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…

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…

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.…

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…

In early 2008 researchers from the University of Melbourne's "New Technologies for Teaching Mathematics" project created a lesson for the Year 10 students at their Victorian research schools. Two important goals of secondary school mathematics education are to build students' conceptual knowledge and to teach students to think…

Work with PLATO, a computer-based teaching system which provides a means for individualizing instruction, is described. Children sit at terminals and respond to directives and questions on the screen by touching it or by typing a message. PLATO responds, and prescribes work in accordance with the child's previous performance. Curricular materials…

This package contains student and teacher handbooks and a report summarizing a project during which the handbooks were developed as part of a numeracy education course for adult basic and literacy education students. Discussed in the project report are the following: development of the course's 7 numeracy education units, field testing of the…