This article focuses on the criticisms of current approaches in educational research methodology. It summarizes rationales for mixed methods and argues that the mixing quantitative paradigm and qualitative paradigm is problematic due to practical and philosophical arguments. It is also indicated that the current rise of mixed methods work has…

This paper uses a series of models to illustrate one of the fundamental processes of model building--that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework. The process encourages students to think about the…

We investigated students' understanding of proportional, inverse proportional, and affine functions and the way this understanding is affected by various external representations. In a first study, we focus on students' ability to model textual descriptions of situations with different kinds of representations of proportional, inverse…

Despite a number of theories in circuit analysis, little is known about the behaviour of ideal equal voltage sources in parallel, connected across a resistive load. We neither have any theory that can predict the voltage source that provides the load current, nor is there any method to test it experimentally. In a series of experiments performed…

Young children spend a much greater amount of time on practicing multiplication facts compared to understanding the concept of multiplication. When students have long-term, foundational concepts rather than a series of fragmented algorithms or facts, they are more likely to understand and generalize the mathematics. Using generalized models that…

This book seeks to illustrate the research on mathematics competencies and disposition in China according to the conceptual development and empirical investigation perspective. Mathematics education in China has a distinguishing feature a focus of attention to mathematical competency. Paradoxically, there has not been an explicit, refined, and…

There has been an ongoing debate of which physical labs or virtual labs are better. To resolve this issue, a remote lab provides an online lab that can do real experiments to obtain real data from a distant physical lab. Instead of relying on a remote lab, this article suggests that students collect experimental data locally with low-cost data…

This study investigates the participation and knowledge growth of children with mathematical difficulties as they work in groups with their classmates on a year-long sequence of modelling tasks. It involves observations of a class of 23 fifth graders, 9 of whom were identified as having difficulties in mathematics. All the students worked for 8…

Recent data from a cross-national assessment, the Programme for International Student Assessment (PISA), place the United States performance in mathematics at 38 out of 71 countries (OECD, 2016)--one clear indication of the ongoing need for the improvement of mathematics education. This improvement relies, in part, on improving undergraduate…

According to the survey of experts, the association of non-cognitive skills in groups according to their classification as object of evaluation leads to the fact that one group includes very different skills - both in volume and in the way of they identify and assess. So, the purpose of the research is the development of mathematical model of…

Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes's reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical…

The purpose of this study is to describe students' ability in solving mathematical representation problems evaluated from mathematical disposition. The subjects are three students of 10th grade of public senior high school (PSHS) in Padalarang, West Java, Indonesia. They were selected from 35 students with high, medium, and low mathematical…

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

The Mathematics Practicum has been offered at St. Olaf College for over 30 years. The Practicum is a 4-week, January Interim course where three teams of five students work on consulting problems solicited from area businesses, government agencies, and non-profit organizations. These problems have significant mathematical, statistical, and…

"Flatland: A Romance of Many Dimensions" is an 1884 novella written by English schoolmaster Edwin Abbott. He describes what it would be like to live in a two-dimensional (2D) world--Flatland. It is fascinating reading that underscores the challenge of teaching three-dimensional (3D) mathematics using 2D tools. Real-world applications of…