The Perplexity Factor

 

“Curiosity is the wick in the candle of learning.” - William Arthur Ward

Try to think about a time when you were truly baffled by something. Did it make you wonder? Were you curious? Did it make you want to try to make sense out of the situation? Or was the idea so complex that you couldn't even begin to try and comprehend it? 

Whenever I introduce a new lesson to my students, I try to provide them with a thought-provoking prompt. The purpose of this is to create a hook that is so captivating that it will sustain their curiosity and interest throughout the lesson.  In her book, Dare to Lead, Brené Brown writes, “To introduce curiosity about a particular topic, it may be necessary to ‘prime the pump’—to use intriguing information to get folks interested so they become more curious” (Brown, 2019).  This type of intriguing information can be in the form of a surprising statement, an image, a video, an audio file, or any other type of media that might serve as prompt to stimulate curiosity.  The challenge, however, is to create a prompt that has the right balance of difficulty level, relevance to the lesson, and application to students' lives. This is what I call, the perplexity factor.

In order for the prompt to be effective, the learning needs to be effortful.  Brown calls this "desirable difficulty" and makes the comparison to feeling a muscle burn when it's being strengthened.  She goes on to say that the brain needs to feel some discomfort when it's learning.  Your mind might hurt for a while—but that’s a good thing” (Brown, 2019).  On the other hand, if the difficulty of the prompt is not desirable, then students will not be interested in learning, and the prompt will be ineffective.  This usually happens when students do not find the prompt meaningful or relevant to their lives.  In the event of oversimplifying a bit, I have provided a visual to help illustrate this concept.

Ability + Difficulty + Relevance + Curiosity = Perplexity


While relevance is important, curiosity is what really inspires us to engage in a perplexing prompt.  This is because we feel an overwhelming urge to understand something that doesn't make sense to us. In fact, George Loewenstein, a professor of economics and psychology at Carnegie Mellon University, proposed that curiosity is the feeling of deprivation we experience when we identify and focus on a gap in our knowledge. This means that we have to have some level of knowledge or awareness before we can get curious (Brown, 2019).  In other words, it's like trying to find the missing piece of a puzzle.  The missing piece represents the gap in our knowledge, and the puzzle is the background knowledge that we already possess.  I don't know about you, but I would be on my hands and knees searching for that missing puzzle piece.  That is the feeling of deprivation that Loewenstein is proposing that drives us to fill the gap in our knowledge.  And this is why perplexity prompts—when done correctly—are so effective.

I first learned about this idea from Dan Meyer back in 2011 when I was teaching math and science to sixth-grade students. I was already implementing inquiry-based learning into my instruction, but I found that Dan was particularly exceptional at creating highly effective prompts. As a former high school math teacher, Meyer shares on his website that he "taught high school math to students who didn't like high school math."  Therefore, he wanted to find a way for his students to be able to meaningfully connect with his lessons in order for them to reach a deeper level of learning and understanding. But before he could do that, he needed to find a way to allure and sustain his students' interest that was both authentic and puzzling. So, with the help of a camera and a few computer applications, Dan created his own string of visual prompts, which he later published as his free and accessible curriculum, Three-Act Math.

In order to create his Three-Act Math curriculum, Dan asked himself the following questions, which he has posted on his website, Dan Meyer's Perplexity Session.

  • How do we turn the world outside the math classroom into a math problem that's both fun and challenging, not boring and easy?
  • What are three common myths about engagement and how do we counteract them?
  • How does paper distort mathematical problem solving and how can digital media correct the distortion?
  • What technology and tools are essential for designing perplexing math application problems?
  • If math is aspirin, then what is the headache and how do we create it?
  • How do you generate engaging and challenging curriculum from the math you encounter in your own life?

Dan's cleverly crafted questions enabled him to discover answers that ultimately resulted in developing his highly successful platform.  His platform launched a movement that—in my opinion—completely revolutionized not only math instruction, but instruction for all content areas.  He once shared an analogy that really resonated with me: 

"If math is basketball, let students play the game." - Dan Meyer

What Dan so brilliantly realized was that kids play the game of basketball well before they join a team where they practice drills, ball-handling, and free throws. It is only after they become interested in the game of basketball, do they fully understand the need for practice in order to improve their skills.  Meyer further claims, "Drills aren’t a basketball player’s first, only, or most prominent experience with basketball. Drills come after a student has been sufficiently enticed by the game of basketball – either by watching it or playing it on the playground – to sign up for a more dedicated commitment. If a player’s first, only, or most prominent experience with basketball is hours of free-throw and perimeter drills, she’ll quit the first day – even if she’s six foot two with a twenty-eight inch vertical and enormous potential to excel at and love the game" (Meyer, 2012).

