Week+5+-+Math+Trek+and+Introduction+to+GSP

**Week 5 Thoughts and Reflections** Here are some thoughts about how and when you may wish to use GSP. I would encourage all of you to complete the GSP task with triangle explorations to both give you practice with this amazing tool, but also because I think you'll find the exploration engaging and interesting and may offer furthe insights into the geometric properties of triangles. I'll post up my GSP file so that you can, at least, get a feel for some properties of Euler's line. //Bye the way, thanks for the corrections and suggestions to improve the wording on the worksheet. These edits are now included in the worksheet on the website.//

Geometer’s Sketchpad is “dynamic geometry software” which allows you to construct lines and objects and then move them around, or vary the value of a coefficient in an equation and see the effect on the graph of the function. You can even animate objects. Students will grasp the “big picture” more readily because they can observe an object in transition from one state to another. **// What can you do with it? //** Geometer’s Sketchpad can be used throughout the entire high school curriculum.
 * // What is Geometer’s Sketchpad? //**
 * In Grade 9 **, you can investigate the Pythagorean Theorem, the Parallel Line Theorem, properties of triangle centres, slope and the //y// intercept, and make algebra more concrete by representing polynomials as areas and volumes.
 * In Grade 10 **, you can demonstrate how changing the values of “//a//”, “//h//”, and “//k//” in affects the graph of the parabola, and why.
 * In Grade 11 **, you can unwind the unit circle to generate the sine and cosine curves, and animate transformations of the trigonometric functions. The conic sections can be constructed from their locus definitions, and their reflector properties demonstrated with great effect.
 * In Grade 12 **, you can animate classic Calculus problems and transformations of the new families of functions your students will encounter (absolute value, exponential, logarithmic). Graphing in general is easily done with GSP and the graphs can be copied and pasted into other documents. Also, when solving equations, students often find it helpful to see the problem represented graphically.

Kirsten asked an interesting question about how to manage the diversity of students who are more or less willing to participate and engage in mathematical discussions in class. This is an important question and a challenge for many teachers. Upon reflection, I should have directed this question back to the whole class for pair, group, table discussion. The Boaler readings for next week (ch. 6 and 7) examines this problem in detail. As you read, think about how you would answer the following questions: (We shall discuss them during class next week)
 * Discussions around equitable student participation**
 * Students vary in their readiness or willingness to take part in group discussions and can often feel isolated and anxious when asked to explain their solutions. What can a teacher do to encourage equitable participation of all students?
 * What is the purpose of small-group discussion, whole-group discussion?

Many thanks to Steve M. and Claudia, Erika and Isabelle, Jason and Ryan and Heather J. and Deepika for agreeing to move their activity stations to week 7. This will allow us to have more time on week 8 to share ideas and discuss any concerns prior to your practicum. I have altered the course notes on the website to reflect this.
 * Student Candidate activities on week 7 (22 October)**

For next week (week 6) activity stations, don't forget to contact me if you need any resources from the LRC
 * Remember**

Until next time... Adrian