Using a Journal Article as a Professional Development Experience

**Technology**

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**Title: **Technology Enhances Student Learning across the Curriculum

**Authors:** Jean McGehee & Linda K. Griffith

**Journal:** *Mathematics Teaching in the Middle School*

**Issue:** February 2004, Volume 9, Issue 6, pp. 344-349.

**Rationale/Suggestions for Use**

This article demonstrates several forms of technology that can enhance basic understandings and skills of middle school mathematics concepts.

Technologies such as Calculator Based Ranger (CBR), Spreadsheets, and Geometer's Sketchpad are all discussed.

**Procedures/ Questions**

- If you have access to and experience with the CBR, then proceed as follows:
- Start with Figure 1, on page 345 of the article and note that the teacher asked the students for their interpretation of the graph. Ask teachers to discuss what students might share and, in particular, students possible misconceptions with the graph.
- Ask for two volunteers to use the CBR to match the graph in Figure 1. Discuss as a group.
- Have teachers match at least one of the graphs in Figure 2, on page 346 of the article. Discuss how their movement matches the graph.
- Discuss how you might make a graph that is like the letter V. Have the teachers try it.
- Discuss how you might make a graph of a circle. Have teachers try it. What did the teachers conclude?

- If you have access to and experience with the Geometer's Sketchpad software, then proceed as follows:
- Ask participants if centroid is included in their middle school curriculum.
- Explore the meaning of centroid and how to find the centroid in several triangles by paper folding. Share what was noticed about the centroid of different triangles.
- Participants now use Sketchpad to find the centroid of a non-equilateral triangle. Explore measurement opportunities. See edited Figure 6 from page 348 of the article (at end). Discuss findings.
- Discuss how the use of this technology facilitates exploration of the properties of a centroid.
- Why is finding the centroid of a circle useful in mathematics?
- The orthocenter of a triangle is the intersection of the altitudes. Construct the orthocenter and determine what happens to the orthocenter if the triangle is acute, if obtuse, if right? Why is finding the orthocenter of a circle useful in mathematics?

- If you have access to and experience with TI-73 or spreadsheets, pose the following to participants:
- Assume you were a specialty shoe store catering to educators, how would you order different shoe types in these categories: shoes that lace up, shoes with fasteners (Velcro or buckles), and shoes that slip on? See page 349.
- Collect shoe data from participants in the group.
- Use technology to create a circle graph of the data. Analyze.
- Extension: At the NCTM Illuminations website, an online spinner can be found that will allow further exploration of the above scenario. http://illuminations.nctm.org/ActivityDetail.aspx?ID=79

- If you have access to and experience with a handheld calculator (minimum 8-digit display), then proceed as follows:
- Discuss strategies for helping students understand that . This is a common error. In the article a spreadsheet is used to explore patterns of dividing by 9 (Figure 5). This same problem can be explored using a calculator and recording results.
- Ask: "Can you predict if a fraction will terminate or repeat when represented as a decimal?"
- Have different groups explore the decimal representation of fractions with denominators from 2 to 25 using a calculator (or spreadsheet). Discuss the role of the prime factors of the denominator in determining if a fraction repeats or terminates, and if it repeat, what patterns are expected?
- Extension: Fill spreadsheet with fractions that have denominators from 2 to 48. What did you notice when denominator was a multiples of 2 or 5? What do you notice when the denominator was a multiple of 3? Multiple of 4?

**Next Steps**

**Connections to Other NCTM Publications**

- Beckmann, C. E., & Rozanski, K. (1999, October). Graphs in real time.
*Mathematics Teaching in the Middle School*, *5*, 92-99.
- Beigie, D. (2000, January). Zooming in on slope in curved graphs.
*Mathematics Teaching in the Middle School*, *5,* 330-334.
- Beigie, D. (2002, April). Investigating limits in number patterns.
*Mathematics Teaching in the Middle School*, *7*, 438-443.
- Beigie, D. (2005, February). Computer-generated fractal art.
*Mathematics Teaching in the Middle School,* *10*, 262-268.
- Crocker, D. A., & Long, B. B. (2002, March). Rice + technology = an exponential experience!
*Mathematics Teaching in the Middle School*, *7*, 404-407.
- Edwards, T. G. (2000, March). Pythagorean triples served for dessert.
*Mathematics Teaching in the Middle School*, *5*, 420-423.
- Eisen, A. P. (1999, October). Exploring factor sets with a graphing calculator.
*Mathematics Teaching in the Middle School*, *5*, 78-82.
- Erbas, A. K., Ledford, S., Polly, D., & Orrill, C. H. (2004, February). Engaging students through technology.
*Mathematics Teaching in the Middle School*, *9*, 300-305.
- Flores, A. (2002, March). A rhythmic approach to geometry.
*Mathematics Teaching in the Middle School*, *7*, 378-383.
- Glass, B. (2004, March). Transformations and technology: What path to follow?
*Mathematics Teaching in the Middle School*, *9*, 392-397.
- Johnson, I. D. (2000, October). Mission possible! Can you walk your talk?
*Mathematics Teaching in the Middle School*, *6,* 132-134.
- Little, C. (1999, February). Teacher to teacher: Geometry projects linking mathematics, literacy, art, and technology.
*Mathematics Teaching in the Middle School*, *4,* 332-335.
- Masalski, W. J., & Elliott, P. C. (Eds.). (2005).
*Technology-supported mathematics learning environments: 2005 Yearbook of the National Council of Teachers of Mathematics*. Reston, VA: National Council of Teachers of Mathematics.
- McCoy, L. P., & Shaw, J. M. (2003, September). Patchwork quilts: Connections with geometry, technology, and culture.
*Mathematics Teaching in the Middle School*, *9*, 46-50.
- Mittag, K. C., & Taylor, S. E. (2006, September). Hitting the bull’s eye: A dart game simulation using graphing calculator.
*Mathematics Teaching in the Middle School*, *12*, 116-120.
- Murphy, D. E., & Gulley, L. L. (2005, April). John Henry – the steel driving man.
*Mathematics Teaching in the Middle School*, *10*, 380-385.
- Nickerson, S. D., Nydam, C., & Bowers, J. S. (2000, October). Linking algebraic concepts and contexts: Every picture tells a story.
*Mathematics Teaching in the Middle School*, *6*, 92-98.
- Russo, L. M., & Passannante, M. R. C. (2001, February). Statistics fever.
*Mathematics Teaching in the Middle School*, *6*, 370-376.
- Schooler, S. R. (2004, October). A chilling project integrating mathematics, science, and technology.
*Mathematics Teaching in the Middle School*, *10*, 116-121.