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June 17 - 21
Monday:
- 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 Tuesday AM.
- For Tuesday, work on your principles and standards project. Remember that your group will teach to
the class a high-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:
http://www.mste.uiuc.edu/courses/ci302sp02/nctmProjGuidelines.html. The only difference is that you
will not do the textbook analysis this summer, although we will look at sample texts next week.
- For Tuesday, 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.
- Read chapter 5 in Brahier.
Tuesday:
- 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.
- Read Chapters 3 & 4 in Brahier. Respond to the following questions:
- 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.
- 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?
Wednesday:
- In class, we will do a math activity and explore a new piece of software, Fathom. We will explore it
more on Thursday and next week.
- Read 6 in Brahier.
- Complete the homework activity assigned by one of the student groups on distributive properties in
algebra from a geometric point of view
Thursday:
- In class, you will present your standards projects. Point us to where your summaries are online,
briefly (1 minute) describe your middle school activity, and then do the high school activity. Each group
will have roughly 20 minutes. After the first two hours, we will do a math activity and discussion.
- 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?
- Chapter 6 discusses the professional responsibility of a teacher to develop "worthwhile mathematical
tasks & activities" that promote conceptual understanding of mathematics topics from various perspectives
and on different levels. Pick one topic from middle school or secondary mathematics. Then, search/research
3 different approaches to address that topic and describe. No formal lesson plan is needed, but a good
description of the activities with an example or links is required. One approach should involve something
"hands-on" to make sense of the concept. One approach should involve visual understanding of the content
and how that connects to symbolic/numeric understanding. One approach should invoke a deeper understanding
of the topic, such as connecting it to real life, other fields of study, other parts of mathematics, etc.
OH--at least one of the 3 approaches should involve use of instructional technology that supports the notion
of "added value" and at least one of the approaches should involve either cooperative work or active classroom
discourse! Be prepared to share ONE of your ideas in class on Monday in 1-2 minutes
- Your GSP/Conic section constructions and analysis are due in your folder by Monday AM, June 24, next week.
Make sure that files are either HTML files or GSP files.
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