Which mechanics research-based assessment should I use in my class?

posted April 10, 2021 and revised September 28, 2021
by Adrian Madsen, Sarah B. McKagan, Eleanor C. Sayre

This recommendation initially appeared as an article in the American Journal of Physics:  A. Madsen, S. B. McKagan and E. C. Sayre, Resource Letter RBAI-1: Research-Based Assessment Instruments in Physics and Astronomy, Am. J. Phys. 85, 4 (2017).

The topic of mechanics has the largest number of RBAIs, because so many students take introductory mechanics courses at the university level and the content is very standardized. These mechanics RBAIs cover kinematics and forces, energy, rotation, and density (Table 1). Because of the wide variety of topics taught in introductory mechanics courses, there is no assessment where all course content is covered. Instead these assessments have a more narrow range of topics, so that you can probe your students’ understanding of each sub-topic in mechanics more thoroughly. There is also one mechanics RBAI for intermediate and upper-division mechanics courses discussed in this expert recommendation.

Table 1. Introductory mechanics research-based assessments. 

Title Content Intended Population Research Validation Purpose 

Kinematics and forces

Force Concept Inventory (FCI) Kinematics, Forces: 1D and 2D Intro college, high school Gold To assess students’ understanding of the most basic concepts in Newtonian physics using everyday language and common-sense distractors.
Force and Motion Conceptual Evaluation (FMCE)  Kinematics, Forces: 1D  Intro college, high school  Gold To assess students’ understanding of Newtonian mechanics.
Mechanics Baseline Test (MBT) Kinematics, forces, energy, momentum Intro college, high school Bronze To assess more formal dimensions of basic Newtonian physics.
Inventory of Basic Conceptions-Mechanics (IBCM) Kinematics, forces  Intro college Silver To assess the basic threshold of meaningful understanding of Newtonian theory.
Test of Understanding of Graphs: Kinematics (TUG-K & TUG-K2) Kinematics graphs Intro college, high school (use TUG-K2) Gold To assess students’ ability to interpret kinematics graphs.
Force, Velocity and Acceleration Test (FVA) Force, velocity, acceleration Intro college Bronze To assess students’ understanding of the relationships between force, velocity, and acceleration.
Energy

Energy, momentum

Intro college

Gold

To assess conceptual understanding of energy and momentum for standard introductory mechanics courses.

Energy principle, forms of energy, work and heat, absorption & emission spectra, specification of appropriate systems

Intro college

Silver

To assess conceptual understanding of students in the matter & interactions (M&I) Mechanics courses

Rotation

Rotational motion

Intro college

Silver

To assess students’ understanding of rotational and rolling motion con- cepts typically covered in a standard introductory physics course

Rotational kinematics

Intro college

Bronze

To assess students’ understanding of angular velocity and angular acceler- ation of a particle in standard intro- ductory physics contexts

Density

Mass, volume, density

Intro college, high school

Bronze

To assess students’ understanding of density

Kinematics and forces assessments (intro courses)

Overview of kinematics and forces research-based assessment instruments

There are six research based assessment instruments (RBAIs) which cover kinematics and forces: The Force Concept Inventory (FCI) (Hestenes 1992), Force and Motion Conceptual Evaluation (FMCE) (Thornton 1998), Test of Understanding of Graphs in Kinematics (TUG-K) (Beichner 1994), Mechanics Baseline Test (MBT) (Hestenes et al. 1992), Force, Velocity, and Acceleration (FVA) test (Rosenblatt et al. 2011), and Inventory of Basic Conceptions in Mechanics (IBCM) (Halloun 2007). Research and development of kinematics and forces RBAIs has been occurring since the early 1990s, with the FCI being the first published RBAI in physics. The kinematics and forces RBAIs are all used in introductory classes at the university level, and some are also appropriate for high school students.

Force Concept Inventory (FCI)

The most commonly used test of forces and motion is the Force Concept Inventory (FCI) (Hestenes 1992). This is a multiple-choice pre/post conceptual assessment about the most basic concepts of force and motion appropriate for introductory university level physics courses and high school courses. The FCI was the first RBAI in physics that presented answer choices consisting of Newtonian concepts and common-sense alternatives that were based on research into student thinking. Understanding which of these common-sense alternatives students choose is just as important as looking at the number of correct answers, as this information helps instructors learn how to improve their teaching. About half of the questions on the FCI come from an earlier test called the Mechanics Diagnostic Test (MDT) (Hestenes 1995). Questions on the MDT were developed using students’ ideas from open-ended responses.

