Illinois State University Mathematics Department

MAT 326: Technology Tools for Secondary School Mathematics

Dr. Roger Day (day@ilstu.edu)



Session #4

10 September 2012

Warming Up: Free Rice, Anyone? or Make 24?

Exploration: Quadratics Functions and Their Graphs

Each small group should come to class with proofs of the three conjectures regarding the parameters a, b, and c. We discussed in class last time what constitutes proof (see pics of board writing related to each parameter). Tonight, each group is to have ready a draft of responses to all four stages of the exploration.

Tonight we'll look at and discuss the draft proofs brought in by each group. I'll collect those tonight as well.

Extending the Technology: Parameters, Sliders, and Polynomials

    You created and emailed to me GGB files that mimicked the previously used GSP file for exploring graphs of quadratic functions, focusing on changes in the graphs based on changes in the parameters:

    • y = ax2 + bx + c
Using the previously created GSP5 quadratic explorer file, edit it to insert locus of points for each of the three parameters (a,b,c). Then, create Hide/Show buttons for each locus of points. Show me this modification during class tonight.

    You created and emailed to me GSP files with sliders to explore graphs of linear and cubic functions, focusing on changes in those graphs based on changes in the parameters:
    • y = ax + b and
    • y = ax3 + bx2 + cx + d
Linear Explorations

On your linear explore GSP page, insert Hide/Show buttons for each of the following questions or statements. Then, on that GSP page, type in your conjectures related to each statement. Test and revise each conjecture as needed. Show me these modifications during class tonight.

  1. Describe the family of functions produced when you vary a in y = ax + b.
  2. Describe the family of functions produced when you vary b in y = ax + b.
  3. Describe the family of functions produced when you vary a and b, at the same rate and in the same direction, in y = ax + b.

Cubic Explorations

On the GSP cubic page, determine and plot points representing each local maximum and minimum, if they so exist. You'll likely need to use the derivative feature of GSP. Once you have extrema plotted, commence with an analogous exploration to that of the quadratic exploration you previously undertook. Add locus of points for each of the four cubic parameters as well as Hide/Show buttons for each. Show me your progress on this during class tonight.

  1. Clearly state what you are investigating.
  2. Generate a conjecture for that investigation.
  3. Test your conjecture using your geometric construction.
  4. Prove your conjecture.
  5. Based on your cubic and quadratic explorations, draw a generalization between the quadratic and cubic cases.


During Session #4, we'll discuss uses of this sort of technology and discuss at what points in the school mathematics curriculum  we might  encounter the mathematics you've explored.
     
Parameters, Variables, Equations, Functions, and More

For each equation shown here, explain what the letters represent. Then, discuss the similarities and differences in those letters from equation to equation.
y = 3x + 4
y = mx + b
3x = 6

Techno Tools

On GSP: locus of points, trace, tables, plotting points; parameters, derivatives, evaluating a function at a specified input value

Technology for Teaching and Learning

What should be the role of technology in your high school classroom? Generate some specific examples of appropriate technology use and some specific examples of inappropriate technology use. Be specific.

Technology and Document Creation

Between Session #2 and tonight, you used Equation Editor to create typeset equations, expressions, and functions as part of a sample quiz I provided for you. What other document creation skills and processes will be useful for you as a mathematics teacher?

Mobile Apps: A Preview

Here's an example of an iPad app that a school mathematics teacher might use.


Assignments for Session #5 (17 Sept 2012)

  • Complete any follow-up group work on your Quadratic Graphs exploration proofs, based on today's discussions. There may be a required turn-in here!
  • Continue the cubic GSP explorations described and initiated tonight. No turn-in yet!
  • Review the Techno Tools videos (see above) to be able to use these GSP features. No turn-in required.
  • Read the following articles related to using electronic spreadsheets in school mathematics.
    • Teaching and Learning Mathematics with Interactive Spreadsheets
    • Teaching Mathematics Through Spreadsheet-Oriented Problem Solving
    • Spreadsheets in the Classroom
    • When you have read and studied all the articles, create a three- to four-paragraph summary and analysis to address these two questions:
      • (a) How can the spreadsheet be an effective tool to help teach and learn high school mathematics?
      • (b) What are some concepts and skills that I (that is, you, the MAT 326 student who's becoming a teacher) need to develop or improve upon to begin such uses of the spreadsheet for teaching and learning?
    • Submit these required responses to me in an email message. After class tonight or sometime tomorrow, I'll send you an email template to which you can simply REPLY with your responses. Your responses are to be submitted to me via email by 8:40 am on Sunday, September 16, 2012. Please use the reply template I send to you.
  • Continue to look for and critique mobile apps that focus on school mathematics, preferably secondary school mathematics. More info on this to follow.




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