Imagine the following scenario. Your university is offering dozens of sections of your course, of which only a handful will stay active past the first week of classes; the rest will be closed. During that week, students can attend as many sections as they wish. What would you do to convince your students they will get the most out of the course if they stick to your section?

This is an unlikely scenario… Yet, there is an ever increasing collection of free courses students can use for learning (MIT’s OpenCourseWare, edX, Coursera, etc), which combined with the high cost of higher education and student debt problem (1.5 Trillion!), make a compelling case to go that route (at least for some students). So, what’s the benefit of in-person courses and what will our roles be in the future? A possible answer is that one of our roles should be to model learning in our classrooms. In a typical lecture-based course (like the ones in the platforms mentioned above), we model knowing, not learning. In courses with active learning components, we model and encourage engagement and discussions of the material, hopefully leading to deeper learning experiences.

So, how do you get started if you want to add tools to your teaching kit that encourage students to be active members in the classrooms? My best suggestion is to read the MAA Instructional Practices Guide (MAA IPG); it has the answer to EVERY question you might initially have (if you don’t believe me, try it! You might prove me wrong but it will get you to read it :-)). To complement the MAA IPG, I want to present here five first day activities (plus some freebies at the end) you can try this coming semester to foster conversations and collaboration among your students. I’ll share my goal for each activity. The first three are more general activities about learning, mindset, and collaboration. They can be adapted to pretty much any course. The last two are content-based.

**I. Setting the Stage, created by Dana Ernst**

Partition your class into subsets of 3 or 4 students and ask them to discuss the five questions presented below (or, if you prefer, a subset of them), one at a time, with ample time for discussions. I have used a think-pair-share approach, in which students first think about the question, then discuss with their group mates, and then share with everyone.

- What are the goals of a university education?
- How does a person learn something new?
**What do you reasonably expect to remember from your courses in 20 years?**- What is the value of making mistakes in the learning process?
- How do we create a safe environment where risk taking is encouraged and productive failure is valued?

**Goal**: My goal in this activity is for students to convince themselves that learning math is not much different than learning to play an instrument, sports, arts, or any other human endeavor. It requires a combination of practice, guidance, collaboration, perseverance, and mindset. Questions 2, 4, and 5 have been key for my students to buy into some of the active learning activities we do throughout the semester and to set up our norms for collaboration.

Question 3 is perhaps my favorite. It gets students to reflect on their long-term goals. In fact, it gets me to think about their long-term goals. I want to share a question Michael Starbird recently asked a group of mathematicians in a workshop: **What do we expect our students to gain from our courses that will still help them 20 years from now?** Here are some possible answers: for our students *to become intellectually curious, love and enjoy learning, be resilient and persistent, consistently engage in creative problem solving, increase how long they are willing to think about a problem, improve how they work with others, learn from mistakes, and understand simple things deeply. *

Wouldn’t it be great if we can model learning in a way that students can achieve these goals? They would live a richer life and potentially become life-long learners. I think, at the very least, we should try!

**II. The Marshmallow Challenge, originally presented by Dennis Boyle**

Divide students in groups of 3 or 4. The idea of this challenge is simple: build the tallest free-standing structure in 18 minutes using 20 sticks of spaghetti, a pair of scissors, 1 yard of tape, 1 yard of string, and 1 marshmallow. I forgot a detail: build the tallest free-standing structure with the (full) marshmallow on top! (I’ve had students break the marshmallow and use it as glue). Sounds simple? Try it :-). Oh, Kinder-garteners do better than CEOs!

**Goal**: My goal in this activity is for students to face a difficult (yet fun and approachable) challenge while interacting with each other. I love how conversations happen instantly. It works great as an ice-breaker. The challenge is simple enough that they get started quickly but complicated enough that’s actually hard to complete it. The only negative I find is that it takes too long to combine both the Marshmallow Challenge followed by Setting the Stage. In the past, I have complemented it with a shorten version of Setting the Stage.

**III. Video Reflections**

This is perhaps a first homework rather than a first day of class activity but it still makes the list. In the past, I have asked students to watch videos and reflect on them. Here are my favorites:

**Jo Boaler‘s (and her students’) Four Boosting Messages video.**I ask the students to mention the four boosting message mentioned in the video and reflect on them (e.g. Do you agree/disagree with them? Why?).

**Goal**: My goal is simple here, for students to hear about math education research and reflect on the following four messages Jo and her students share in the video: there is no such thing as a “math person” as any person can learn math at a high level, having a growth mindset is helpful in the learning process, struggles and mistakes are really important, and speed is not important when it comes to learning math.**Neuroplasticity**: There are two short videos I like: Growing your Mind (Khan Academy) and Neuroplasticity (Sentis). I then ask: What are your thoughts about neuroplasticity? Had you heard about it before? How is it related to the process of struggling while learning new mathematics?

