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…

Developing models and using mathematics are two key practices in internationally recognized science education standards, such as the Next Generation Science Standards (NGSS). However, students often struggle with these two intersecting practices, particularly when developing mathematical models about scientific phenomena. Formative…

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…

In this dissertation study, I report on six middle school students' construction and interpretation of graphs and associated dynamic situations. Constructing and interpreting graphs represents a critical moment in middle school mathematics due to its opportunity to provide a powerful foundation for learning. Nevertheless, researchers have…

The Dijkstra's algorithm is an algorithm that determines the shortest paths needed to go from a starting node to any node in a graph. In this article, the process and results of an activity that included route formation among the provinces in the Aegean region using Dijkstra's algorithm are shared. The activity was designed based on a mathematical…

As a group of middle school mathematics teachers and teacher educators, the authors have focused their attention on using innovative practices coupled with high cognitive demand tasks to engage students, pique their interest in mathematics, and promote conceptual understanding. This article explores their three-act task design. In act 1, students…

Modeling and argumentation are two important scientific practices students need to develop throughout school years. In this paper, we investigated how middle and high school students (N = 512) construct a scientific argument based on evidence from computational models with which they simulated climate change. We designed scientific argumentation…

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

"Who has been to Dairy Queen® and purchased a Blizzard?®" Ms. Bosetti asked her students. During the summer, Bosetti had seen many of her former and future students at the local Dairy Queen enjoying Blizzard desserts and wondered, "Which Blizzard size is the best value?" She used this context for a ratios and proportions task…

This study examined how 12- and 13-year-old students' mathematics and science background knowledge affected line graph interpretations and how interpretations were affected by graph question levels. A purposive sample of 14 students engaged in think aloud interviews while completing an excerpted Test of Graphing in Science. Data were…

In this article, the author focuses on possible ways to develop the concepts of joint variation and function through the upper primary and lower secondary years of education. The examples demonstrate the building of a range of important mathematical ideas by modelling life-related situations using students' informal and intuitive knowledge. Over…

This article describes a lesson unit in which students constructed tables and graphs to represent the growth of different trees. Students then compared the graphs to develop an understanding of slope.