## 3D Printer Models for MAT 232

This semester, I am teaching MAT 232 Multivariable Calculus. We often talk about level curves and use the saddle surface as a key example. Every time it comes up, I ask students to stare at the part of their hand where the thumb meets the palm. Of course, they stare at me like I am crazy! This region of the hand is a good model for a saddle surface. If you start looking around at biological examples, you’ll see saddle surfaces everywhere.

I got interested in getting some 3D printed models of saddle surfaces to hand around the class. I found a great project 3D Printed Models for Multivariable Calculus put together by John Zweck. The STL files for the models are freely available, and I asked Reinhard Grassmann of the Continuum Robotics Lab if he could 3D print some models of saddle surfaces and the paraboloid for me.

They arrived yesterday and they turned out GREAT! You can clearly see the level curves in one model, and the coordinate grid in another. They feel great to hold and are durable enough to hand around to a class of students.

## UTM Math Club — The Diamond System

I gave a string workshop at the UTM Math Club. It was very experimental. I wanted to highlight the algorithmic aspect of string figures. We were going to do the first bit of inoli’s Diamonds System.

## Math Learning Center Orientation

Today I gave a little bit of an orientation to the Math Learning Center at MCS TA Professional Development day.

Professional development for TAs is where people get started on their teaching careers. These mini-workshops for incoming TAs are a valuable opportunity to share our hard won insights in to teaching and learning with people who are at the front lines. Teaching assistants interact directly with students, and are often the part of a course that students related to best. Almost all of out teaching assistants are themselves students at UTM. They have the freshest perspective on how these courses are taught.

My contribution to the program for TA Professional Development was communication strategies for use in one-on-one interaction with students. I wanted to get across two ideas: “asking is more important than telling” and “students don’t know”. I tried to bundle these together in a communication exercise.

The teaching assistants were all given a simple picture, and asked to describe the picture “mathematically” to their neighbour. The task is difficult because the person describing the picture could not directly describe the subject.

## Symmetry Groups at Science Unlimited

I gave a talk about symmetry groups at Science Unlimited 2019.

The slides are available here, for the curious.

## MSLC Summer Seminar

- May 30th “Derivation and applications of the gamma function” by David Salwinski
- June 6th “An Extension of Heron’s Formula” by Zohreh Shahbazi
- June 13th “What is Homology?” by Parker Glynn-Adey
- June 20th “Exploring Mathematics Learning Support Across Canadian Universities” by Rubina Shaik and Shrijan Rajkarnikar
- June 27th “Liouville numbers and irrationality measure” by David Salwinski
- July 4th “Representation theory” by Lisa Jeffery
- July 11th “Geodesics on Surfaces of Revolution” by Amanda Petcu
- July 18th “An (informal) Introduction to Model Theory and Skolem’s Paradox.” by Yasin Mobassir
- July 25th “Geometric Reflections” by Parker Glynn-Adey
- August 1st “The Inscribed Square Problem” by Amanda Petcu

## Geometric Reflections

There is something pleasing to a mystic in such a land of mirrors. For a mystic is one who holds that two worlds are better than one. In the highest sense, indeed, all thought is reflection — Chesterton

## A Community of Mathematicians: Using a Wiki in a Large Calculus Class

PCMI 2019 Workshop on Equity and Mathematics Education

2019 Organizer: Rochelle Gutiérrez, University of Illinois College of Education

Participants will further develop their understanding of equity (identity & power issues) in mathematics and consider how to expand our goals to rehumanize mathematical experiences for those with whom we engage. In this workshop, we will explore different perspectives/theories, reflect on our own practices, learn from experts in the field who have been altering their practices, and create our own action plans for work we intend to carry out after the workshop ends.

Ideal participants will include mathematicians, mathematics teachers, and mathematics education professors who have a specific project upon which they would like to focus. For example, you may have in mind a course you would like to alter in some way; a new initiative to launch; a summer camp or bridge program; a professional development or teaching activity to update; or simply a new way to think of assessments or evaluations. By the end of the session, you will leave with a more developed action plan and feedback from others so you can put your best foot forward in your future work.

