There have been changes to the notes for Monday & Thursday!
Changes are indicated in red
Monday:
Post:Metalesson
Read: For Tuesday, Brahier, Chapter 5. There will not be any questions to answer on this chapter in writing.
Read: Also, read carefully your assigned section of the content and process standards from the Principles and Standards document. Work with your group to prepare your summaries, activities, etc. These will be due next Thursday in class.
Post and prepare to present: Concept attainment activity: Select a concept in mathematics, e.g., 'closed polygons' was the example in the text. Now, create a short "concept attainment" activity that employs inductive learning by creating several examples and non-examples of this concept. However, do not identify upfront which are examples and which are non-examples. Be prepared to share this activity from your folder on Tuesday/Wednesday. Class members will try to discern what concept you are presenting by characterizing the common properties of examples. There is an example in the text on page 44.
Tuesday:
Post: Metalesson
In-class: We will work on inserting image files into web pages.
Prepare and Post: For today, prepare to present your concept attainment activity. All of these should be located in your folders online. We will do as many as possible, and finish the remainder on Wednesday AM.
Work: Continue to work on your Standards Project. Remember that your group will teach to the class a high-school or middle-school level lesson in your content standard area that highlights the process standard you are assigned as well. For the detail of the content to be included in the summaries, you can look at the following URL:.
Work and Post Eventually: For Wednesday, continue to work on your Geometer's Sketchpad assignment to unpack the conic sections. You should explore both ellipses and hyperbolas, and you should include the following things in your assignment:
A patty paper folding activity--include instructions as how you would have students do this activity
A Sketchpad file that replicates the patty paper construction, along with instructions for students to guide them in building the construction of the conic section.
A proof that the objects you have constructed are indeed an ellipse and a hyperbola that meets the following definition: The locus (set) of all points that are equidistant from a given point and a given circle. Once proven, demonstrate (prove further) that the standard properties of ellipses/hyperbolas hold. In the case of the ellipse, this means that the sum of the distances from a point on the ellipse to the two foci is a constant. In the case of the hyperbola, the difference is a constant.
MacGyver-ish problems. Posted on the website are 5 problems similar to MacGyver Problems, and ask you to pick 3 to respond by the weekend. We will do the same 3 problems at the end of the course.
In-Class: In class, we will discuss the remaining concept attainment activities, we will examine screen shots of images to include in worksheet instructions for Sketchpad,etc., we will do a math activity, and we will have time to work on both of your ongoing projects for the week.
Work and Post: Continue to work on Standards Project. Be prepared to teach lesson tomorrow. Your group will have 15-20 minutes total. Your entire project website should be posted by Sunday evening at 5 PM.
Work and Post: Continue to work on Geometer’s Sketchpad project with conic sections. Your work should be posted by Monday.
Read: Chapters 3 and 4 of Brahier. Questions to answer over the weekend.
Post: Create a list of 10 "BIG IDEAS" in mathematics that you feel are vital for all students to know about mathematics by the time they leave high school. Can you categorize these big ideas in any way?
Thursday:
Post: Metalesson
In-Class: You will present your standards projects. Point us to where your summaries are online, briefly (1 minute) describe one of the two lessons, and then do the other lesson activity. You may choose whether to do the middle school lesson or the high school lesson. Each group will have at most 20 minutes, including feedback. After the first two hours, we will do a math activity and discussion.
You should prepare enough materials for the rest of the class to do your lesson activity. There are 12 other students plus Erica and Tim. Please let Erica or Tim know if you need any assistance with equipment, manipulatives, or other resources by Wednesday AM.
Post over Weekend: In Chapter 5 of Brahier, it mentions the idea of "lesson imaging"--page 131ff. Create a lesson image for the lesson you taught today that addresses the following types of questions: How did it go? Did the students respond to the activity in ways that you anticipated? What did you expect them to do/say/respond? In what ways did they respond differently than you expected? What would you do differently in a classroom of live actual high school students? Are there modifications/adaptations that you would make to meet needs of diverse learners?
In Chapter 3, Brahier summarizes some of the vision in the NCTM Standards and describes several curricular models for secondary mathematics. Describe the curricular model of mathematics you experienced in high school. Was it a "tracked" curriculum? What is a tracked curriculum, in your mind? Do you believe that secondary mathematics curriculum should be tracked along ability grouping? Why or why not? What are the pro's and con's of tracking in school curricula?
Suppose that you are beginning a unit on quadratic functions in Algebra II. Create a set of affective and cognitive objectives (at least one at each level) for the topic of quadratic functions.
Respond to question 8, on page 104.
Read: Chapter 6 in Brahier. Be prepared to discuss.
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