| Jan. 21 |
Introduction. About this
course. New Topic: Triangle Area. Topic
Page. Pre-test; see
report. |
| Jan. 26 |
Triangle area continued.
Lecture about the readings. See assignments at the topic
page. |
| Jan. 28 |
Triangle area continued. Class discussion. |
| Feb. 2 |
Post-test on
triangle area; see
report.
New topic: Parallelograms. Topic
Page. Pretest.
Introduction. |
| Feb. 4 |
Parallelograms continued. Discussion
of definitions; see readings on definitions. Discussion of parallelogram
theorems. HW: Write
proofs of the equivalence of items i)-iv) I of
the Parallelogram
Theorem. |
| Feb. 9 |
Parallelograms continued. Review of
some geometric contstructions with ruler and compass(approx. 50 minutes).
Discussion of student work from last year
(approx. 30
minutes). HW:
Write final versions of your proofs of the Parallelogram Theorem.
Extra credit: 1) Prove or disprove Roseanne's conjecture.
2) Prove or disprove John's Conjecture. |
| Feb. 11 |
Discussion of pre-/post tests, grading, teaching styles (20 minutes).
Parallelograms continued. In groups
of 3 to 6, students read, compared, discussed and revised proofs from
their homework (40
minutes). Several proofs were put on
the board,
presented and discussed (15 minutes). HW: 1)
Revise your proofs again, and submit on Monday. 2) Read Euclid Book
I;
see Euclid
Topic Page. |
| Feb. 16 |
New Topic: Euclid. Pre-test: "What
is a definition? A postulate? A theorem? What role do these things
play in a logical deductive
system?" (10 minutes).
Lecture Euclid, Book I, Propositions
1-26.
1-3 |
various ways of reproducing line segments |
4-8 |
triangles: (4) the SAS criterion for congruence,
(5-6) properties of isosceles triangles,
(7) the ASA criterion for congruence and
(8) the SSS criterion for congruence
|
9-12 |
basic ruler and
compass constructions: bisecting angles and segments
and drawing a perpendicular to a given
line through a given point
|
13-15 |
the angles formed when two lines meet, including the fact that vertical angles
are congruent
|
16-21 |
inequalities between various
parts of a triangle: (16) an exterior angle is greater
than either of the opposite interior angles;
(20) the
total length of any two sides exceeds the length of the
third
|
22-23 |
constructions of triangles |
24-26 |
inequalities involving comparisons between two triangles
and (26) the AAS criterion for congruence. |
HW:1) Read all the propositions in Euclid
Book I. 2) Continue the grouping, above, through Proposition
48. I want you to study the proofs until you understand them
and
can
reproduce
them in
your own words and explain them to other people. (This
will take many readings and a lot of work. I am asking for a lot,
here.) |
| Feb. 18 |
Students turned in their work on parallelograms. Geometer's
Sketch Pad. Students were introduced to GSP. Running it
on laptops, they carried out the constructions in Euclid
I.2 and I.16. HW: Continue
assignment from 2/18. |
| Feb. 23 |
Lundi avant Mardi Gras |
| Feb. 25 |
Gueule de bois
Mercredi |
| Mar. 1 |
Euclid Book I (continued). Continued the
overview of the structure of Book I. Described the role of the Parallel Postulate.
(See the commentary accompanying Proposition
29 in Joyce's web edition of Euclid.) Noted relations to specific topics
and themes from the high school curriculum, e.g., "alternate
interior angles", the parallelogram theorems, triangle area. Discussed
the TIMSS video of the 8th-grade Japanese geometry lesson. |
| Mar. 3 |
Dr. C.N.Delzell discussed Euclid's proof
of the Pythagorean Theorem, then led an activity from the book, 101
Great Ideas... by Posamentier and Hauptman illustrating how subtleties
of definitions, if overlooked, can cause errors. |
| Mar. 8 |
Post-test on Parallelograms. Lecture: "How
logically sound is Euclid?" Although
Euclid was THE model of logical rigor for over two millennia, in the 19th
century mathematicians realized that there were some subtle flaws in Euclid.
What are these flaws? (Russell) Can they be fixed? What is the significance
of this and the relevance to teaching high school? More discussion
of definitions. |
| Mar. 10 |
Discussion and analysis of some student work (proofs). |
| Mar. 15 |
Test |
| Mar. 17 |
Activities related to ratio and proportion: TEXTEAMS "Perplexing
Puzzle". Using a rubber band to dilate a figure. Lecture: Similarity of triangels,
AAA criterion, measuring distant objects by triangulation. HW. Read the report
by the Olberdings on activities they designed. |
| Mar. 22 |
|