When we think about this concept and apply it to math instruction, we begin to see some similarities.  If we present students with problem sets and formulas in math class before they even have a chance to explore the real world application of the lesson, then we have lost them before we even get started.  What we should do instead is present them with a real world scenario where they have to identify the problem, then grapple with different strategies for which they can solve the problem.  It is only after they fully understand the purpose of the lesson, will they be more receptive—and hopefully intrinsically motivated—to practice their math skills. 

The great thing about this concept, is that it can be applied to any grade level, in any content area.  As a math and science teacher, I naturally started with creating my own math prompt for my sixth-grade students.  Here is a prompt that I created and later presented to my students as an introduction to our unit on perimeter and area (See Figure 1). 
Figure 1: Pizza Pies


My hope was that students would observe the prompt, process it, and intuitively think of the question, "Which pizza pie is bigger?"  Students would then be able to use the given information of the diameter of the circular pizza, and the width of the rectangular pizza in order to calculate the area of each pie.  They would also have to realize that they need to know the length of the rectangular pizza in order to accurately calculate the area.  The perplexity factor in this example was just right.  The level of difficulty was developmentally appropriate, pretty much all students love pizza, and the lesson topic addressed the sixth-grade state and national standard of calculating perimeter and area for circles and polygons.  The best part was that I had intentionally chosen to present this prompt before introducing the area formula of a circle. This allowed students to engage in productive struggle as they grappled with finding solutions. Not surprisingly, students found this method of instruction way more engaging than the traditional word problem in Figure 2. 

Figure 2: Word Problem


I was so proud of this prompt, that I even submitted the image as an entry on Dan Meyers 101questions website.  Dan created this site to encourage people to upload their own photos and videos that they perceived to be perplexing.  Once you submitted a media file to the website, it was up to the public to determine its perplexity score.  For example, with every photo that was submitted, users would view a photo at random and choose whether they wanted to either skip the photo, or type in a response to the following question, "What's the first question that comes to your mind?" The decision on whether someone chose to skip or answer the question calculated into the photo's perplexity score.  So naturally, the more people that answered the question, the higher the photo's perplexity score.  The website even has a Top 10 category of photos and videos for both "right now" or "all time" which I still glance at from time to time. 

After I got comfortable with creating these types of prompts for math, I decided to take a slightly different approach in science.  In this example, I created a prompt to introduce a Problem-Based Learning project with my sixth-grade science students (See Figure 3).


Figure 3: Problem Based Learning Prompt


In this example, I presented my students with a real world scenario in which they had to identify the problem before they could begin working on their project.  The perplexity factor in this example was also just right—the level of difficulty was age-appropriate, the scenario involved their own school and local government, and the lesson addressed the state and national standard of renewable and nonrenewable energy sources.  For this project, I grouped my students in teams where they collaboratively identified the problem, asked meaningful questions, conducted research, and presented their solutions to an authentic audience of local scientists.  

When I began teaching technology, I used the photo in Figure 4 as a prompt to spark curiosity in my students.  The great thing about this photo is that none of my students had ever seen a photo quite like this one.  The perplexity factor for this photo was perfect.  Since this was a photo, it afforded equitable access to the content, students made a connection to operating various technology devices, and the lesson addressed the state and national standards of programming in computer science, as well as World War II in social studies.  What's more, the perplexity factor in this photo is so versatile that I even use it when I lead workshops with teachers. 


Figure 4: "ENIAC" flickr photo by thekirbster shared under a Creative Commons (BY) license

  
Spoiler-alert! This is an actual photo of the first computer programmers using the ENIAC computer during World War II.  What makes the perplexity factor so high in this photo is the fact that a) women were the world's first computer programmers and b) this story was kept a secret for such a long period of time.  I am always amazed that both children and adults find this photo to be equally fascinating whenever I use it as a prompt.

