This study explored how students develop meaning of functions by building on their understanding of expressions and equations. A teaching experiment using design research was conducted in a sixth-grade classroom. The data was analyzed using a grounded theory approach to provide explanations about why events occurred within this teaching episode…

This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications…

This paper gives a grounded cognition account of model-based learning of complex scientific knowledge related to socio-scientific issues, such as climate change. It draws on the results from a study of high school students learning about the carbon cycle through computational agent-based models and investigates two questions: First, how do…

This study aims to determine the effect of the application of the Search, Solve, Create, and Share (SSCS) learning model to the mathematical reflective thinking skills and the students' mathematical problem-solving abilities. This research is a type of Quasi-Experimental Design research with a 2x2 factorial research design. Data collection…

The study aimed to analyze the interaction effect teaching models and cognitive style field dependent (FD)-field independent (FI) to students' mathematical problem-solving ability (MPSA), as well as students' MPSA differences based on teaching models and cognitive styles. Participants in this study were 145 junior high school students, with…

The purpose of this article is to demonstrate how exponential functions and patterns can be taught by well-structured lessons composed of classroom activities, mathematical questions, discussions, and solving problems. Sawyer (1943) used a rope-and-post system to introduce the concept of logarithms and to calculate a product by adding the…

This article discusses how technology, in conjunction with carefully designed tasks and orchestrated discussions, has the potential to both reveal students' mathematical practices and to provide opportunities to shape those practices. Four specific mathematical practices that tend to be associated with problem-solving situations are examined: (1)…

This paper builds on two concepts, the first of which is the extended information processing model of expert design cognition. This proposes twelve internal psychological characteristics interacting with the external world of expert designers during the early phases of the design process. Here, I explore one of the characteristics, hierarchical…

This article elaborates a new direction for studying the construction of novel strategies that enables researchers to model the conceptual underpinnings of students' observable strategic actions during episodes of mathematical problem solving. The nature of the relationship between conceptual and procedural knowledge has been persistently debated…

Should the topic of judgment have a place in the preparation and development of school leaders? This question serves as the focus for an examination of the nature of judgment and obstacles to good judgment. Judgment is defined as the ability to arrive at and make a choice when faced with incomplete information, uncertain conditions, and/or…

The need for methods, techniques and approaches that we can develop high-level thinking skills in important activities increases day by day in order to achieve effective use of technology and change in information and communication technologies. In particular, the diversity, complexity of technical skills and to gain technical skills required to…

Socio-cultural theories in mathematics education field recently emphasize the importance of the collective argumentation within small-group work. Since mathematical modelling tasks require a process in which students search for a solution for real life problems through small-group work, the arguments in this process become an issue of concern.…

One of the essential problems, in educational data mining, is to predict students' performance on future learning materials, such as problems, assignments, and quizzes. Pioneer algorithms for predicting student performance mostly rely on two sources of information: students' past performance, and learning materials' domain knowledge model. The…

Formulating a mathematical model is a dynamic process, and attending to changes in students' models as they engage in modeling tasks is critical for informing pedagogical interventions. In this report, we coordinate constructs from literature on mathematical modeling, quantitative and covariational reasoning, and semiotics to characterize changes…

This paper presents a model for mastery learning. The framework for this model overlays the cognitive and knowledge dimensions from Krathwohl's revision of Bloom's Taxonomy, the Revised Taxonomy, with Polanyi's theory of personal knowledge. A simplified framework integrates Polanyi's concepts of subsidiary and focal awareness with the Revised…