Multidimensional Profiles of Critical Thinking in Physics Labs: Latent Structure, Instructional Change, and Connections to Physics Identity

Using latent profile analysis on a large multi-institutional dataset, this study reveals that physics lab critical thinking consists of two distinct multidimensional profiles with significant instructional shifts, and identifies belonging as the primary upstream predictor of both these performance profiles and students' affective development, including recognition, self-efficacy, and agency.

The Gist

Imagine a physics lab not as a place where students just follow a recipe to get the right answer, but as a bustling kitchen where they are learning to be chefs. The goal isn't just to cook a meal; it's to learn how to taste the food, critique the recipe, and decide what to cook next.

This paper is a deep dive into how students learn to be those "chefs," and it uses some fancy statistical tools to see what's really happening under the hood. Here is the story of their findings, broken down into simple concepts.

1. The Problem with "One Big Score"

For a long time, teachers and researchers looked at a student's critical thinking like a single number on a report card. If you got an 80, you were "good"; if you got a 40, you were "bad."

But the authors argue this is like judging a musician only by their overall "musicality score." It misses the details! A student might be amazing at reading sheet music (evaluating data) but terrible at improvising a solo (proposing next steps).

The New Approach: Instead of one score, they looked at three specific skills:

1. Evaluating Data: Can you tell if the numbers make sense?
2. Evaluating Methods: Can you tell if the experiment was set up correctly?
3. Next Steps: If the experiment failed, what do you do next?

2. The "Two Teams" Discovery (Latent Profiles)

The researchers looked at over 5,500 students from many different universities. They used a method called Latent Profile Analysis, which is like sorting a giant pile of mixed-up LEGO bricks into distinct, recognizable shapes.

They found that students naturally fell into two main "teams" or profiles, both before and after the class:

• The "Struggling Team" (Profile 1): These students were shaky on all three skills. They didn't know how to check their data, they weren't sure about the methods, and they had no idea what to do next.
• The "Balanced Team" (Profile 2): These students were decent at all three things. They weren't necessarily geniuses, but they had a consistent, working approach.

The Big Twist: When the semester ended, the teams swapped members!

• About 48% of the "Struggling Team" students improved enough to join the "Balanced Team."
• But here's the surprise: About 44% of the "Balanced Team" students actually dropped back down to the "Struggling Team."

The Lesson: Critical thinking isn't a fixed trait like eye color. It's like a muscle that can grow or shrink depending on how the class is taught. The "recipe" of the class matters a lot.

3. The Emotional Engine Room (Physics Identity)

The second part of the study asked: What drives these changes? They looked at four emotional factors:

• Belonging: "Do I feel like I belong in this lab?"
• Recognition: "Do my teachers and peers see me as a capable scientist?"
• Self-Efficacy: "Do I believe I can actually do this task?"
• Agency: "Do I have the power to make my own decisions?"

They built a model to see which factor was the "boss" and which was the "follower."

The Chain Reaction

1. Belonging is the Foundation: Imagine a house. Belonging is the concrete foundation. If you don't feel like you belong in the lab, the rest of the house (confidence, recognition, skills) is shaky. The study showed that feeling like you belong first leads to feeling recognized, confident, and having a say in the work.
2. Agency and Confidence are Dance Partners: Agency (making decisions) and Self-Efficacy (confidence) helped each other, but one led the dance. When students were given the power to make decisions (Agency), their confidence (Self-Efficacy) grew. But just feeling confident didn't necessarily make them take charge.
3. Recognition is the Trophy: Recognition (being seen as a scientist) mostly came after the other factors. It was the result of feeling like you belong and having the confidence to act, rather than the thing that started the engine.

4. The Surprising "Trap"

There was one weird finding. The study found that sometimes, when students felt they had a lot of Agency (they were making lots of decisions), their critical thinking skills actually went down slightly.

The Analogy: Imagine giving a kid a car and saying, "You drive!" (High Agency). If they just drive around aimlessly without a map or a destination, they aren't actually learning to drive well. They are just busy.
The researchers suggest that being active isn't enough. You need to be active in the right way (checking data, testing models). If students are "doing" things but not thinking deeply about why, their critical thinking skills might not improve.

The Takeaway for Teachers and Students

1. Don't just grade the score: Look at how a student thinks. Are they good at data but bad at planning? Fix that specific gap.
2. Build the Foundation First: Before you can teach complex science, you must make sure students feel like they belong in the room. If they feel like outsiders, they won't engage.
3. Give Power, but with a Map: Let students make decisions (Agency), but make sure those decisions are about thinking and testing ideas, not just moving equipment around.
4. It's a Rollercoaster: Learning isn't a straight line up. Students can improve and then slip back. Teachers need to keep supporting them throughout the whole ride, not just at the start.

In short, this paper tells us that becoming a critical thinker in physics is a complex dance between what you know, how you feel, and what you are allowed to do. To get the best results, you need to nurture all three at the same time.

Technical Summary

1. Problem Statement

Physics laboratory courses are resource-intensive but often fail to produce measurable gains in critical thinking when used merely to reinforce lecture content. While the Physics Lab Inventory of Critical Thinking (PLIC) has been validated to measure three distinct components of critical thinking (evaluating data, evaluating methods, and proposing next steps), prior research has largely treated PLIC data as a unidimensional composite score.

This approach obscures the specific configurations of student competence. Furthermore, the longitudinal relationship between students' epistemic performance (critical thinking skills) and their affective identity constructs (belonging, recognition, self-efficacy, and agency) remains unexplored. The study addresses two primary gaps:

1. What are the latent profiles of critical thinking across the three PLIC scales in a large, multi-institutional dataset, and how do they shift over instruction?
2. How do these profile transitions longitudinally relate to physics identity constructs?

