Mathematical modelling is an interlinking process between mathematics and real-world problems that can be applied as a means to increase motivation, develop cognitive competencies, and enhance the ability to transfer mathematical knowledge to other areas of science, such as engineering disciplines. This study was designed to investigate the effect…

This paper is written as a guide for any instructor seeking to develop the mathematical modeling process or open-ended problem solving in their courses. We describe a pedagogical approach to create mini modeling problems to develop the modeling process. These are problems that fall between traditional homework problems and open-ended modeling…

This research was performed as a single group pretest-posttest experimental design to determine the effect of mathematical modeling instruction on pre-service primary school teachers' (PPSTs) problem-solving skills and attitudes towards mathematics. Based on an online intervention due to the pandemic, the study involved 12 PPSTs who participated…

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…

The purpose of this systematic review is to reveal the research findings that suggest instructional practices to foster the creativity of students in mathematics. Although several studies have investigated the effects of various instructional practices influencing the mathematical creativity of students, little is known about how the findings of…

We conducted a comprehensive synthesis of computer-assisted instruction (CAI) research that aimed to facilitate the learning of mathematical word problem solving involving elementary and secondary school students with learning disabilities or difficulties in mathematics. We examined a total of 13 studies under the four instructional categories:…

Two major challenges in mathematics teacher education are developing teacher understanding of: (1) culturally responsive, social justice--oriented mathematics pedagogies; and (2) mathematical modeling as a content and practice standard of mathematics. Although these challenges may seem disparate, the innovation described in this article is…

Many engineering subjects rely on the interpretation of symbolic, numeric and graphic representations. Engineering students have challenges pertaining to their mathematical understanding of their actions with a computer algebra system (CAS). We investigated how a mathematical modelling task could mediate varied levels of mathematical…

A theoretical model of metacognition in complex modeling activities has been developed based on existing frameworks, by synthesizing the reconceptualization of metacognition at multiple levels by looking at the three sources that trigger metacognition. Using the theoretical model as a framework, this multiple-case study explores students'…

The purpose of the study was to investigate the effects of the instruction with mathematical modeling on pre-service mathematics teachers' mathematical modeling performance. The participants were 24 pre-service elementary mathematics teachers. A mixed method approach was used to conduct the research. Each week, the participants were given two…

US high school (HS) students are lagging behind their foreign peers in math performance. It is thus necessary to design teaching modules that motivate US HS students to learn more math and to improve their math skills. Our study set out to test two different software programs designed for the development of such skills. MATLAB Simulink provides a…

The implementation of teacher-independent realistic modelling processes is an ambitious educational activity with many unsolved problems so far. Amongst others, there hardly exists any empirical knowledge about efficient ways of possible teacher support with students' activities, which should be mainly independent from the teacher. The research…

The aim of this study is to investigate whether the model method is effective to assist primary students to solve word problems. The model method not only provides students with an opportunity to interpret the problem by drawing the rectangular bar but also helps students to visually represent problem situations and relevant relationships on the…

At the end of primary school all children more of less know what a percentage is, but yet they often struggle with percentage problems. This article describes a study in which students of 13 and 14 years old were given a written test with percentage problems and a week later were interviewed about the way they solved some of these problems. In a…

In an introductory chemical engineering course, the conceptual framework of a holistic problem-solving methodology in conjunction with a problem-based learning approach has been shown to create a learning environment that nurtures deep learning rather than surface learning. Based on exam scores, student grades are either the same or better than…