## Denlow Public School

I visited Denlow Public School and did two workshops for the Grade 4 and 5 students. The Grade 4s played with probability, learned to play Pig. This simple dice game has been subject to a lot of deep analysis. Some folks at Gettysburg College have given an optimal solution to the game.

The Grade 5 students learned about Cat’s Cradle. They were very excited, and wanted to learn more. Many students already knew a figure or two. We covered Half Second Star, Cup and Saucer, and Jacob’s Ladder. I’m told that they’re still playing with the string that I gave them.

## NIBL&T 2019 Day 1

I just finished up my first day at the Inquiry Based Learning and Teaching Conference in Denver, Colorado. It is great to see my friends from the Inquiry Based Learning Workshop last summer. My colleagues Alex Rennet and Jaimie Thind from UTM are here as well. A couple people at the conference have commented on what a strong IBL presence we have at UTM. Woot!

Setting the Stage for Small Group and Whole Class Discussions: Eliciting and Building on Student ThinkingKaren Keene, National Science Foundation & Nicholas Fortune, Western Kentucky University

Description: During this workshop, faculty will focus on two main themes: 1) how to set up their classrooms’ norms and environment to be able to have productive small group and whole class discussions, and 2) what teacher moves they can use during small group and whole class discussions to directly elicit their students’ thinking and build on that thinking. Each of these main themes will come with a mini-activity to gain first-hand experience. Topics for the first theme include but are not limited to ways to set up groups, how to provide an encouraging environment where it is acceptable to make mistakes, and using challenging tasks. Topics for the second theme include but are not limited to eliciting and building on students’ thinking, revoicing, peer to peer interactions, and connecting small group work to whole class discussion.

An active approach to calculus II and how it can help address (and create?) challengesJeanette Mokry, Dominican University; Aliza Steurer, Dominican University

Description: In addition to the new content that calculus II brings to our students, it also requires more decision-making and explanations of solutions than calculus I. Many topics in calculus II require students to make a decision. For example, “What series test should I use?” After deciding what series test to use, students must correctly interpret the results of the test and/or explain their reasoning. This can make the material quite challenging for students. Also, much of the content builds on prior knowledge, which can create challenges for the instructor, such as needing to present new material and also connect with the “old.” Mathematics also requires great attention to detail, including derivative notation, limit notation, and proper use of an equals sign. In the face of these challenges, how do we keep students motivated and help them see that, contrary to what they may have heard about the course, the material is doable? We will discuss how we have used active-learning worksheets to address some of these challenges as well as new challenges this approach can bring to the students and the instructor. At the beginning of our presentation, we will ask the audience what challenges they and their students have encountered with calculus II. Participants will also complete a short worksheet and, together as a group, we will discuss how that worksheet might address or create challenges in our classrooms.

From Place Values to Place Matters: An Indigenous Perspective on Calls for Diversity, Equity, and Justice in Mathematics and Mathematics EducationBelin Tsinnajinnie, Santa Fe Community College

Abstract: Despite perspectives that view mathematics as universal and culture free, policies and practices in mathematics education continue to perpetuate forces of settler colonialism and assimilation. Failed U.S. policies in Native American education illustrate the damaging impacts of assimilation and settler colonialism in education. What practices in our mathematics programs perpetuate settler colonialism and assimilation? In what ways can attenuating to our sense of place better serve goals of equity, justice, and inclusion?

## 10,000 PhD Project

The University of Toronto just released a huge study of the job outcomes of recent graduates, the 10,000 PhDs Project. It is really eye opening. I wish that I had seen this data when I was in the dregs of grad school job despair. It is really remarkable that 30% of people wind up in tenure stream appointments. Those are incredibly good odds. If I had had to guess, I would have estimated it at less than 10%.

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