increasingly need proficiency with computational thinking (CT), systems thinking (ST), and computational modeling. One aspect of computational modeling that can support students with CT, ST, and modeling is testing and debugging. Testing and debugging enables students to…

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…

Econometrics has become increasingly important in Economics and Business degrees, since it appears to be narrowly related to several main skills and competencies as information management, creativity, problem-solving or decision-making. Furthermore, the development of information technologies, including econometric software, makes it possible to…

Preparing the new generation to be data-literate citizens is a pressing challenge, and some explorations have been made to cultivate K-12 students' data science skills and attitudes. However, there is a lack of instructional models to guide the design of data science programs in K-12 due to its complex and interdisciplinary nature as well as the…

A hallmark of effective teaching is that it grants learners not just a collection of facts about the world, but also a toolkit of abstractions that can be applied to solve new problems. How do humans teach abstractions from examples? Here, we applied Bayesian models of pedagogy to a necklace-building task where teachers create necklaces to teach a…