The fields of quantitative and covariational reasoning boast a wide range of powerful theoretical tools, which are described carefully in the literature. Less frequent and explicit attention, however, has been paid to writing down detailed, practical guidance for operationalizing these theoretical constructs. Some guidance is provided by…

Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

Understanding and analyzing data is a crucial aspect of quantitative literacy in the 21st century, leading scholars and policy makers to push for more rigorous instruction in this area rooted in statistical investigation. In this study, we examine 144 upper-elementary mathematics lessons on data and statistics topics to assess the extent to which…

Understanding and analyzing data is a crucial aspect of quantitative literacy in the 21st century, leading scholars and policy makers to push for more rigorous instruction in this area rooted in statistical investigation. In this study, we examine 144 upper-elementary mathematics lessons on data and statistics topics to assess the extent to which…

This article is a presentation of a three-day sequence of lessons that engaged fifth-grade students in an exploration following the activities of scientists. From asking questions and analyzing data, to engaging in scientific modeling, to defending their theories to the scientific (classroom) community, these fifth graders were mirroring how…

The lesson set in this article describes an introductory learning experience using wildlife camera-based citizen science projects hosted on Zooniverse (http://www.zooniverse.org). Wildlife camera projects were chosen due to the charisma of the study organisms, student engagement while looking at images, ease of access to projects, ease of teaching…

The purpose of this case study was to examine prospective mathematics teachers' lessons in the context of choice and use of representations while teaching limit. The participants were four senior prospective mathematics teachers. The data were obtained from the participants' lessons plans, the video recordings of their lessons, and the…

Reasoning about graphical representations representing dynamic data (e.g., distance changing over time), including interpreting, creating, changing, combining, and comparing graphs, can be considered a domain-specific operationalization of the general twenty-first century skills of creative, critical thinking and solving problems. This paper…

Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

Using an interactive map-based PDF, students learn key concepts related to biodiversity while developing data-analysis and critical-thinking skills. The Bird Island lesson provides students with experience in translating geospatial data into bar graphs, then interpreting these graphs to compare biodiversity across ecoregions on a fictional island.…

This paper compares lessons on linear equations from the same curriculum materials taught by two teachers of different levels of mathematical knowledge for teaching (MKT). The analysis indicates that the mathematical quality of instruction in these two classrooms appears to be a function of differences in MKT. Although the two teachers were…

In the Walking Out Graphs Lesson described here, students experience several types of representations used to describe motion, including words, sentences, equations, graphs, data tables, and actions. The most important theme of this lesson is that students have to understand the consistency among these representations and form the habit of…

My NASA Data (Chambers et al. 2008) is a teaching tool available on NASA's website that offers microsets of real data in an easily accessible, user-friendly format. In this article, the authors describe a lesson plan based on an activity from My NASA Data, in which students explore parts of the United States where they would want to live if they…

In this article, the author suggests a framework for developing lesson ideas involving variation. This idea was demonstrated by Rebecca Davey at a conference bringing together teachers from the seven schools participating in the TI-"n"spire pilot research project overseen by Alison Clark-Wilson of the University of Chichester. It uses information…

From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater…