Blake E. Peterson

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Math Ed 562 Assignments

Days to remember: The midterm exam will be handed out on July 19 and collected on July 26.
The second paper will be assigned on July 28 and due on August 4.

Date Given
Date Due
Assignment
June 21
June 23

Read Devillers paper on Roles of Proof

Work on the Hinged square problem for 20 minutes.

June 21
June 28

Section 1.1 #3, 4, 7, 12 (L is on BC), 14, 17


Read 1989 & 2000 Standards about geometry for all grade levels, write a 3-4 page paper about the standards addressing the following questions:
What is the general focus of the geometry standards?
What is the role of proof in the geometry standards?
What are the changes from 1989 to 2000?

June 23
July 5

Solve Hinged Square Problem

Section 1.2 #2 a, b, f, g #5

Given B, D, D', C are collinear and BD/DC = BD'/D'C prove D=D'

Read "Types of Student Justifications" (Sowder & Harel, MT Nov. 1998); "Geometry Proof Writing: A Problem Solving Approach a la Polya (McGivney &DeFranco, MT Oct 1995); "Characterizing Students' Understandings of Mathematical Proof" (Knuth & Elliot, MT Nov. 1998); "Teachers' Conceptions of Proof in the Context of Secondary School Mathematics" (Knuth, JMTE Vol. 5 2002). Be prepared to discuss these papers.

June 28
July 7

Read "Ten Things to Consider when Teaching Proof"

Section 1.3 #5, 9, 11

Spend 30 minutes on the attached problem

July 5
July 12

Section 1.3 #1, 4

Use Ceva's theorem to prove that the altitudes of a triangle are concurrent.

On tri ABC, let D cut seg BC into a 2:1 ratio and E cut CA in a 3:1 ratio. If AD, BE, and CF are concurrent, how does F cut AB?

Read up through chapter 5 of the Usiskin book.

July 7
July 12
Work on triangle problem for 30 minutes
July 7
July 14

Midterm: Proof paper

Read pages about van Heile from Mathematics for Elementary Teachers (Musser, Burger and Peterson, 2011); Read article "Characterlizing the van Hiele Levels of Development in Geometry" (Burger & Shaughnessy, JRME Vol 1, 1986); Read copied chapter from "Structure and Insight" (van Hiele, 1986)

July 12
July 19

Work on the triangle problem for 30 minutes for Thursday July 14.

Section 1.4 #3, 9, 11

Read article "van Hiele Levels and Achievement in Writing Geometry Proofs" (Send, 1989); "The van Hiele Model of the Development of Geometric Thought" (Crowley, 1987)

July 14
July 21

Finish the ISOSCELES triangle problem, Section 1.4 #4, 6

Read chapters 6-11 in the Usiskin book

July 19
July 26

Midterm exam

Complete the van Hiele interview and write the 2-3 page assessment of the van Hiele level of the person you interviewed.

July 21
July 26
Perform the compass and straightedge constructions for the translation and rotation on the worksheet.
July 21
July 28

Section 2.1 #1, 2, 3

Section 2.2 #1a-e, 2, 3

July 26
Aug 2

1. On Geometer’s Sketchpad construct R(O,a) R(l) (tri ABC) (this means draw triangle ABC, reflect it about l and then rotate the image around point O with an angle of a) and then find line m and vector XY such that T(XY)R(m) where XY is parallel to m accomplishes the same transformation.

2. Prove that a reflection in two parallel lines is equivalent to a translation with a translation vector that is perpendicular to the parallel lines and twice as long as the distance between the lines.

3. Prove that a reflection in two intersecting lines is equivalent to a rotation with a center of rotation at the intersection of the lines and the angle of rotation is twice as large as the angle between the lines.

4. In triangle ABC with midpoints DEF, find and describe an homothety that maps triangle ABC to triangle DEF. COMPLETE THIS PROBLEM BEFORE THURSDAY'S CLASS

Section 2.2 #5, 10, 13

July 28
Aug 2
Find 5 examples of integer isosceles triangles (use Ptolemy's theorem)
July 28
Aug 4

Spend 30 minutes searching for a perfect box

Read Zal Usiskin article about what should not be in the Algebra and Geometry curricula

Prove Ptolemy's Thorem: "In a cyclic quadrilateral, the sum of the products of the lengths of the opposite sides is equal to the product of the lengths of the diagonals"