2. Methodology

The study utilized a large, multi-institutional dataset of 5,513 matched pre/post student records from introductory and sophomore-level physics labs across North America.

Study 1: Latent Profile Analysis (LPA)

• Goal: To identify subpopulations of students sharing similar configurations of scores across the three PLIC subscales.
• Technique: Used the flexmix package in R to model a finite mixture of unobserved subgroups.
• Model Specification: Gaussian components for "models" (data) and "actions" (next steps) subscales; multinomial component for the "methods" subscale (due to categorical scoring).
• Model Selection: Evaluated 1–4 profile solutions using AIC, BIC, ICL, and entropy. A two-profile solution was selected for both pre- and post-instruction based on fit and interpretability.
• Transition Analysis: Computed transition matrices to track student movement between profiles from pre- to post-test. Chi-square tests assessed associations with course types (Calculus-based, Algebra-based, Sophomore).

Study 2: Cross-Lagged Panel Models (CLPM)

• Goal: To examine directional relationships between PLIC profile membership and identity constructs (belonging, recognition, self-efficacy, agency).
• Technique: Used the lavaan package in R with Maximum Likelihood Estimation with Robust Standard Errors (MLR).
• Variables: Pre/post measures of the four identity constructs and the posterior probability of belonging to the "higher-knowledge" profile (Profile 2).
• Model Testing: Compared a saturated model against a trimmed model (constraining non-significant paths to zero) using chi-square difference tests.
• Invariance Testing: Conducted multigroup CLPMs to test if structural relationships differed by course type.

3. Key Results

A. Latent Profiles of Critical Thinking (Study 1)

• Profile Structure: A two-profile solution best fit the data at both timepoints.
  • Pre-Instruction:
    • Profile 1 (12.7%): Low performance on methods and next steps; moderate data evaluation.
    • Profile 2 (87.3%): Relatively uniform performance across all three components.
  • Post-Instruction:
    • Profile 1 (44.6%): Moderate, uniform performance across all components.
    • Profile 2 (55.4%): High performance specifically on data evaluation, with moderate scores on methods and next steps.
• Instructional Impact: There was substantial bidirectional movement.
  • 48.4% of students in the lower-performing pre-test profile transitioned to the higher-performing profile post-test.
  • 43.6% of students in the higher-performing pre-test profile regressed to the lower-performing profile.
• Course Type: While statistically significant, course type (Calculus vs. Algebra) had a small effect size (Cramér's V ≈ 0.10) on profile membership, suggesting broad curricular categories do not strongly dictate critical thinking configurations.

B. Longitudinal Identity Dynamics (Study 2)

The trimmed CLPM revealed the following structural relationships:

• Belonging as the Upstream Predictor: Pre-instruction belonging significantly predicted post-instruction recognition, self-efficacy, agency, and membership in the higher-knowledge profile. It is the foundational condition for other outcomes.
• Reciprocal Agency–Self-Efficacy Loop: A reciprocal but asymmetric relationship exists. The path from Agency $\to$ Self-Efficacy ($\beta = 0.136$) was significantly stronger than Self-Efficacy $\to$ Agency ($\beta = 0.038$). This suggests that taking action (agency) drives confidence (efficacy) more than confidence drives action.
• Recognition as a Downstream Construct: Recognition was predicted by belonging and agency but did not significantly predict other constructs, functioning primarily as an outcome rather than a driver within a single term.
• The Negative Agency Path: Surprisingly, pre-instruction agency negatively predicted post-inclusion in the higher-knowledge profile ($\beta = -0.084$). This effect persisted after suppression checks, suggesting that behavioral participation (agency) does not automatically equate to high-quality epistemic engagement.
• Stability: PLIC profile membership showed low autoregressive stability ($\beta = 0.102$) compared to identity constructs (e.g., belonging $\beta = 0.514$), indicating critical thinking profiles are highly malleable to instruction, whereas identity is more stable.

4. Key Contributions

1. Person-Centered Characterization: This is the first study to apply Latent Profile Analysis to PLIC data in a large, international dataset, moving beyond composite scores to reveal that critical thinking exists in distinct, multidimensional configurations.
2. Instructional Malleability: The study demonstrates that critical thinking profiles are not fixed; nearly half of students shift profiles based on instruction, highlighting the potential for pedagogical intervention.
3. Identity-Epistemic Integration: It establishes a longitudinal framework linking identity and epistemic outcomes, identifying belonging as the primary upstream driver of both identity development and critical thinking gains.
4. Nuanced Agency Findings: The discovery of a negative path between agency and epistemic profile membership challenges the assumption that "more participation" always equals "better learning," suggesting a need to distinguish between behavioral agency and epistemic agency.

5. Significance and Implications

• For Assessment: Researchers and practitioners should move away from treating critical thinking as a single continuum. Instead, they should diagnose specific configurations (e.g., strong data evaluation but weak method evaluation) to tailor instruction.
• For Instructional Design:
  • Climate First: Creating inclusive lab climates that foster belonging is a prerequisite for developing critical thinking skills.
  • Structured Agency: Labs should provide structured opportunities for student decision-making to build self-efficacy, but these activities must be explicitly designed to ensure the quality of reasoning (epistemic agency), not just the act of participation.
  • Focus on Data Evaluation: The results suggest that data evaluation (model testing) is the dimension most responsive to instruction, aligning with skills-focused lab curricula.
• Future Research: The authors recommend Latent Transition Analysis (LTA) to model transitions probabilistically and the development of measures that separate behavioral agency from epistemic agency.

In summary, the paper argues that physics lab learning is a complex interplay where social belonging enables agency, which in turn drives self-efficacy and critical thinking, but only if the agency is directed toward high-quality epistemic work.