Active Learning Activities - Abra Brisbin, Math

Tragically, many students come to college with very little modeling experience. Not modeling in the sense of fashionably wearing retail clothing or modeling in the sense of painstakingly gluing tiny pieces together in order to make ostentatious little cars, but modeling in the sense of deriving mathematical equations to represent real-world phenomenon. Dr. Abra Brisbin, Department of Mathematics, utilizes an active learning teaching technique called “information search” to get her students to interact with models in a meaningful way.

Setting: Activity utilizing pod groups (5 pods with 3 students per pod), groups reporting out, and a discussion involving the whole class

Setup for the activity: Students were assigned to read two papers ("Just modeling through: A rough guide to modeling" by Michael Pidd and "It's the findings, stupid, not the assumptions" by Stephen Shugan) and write answers to three questions about the papers before class.

How the activity unfolded in the classroom: I assigned each group one of the first 5 principles of modeling discussed in Pidd's paper. They discussed their assigned principle within their pod, and used the whiteboards to write answers to the following questions: What does this principle mean? Why is it important? Give an example of applying the principle. While discussing within their pods, several groups used the computers at each table to bring up a copy of the paper to refer to.

After about 15 minutes, I asked a member of each group to explain their answers to the rest of the class. I solicited discussion on connections between the principles and students' prior knowledge by asking, "Did any of the principles surprise you?" and "How could this principle apply to the model of the wolf population we worked on last week?"

After the activity: The presentation by students and discussion were part of the activity. On a subsequent homework problem, students were asked to build a model of the number of restaurants in the United States, and write a paragraph describing how their model-building process illustrated a principle of modeling.

Additional comments from the instructor: "I was pleased that this activity got students to think about the broader context of modeling, in contrast to the specific mathematical tools for modeling that are the focus of most of the course. In the future, I would like to spend more time discussing the Shugan paper (most of the time was spent discussing the Pidd paper), and integrate additional questions throughout the term to call students' attention back to this activity."

Tip provided by Abra Brisbin

Write-up by Jon Pumper

Active Learning Activities- Ursula Whitcher, Math

While John Conway’s Game of Life (a cellular automaton) appears to be quite different from Milton Bradley’s Game of Life (a rather trite board game), there are a few prevailing similarities. For instance, both represent scenarios where there is a finite number of situations a player can occupy; both involve witnessing the overall evolution of its players; and both can be considered “zero-player” games, in the sense that Conway’s Game of Life requires no players and Milton Bradley’s Game of Life should really never have any players, especially if Klaus Teuber’s Settler’s of Catan is within easy reach. Dr. Ursula Whitcher, Department of Math, focuses less on the comparison of complex mathematical phenomenon to popular board games and more on just the mathematical phenomenon part in her active learning activity featuring John Conway’s Game of Life:

Setting: 20-minute activity implemented in a 100-level course; 6 pods with 5 students per pod

Purpose of the activity: Students explore and discuss Conway's Game of Life using the Google Easter egg, as displayed on pod computers.

Setup for the activity: Googling Conway's Game of Life produces an implementation of the cellular automaton "game."  The game can be paused and restarted.

How the activity unfolded in the classroom: Groups explore different starting configurations, trying to answer three questions:

• Can you make a pattern that stays the same for several seconds?
• Can you make a pattern that oscillates between a couple of states?
• Can you make a pattern that moves across the screen?

This activity leads into a discussion of the formal rules of the "game."

After the activity: Students use the formal rules of Conway's Game of Life on homework and exam problems.  Cellular automata are also a possible example for a final exam essay.

Additional comments from instructor: Other possible prompts to explore with this activity include:

• Can you make a pattern that disappears/dies out?
• Can you guess some of the rules of the game?

Active Learning Activities - Carolyn Otto, Math

Anyone who has struggled to communicate with another person—or even worse, witnessed another person struggling to communicate with another person—has experienced (or witnessed) the linguistic phenomenon that people relate to words in many different ways. Words such as “palette,” “illicit,” or “please go get me a cup of coffee” are constantly confused, little to the fault of any artist, bank robber, or writing intern involved. But there are some words that are so confusing that they can hardly ever be used in conversation without immediately invoking panicked faces, nervous sweating, or frantic wikepedia surfing. “Fractal” is one such word, a “natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale.” ¹ Dr. Caroyln Otto, from the Department of Mathematics, devotes an entire class period to the exploration this confusing topic, and describes the lesson plan in today’s issue of “Active Learning Activities.”

Setting: Activity utilizing pod groups (6 pods with 4-6 students per pod)

Setup for the activity: The activity involved the definition of fractals. The students didn’t have any outside information about the topic beforehand. This was introduced during class.

How the activity unfolded in the classroom: At the beginning of class, each pod was given a list of questions to discuss. These questions included what is the definition of a fractal, how would we use them, and can you give an example of a fractal. After the students turned in a written summary of their thoughts, the class watched a PBS documentary on fractals.

After the activity: After the video, their summaries were returned and the pods were asked to type up a new summary on their Pod computers. I went around to each Pod to discuss their early answers and new answers. Each Pod emailed me a new summary.

