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 34 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 611 in the Usiskin book 
July 19 
July 26 
Midterm exam
Complete the van Hiele interview and write the 23 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 #1ae, 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"











































