Energy and Momentum Conceptual Survey

• Energy and Momentum Conceptual Survey is a diagnostic instrument that evaluates undergraduate grasp of core physics principles via scenario-based, multiple-choice items.
• The survey targets fundamental areas like scalar/vector distinctions, conservation laws, and multi-step processes, using distractors rooted in common student misconceptions.
• Empirical studies using the EMCS reveal persistent conceptual gaps and suggest integrative teaching strategies to enhance students' physical reasoning.

The Energy and Momentum Conceptual Survey (EMCS) is a research-based diagnostic instrument developed to probe the conceptual understanding of key physics principles—specifically energy and momentum—among undergraduate students at both introductory and advanced levels. The EMCS synthesizes insights from physics education research (PER) to construct multiple-choice items that reveal specific alternative conceptions and systemic challenges in learning foundational physics. Since its introduction, the EMCS has been the primary focus of several empirical studies, which collectively establish its reliability, delineate persistent student difficulties, and elucidate limitations of conventional instructional paradigms in fostering robust conceptual understanding.

1. Survey Design: Structure, Content, and Blueprint

The EMCS comprises 25 multiple-choice items targeting the conceptual domains of energy and momentum, specifically as addressed in introductory physics curricula for science and engineering majors (Singh et al., 2016, Singh et al., 2016, Brundage et al., 2023). Each item is scenario-based and accompanied by four well-researched distractors constructed from empirical analyses of common student misconceptions.

The surveyed principles include:

• The work–energy theorem, mechanical energy conservation, gravitational and frictional work.
• Linear momentum definition and conservation (elastic/inelastic collisions), impulse–momentum theorem.
• Application of energy and momentum conservation in multi-step processes (e.g., ballistic pendulum, projectile collisions).
• Distinctions between scalar and vector quantities (e.g., recognition that work and energy are scalars; momentum is a vector).
• Application and interpretation of key formulas:
  • Kinetic energy: $K = \frac{1}{2} m v^2$
  • Gravitational potential energy: $U = m g h$
  • Linear momentum: $p = m v$
  • Work–energy theorem: $W = \Delta K$
  • Impulse–momentum theorem: $F \Delta t = \Delta p$
  • Conservation of mechanical energy: $K + U = \mathrm{constant}$
  • (Singh et al., 2016, Brundage et al., 2023).

The survey blueprint ensures that questions span a range of cognitive complexities (recall, interpretation, application) and avoids less relevant topics (e.g., center-of-mass frame analysis, harmonic motion). Item development integrates free-response student data and in-depth interviews, ensuring that distractors correspond closely to observed conceptual confusions (Singh et al., 2016, Singh et al., 2016).

2. Major Empirical Findings: Student Performance and Alternate Conceptions

Comprehensive administrations of the EMCS to populations exceeding 3,000 students consistently reveal limited conceptual grasp of energy and momentum principles. Key results include:

• Post-instructional average scores for introductory courses cluster around 49–51%; normalized gains are modest (overall $g \sim 0.25$), with upper quartile students achieving $g \sim 0.45$ and lower quartile $g \sim 0.16$ (Singh et al., 2016).
• Upper-level (advanced) undergraduates display only marginally higher correct response rates on the most challenging items: for every item in which introductory post-test success was below 50%, fewer than two-thirds of upper-level students selected the correct answer post-instruction (Brundage et al., 2023).
• Persistent alternate conceptions include:
  • Misapplication of scalar and vector distinctions (e.g., attributing direction to energy or treating momentum as a scalar).
  • Confusion between the work performed by different forces and the total work, especially regarding path independence for gravitational work.
  • Erroneous beliefs in mass dependence of speed at the base of frictionless slides or after projectile flight, contrary to energy conservation (Singh et al., 2016).
  • Inability to select the correct “system” for applying conservation laws in collisions; misattribution of conservation principles to individual rather than composite systems.
  • Difficulty integrating energy and momentum concepts in two-stage processes (e.g., the ballistic pendulum).
  • Frequent reliance on surface features of problems (e.g., slide angle, object shape), impeding recognition of deep invariants like vertical displacement (Singh et al., 2016).

The table below summarizes recurring misconceptions:

Survey Topic	Typical Misconception	Context/Item
Scalars vs. Vectors	Assigns direction to kinetic energy	Items 1, 22
Work by Gravity	Belief that path alters work done by gravity	Items 6, 15
Mass Dependence	Speed at bottom increases with mass	Items 15, 22
Collision Physics	Individual, not system, momentum conserved	Items 3, 11, 16
Impulse–Momentum	Confuses time interval with impulse concept	Items 19, 23

Fragmented, context-dependent reasoning patterns are systematically observed in both written and oral responses—even after standard instruction.

