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.

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May 2020 For the Love of Mathematics Jokes

### 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.

Over the past 100 years, technology has evolved in unprecedented fashion. Calculators, computers, and smart phones have become ubiquitous, yet school mathematics experiences for many children still remain without many powerful technological tools for the exploration of mathematics. We consider the evolution of some tools as we imagine a future.

### Anne Quinn

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.

### Lindsay Reiten and Susanne Strachota

A free tool encourages students to engage in the authentic practices of statistics and data analysis.

## Quick Reads: Using Technology to Build a Pen for Browser

### a good idea in a small package

### Leigh Haltiwanger, Robert M. Horton and Brooke Lance

Making mathematics meaningful is a challenge that all math teachers endeavor to meet. As math teachers, we spend countless hours crafting problems that will energize students and help them connect mathematical topics to their everyday lives. Being successful in our efforts requires that we allow students to explore ideas before we provide explanations and demands that we ask questions to promote a depth of thinking and reasoning that would not occur without such probing (Marshall and Horton 2009).

### Alfinio Flores

The striking results of this coin-tossing simulation help students understand the law of large numbers.

### Ayanna D. Perry, Emily P. Thrasher and Hollylynne S. Lee

The use of iPads® in the classroom is growing. In the 2013–14 school year, 57 percent of schools planned to invest in iPads (Netop 2013). This investment can benefit mathematics classrooms only if teachers know which apps they can use to help students develop deeper mathematical understanding. Although learning about and developing facility with various apps is valuable for mathematics teachers, the process can be difficult, overwhelming, and time-consuming. To get started, we recommend one app, Dropbox, that can be used to share materials within the classroom setting, and then we suggest three free, easy-to-use mathematics apps: Sketchpad Explorer, Data Analysis, and MathGraph (see the **table** on p. 711).

### Hollylynne S. Lee, Tina T. Starling and Marggie D. Gonzalez

Research shows that students often struggle with understanding empirical sampling distributions. Using hands-on and technology models and simulations of problems generated by real data help students begin to make connections between repeated sampling, sample size, distribution, variation, and center. A task to assist teachers in implementing research-based strategies is included.