**Goal**: Similar to the previous one, my goal is simply for students to realize that there is research out there on how our brain works and to be informed about and in charge of their own learning experience.**Carol Dweck‘s work on Growth Mindset**: I like The Power of Belief video by Eduardo Briceno. I ask students to reflect about the video and answer two questions:

[After watching the video once, stop at 1:57] What are your initial reactions to the phrase: “*The moment we believe that success is determined by an ingrained level of ability, we will be brittle in the face of adversity.*” by Josh Waitzkin.

[Stop at 5:36] Discuss differences in growth mindset and fixed mindset by answering the following three questions: What do people with fixed mindsets focus on the most? How do both mindsets view effort? How do both mindsets view obstacles?**Brené Brown‘s work on vulnerability**: I have not actually assigned any video on this topic, mainly because it was not until early this summer that I became aware of Brené’s work. The key arguments I take from Brené’s work are summarized by two of her quotes: “Vulnerability is the birthplace of innovation, creativity, and change” and “Learning is inherently vulnerable. No vulnerability, no learning.” When we ask students to share their opinion, comment on a problem, present a solution, we are asking them to be vulnerable. Brené does an excellent job at presenting a case of why it’s to our benefit to be vulnerable.

**IV. Model Usain Bolt’s Performance [Calculus 1]**

Divide students in groups of 3 or 4 and show a clip of Usain Bolt running a 100 meter dash. Then ask the students to estimate the position, velocity, and acceleration functions of Usain Bolt during the 10 seconds it usually takes him to complete the dash. I’m sure many people have done activities like this one before, but this particular version I got from Steven Strogatz‘s new Infinite Powers book and his Quanta article.

**Goal**: My goal here is twofold. I love to have students interact and get active on the first day and this activity accomplishes that. The second goal is for students to play with the concept of functions, modeling, derivatives (through velocity and acceleration) and their connections, and to test their models against their intuition and the reality of Usain’s race.

**V. Maximize… on the First Day of Classes [Calculus 1] by Roberto Soto**

Divide students in groups of 3 or 4 and ask them to help their company design a box with maximum volume given the following constraints:

- The box must be made from the following material – an 8.5” by 8.5” piece of cardboard.
- To create the box, you are asked to cut the same size square from each corner of the 8.5” by 8.5” piece of cardboard and to fold the remaining cardboard as in Figure 1.

**Goal**: The goal of this activity, much like the previous one is to establish a culture of collaboration, including norms, establish the role of functions in our world and the many ways that we can analyze them without calculus, and establish the fact that we need to do the work – just seeing a professor solve a problem is not enough. Later in the semester, we will see how to solve the problem using Calculus tools.

In fact, Roberto spices up the activity by assigning roles to students. There are four roles: Interrogator (allowed to ask the professor), Investigator (allowed to visit other groups), Reporter (responsible for sharing the group’s work), and Crew (responsible for handling tools for the activity… like actual cardboard and scissors).

I haven’t tried this activity but am excited to try it soon! First, it accomplishes the goals of collaboration, modeling, and hands-on approach. It’s nice one can come back to the problem later in the semester when discussing optimization. I’ll try it this Fall…

**Final Thoughts**

- In my experience, getting students to talk to each other from day 1 is the best way to avoid the awkwardness of asking them to work together midway through the semester when they have not done it before. Once you set an expectation and consistently apply it, it then becomes the norm.
- I have found that these messages get forgotten if they are only discussed or practiced during the first day of class. Francis Su (Five reflective exam questions that will make you excited about grading) and Ben Braun (The Secret Question, Mathematical Cultures Beyond the Classroom) have written great articles that might get you to think about other ways to continue this conversation throughout the semester and why should we do it. In particular, I hope these readings can spark new ideas in you that may better fit your own courses.
- Alex McAllister uses a few other videos I like: Grit: the power of passion and perseverance, How to escape education’s death valley and Mental Toughness: Think Differently about your World.
- Want more content-based activities? Here are some activities my academic brother Tom Edgar has tried in his classes: Puzzles for an intro to proof class; counting problems for a combinatorics class; other content-related questions for abstract algebra, linear algebra, and discrete math. Games like SET and Spinpossible (Danna Ernst’s IBL Algebra book has an activity with it) are fun ways to introduce initial important concepts in algebra (e.g. operations on a set, associativity, commutativity, inverses, etc).
- Jo Boaler recently published a document (with cartoons from Ben Orlin) about “What does it mean to be great at maths?“

What are some of the first day activities you do? Please share them with me (alexander.diaz-lopez@villanova.edu). I hope to write a follow up post if I get enough submissions; but one way or another I will share with everyone the ones I receive.