## 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.

## IBL Geometry Materials

Turns out that JIBLM has a lot of resources for Geometry!

- Euclidean Geometry: An Introduction to Mathematical Work by TJ Hitchman
- Hilbert Geometry: A Guided Inquiry Approach by David Clark
- Modern Geometry I by Nathaniel Miller
- Modern Geometry II by Nathaniel Miller
- Euclidean and Non-Euclidean Geometries by Charles Coppin

Tonnes of excellent material to work with!

## 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.

## Some Mathematical Reading

I just stumbled on this excellent list “Readings for Math Teachers” by Theron Hitchman. Lots of great stuff to read and ponder.

An absolutely spot-on quote from one of the articles:

The teaching of mathematics, like mathematics itself, is an endless journey of study. I believe that teaching mathematics can be as intellectually demanding as doing mathematics. If our society could come to see teaching as a job that is emotionally, physically, and intellectually demanding, we would then be able to give teachers the respect they deserve, attract more talented people to the profession, and speed up the pace of pedagogical innovation through the study of teaching. — Adventures in Teaching, Darryl Yong

## 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 Day 3

Team-Based Learning in a Large Calculus ClassHeather Bolles, Iowa State University; Amanda Baker, Iowa State University; Travis Peters, Saint John’s University; Elgin Johnston, Iowa State University; Darin Wohlgemuth, Iowa State University

Description: Implementing Team-Based Learning in a large-enrollment calculus class (more than 150 students) involves significant planning, stamina, and buy-in from students, instructors, and administrators. In this session, we share how we adapted the TBL flipped model to both Calculus I and II, the collaborative approach in developing and implementing materials, the continual evolution of the process, and the resources and classroom spaces we found helpful. Qualitative and quantitative data gathered over a three year period provide indications of success and identify where adjustments are yet needed. During the session, we will briefly model how we engage students in an application exercise following the Readiness Assurance Process, where students gain initial exposure to the topic.

Disseminating IBL via GeometryDavid M. Clark, SUNY New Paltz; Samrat Pathania, Wallkill High School

Description: This talk will report on a multiyear project to advance the use of IBL through the teaching of geometry. Currently the speaker is co-authoring a nearly completed book with Pathania entitled “High School Geometry: A Full Axiomatic Development”. Directed to college/university instructors, it will give them the full theoretical underpinnings of the speaker’s 2012 undergraduate text, “Euclidean Geometry: A Guided Inquiry Approach”.The 2012 text is primarily intended to give pre-service and in-service high school teachers (1) a personal learning experience through IBL and (2) an in depth understanding of exactly the topics they will need to teach. Whether or not they eventually do teach geometry, they will leave this course with a sound knowledge of what IBL is and how it is implemented so that they can draw on it for whatever they do teach.

High school students need to learn how to make evidence based arguments and judge when others are successfully doing so. This project will foster that goal by offering a vertically coherent view of geometry, giving high school students, high school teachers and research mathematicians a common basis for understanding this key subject.

Inquiry-Oriented Instruction as Principled ImprovisationDarryl Yong, Harvey Mudd College

Abstract: A very common IBL instructional routine involves posing tasks to students, monitoring their progress, and providing support as students tackle those tasks. The monitoring and supporting phases of instruction are often highly improvisational because they are less scripted and more dependent on what students do and say. What principles guide you during these phases of instruction? How can we work toward greater mathematical understanding, greater equity and inclusivity in our classes during this phase of instruction?

Oh! One more thing.

3D Printed Manipulatives for CalculusSebastian Bozlee, University of Colorado Boulder; Faan Tone Liu, University of Denver; Caroline Matson, University of Colorado Boulder; Cherry Ng, University of Colorado Boulder; Athena Sparks, University of Colorado Boulder; Porsche Adams Wootton, University of Colorado Boulder

Description: Intermediate students in calculus are often challenged by visualizing the applications of calculus in 3-dimensions. As we generalize curves in 2-dimensions and areas under a curve to surfaces and volumes constructed from functions, students benefit from a variety of approaches. We have used a 3D printer to develop numerous models and activities for our Calculus sequence. We will present an activity investigating solids with known cross-sections and various homework and lecture models for Calculus 2. We will discuss how these models are integrated in the classroom, how we developed the codes for and produced these models, and what plans are in progress to extend this work. We will also discuss how we established the 3D printer as a department resource including the expenses and support involved.

A brief description is available at: https://cu3d.github.io/

## NIBL&T Day 2

Oh man! Today was fantastic. I attended an online workshop by Tim Brzezinski on GeoGebra 3D. We did some 3D modelling, and did a worksheet. I’m amazed by all the stuff that GeoGebra can do. Previously, I’d only ever used it for simply graphing for my students. Now that I’m aware of its powerful geometric toolkit, it seems like the sky is the limit.

Towards the end of the session, we got to use GeoGebra 3D on our phones to do augmented reality stuff. Tim modeled a Toblerone bar, and then virtually super-imposed it on the real thing. Tim’s Geogebra page is full of amazing geometric stuff. He constantly tweets interesting math ed material at @dynamic_math. I encourage you to check it out. I’m definitely going to be using the augmented reality features soon.

Tim’s GeoGebra 3D with AR (Google): Explorations & Lesson Ideas

Steve Phelps’ Pythagoras Proofs without Words

The second session that I attended was a round table discussion on using inquiry to promote productive failure, resilience, grit, and growth mind set. We shared various metaphors that we use to explain growth mindset to our students. I often talk about math exercises as a form of weight lifting. Usually, I say this to make the point that watching me solve exercises doesn’t build up that skill in my students. The folks that I was chatting with developed the metaphor in a bunch of new directions, weight lifting involves: pain (productive failure), works best on a regular schedule, benefits from a minimum of expert guidance, prepares us for non-weight lifting tasks.

People have been giving five minute talks here. I love the format. You get to hear someone give a good pitch in a short, concise, and often simple way. The take away for me today was the notion of a MathsJam, a social gathering of people at a pub to talk about math. Brilliant!

## 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?

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