instruction,  math in real life

Pablo Escobar’s Hippos and Levels of Inquiry

As a school, JQUS has been working over the past two years to bring inquiry-based teaching to both our International Baccalaureate (IB) Middle Years Programme (MYP) and Diploma Programme (DP) classes. The IB unit planner starts with a Statement of Inquiry (SOI) that brings together common key and related concepts to create a big idea / conceptual understanding (kind of like an essential question / enduring understanding). For example, my exponential functions unit last year was based on the SOI “Relationships show how change in population and demography connects to the impact of decision-making on humankind and the environment,” with the aim of getting students to apply exponential functions to population growth so that the math content could have a meaningful context.

Trevor MacKenzie represents how “a teacher can gradually remove scaffolds to give learners more independence” with a visual metaphor of an instructor teaching a whole class how to swim, having them swim with kickboards, having them swim in the pool, and then releasing them to swim in the ocean to represent how students move between the levels of inquiry (structured, controlled, guided, and free). Our teachers have grown more comfortable with developing SOIs and the related factual, conceptual, and debatable inquiry questions. This year, we seek to support teachers in getting comfortable with designing inquiry-based learning experiences with that gradual removal of scaffolds. The MYP Personal Project, DP Internal Assessments, and DP Extended Essay are all prime examples of free inquiry: students must design their own research questions before applying their content knowledge and demonstrating their understanding.

One of my “aha!” moments this year was realizing that I wasn’t making that progression from structured –> controlled –> guided –> free explicit or visible to my students (or myself). With the exponential functions unit I referenced above, I turned a student question into a controlled inquiry on Pablo Escobar’s hippos. I had planned to use an invasive species task from Illustrative Mathematics to support students in understanding how to solve DP exam problems. I happened to say in class “we’re going to use these functions to look at invasive snails.”

One of my students responded with “Miss, what if we looked at Pablo Escobar’s hippos?”

In my next planning period, I immediately googled “pablo escobar hippos” (thankfully not flagged for inappropriate content) and started planning a way to bring exponential functions to the rampant Colombian hippos. With this student question, I hoped to spark inquiry-based teaching that incorporates visible thinking practices, technology, and real-world connections. Inquiry challenges learners to engage with significant ideas and promotes meaning and understanding. The hippo population growth (which exploded from the original four brought over from Africa in the mid-1990’s to over 50 in December 2018) can be modeled using an exponential functions (significant math idea). The cascade of effects on the surrounding towns required the government, scientists, and many other stakeholders to explore solutions to the hippo problems (significant connections to other disciplines and to the real world).

After viewing a Vox video on the hippos and learning how to model exponential growth based on the initial population and December 2018 population, the students came up with various solutions (e.g., hippo castration, walking them to the neighboring country) and explained their understanding of the math via Flipgrid. I brought the activity to the 8th-12th grade team and had mixed groups of teachers do it too–they got very into it with solutions like Hippo Planned Parenthood or an entreaty to be humane and take the hippos back to Africa on boats.

Controlled Inquiry

The goal was to get the students to practice modeling exponential growth related to one of the themes from the World of 7 Billion Student Video Contest.

I brought the hippo inquiry to the 2019 Joyful Learning Symposium and processed my learning in a small group using the Success Analysis Protocol.


I am proud of the small successes I’ve had this year and realize now that I hadn’t made the progression between levels of inquiry visible or clearly defined the student’s role at each level. Many students struggled with putting together the math and addressing the SOI, debatable question, and Theory of Knowledge (TOK) question. However, I am inspired to keep on making improvements, starting with co-planning our whole-school beginning of year staff retreat, attending the GIBS New England Conference (where Trevor MacKenzie is giving the keynote address), and co-planning our professional development (including peer video feedback and looking at student work).

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