Lessons from pendulums: A design comparison of three lab activities

This paper compares three pendulum lab designs to demonstrate how differing institutional expectations, ancillary goals, and interpretations of shared theoretical commitments can lead to divergent curriculum choices, thereby highlighting the complex relationship between theory, goals, and design while advocating for transparent reasoning and responsive adaptation.

The Gist

Imagine three different chefs, all working in different kitchens, who have decided to teach a cooking class with the exact same goal: to stop students from just following a recipe and start teaching them how to actually be chefs.

They all agree that the old way of teaching (where the teacher says, "Chop this onion, stir that pot, and you will get the perfect soup") is boring and doesn't teach real cooking skills. They want their students to figure things out, make mistakes, and learn how to taste and adjust the food themselves.

But here's the twist: Even though they all want the same result, they designed their classes very differently.

This paper is like a behind-the-scenes documentary where these three chefs (physicists from Cornell, Tufts, and the University of Washington Bothell) sit down to explain why they made the choices they did. They all use the same "philosophy" (a resource-based view of learning), but their "recipes" for the lab look nothing alike.

Here is the breakdown of their three different approaches, using simple analogies:

1. The Cornell Chef: "The Detective Game"

The Setup: The Cornell team hands the students a "suspect" (a famous physics equation that says a pendulum's swing time shouldn't change based on how wide it swings).
The Strategy: They tell the students, "Here is the rule. Now, go test it. We bet you'll find a clue that the rule is actually wrong."
The Metaphor: It's like a mystery novel. The students are detectives. They are given a specific theory to investigate. The goal is to find the "plot hole" where the theory doesn't match reality.

• Why they did it: They think students need a clear target to aim at. By giving them a rule to break, the students naturally start asking, "Wait, why isn't this working?" This forces them to use tools (like statistics) to prove their point.
• The Guide: They give the students a very detailed map (instructions) on how to set up the experiment, but the destination (the conclusion) is up to them.

2. The Tufts Chef: "The Wild West"

The Setup: The Tufts team hands the students a blank piece of paper and says, "Figure out how to measure a swinging weight. Oh, and by the way, Galileo (a famous scientist) said it doesn't matter how wide the swing is. Do you believe him?"
The Strategy: They give almost no instructions. No recipe, no map, no specific steps.
The Metaphor: It's like survival camping. The students are dropped in the woods with a goal. They have to build their own shelter, find their own water, and decide what tools to use.

• Why they did it: They believe that if you give students a list of steps, they will just "do school" (follow orders without thinking). By removing the steps, they force students to feel a little uncomfortable and confused. They believe that wrestling with that confusion is where the real learning happens.
• The Guide: The teachers (TAs) act like camp counselors who don't give answers but ask, "What are you thinking?" and "How does that make sense to you?"

3. The UWB Chef: "The Community Workshop"

The Setup: The UWB team starts with a neutral question: "Does the swing width change the time?" They don't mention Galileo or any specific equation at first.
The Strategy: They give students some tools and a scaffold, but they focus heavily on the process of working together.
The Metaphor: It's like a community garden. Everyone has a plot, but they have to agree on how to water the plants, how to measure the growth, and how to decide if the plants are healthy.

• Why they did it: They want to build a culture where science is something people do together. They give students specific tools (like making a histogram chart) to help them organize their thoughts, but they let the students decide what those charts mean.
• The Guide: They provide a "team agreement" so students know how to work together, and they slowly remove the training wheels as the semester goes on.

The Big Reveal: Why the Differences?

The authors realized that even though they all believe in the same "theory" of learning, their designs differ because of three main things:

1. Who the Students Are:

   • At Cornell and Tufts, the students are likely to have heard of Galileo or the physics equations before. So, the teachers use that knowledge to create a conflict (a "productive failure") to shake up their thinking.
   • At UWB, the students might not know those things yet. So, the teachers start neutral to let the students build the facts from scratch.