Additional comments from the instructor: “The students were engaged at all stages of this activity. There was a lot of communication between the students and myself as well as attention to the film. The students were excited about the subject and many brought that excitement to the next days of class.”

¹ See http://en.wikipedia.org/wiki/Fractal

Tip provided by Carolyn Otto

Framing provided by Jon Pumper

Active Learning Activities - Richard Spindler, Math

What do pancakes, classrooms, and The Bird have in common? They can all be flipped! Professor Richard Spindler from the Department of Mathematics speaks to his success in flipping the classroom in this active learning activity post:

Setting: Problem-solving activities utilizing pod groups (6 pods with 3-4 students per pod) and Q&A, as needed

Setup for the activity: Students were required to watch a video and read an assignment on the topic before coming to class. I then provided questions and problems they would work on together in class, and I circulated in the classroom to answer questions.

How the activity unfolded in the classroom: The students began their work together in their pod groups, discussing each problem. As they worked, they called me over with questions, and I discussed the issues either with the entire group or with the one or two students who had the question. Occasionally, if a common issue arose, I discussed it with the entire class, using the projector.

After the activity: I summarized any important points or issues that arose. After class, the students took a D2L Quiz on the topic.

Additional comments from instructor: "The students are more engaged, relaxed, and they are more likely to ask questions. In addition, the flipped nature of this activity allows me to work with them on problems as opposed to a lecture format where I would have much less time for that. From past experience, many of them typically could not do the problems independently outside of class."

Teaching Tip: Dr. Sherrie Serros on Snowball Activities

These last few gorgeous days have tempted even the most cynical Wisconsinites to believe that winter is finally over (for those that remember last year, however, cynicism might still be fully present). But if you don’t want to embrace the warmth like the myriad of college students in shorts now (it’s still only 40 degrees, people) try introducing one or both of these “snowball” activities that Dr. Sherrie Serros, Department of Mathematics, provides below:

Snowball fight:  This activity enables students to anonymously participate in a process-oriented problem and ensures 100% participation. I put a couple of different solutions on the board that provide the same answers, but structurally are very different. Students have to decide which one demonstrates valid mathematics. If I were to just openly ask the class, I wouldn’t necessarily get a lot of eager responses: student are often afraid to raise their hand and assertively declare which one is right and which one is wrong.  So instead, I have each of them take a slice of paper on which they have to write out what solution they think is correct and their reasoning behind it. Nobody else knows what they’ve written; I instruct them not to write their names on the piece of paper. Then, they crumple up the piece of paper into a little ball and throw it across the room. Students then pick up whatever “snowball” is nearest to them and they read what it says. In this way, I get to hear everyone’s thinking process and I can focus on the misconceptions present in the classroom without ever putting a single student on the spot. Additionally, when we do focus on the misconceptions, people can hear that others had the same thoughts and feel that they were not alone. Students really like this activity (who doesn’t like throwing snowballs?) and I benefit by hearing everyone’s thought-process in the classroom.

Rolling Snowball: This activity is useful when you want to generate a big idea based on a small core. My example for this comes from my education classes when I want the students to work on lesson design. I separate them into groups and start by providing them with the content of the lesson, and then have each group add an additional facet to the lesson (i.e. the diversity of learning styles, or the diversity of learning abilities, or assessment). By the time we go around the room and gather everyone’s contributions we have a big unit formed that addresses many crucial facets of lesson design. The metaphor I use for this is that of a snowball rolling down the hill because as each layer is added our lesson design becomes bigger, more fleshed-out, and more involved. 

Interview by: Jon Pumper

Active Learning Activities - Carolyn Otto, Math

The "Active Learning Activities" series will focus on what its name suggests: activities provided by our very own professors to be utilized in active learning classrooms. This post focuses on Dr. Carolyn Otto's use of "Artifacts" - visual representations and/or handheld objects" - to stimulate discussions on the different types of mathematical infinity. 

Setting: Activity utilizing pod groups (6 pods with 4-6 students per pod)

Setup for the activity: Our class was learning about different types of infinity.  In order to do this, I discussed the notion of 1-1 correspondence.  I brought in a set of plastic bags each filled with a different amount of skittles, rubber bands, and M&Ms with one paper plate.  I wrote a power point on the definition of 1-1 correspondence and gave them a sheet explaining what to do with the plastic bag of supplies (1 per pod).

How the activity unfolded in the classroom: Each pod completed the questions on the sheet by manipulating the objects in the bags with their hands.  They were given thought questions about how to find the needed correspondences and what that meant.

After the activity: After the activity, I went around to each pod to discuss the activity.  Then each student had to complete an assignment outside of class that recapped the activity and built on the ideas.

Additional comments from instructor: "The students worked well together to figure out the activity.  The talk in the room focused on the activity and good questions were asked.  The assignment was well received and most students received 100% on it."

For additional examples of active learning from UW Eau Claire instructors, follow this link to our website or click on the "Active Learning" tag located on the right side of the blog.

Tip provided by Carolyn Otto