No New Homework.

Continue working on Project #3, adding Problem #4 from the Investigating Polyhedra Activity.

Continue working on Project #3.

Continue working on those specific problems on Project #3.

• Study for the Constructions Assessment, which will be given tomorrow, Wednesday, 4/01/2026.
  
• Continue working on those specific problems on Project #3.

• Continue working on those specific problems on Project #3.
• A Note about Class and Office Hours this Week:
• Wednesday, 4/01/2026: morning office hours are cancelled as I am giving oral exams in my Modern Geometry class during that period.  However, I will have office hours from 1:30-2:30 PM that day.
• Thursday, 4/02/2026: office hours cancelled; classes will be held as usual.
  
• Friday, 4/03/2026: office hours cancelled; classes will be held as usual, but I won't take attendance this day, so if you need to go home for Easter weekend, just be sure to watch the video.
• Monday, 4/06/2026: office hours cancelled.  Beginning Tuesday, everything should be back to normal.

No New Homework.

You may download the new version of Project #3, which contains the problem regarding the self-working card trick.

• Your Constructions Assessment will be held next Wednesday, 4/01/2026 between 8:00 and 11:00 AM.  Please sign up for a slot here.
• You may now download Project #3, and being working on Problems 1.1a, 1.1b, 3.4, and 3.5.  For one of the problems on Project #3, you will need the following videos:
• Hexaflexagons 1
• Hexaflexagons 2
• How to Fold a Hexaflexagon
  

Read this Article on the Physiology of Beauty and write a one paragraph reflection on one or two items in this article that you found most surprising or interesting.  Turn this in on Tuesday, 3/24/2026.

Read this Article on the Physiology of Beauty and write a one paragraph reflection on one or two items in this article that you found most surprising or interesting.  Turn this in on Tuesday, 3/24/2026.

• For those who did not master the proofs in Project #1:
• Watch this short video explaining the new assignment.
• Complete the new version of Project #1 by Tuesday, 3/31/2026.
• Here is a list of the potential problems on the Constructions Assessment.

No New Homework.

• Here is an 8-minute video clip from a previous year's class regarding the teaching of the Law of Cosines and Law of Sines as an extension of right triangle trigonometry.
• The full version of the project, including the trigonometry problems, is available under Assignment #16 (you may have to press the refresh button after the PDF loads).  This includes the addendum that I handed out in class.

We will begin working on Project #2 in class tomorrow.

Complete Quizzes #7, #8, &#9, as delineated under Assignment #14.

• Quizzes #5 & #6: Read the article, Ten Things to Consider when Teaching Proof by Michelle Cirillo.  Write a paragraph or two identifying two of the ten items that most resonated with you and explaining why they resonated with you.  This will count as Quizzes #5 & #6 and will be due on Monday, 2/09/2026.
• Quizzes #7, #8, & #9:
• Read this Summary of Euclidean and Non-Euclidean Geometries.
• We will watch a Documentary on Non-Euclidean Geometries in class on Monday, 2/09/2026.
• Complete Quizzes #7, #8, & #9 by Monday, 2/16/2026.

Study for Test #1, Part #2, which will be given Thursday, 2/05/2026.

Study for Test #1, Part #1, which will be given tomorrow, Tuesday, 2/03/2026.

No New Homework.

• No New Homework.
• I will be addressing this in class tomorrow:  Here is a very short summary of the importance of both Horace Mann and John Dewey in the history of education in the United States, along with the link to Winona State University.  It is purely for enrichment; I believe that no education major should leave WSU without at least being exposed to  this information.

• Project #1 will be due on Friday, 1/30/2026.

