Marggie D. Gonzalez www4.ncsu.edu/~mdgonza2 April McLamb www4.ncsu.edu/~ajmclamb Donovan, J.E. (2006). Using the dynamic power of Microsoft excel to stand on the shoulders of giants. The Mathematics Teacher, 99 (5), p

“If I have seen further than others, it is because I have stood on the shoulders of GIANTS” – Isaac Newton

 Problem Solving  Present a classic algebraic problem and expand it through dynamic representation.  Communication  Share ideas and discuss conjectures.  Connection  Connect algebra with finance math.  Representation  Different representations are used to display the data (sliders, table, and graph).

Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning (NCTM, 2000, p. 24).

 Connection between different representations  Being able to understand and explain the meaning of variables using tables, and graphs  Being able to make generalization using parameters

Person A sets out in a car going at 50 mph. Starting 3 hours later, person B tries to catch up (along the same route). If person B goes at 75 mph, how long does it take to catch up? Solution: t = 9 hrs Equation: 50 t = 75( t - 3)

Generalization involves varying the speeds by assigning variables to traditional constant values. In this case assign: v 1 as the speed for person A and v 2 as the speed for person B. Rewrite the equation including these variables and solve for t. What questions will you include in this task in order to elicit students’ conceptual understanding of rate of change? Could you extend this task further? Explain.

 Twin 1 and Twin 2 are planning to save for retirement. Twin 1 will save $2000 per year from age 25 through age 34 and then no longer make annual contributions. Every year on her birthday she makes a $2000 deposit. Twin 2 wants to “live it up” while she is still young and plans to start saving $2000 per year when she hits age 35. Beginning on her 35 th birthday she deposits $2000 per year on her anniversary of her birth. Which twin will have more money when they retire on their 65 th birthday? Assume an interest rate of 8% compounded annually.

 What do you found?  Twin 1 will have more money than Twin 2 at their 65 th birthday.  Do you think the result will surprise your students?  WHY?  The task “deliberately confuse students to draw their attention to subtle relationships” (Sinclair, 2003)  Cognitive Conflict (Hollebrands, Laborde, & Strober, 2008)

 Create a slider and attach it to cell F4.  Create an XY scatter plot with Twin 1 and Twin 2 plotted on the same graph.  Explore the effects of changing the interest rate.

At what interest rate will the twins have the same amount of money at their 65 th birthday? %

Summarize your conjectures about the effects of each: a: b: c:

 What do you notice about the vertex of the function as you change parameters?  Which parameters affect the vertex?  How can you determine the location of the vertex using those parameters?

 The authors did not specifically stated the learning goals.  The activity was used in a professional development with practicing teachers.  Idea of generalization problems in algebra and showing students the influence the value of variables has in a problem.  In the twins example, the money Twin 1 or Twin 2 will have at the end depending on the amount of years they will be saving as well as on the interest rate they receive.

 Sliders  Creating vs. Given  More Money  Have the table of values created for students.  Quadratic Formula  Negatives values and fractional values for coefficients

 No changes if use with teachers in a professional development.  If use with students:  In Task 1 - Sliders created  In Task 2 - Table created and have students create the slider

Donovan, J.E. (2006). Using the dynamic power of Microsoft excel to stand on the shoulders of giants. The Mathematics Teacher, 99 (5), p Buckley, M.A., and Kelly, S. (2003). Transforming spreadsheets into dynamic interactive teaching tools. On-Math, 2 (2), National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: The Council. Hollebrand, K.F., Laborde, and Strober (2008). Technology and the learning of geometry at the secondary level. In M. Kathleen and G. Blume (Eds.). Research of Technology and the Teaching and Learning of Mathematics: Volume I. Research Syntheses, Greenwich, CT: Information Age. Sinclair (2003). Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials. Educational Studies in Mathematics, 52, p