We examine the meanings students give to points when they are graphing relationships between quantities in dynamic, experiential contexts. Using data from teaching experiments with middle-grades students, we illustrate two main categories of meanings: iconic and quantitative. We then introduce four distinct subcategories of meanings: (a) iconic…

This study aims to determine the graphical literacy levels of middle school mathematics teachers. The participants of the study consisted of 33 middle school mathematics teachers working in different provinces. The data of the study were collected with the help of the graphical literacy test created by the researchers. The data were analyzed by…

In the context of an afterschool program in which students explore relatively large authentic datasets, we investigated how 11- to 14-year old students worked with categorical variables. During the program, students learned to use the Common Online Data Analysis Platform (CODAP), a statistical analysis platform specifically designed for middle and…

The construct of static and emergent shape thinking (Moore & Thompson, 2015) characterizes differences in students' reasoning about graphs. In our previous work with middle school students, we found that this construct may also be useful in characterizing students' reasoning about other representations such as simulations and tables. In this…

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…

Emergent graphical shape thinking (EGST) involves interpreting or constructing a graph as dynamically generated, which is useful across science, technology, engineering, and mathematics fields. Although evidence suggests that students as young as middle school can engage in EGST with support, other research indicates most college students and U.S.…

A group of eighth-graders was presented with a two-day lab exploring graph theory as an enrichment experience. With the school's winter break looming, students were weary of solving linear equations, and this topic was intended to inject some new life into the classroom. In addition to learning about a completely new topic, they would be exposed…

Although there is much research exploring students' covariational reasoning, there is less research exploring the ways students can leverage such reasoning to coordinate more than two quantities. In this paper, we describe a system of covariational relationships as a comprehensive image of how two varying quantities, having the same attribute…

This case study examines how material resistance (limitations posed by the physical world) and graph interpretation intersected during a high school biology investigation using digital sensors. We use an extended episode from a small group to illustrate how, in an inquiry-based unit, measuring near the resolution limit of a sensor caused scaling…

This article describes an activity and resource from The New York Times that can be used to help learners cultivate critical statistical literacy. Critical statistical literacy involves understanding, interpreting, and questioning statistical information to make informed decisions (Casey et al., 2023; Franklin et al., 2015; Weiland, 2017). It is a…

This study examines in-service mathematics teachers' problems on linear relationships that they posed in a semi-structured problem posing situation with a group and their ideas about the factors affecting the quality of the posed problems. Eight groups of 24 teachers participated in the study. Teachers' problems, written group work, and class…

Despite the increasing interest in data science education in the world, its teaching is not included in the curricula (junior secondary) and there is little information about it. Google Trends is discussed as a tool and database in school data science. Also, in different subjects, students were able to create and interpret graphs using this tool.…

The ability to interpret and compare data distributions is an important educational goal. Inherent in the statistical concept of distribution is the need to focus not only on individual data points or small groups of data points (so-called local view), but to perceive a distribution as a whole, allowing to recognize global features such as center,…

This design case details the ten-year (2014-present) iterative process to design and develop a graph-based computer-assisted program to support middle school students' development of collaborative argumentation. We begin by describing the first two iterations of the design and discuss how we learned from the process failures. This paper focuses on…

Six 7th-grade students engaged with an instructional sequence involving the use of the "TinkerPlots" software to organize data sets in ways intended to help them construe two attributes: the location of quarters of the data within a sub-range of the entire set, and the spread of those portions. We present evidence of students' thinking…