Promoting Inquiry and Exploration with Primary Resources

If you have never visited the Library of Congress, I highly recommend checking it out.  When I visited the Library of Congress back in 2012, I became inspired by reading all of the educational quotes on the walls, and seeing statues of historical figures that represent the eight categories of knowledge: philosophy, art, history, commerce, religion, science, law, and poetry. Each one of these categories is considered symbolic of civilized life and thought. 

The mission of the Library of Congress is to collect and organize America's resources and make them universally accessible and useful.  One of the ways that the Library of Congress is reaching out to teachers is by providing them with a wealth of resources and tools to supplement curriculum, instruction and assessment in the classroom.  Moreover, the Library of Congress states on its website that it offers " ... classroom materials and professional development to help teachers effectively use primary sources from the Library's vast digital collections in their teaching."

Teachers can find Library of Congress lesson plans and more that meet Common Core standards, state standards, and the standards of national organizations. However, what I find to be the most helpful is their curriculum that uses primary resources to promote inquiry and exploration.  When I visited the Library of Congress, I participated in a workshop where I learned how to implement their curriculum in the classroom. When using these primary resources, it recommends that teachers facilitate the following learning tasks:

  1. Have students identify and note details
  2. Encourage students to generate and test hypotheses about the source
  3. Have students ask questions to lead to more observations and reflection

In order to help students with this process, The Library of Congress encourages teachers and students to use the following terminology:

  • Observe:  I see ...
  • Reflect:  I think ...
  • Question:  I wonder ...

And by engaging in this workshop, I also learned that they also recommend these highly effective instructional strategies to get students interacting with the content, as well as each other:

  • Encourage students to perform this process as a Think-Pair-Share Activity
  • Encourage students to perform this process in groups with a JigSaw activity
  • Encourage students to think of a creative title that would capture the major concepts or themes of the primary source
  • Encourage students to create a short story or poem based on factual information from the primary source.

As I stated earlier, the whole purpose of using primary sources in the classroom is to promote inquiry, exploration, and research for our students.  We need to empower our students to ask their own questions that are important to them to make their learning more meaningful.  Let's help our students to craft questions that lead to further investigation, and to develop a research strategy for finding answers.


Final Thoughts

In our current education system, there are many factors that are out of our control—the who, what, when, and where of education.  We cannot change our students, our content, our schedule, nor the location of our schools. However, there are two important factors that we do have control over.  We have control over, the why and how of education.  Put simply, we have autonomy over why we teach and how we teach.

We as teachers have the opportunity to teach in a way that we believe will yield the greatest learning outcomes for our students.  And what we believe to be true about best-practice teaching will significantly impact our instructional decisions we make in the classroom.  In my experience, I have found inquiry-based learning to be the most effective strategy to engage students in the learning process.  Not only because it empowers students to become a steward of their own learning, but because it ignites a sense of inherent curiosity that will act as fuel for their learning journey.

I challenge you to continue to inspire and motivate your students.  Continue to provide them with authentic learning experiences where they have agency over their learning.  And continue to find ways to integrate perplexity into your lessons that are appropriately challenging, relevant to the lesson, and applicable to their lives.


References
  1. Brown Brené. Dare to Lead Brave Work. Tough Conversations. Whole Hearts. Ebury Digital, 2019.
  2. Meyer, Dan. “Dan Meyer's Perplexity Session.” Dan Meyer's Perplexity Session, http://perplexity.mrmeyer.com/. 
  3. Meyer, Dan. “If Math Is Basketball, Let Students Play the Game.” Dy/Dan, 10 July 2012, https://blog.mrmeyer.com/2012/if-math-is-basketball-let-students-play-the-game/. 
  4. Meyer, Dan. “About.” Dy/Dan, 19 Feb. 2018, https://blog.mrmeyer.com/about-2/.
  5. Meyer, Dan. 101questions, https://www.101qs.com/. 
  6. Meyer, Dan. “The Three Acts of a Mathematical Story.” Dy/Dan, 6 Aug. 2016, https://blog.mrmeyer.com/2011/the-three-acts-of-a-mathematical-story/. 
  7. “About This Program: Teachers: Programs: Library of Congress.” The Library of Congress, https://www.loc.gov/programs/teachers/about-this-program/

Comments