*Contributing author Catherine Case is a lecturer at the University of Georgia and the lesson plan editor for Statistics Teacher.*

This post is really inspired by a plenary talk given by Jim Stigler at USCOTS 2015. He’s a psychologist at UCLA, and in his USCOTS talk, he emphasized the idea of productive struggle. He talked about different teaching cultures around the world, and how American classrooms often feature “quick and snappy” lessons as opposed to “slow and sticky” lessons, despite the fact that making the process of learning harder can actually lead to deeper, longer-lasting understanding.

His ideas really challenged me, because I often teach fairly large classes (120 – 140 students per section), and nowhere is “quick and snappy” more highly valued than in a large lecture. There’s definitely tension in large classes between efficiency and productive struggle.

Efficiency | Productive Struggle |

Statistical questions are clearly defined in the textbook. | Students carry out the full problem-solving process. |

Teacher solves all problems (correctly and on the first try). | Students wrestle with concepts before strategies are directly taught. |

Students use formulas and probability tables proficiently. | Students use appropriate data analysis tools. |

At first, this tension was overwhelming to me. In the stat ed community, we’re surrounded with inspiring, innovative ideas, but the gap between where we are and where we want to be can be paralyzing. To counter that, let’s start small with a simple classroom activity that allows students to struggle through the statistical process. Along the way, I’ll mention tricks that make it easier to pull off, even with lots of students in the room.

**Example: A Survey of the Class**

**Formulate Questions**

This activity is great for the beginning of the semester, because it only requires knowledge of a few statistical terms – statistical vs. survey questions, explanatory vs. response variables, categorical vs. quantitative variables. It also challenges students’ expectations about what’s required of them in a large lecture class, because right off the bat, they’re being asked to collaborate and communicate their statistical ideas.

- First, students work in groups to write a statistical question about the relationship between two variables that can be answered based on a class survey. Then they pass their card to another group.
- After receiving another group’s card, students break down the statistical question into variables. Which is the explanatory variable and which is the response? Are these variables categorical or quantitative? Then they pass their card to another group.
- Students write appropriate survey questions that could be used to collect data – one survey question per variable.

I’ll admit that in many of my lessons, I have a well-defined statistical question in mind before class even starts. This activity is different, because students experience the messy process of formulating a statistical question and operationalizing it for a survey.

**Collect Data**

Before the next class period, I read their work (or at least a “random sample” of their work ☺) and I try to close the feedback loop by discussing common issues that I noticed. Do some questions go beyond the scope of a class survey? Are certain kinds of variables commonly misclassified? How can we improve ambiguous survey questions? Even though my class is too large to talk to every student individually, this gives me an opportunity to respond to and challenge student thinking.

Later we can use student-written questions as the starting point for data collection and analysis. I usually choose 10-15 survey questions (ideally relevant to more than one statistical question), and collect their data via Google Forms. When students answer open-ended questions like, “How many hours do you spend studying in a typical week,” it generates data that’s messy but manageable. It feels more authentic than squeaky clean textbook data, plus the struggle of cleaning a few hundred observations by hand may help students understand the need for better data cleaning methods.

**Analyzing Data Using Appropriate Tools**

“Appropriate tools” certainly aren’t one-size fits all, but for this activity, I need a tool that…

- Can handle large(ish) datasets
- Is accessible for students – preferably free!
- Makes it easy to construct graphs and calculate summary statistics

At UGA, we have a site license that makes JMP free for students, and many regularly bring their laptops to class, so JMP works well for us with students working in pairs. If I didn’t have access to JMP, I might consider CODAP, which looks a lot like Fathom (friendly drag and drop interface!) except it’s free and runs in a web browser.

Speaking of a friendly interface, another hurdle in a large class is how to trouble-shoot technology for students, especially if you don’t have smaller “lab” sections or TA support during class. For me, it’s a delicate balance of scaffolding and classroom culture…

After demonstrating how to construct graphs and calculate summaries using software, I assign some straightforward data analysis questions with right/wrong answers. For this, I use an app called Socrative, which works similarly to clickers, except that it allows for both multiple choice and free response questions. Socrative allows me to give immediate feedback – for example, if they miss a question, I can provide them with the software instructions they need. In addition to feedback through Socrative, I try to normalize the process of struggling with new technology and encourage them to help each other. I remind them it’s impossible for me to help everyone individually, but I’m confident they can work together and solve most problems without me. Students generally rise to the challenge and accept that there are multiple sources of knowledge in the room.

Once I’m confident students know how to use the necessary data analysis tools, we can try more challenging, open-ended questions. For example, I may choose a response variable and ask students to explore the data until they find a variable that’s a good predictor, then write a few sentences about that relationship. They need to use graphs and calculate statistics to answer this, but I’m not explicitly telling them which graphs and statistics to use, and I’m certainly not giving them “point here, click here” style instructions. There’s a little productive struggle involved!

**Interpret Results in Context**

In the following class, I present student analyses as a starting point for our interpretations. They already have a foundation for discussing effect sizes and strength of evidence, because they’ve considered the relationships among variables themselves. Students can offer deep insights about the limitations of the analysis (e.g., sampling issues, measurement issues, correlation vs. causation), because they’ve been involved with the investigation at every stage.

**Look Back and Ahead**

The authors of the ISI curriculum (Tintle, et al.) include “look back and ahead” as the final step of the statistical process. At this step, students consider limitations of the study and propose future work.

This concept is really helpful in my teaching too. Earlier I mentioned students’ expectations, but I’m also working on managing my own expectations. I can’t let the idea of a perfect active learning class keep me from taking steps in the right direction. I don’t have to change everything in one semester and I can’t expect every activity I try will work. The best I can do is to make a few small changes right now, keep a journal to learn from my experiences, and keep moving forward.