To what extent should humans rely on hidden statistical methodologies to make decisions on where they or their children go to college? When does methodology become mythology in college selectivity? And, where do we see our deep-seated biases reflected in our use of mathematics, and what should we do about it?
Malcolm Gladwell wrestles with some of these questions in the sixth season of his podcast Revisionist History, and they are wonderful cues for students to tackle in statistics, history, and English language arts classes.
Or, perhaps we should ask how we should best prevent invasive species from spreading? To what extent can we prevent malaria-carrying mosquitoes from migrating to other regions as the world warms? How do we regulate fishing in areas that no one “owns”? Or, what is our ethical responsibility for bringing back extinct animals using technology or preventing ourselves from delving into a world of creating new living things? These are equally interesting questions that span middle and high school classrooms.
If we wanted to have students go after the aforementioned questions, how should we go about doing it? One approach is to use a hexagonal-thinking strategy within a rigorous project-based learning (PBL) methodology.
One way to define rigor is the equal intensity and integration of the following levels of learning:
- surface (I know ideas or skills),
- deep (I can relate ideas and/or skills), and
- transfer ( I can apply ideas or skills in multiple contexts).
Rigorous PBL is an inquiry-based methodology that follows a distinct pathway of learning that organizes levels of rigor into a particular sequence. The process integrates all levels of learning through six steps. In this way, students experience all levels of complexity and the need to learn each level to accomplish a challenging task. The initial moment when students encounter a challenging task and build the need for surface and deep learning is called the entry event. One interesting way to do this is through hexagonal thinking.
The 6 Steps of Hexagonal thinking
Step 1: Launch. Provide a challenging context (or set of contexts) to initiate intellectual engagement for students. For instance, you may have students listen to the Revisionist History podcast on college rankings or view the introductory video of bringing back the woolly mammoth.
Step 2: Surface exploration. Provide students with a set of hexagonal shapes (e.g., a set of hexagonal sticky notes or a free electronic version) that enable them to write down key terms that are important. Share with students that one color should represent contexts (situations in which the content applies) and another color should represent the content (specific knowledge or skills that students must learn and apply to other situations). One scaffold that may be helpful to start this process is to provide students a word bank.
Step 3: Deep-level connections. This step is conducted in two parts or substeps. First, ask students to find connections between the hexagons they have labeled. Here, students should discuss (or write down) the connections between content, between contexts, and across both content and contexts. Next, have students compare and contrast their hexagonal structures and rationale for each connection with other students (or student groups).
Step 4: Transfer-level extensions. Ask students to generate additional contexts and/or content to consider in this project. This is an opportunity to prompt students to
- create analogies,
- compare contexts within and across groups,
- generate hypotheses on how their configurations will change over time, and
- draft questions they want to solve.
Step 5: Driving questions and learning goals. Have students share their thinking from step four with others as a means to identify the driving question, learning intentions, and success criteria. One way to do this is to use structured protocols (e.g., chat stations).
Perspectives (Chat 1): What are potential perspectives that emerge from this problem? What is your current “position” on this problem? What else would you want to know about this situation?
Problem (Chat 2): What do you see as potential driving questions from the connections made between different groups?
Potential Outcomes (Chat 3): What do you think we will need to learn to address these questions and to understand the connections more deeply?
Patterns and Potential Connections (Chat 4): What other contexts can you think of that connect to this work? Do you see any recurring patterns?
Step 6: Develop knows/need to knows. During this final step, students and teachers determine which driving question or set of questions they will work to answer. As a part of answering this question, teachers provide a rubric and ask students to compare and contrast their thinking of what they are learning with that of the teacher.
This is an opportunity for students to write down what they “know” from the rubric as well as what they “need to know” to meet the expectations on the rubric and address the driving question. Students then draft any next steps they will take to answer the driving question(s) and meet the learning intention(s) and success criteria. Finally, students generate hypotheses on how their hexagonal configurations will change over time.