Amy Hogan is an AP Stats teacher and math team coach at Brooklyn Technical High School, a specialized public high school in New York City. Amy is an AP Exam reader, a three-time recipient of the Math for America Master Teacher fellowship, and a member of the ASA/NCTM Joint Committee on K-12 Education in Statistics and Probability. You can read her blog A Little Stats and find her on twitter as @alittlestats.

When the pandemic first hit, my students were forced to finish the year in emergency remote instruction with very little synchronous interaction with me. My school and many others had not anticipated the extended length of the lockdown and or how strange and challenging learning remotely would be for everyone. My statistics colleagues and I went from not wanting to give a final at the end of the school year (because hadn’t these children been through enough already!) to wanting a final that would have some options for curriculum content and some reflective writing.

We wanted the final to allow for creativity, flexibility, and be a loving way to give our students closure to a year that no doubt they would someday tell their grandchildren about. We were deeply inspired by Francis Su’s lovely post: “7 Exam Questions for a Pandemic (or any other time)” and I highly encourage you to read it if you haven’t done so already. In the end, we came up with a final we felt would help students demonstrate some content knowledge and reflect on a year of learning.

Here I’ll outline the general structure and format of the final, with some edits to what I would do now.

## Part I: Content

Give students a choice of how they want to demonstrate their content knowledge. We gave students three options and they had to choose one.

Write an original problem and then show the solution. Create an original scenario, statistical question, and complete solution for which you can demonstrate your understanding of either a two-proportion z-test, chi-square test of independence, or a two-sample t-test. [Want to add a fun twist? Give them a specific total sample size and/or interval for their resulting p-value.] For more ideas here, check out the Stats Medic post about the student created inference exam.

Explore some regression analysis of a data set. Create a scatterplot, describe the relationship, generate the linear model, interpret the values, assess the model, maybe even some regression inference. Voila! I like the Census at School random sampler for this, although beware the resulting data is messy and you may need to assist students with some data cleaning.

Explore a topic slightly beyond the curriculum. Some ideas: a bootstrap confidence interval for a median (à la Emma’s Apartments #6), ANOVA, or multivariable regression. If needed, again, give students a dataset from which they will randomly sample.

## Part II: Reflection

We gave students a list of possible topics and had them choose one or two. Here’s where we really channel our inner Francis Su.

Pick a recent artifact: an article, graph, quote, etc. Explain how this course influenced the way you understand, interpret, or have a new perspective about your chosen artifact with regards to statistics.

We have emphasized the importance of productive struggle in statistics – that it’s normal and part of the learning process. Describe a specific instance in this course where you struggled with a problem or concept, and initially had the wrong idea, but then later realized your error. In this instance, in what ways was the struggle or mistake valuable to your eventual understanding?

Choose any career, perhaps one in which you are potentially interested. Research how statistics training would help in that career and give one specific example of how a person in that career might utilize statistics to do their work.

Consider one statistical idea from the course you have found beautiful and explain why it is beautiful to you. Explain in a way that could be understood by a classmate who has not yet taken this class and address how this beauty is similar to or different from other commonly-believed objects of beauty and/or from other mathematics.

What is one of the big ideas from this course? State the idea, define it using appropriate terminology, and relate it to your prior understanding of statistics. How has your understanding of statistics changed because of it?

Create an original cartoon or meme that utilizes a specific statistics topic or fact you learned in this course.

What statistical ideas are you curious to know more about as a result of taking this class? Give one specific topic from the curriculum you'd like to explore further, and describe why this is interesting to you.

## How to Grade This Exam

As for grading, I would recommend creating a holistic rubric with components you’d like to see for an ideal response to each question. Students get a base score for turning in a complete response to the assignment, let’s say, and then additions for each question based on the rubric. For example, if you’d like to see two components in a particular response, it’s easy to award full credit if both are present, half if one is present, and 0 if none are present in the student’s response. Or if the response is a reflection – full credit if the response is done well, partial credit if done but not as well, and no credit if not done at all. Having a rubric (much like the AP Statistics exam but with less specifics) will make it more straightforward to score unique responses based on what is present and what is missing from the response.

Take both parts or just one part for a final. I like leaving some room for student creativity and interpretation. By all means, if there are things your students would want to do that don’t fall under the above… I think it would be nice to also add a ‘design your own’ option. If you choose to use both parts, you can also decide how you want to weight them. You can weight the content more, the same, or less than the reflection based on your needs and intent.

I feel our final exam that year accomplished our goals. Students were highly engaged with this assignment, and I felt they were able to demonstrate a lot about their learning and understanding with this format. We allowed for student input, gave some appropriately challenging prompts, and encouraged our students to inject their personalities in their work. Although grading it took some time, reading the submissions was more joyous than any final I’ve ever given. For these reasons, I would absolutely give an exam like this again. Overall, I feel this structure for a statistics final exam humanizes our students, highlights virtues and learning as a journey rather than just skills.

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