2. The "Safety" vs. "Struggle" Trade-off:

   • The Cornell and UWB teachers worry that if they give no instructions, students will feel lost, frustrated, and quit. So, they give enough structure to keep students moving forward.
   • The Tufts teacher believes that feeling lost is actually a good thing! He thinks struggling with the confusion is a vital skill (called "meta-affective learning") that helps students become resilient scientists.

3. The Teachers' Role:

   • At Cornell and UWB, the instructions are so detailed that even a new teacher can run the class perfectly.
   • At Tufts, the instructions are so minimal that the teacher must be an expert at reading the room and adapting on the fly. It puts a huge responsibility on the teacher to guide the students through the confusion.

The Takeaway

The main lesson of this paper is that there is no single "perfect" way to teach.

Just because two teachers believe in the same educational theory doesn't mean they will design the same class. Their choices depend on their specific students, their specific goals, and how much they are willing to let students struggle.

The authors argue that instead of just copying a "best practice" lab, teachers should understand the reasoning behind the design. If you know why a teacher gave a specific instruction (or didn't), you can adapt it better to your own classroom.

In short: Good teaching isn't about having the same recipe; it's about understanding why you chose your ingredients and how to adjust them for the people you are feeding.

Technical Summary

1. Problem Statement

Physics Education Research (PER) has long established that traditional "cookbook" laboratory activities (which verify known results via prescriptive instructions) often fail to foster genuine scientific inquiry or epistemic agency. While researchers agree on the theoretical goal of shifting students from "doing school" (following instructions to get a grade) to "doing science" (constructing knowledge through empirical study), there is a gap in understanding how theoretical commitments translate into specific curriculum designs.

Existing literature (e.g., Boudreaux & Elby) has shown that different theoretical frameworks lead to different designs. However, this paper addresses a more nuanced problem: How can designers with the same theoretical perspective (a resource-based view of student knowledge) and similar goals (promoting epistemic agency) arrive at significantly different curriculum designs? The authors seek to uncover the "hidden decisions" and "pedagogical judgments" that drive these divergences.

2. Methodology

The authors employ a comparative case study of three pendulum laboratory activities implemented at three distinct institutions:

• Cornell University: A large, private research university.
• Tufts University: A small, private research university.
• University of Washington Bothell (UWB): A small campus of a large public research university.

Data Sources:

• Curriculum Analysis: The authors analyzed the instructional materials (lab manuals, prompts, assessment rubrics) for the pendulum labs at all three sites.
• Reflective Inquiry: The authors engaged in a collaborative self-study to articulate their own design reasoning, moving beyond surface-level descriptions to examine the underlying "working models" of students and the trade-offs they made.
• Contextual Review: They examined institutional constraints, including class size, instructor type (Graduate TAs vs. Professors), course structure (stand-alone vs. lecture-linked), and student demographics.

Theoretical Framework:
All authors operate under a Resource-Based Framework (specifically regarding framing and epistemic agency). They view student knowledge as composed of context-sensitive "resources" that can be activated or suppressed by instructional cues. The goal is to design labs that cue students to frame the activity as genuine inquiry rather than verification.

3. Key Contributions

The paper makes three primary contributions to the field of PER and curriculum design:

1. Identification of Design Divergence Drivers: The authors identify three specific factors that cause curriculum divergence even among designers with aligned theoretical goals:

   • Institutional Expectations of Students: Differences in what designers believe students already know (e.g., familiarity with Galileo or harmonic oscillator equations) and their affective states (e.g., tolerance for confusion).
   • Ancillary Pedagogical Goals: Secondary goals such as TA training (Tufts) vs. standardized implementation (Cornell/UWB) or specific statistical skill acquisition.
   • Nuanced Interpretations of Theory: Different interpretations of how to handle "productive failure" and student "doing school" behaviors (e.g., using instructions to scaffold vs. removing instructions to force agency).