• Test #1 Study Guide:  You may download this Test #1 Template in order to better understand the structure of the test.  Test #1 is scheduled for Tuesday, 2/3/2026 and Thursday, 2/5/2026 and will cover the material from the reading and notes on the History of Geometry and Reason as delineated below.
• History from the Class Lecture:
• Observations about the need for rigor
• Proper vs. Improper Knowledge
• What is Rigor?
• How to correctly argue from a picture
• Examples of establishing a logical link between assumptions and conclusions
• Example of how pursuit of a rigorous proof can lead to developments of many sub-discplines with their own applications
• Inductive and Deductive Reasoning
• The 5 differences between the two as delineated on the handout.
• Quote from the BOT Standards regarding empirical fact and formal proof.
• Which truth value is established by deductive reasoning?  Not the truth value of p, nor of q, but of the implication p --> q.
• History as Delineated in the Power Point Talk:  From these, you should know: (1) significant contributions of individuals (e.g. Euclid, Archimedes, etc.), cultures (e.g. Babylonians, Muslims, etc.), or schools (e.g. Ionian or Pythagorean), (2) major events or controversies (e.g. Thales-Aristotle vs. Pythagoras-Plato, Crusades, Renaissance, etc.), (3) general ordering of events into time periods, but knowing exact years are not necessary.  You may download the (flawed but still very worthwhile) timeline created by previous students.
  

• History as Delineated in the Power Point Talk:  Pay particular attention to the slides on Galileo, because they ultimately trace the main threads of how mathematical and scientific thought progressed through the Renaissance and into the modern day.  In particular, some phrases and concepts with which you should be familiar from that section are:
• Saving the appearances.
• "New theory of the nature of theory."
• The role of the Aristotelians.
• Legitimate criticisms of Galileo's ideas, including the one that wasn't answered until 1838.
• What Timothy O'Neill meant when he said that the "Renaissance was a curiously conservative and retrograde movement in many ways."
• History Reading from Sections 1.1, 1.2, and 1.4: as indicated on the reading guide for those sections.  You may download some proposed answers to the questions about the reading as a study aid.
• Axiomatic Systems:
• Definitions relevant to axiomatic systems.
• Motivation for the axiomatic system: harmony of proportion and perfection of reason.
• Two pitfalls in creation of axiomatic systems and the solutions proposed by Greek thinkers.
• Aristotelian Logic and Law of Excluded Middle (its precise statement and its purpose).
• Three elements of an axiomatic system and how they are established.
• Modern work of David Hilbert, Bertrand Russell, and Kurt Gödel.
• Article on van Hiele Levels:
• Be able to list the various van Hiele Levels in order.
• Give a concrete example of each.

Continue working on Project #1, which will be due on Friday, 1/30/2026.

• If you wish, you can download the actual Power Point Slides, complete with all of the hyperlinks to sources, etc.
  
• Continue working on Project #1, which will be due next Friday, 1/30/2026.

Continue working on Project #1, which will be due next Friday, 1/30/2026.

• Here is the Handout with the Power Point Slides, on which you may take notes if you wish.
  
• Continue working on Project #1, as delineated under Assignment #1.

Continue working on Project #1, as delineated under Assignment #1.

Study for Quizzes #3 & #4, which will be given tomorrow, Friday, 1/16/2026 and will cover the material from the textbook reading, as delineated under Assignment #1.

Continue working on the Reading Assignment and Project #1 as delineated under Assignment #1.

• Tutoring Opportunity:  If you are interested in the opportunity I shared in class today, please download this handout.
  
• Preliminary Tasks:
• Quiz #1: Complete the Student Profile Survey before Wednesday 1/14/2026.  This will count as Quiz #1 (0% if you don't complete it, 100% otherwise).  But, read the next bullet before completing the survey.
• Quiz #2: Carefully read through your syllabus.  In it you will find embedded words that very clearly do not belong; for example, the word "giraffe" may appear in the middle of a sentence, or some such word.  In the appropriate box on the Student Profile Survey, list all of the words that don't belong in the syllabus.  This will count as Quiz #2.

• Grades and Textbook:
• Download the Textbook from D2L.
• Your updated grades will also be published on D2L after each graded assignment.  These are the only two things for which you will need D2L in this class.

• First Assignments:
  
• Quizzes #3 & #4:  Read Sections 1.1, 1.2, and 1.4. This reading guide may help you focus your reading to most efficiently extract the important information from them for the reading quiz, which is tentatively scheduled for Friday, 1/16/2026.
• Project #1: You may begin working on Project #1 -- Review of High School Geometry.   It will be graded according to this rubric.