# TPC Functions Course I

## Schedule

 Date In Class Assignment July 17 Agenda Introductions, consent forms, course forms (30) Frame course purpose (15) Discuss course "Rules of Engagement" (30) Box Problem Box lesson logic (60) Introduce Graphing Calculator (30) Jul 18 Agenda Continue discussion of box problem (15) Discuss Graphing Tips 1 in the context of the box problem (30) Administer Function Inventory (30) Discuss and whiteboard standard bottle problem (30) Discuss gas guage problem (15) Discuss teacher responses to the Teaching Gap assignment (30) Jul 19 Agenda Discuss modeling homework (45) Function composition/circle lesson (60) Distance time coordination -Walking, moving dots (45) Video analysis assignment Course Forum: Give your thoughts on the logic of the moving dots activity that we discussed in class. July 20th Agenda Discuss solutions to over and back video Explore and explain circle task using graphing calculator Ladder problem Ladder and gas guage problems Course Forum: Review video link from syllabus on "speaking in meaning." Explain what is involved in "speaking in meaning". Discuss what changes/improvements you will neet to make in yourself to speak more meaningfully when participating in discussions during class. July 24th Agenda Discuss ladder problem and gas guage problem (30) Introduce notion of lesson logic: model the development of a "lesson logic" for the composition problem (45) Introduce City A and City B activity (60) Discuss responses to the Ma assignment (30) Develop a lesson logic for the ladder problem Course Forum: Discuss the process and purpose of a lesson logic. Did you engage in new thinking when developing your lesson logic? July 25th Agenda Discuss lesson logics; Discuss Ma assignment. Quiz Explore City A, City B phenomena Select a task that has the potential to engage students in covariational reasoning. Create a lesson logic to use this task with your students. Continue to explore City A, City B phenomena. Download GSP file and tasks (see course forum). Complete level two assignement on the worksheet you downloaded. Provide an explanation of the reasoning you used to construct each of the three graphs on level two of the worksheet. July 26th Agenda Discuss ladder problem Lesson Logics Work expanding sphere problem. Discuss Intro to Graphing Introduce angle measure Intro to Trig Review Intro to Graphing Use definition of angle measure and trig functions to solve problems intuitively July 27th Review notion of angle measure, conversion of degree measure to radian measure, etc. Discuss solving problems intuitively Introduce sine and cosine functions with finger tool Explore behavior of sin (2x), sin (4x)... sin (nx) Explore behavior of cos (sin (2x)), etc. Re-work 4, 5, AND 6 (solving problems intuitively). Be sure to write meaningful explanations, using figures as needed, to explain your answers. Complete Trig Functions Aug. 24th Agenda Hand back tests and discuss select problems (i.e., composing functions by graphing, lesson logic) Describe resubmit options for select test items Discuss Trig Functions assignment Resubmit test items 1 and 2 for 4 points each. Details regarding resubmission guidelines will be provided in clas.. Finalize Trig Functions homework. Be sure to "speak in meaning" when providing your explainations! September 7th Agenda Whiteboard important things you want students to learn when teaching trig. Whiteboard strategy for connecting triangle trig. and trig. on a unit circle. Hand out final project Rate of change assessment Develop a three day unit plan to introduce trigonometry. The plan should include a logic that conveys the ideas to be developed and how you will develop them. Prepare lesson logics for individual days or groups of days that details how the ideas will be developed. Prepare activities by which you will teach and by which students will learn what you intend them to learn. Course Forum: Discuss the process and purpose of a lesson logic. Did you engage in new thinking when developing your lesson logic? Sept. 21, 2006 Agenda Discussion of connections between triangle trig., unit circle trig., and the trig. functions Review of trig. ideas Promoting Covariational Reasoning: More practice composing trig. functions (e.g., sin (cos (2x-1)) Connecting function composition of trig. functions to standard translations--why do the rules work? Homework: Composition of Trig. Functions and Review of Proportionality Course Forum: As you reflect on your teaching and your students' learning, are you still focussing more on what you say, or are you beginning to focus on your students' meaning making and conceptual knowledge? What specifically are you doing if anything to realize these shifts and what successes have you experienced? Oct. 3 Agenda What does it mean to reason proportionally? What is the meaning of constant rate of change? Thinking about teaching linear functions Homework and activities from Shannon's class. Thinking about teaching linear functions homework (to be determined) Nov 14 Agenda Importance of precision when creating mathematical models Action vs Process Functions as Models Extension of in-class example regarding action versus process conceptions Nov 21 Reprise of Action vs Process conceptions of formulas Review of f(x) = x2 mod cos(x) Why does it break where it does? Why do we get some regions of "increased activity" and some regions of "little activity"? What does this have to do with teaching high school math? Inequality activity Course evaluation Logic of inequality activity Inequalities from a broader perspective Nov 28 Thanksgiving Thanksgiving Dec 5 Play with polynomials What is the difference between y = x2 and y = x3? Create "live" tangent for any function Thinking about the influence of terms and coefficients. Dec 12 Final Projects due Complete expanding sphere activity Intro to Graphing Discuss Discuss videos and analyses (15) Discuss the motive for this assignment Discuss textbook assignment Revisit the Box Problem Hand out computers Discuss issues involved in thinking with graphs Continue intro to Trigonometry Use Using definition of angle measure and trig functions to solve problems intuitively Discussion of Five day unit plan for introducing trig Trig Functions How to help students see trig identities. Agenda Examine student's intuitive trigonometric thinking Quiz Introduction to Polar Coordinates (revisit our discussion by viewing the "Polar Fairy Dust" movie) The nature of graphs Interactions between functions and coordinate systems Revisit polar coordinates In-class activity Present unit plans Covariation of quantities (City A and City B) Covariation as intuition (Sue & Daryl) City A and City B homework Sue's Diagram & Falling Paper Clip Polar Coordinates homework Finish Polar Coordinates homework. Re-view Video #3 of Over and Back. What were the central ideas? What were the important pedagogical moves?