Heather L. Johnson

Interactive classrooms with Jupyter and Python

We describe how to set up and share the Jupyter notebooks as a way to introduce the Python computer language in the mathematics classroom. Additionally, we discuss how to use the Binder application together with GitHub® as a way to share the notebooks with students over the Internet. We conclude with some suggestions for how teachers might use these notebooks in class.

A tale of two sliders

The word slider may conjure up visions of interactive mathematics tools that enable exploration of parameters and graphs. Walker and Edwards discuss ideas for using Desmos, a freely available online calculator, to investigate a scenario about tasty sliders. By automating the construction of sliders, Desmos makes their use more accessible for students and teachers alike.

Creating Mathematical Lessons Using TED-Ed

TED-Ed is a free web-based video service tied to the well-known TED Talks. TED-Ed allows instructors to use videos on the website for students to view as homework assignments. It also has options for educators to build lessons around videos and include their own questions, resources, notes, and discussion board posts. Because the lessons have four sections—Watch, Think, Dig Deeper, and Discuss—students are given multiple opportunities to interact with the content and to reflect on their understanding. In the Discuss section, for example, students are able to respond to a question posted on a discussion board. TED-Ed gives educators the freedom to create personal lessons that can be used for homework, extension assignments, make-up quiz assignments, or project-based instruction.

Improving Approximations for Pi with GeoGebra

Department editors Heather Lynn Johnson, heather.johnson@ ucdenver.edu, University of Colorado Denver; Steve Phelps, sphelps@madeiracityschools .org, Madeira High School, Cincinnati, OH; and Robert Lochel, rlochel@verizon.net, HatboroHorsham High School, Horsham, PA Archimedes’s method of approximating is a powerful pedagogical tool connecting mathematics with historical contexts. Previous Mathematics Teacher articles have featured Archimedes’s method of approximation through technology (e.g., Wasserman and Arkan 2011). Most have mentioned that the approximation of approaches the precise value by making the number of sides of a polygon sufficiently large. However, they did not consider how many sides of the polygon are necessary to satisfy a certain precision of for real-life applications. Thus, although eight to ten digits may be necessary for practical calculations, when we attempted to duplicate Archimedes’s classic process with GeoGebra and 96-sided polygons, we were able to tions of . Inversely, the circumscribed polygons around the circle have a greater perimeter and therefore provide an upper bound of the approximations. Archimedes started with a hexagon, and by successively doubling the number of sides up to 96, he obtained a result

A Teacher’s Conception of Definition and Use of Examples When Doing and Teaching Mathematics

To contribute to an understanding of the nature of teachers’ mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher’s conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical knowledge, the authors give an account of the case of Lily, a prospective, then beginning, teacher who conceived of mathematical definition as an object with particular form and function and engaged in purposeful, specialized use of examples when doing and teaching mathematics. Lily’s case illustrates how a teacher’s interpretation of examples (as exemplifications or single instances) and conception of the form and function of definitions can influence her doing and teaching mathematics. An implication is that teacher preparation should foster teachers’ abilities to use examples purposefully to provide students with rich opportunities to engage in mathematical processes such as defining.