2. The Concept of "Design Reasoning": The authors propose a shift in how curriculum is described in research. Instead of just listing design decisions (what was chosen), they argue for foregrounding design reasoning (the why and the trade-offs involved). This includes making explicit the "agentive trade-offs" (autonomy vs. support) and "affective trade-offs" (frustration vs. safety) inherent in the design.

3. Operationalization of Epistemic Agency: The paper provides concrete examples of how the abstract concept of "epistemic agency" is operationalized differently across contexts, ranging from highly structured "invention" activities to minimal instruction requiring TA responsiveness.

4. Results: The Three Lab Designs

The study details three distinct implementations of the pendulum lab:

| Feature | Cornell (Thinking Critically in Physics) | UWB (Adapted Thinking Critically) | Tufts (Minimalist Approach) |
| :--- | :--- | :--- | : |
| Task Presentation | Model-Testing: Students are given the simple harmonic oscillator equation ($T = 2\pi\sqrt{L/g}$) and asked to test it. The goal is to encounter a discrepancy between the model and data. | Neutral Inquiry: The prompt is neutral: "Does the period depend on amplitude?" No external authority or model is cited initially. | Authority-Testing: The prompt cites Galileo's claim that period is independent of amplitude. The goal is to test this specific authority. |
| Written Guidance | High Detail: Instructions include specific tasks (e.g., "make a histogram," "calculate $t'$"), guiding students through statistical tools to find the discrepancy. | High Detail: Similar to Cornell, with specific scaffolding for histograms and statistical comparison ($t'$ statistic). | Minimal: Instructions are half a page long. No specific statistical methods or data visualization forms are prescribed. |
| Statistical Focus | Explicit instruction on using the $t'$ statistic to distinguish data sets. | Explicit instruction on $t'$ and data visualization. | No canonical statistics taught; students must invent ways to quantify uncertainty. |
| Instructor Role | Graduate TAs follow detailed scripts to ensure consistency across sections. | Professors have autonomy to adapt examples but follow the core structure. | TAs (Grad/Undergrad) are the primary agents of instruction, responsible for interpreting student confusion and guiding without scripts. |
| Pedagogical Logic | Scaffolded Agency: Use instructions to guide students into productive scientific practices, gradually reducing support. | Community Construction: Emphasize that science is a community effort; use instructions to build shared norms. | Meta-Affective Learning: Force students to manage uncertainty and "not knowing" to develop resilience and self-directed inquiry. |

Key Finding: Despite these structural differences, all three designs successfully shifted students away from purely "doing school" behaviors, though the path and student experience of that shift varied significantly.

5. Significance and Implications

• For Curriculum Designers: The paper argues that there is no single "correct" way to implement research-based curricula. Designers must explicitly articulate their design reasoning—including their assumptions about student capabilities, affective needs, and institutional constraints—to make their curricula adaptable and generative for others.
• For Instructors: Understanding the reasoning behind a curriculum (rather than just the steps) allows instructors to make responsive adaptations. For example, knowing why a prompt mentions Galileo (to set up a conflict with authority) helps an instructor handle student confusion differently than if the prompt were neutral.
• For PER Scholarship: The paper calls for a move away from purely empirical descriptions of "what works" toward theory-laden design reasoning. It suggests that future research should explicitly map the trade-offs (e.g., autonomy vs. frustration) that designers make, providing "instructionally generative fodder" for the broader community.
• TA Training: The Tufts model highlights that minimal written guidance places a heavy burden on Teaching Assistants, necessitating robust TA training and responsive teaching practices, whereas detailed scripts (Cornell) can standardize implementation but may limit instructor flexibility.

In conclusion, the paper demonstrates that curriculum design is a complex negotiation between theory, context, and human factors. By exposing the reasoning behind their divergent designs, the authors provide a roadmap for creating and adapting physics laboratory curricula that are both theoretically sound and contextually responsive.