In this article we illustrate how one teacher used PhET cannonball simulation as an instructional tool to improve students' algebraic reasoning in a fifth grade classroom. Three instructional phases effective to implementation of simulation included: Free play, Structured inquiry and, Synthesizing ideas.
Manouchehri Azita, Ozturk Ayse, and Sanjari Azin
Katherine Baker, Naomi A. Jessup, Victoria R. Jacobs, Susan B. Empson, and Joan Case
Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.
Amber G. Candela, Melissa D. Boston, and Juli K. Dixon
We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.
Erell Germia and Nicole Panorkou
We present a Scratch task we designed and implemented for teaching and learning coordinates in a dynamic and engaging way. We use the 5Es framework to describe the students' interactions with the task and offer suggestions of how other teachers may adopt it to successfully implement Scratch tasks.
Hamilton L. Hardison and Hwa Young Lee
In this article, we discuss funky protractor tasks, which we designed to provide opportunities for students to reason about protractors and angle measure. We address how we have implemented these tasks, as well as how students have engaged with them.
The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.
John K. Lannin, Delinda van Garderen, and Jessica Kamuru
This manuscript discusses two important ideas for developing student foundational understanding of the number line: (a) student views of the number sequence, and (b) recognizing units on the number line. Various student strategies and activities are included.
Debasmita Basu, Nicole Panorkou, Michelle Zhu, Pankaj Lal, and Bharath K. Samanthula
We provide an example from our integrated math and science curriculum where students explore the mathematical relationships underlying various science phenomena. We present the tasks we designed for exploring the covariation relationships that underlie the concept of gravity and discuss the generalizations students made as they interacted with those tasks.
Jonathan N. Thomas and David M. Dueber
Through the use of rich examples, we examine the non-verbal ways in which teachers and students may communicate with one another. We will explore how gesture may be used to clarify and enrich interactions in the mathematics classroom.
Anna F. DeJarnette and Gloriana González
Given the prominence of group work in mathematics education policy and curricular materials, it is important to understand how students make sense of mathematics during group work. We applied techniques from Systemic Functional Linguistics to examine how students positioned themselves during group work on a novel task in Algebra II classes. We examined the patterns of positioning that students demonstrated during group work and how students' positioning moves related to the ways they established the resources, operations, and product of a task. Students who frequently repositioned themselves created opportunities for mathematical reasoning by attending to the resources and operations necessary for completing the task. The findings of this study suggest how students' positioning and mathematical reasoning are intertwined and jointly support collaborative learning through work on novel tasks.