Many mathematics instructors attempt to insert guided exploration into their courses. However, exploration tasks frequently come across to students as contrived, pertinent only to the most recently covered section of the textbook. In addition, students usually assume that the teacher already knows the answers to these explorations.

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### Nicole R. Juersivich

By using technology, students can conduct an experiment that quickly simulates a large number of random events. Much research has been done on students' conceptions and reasoning about probability (Jones et al. 2007). Recommendations for teaching probability have included just such use of concrete and digital manipulatives to simulate events as well as students' reflection on their initial predictions and analysis of their experiments and their results (NCTM 2000; Van de Walle et al. 2010). In fact, by using Excel® and Visual Basic to simulate coin flipping, students have been able to capitalize on these technological benefits to investigate, conceptualize, and refine their understanding of the law of large numbers.

### Katie L. Anderson

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.

### Adam Poetzel, Joseph Muskin, Anne Munroe, and Craig Russell

Using simple materials, a Mathematica software application, and their knowledge of function transformations, students design and create real mathematical sculptures.

### Darlinda Cassel and Dan Vincent

One of the more challenging aspects of trying to integrate technology into the classroom is finding phenomenon-based activities that can be enriched by technology applications. This article describes a mathscience-technology activity combining students' collection of data with mathematical and scientific analysis that is enhanced by using the iPod Touch (iTouch). The activity focuses on measuring shadow lengths throughout the school year and then organizing and evaluating the data by using the Planets app on the iTouch. Although this particular lesson was created for fifth graders, it could be adapted for students in other grades as well.

### Robinson Marlene

As we launch the 2012–2013 academic year, we find ourselves positioned for the natural renewal of focus and energy that often accompany presidential election years. We recognize that in addition to the weak economy, state and national reductions to education resources can create their own challenges to the mathematics education community as we adopt common curriculum standards. More than forty U.S. states are collectively endeavoring to meet the challenge of understanding and implementing the Common Core State Standards for Mathematics (CCSSM) with fidelity to both the Content and the Mathematical Practices (CCSSI 2010). Other states and regions we serve are also renewing their commitment to quality mathematics instruction and assessment that meets high standards.

### Jennifer Suh and Padmanabhan Seshaiyer

Foundational in understanding place value and our decimal number system, this concept is explored through a practiced-based activity designed to develop teachers' technology knowledge for teaching mathematics. The activity focuses on number sense using online applets and various related models and representations.

### Maurice J. Burke

A tool that combines the power of computer algebra and traditional spreadsheets can greatly enhance the study of recursive processes.

### Dae S. Hong

This article shows how to explore the golden ratio using GSP. Golden rectangles, spirals, triangles, and pentagons are also discussed.