3. Progression with Instruction: Persistence of Conceptual Difficulties

Longitudinal studies using the EMCS pre- and post-instruction demonstrate only moderate improvements in deep conceptual understanding (Brundage et al., 2023). Problematic items that challenge introductory students persist into advanced undergraduate paper. Notably, algorithmic quantitative proficiency does not predict functional grasp of underlying concepts: upper-level students can calculate but often fail to articulate correct reasoning when confronted with novel or conceptual scenarios (Brundage et al., 2023). This suggests that traditional, lecture-based instructional paradigms are insufficient for fostering conceptual transfer or for dislodging entrenched alternate conceptions.

Furthermore, challenging items on invariance of work, proper application of conservation principles, or integration of energy and momentum in multi-step processes remain barriers to conceptual mastery:

• On EMCS items requiring distinction between energy and momentum conservation, upper-level students frequently focus on memorized patterns rather than real physical reasoning.
• Upper-level improvement (normalized gain $\sim 0.14$) is lower than that seen in the upper quartile of introductory students, indicating that progress plateaus with conventional instruction (Brundage et al., 2023).

4. Development Methodology, Validation, and Reliability

The EMCS development combined extensive item blueprinting, free-response diagnostics, and iterative pilot-testing with classical psychometric analysis (item difficulty, point biserial discrimination) to retain only items that differentiate well between levels of understanding (Singh et al., 2016, Singh et al., 2016). Faculty, postdoctoral, and instructor input provided content and face validity.

Statistical metrics:

• Reliability coefficients for the final 25-item survey are in the range 0.68–0.75 for introductory samples, exceeding 0.8 for advanced students. Pre–post correlations with final exam performance validate the instrument’s predictive utility (Singh et al., 2016).
• Think-aloud interviews further corroborate the fidelity of distractors to actual student reasoning (Singh et al., 2016).

Recent advances include the use of LLMs (LLMs, e.g., GPT-4o) for high-throughput analysis of student written responses, enabling categorization of incorrect conceptual resources that extend beyond fixed MC distractors (Savage et al., 20 Aug 2025). Agreement between LLM and human grading is high (0–3% discrepancy, mean Cohen’s kappa $\sim 0.77$), and emergent LLM-derived categories capture deeper reasoning structures than canonical distractors.

5. Educational Implications and Recommendations

Empirical results from the EMCS strongly indicate the need for instructional approaches that promote conceptual integration rather than isolated algorithmic problem solving. The following recommendations are supported by the literature:

• Incorporate explicit scalar/vector distinctions, guided by equations (e.g., $p = m v$, $K = \frac{1}{2} m v^2$), using multiple representations (graphs, diagrams, mathematics) (Singh et al., 2016).
• Employ tasks that demand coordination of energy and momentum concepts in multi-stage processes, accompanied by explanatory reasoning rather than rote calculations (Singh et al., 2016).
• Use bar charts, qualitative diagrams, and explicit reasoning tasks that require students to articulate underlying principles behind computational steps (Brundage et al., 2023).
• Directly confront alternate conceptions through targeted tutorials, peer instruction, and prediction–observation–explanation cycles (e.g., University of Washington PER tutorials) (Singh et al., 2016).
• Leverage lessons learned from LLM-based assessment to enrich formative feedback mechanisms, moving beyond MC performance to deeper diagnosis of student conceptual resources (Savage et al., 20 Aug 2025).

Research suggests that such strategies—implemented in both introductory and advanced classrooms—can measurably improve conceptual understanding of energy and momentum.

6. Extensions, Contextualization, and Role in Physics Education Research

The EMCS occupies a pivotal role in physics education research, both as a diagnostic tool and as a source of empirical data about the efficacy of curricular interventions. Its design aligns with major PER findings that student knowledge in foundational domains is often modular, context dependent, and resistant to change absent deliberate pedagogical scaffolding (Singh et al., 2016). Recent studies leverage the EMCS at multiple curricular stages—K–12 and undergraduate—often linking findings to broader standards mappings (e.g., NGSS) and informing teacher development.

As a specific lens for the intersection of energy and momentum understanding, the EMCS continues to inform curriculum development, diagnostic assessment innovation (e.g., AI-assisted analysis), and the evaluation of instructional transformation efforts across the undergraduate physics landscape.

7. Bibliographic Table of Key EMCS Studies

Reference	Contribution	Notable Findings
(Singh et al., 2016)	Survey development, national administration	Low post-test performance, reliability metrics
(Singh et al., 2016)	Deep dive on alternate conceptions, validation	Interviews confirm MC findings
(Brundage et al., 2023)	Progression to upper undergrad, persistent challenges	Upper-level normalized gain $\sim 0.14$
(Savage et al., 20 Aug 2025)	LLM analysis of written EMCS responses	Broader categories of alt. conceptions

These core studies collectively illustrate the EMCS’s impact and the recalcitrance of foundational conceptual difficulties, reinforcing its centrality in contemporary PER methodology.