Malin Christersson’s Cube Toy
I was looking through the Geogebra site and found this lovely applet Orthographic Projection by Malin Christersson.
This is a lovely tool for investigating one of my favourite facts about hexagons:
The area maximizing orthogonal projection of a cube is the regular hexagon.
It turns out that Malin has tonnes of awesome geometry stuff online!
 Hyperbolic tiler!
 Pythagora’s Tree!
 A whole Tumblr full of great animations!
Awesome math art!
MAT B41 — Week 9
Homework 4 (tex) is now available.
Additional resources:
 Khan Academy on constrained optimization.
 Kristal King on Lagrange multipliers.
Suggested Exercises:
 3.4 Constrained Extrema and Lagrange Multipliers: 1a, 3, 4, 5, 13, 14, 15, 19, 20, 28
Past Finals:
 Final 2016: Find the minimum value of on the closed triangular region in with vertices , , and .
 Final 2015: Find the maximum values of on the solid ball .
 Final 2015: Find the points on the intersection of the paraboloid and the plane that are closest and farthest from the origin.
Notes:
Public Talks for UTSC
MAT B41 — Week 8
Additional resources:
 Khan Academy on multivariate maxima and minima.
 Kristal King on local extrema.
Suggested Exercises:
 Course Notes: Quadratic forms and determinants
 3.3 Extrema of RealValued Functions: 1,2,3,11,13,21,29,31,52
Past Finals:
 Final 2015: Let . Find and classify the critical points of .
 Final 2016: Let . Find and classify the critical points of .
Notes:
IBL Workshop — Day 4
The Daily Reference RoundUp:
 The Calculus Concept Inventory — Jerome Epstein
 A Mathematician’s Lament by Paul Lockhart.
 The 5 Elements of Effective Thinking Edward B. Burger & Michael Starbird
 The Art of Asking Good Questions
 Active learning increases student performance in science, engineering, and mathematics by Scott Freeman, et al.
A couple books that jumped out at me!
 The Shape of Space by Jeff Weeks
 Office Hours with a Geometric Group Theorist by Clay and Margality
Some quick ideas:
 Participation paragraph / class feel paragraph.
 You can use TAs as backup. Make them come to lecture once or twice. If the class has a good learning community then they can cover you, if needed.
The workshop ended today. We had so much fun together. On the very last day, we did a full class video session. We watched a full class taught in IBL style. It was amazing to see all the pieces come together.
At the end of the day we had a graduation ceremony. We did it! We are now IBL practitioners. There was lots of cheering, and celebration. Everyone crowded around the door chatting. I think we’ll be seeing each soon.
IBL Workshop — Day 3
I went to the National Geographic Museum with Blake Madill.
We started off the day with Kittens inspired by Kittens!
A hilarious (and deep) video about “productive” failure: amazing commitment and persistence in skateboarding.
I also bumped in to an essay A Message to Garcia by written by Elbert Hubbard, about the importance of individual committed to a task.
A math circle talk about Sperner’s Lemma by James Tanton, a very nifty highschool teacher.
Dana Ernst has a really nice post about Setting the Stage for an IBL course.
Today at the IBL workshop we did a fantastic bit of playful mathematics. Gulden Karokok introduced us to a mathematical game and encouraged us to play it together. As soon as we had played a couple matches, everyone started to conjecture about winning strategies. One way of teaching induction or formalizing using notation is to bore students with examples until they want to formalize things. The questions emerged naturally from the play and the whole room erupted in discussion. It was a perfect example of the mathematics generating the inquiry.
The game is quite simple: Two players have some number . They have the following moves: they can subtract one or they can “half it”. If is even, you half it by dividing by two. If is odd, you half it by subtracting one and dividing by two. A player loses if the number is zero. Players alternate turns until they reach zero.
The game is a nice little exercise in division. It could be good exercise for people learning arithmetic. However, it gets boring quickly. The natural questions are much more interesting: How wins? What’s the optimal strategy? These questions raise all sorts of fascinating problems both notational and mathematical. Lots of discussion groups puzzled over the question “What is a winning number? Should it be when the current player can force a win or when the next player can force a win?”
After chasing around examples on a page, I decided to take an algorithmic approach. Once I convinced myself that I could write up and algorithm for the problem, I tuned out of the workshop and wrote some code to generate all winning. The code is available here: http://pgadey.ca/teaching/iblgame.py.
We were assigned the reading: Boaler, Jo. “How a detracked mathematics approach promoted respect, responsibility, and high achievement.” Theory into Practice 45.1 (2006): 4046. I wrote up a bit of a response to it.
IBL Workshop — Day 2
“Education research is more like wildlife research than mathematics research” — Sandra Laursen
The Link RoundUp of the Day:

Dan Meyer TED Talk about the systemic problems of math education (and how to make neat problems)
A SelfDirected Guide to Designing Courses for Significant Learning by L. Dee Fink
Instructional Practices Guide: Guide to EvidenceBased Instructional Practices in Undergraduate Mathematics
Bloom’s Taxonomy of educational objectives
Turning Routine Exercises Into Activities that Teach Inquiry: A Practical Guide by Suzanne Ingrid Dorée
The MAA IP Guide has a whole section of queries about course design. I am eager to answer them in writing. I think that it will make my course design much more solid. The coolest thing that I bumped in to while researching my project is that Dana Ernst keeps a point form journal about each of his sessions in class! So Cool!
On a completely different note: Today we did a bit of change ringing! Amy Ksir brought a handmade set of tubular bells and we rang an eightbell plain hunt.
IBL Workshop — Day 1
Some Amazing Resources:
 Journal of InquiryBased Learning in Mathematics (JIBLM)
 Active Calculus
 Discovering the Art of Mathematics (they do Music!)
There are some books that I want to track down:
 Teaching with Your Mouth Shut by Donald L. Finkel
 Scholarship Reconsidered by Ernest Boyer
I think that next year I will draw heavily on Ted Mahavier’s Calculus I, II, & III : A ProblemBased Approach with Early Transcendentals.
We were assigned the reading: Yoshinobu, Stan, and Matthew G. Jones. “The coverage issue.” Primus 22.4 (2012): 303316. I wrote up a bit of a response to it.
MAT B41 — Week 7
Midterms are graded! New list of suggested exercises is available!
There is a new list of suggested exercises available here.
Suggested Exercises
 Chapter 1 Review (p. 71): 1, 4, 5, 7, 8, 16, 18, 20
 Chapter 2 Review (p. 145): 1, 2, 3, 5, 6, 10, 15, 25
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