There are several variations of the FCI: The Gender FCI (or Everyday FCI) (McCullough 2011, McCullough et al. 2001) uses the same questions and answer choices as the original FCI, but changes the contexts to make them more “everyday” or “feminine.” The Animated FCI (Dancy et al. 2006)  takes the original FCI questions and animates the diagrams, so it is given on a computer. The Representational Variant of the FCI (R-FCI) (Nieminen 2010) takes nine questions from the original FCI and redesigns them using various representations (such as motion maps, vectorial and graphical representations). The Familiar Context FCI (Osborn Popp et al. 2009)  presents the original FCI questions with everyday contexts, e.g., falling fruit instead of stones or colliding shopping carts instead of cars. The Simplified FCI (Osborn Popp et al. 2009) was adapted from the original FCI and made simpler for ninth grade physics. The Half-length FCI (HFCI) (Han et al. 2015) uses the questions from the FCI (v95) and creates two equivalent tests (HFCI1 and HFCI2) that are about half of the length of the original FCI (14 versus 30 questions), but have virtually identical total scores. Several high-scoring FCI questions were removed from the Half-length versions, so the scores of on the HFCI1 and HFCI2 are about 5% lower than those for the FCI.

Force Motion Conceptual Evaluation (FMCE)

The Force Motion Conceptual Evaluation (FMCE) (Thornton 1998) is another multiple-choice pre/post conceptual assessment of forces and motion appropriate for introductory university physics courses. The questions on the FMCE are also based on research into student thinking. The FMCE has been used to show that traditional instruction does little to change students’ conceptual understanding of forces and motion.

Many of the questions on the FMCE have a more complex question format, which includes a description of the problem context, a list of answer choices (often more than five), and then several questions about that problem situation. In order to give the FMCE in class, a special Scantron form with room for ten answer choices is needed. The FMCE questions were developed based on student interviews, responses to open-ended versions of the questions and expert review.

Comparing the FCI and FMCE

Both the FCI and FMCE cover forces and motion, but they have different emphases. The FCI covers more topics than the FMCE, but the FMCE has more questions about each topic to more thoroughly assess students’ understanding of each topic. Both tests assess one-dimensional kinematics and Newton’s laws. The FCI also includes questions on two-dimensional motion with constant acceleration (parabolic motion), impulsive forces, vector sums, cancellation of forces, and identification of forces (Thornton et al. 2009). The FMCE includes questions about graphs of motion, whereas the FCI does not. FCI questions 15 and 16 present the same situation as FMCE questions 35–38. FCI question 28 is nearly identical to FMCE question 39. The questions on the FCI each have five answer choices, whereas some questions on the FMCE have more than five. Both tests have a strong research base. There is a strong correlation between FCI and FMCE scores (Thornton et al. 2009). As both of these tests are widely used, there is a large corpus of comparison data (FCI results have been published for over 50,000 students (Von Korff et al. 2016), while FMCE results have been published for over 10,000 students (Von Korff et al. 2016), which can help you understand how your students’ scores compare to others. You can find a list of articles with FCI comparison data on the research tab of the FCI assessment page.

Mechanics Baseline Test (MBT)

The Mechanics Baseline Test (MBT) (Hestenes et al. 1992) is another multiple-choice conceptual pre/post assessment for introductory college mechanics courses. The MBT assesses more formal dimensions of basic Newtonian physics with some conceptual questions and some simple calculational questions. The MBT questions are based on research into student thinking. Some of the questions come from Advanced Placement (AP) exams.

The MBT is meant to be used alongside the FCI to get a well-rounded picture of students’ understanding. The FCI questions can be answered with no previous physics training, whereas the MBT uses more formal language and includes graphical representations of motion and calculational problems that could not be answered without formal physics training. The MBT not only covers kinematics and forces, like the FCI, but also includes questions on energy and momentum, which are not covered in the FCI. The MBT includes just a few questions on Newton’s first and third laws, since these are well covered in the FCI. The answer choices on the MBT include typical student mistakes but not common-sense alternatives like the FCI. The FCI has a stronger research base than the MBT. There is a strong correlation (0.68) between the FCI and the MBT for a group of university students (Hestenes et al. 1992).

Inventory of Basic Conceptions in Mechanics (IBCM)

The pre/post multiple-choice questions on the Inventory of Basic Conceptions in Mechanics (IBCM) (Halloun 2007) also assess introductory students’ conceptual understanding of Newton’s laws and forces. The IBCM uses questions from the FCI, MBT, and MDT, but makes slight changes to the wording and answer choices. The IBCM was developed in Lebanon. Since the IBCM takes questions from the FCI and MBT, it is very similar to both of these tests. The IBCM concentrates on Newtonian theory with only two basic models: the free particle and uniformly accelerated motion. It does not include centripetal and centrifugal forces. There are no peer-reviewed publications presenting IBCM results.

Force, Velocity, and Acceleration test (FVA)

The Force, Velocity, and Acceleration test (FVA) (Rosenblatt et al. 2011)  is a pre/post multiple-choice conceptual assessment that probes students’ understanding of the relationships between force, velocity, and acceleration. Each question presents a scenario with information about either the force, velocity, or acceleration vectors and then asks students about what this means for one of the other vectors. The FVA test provides a coherent picture of student understanding of the relationships between these three by probing six possible conditional relations between them. The FVA test questions were developed using students’ responses to open-ended questions and revised using student interviews. The relationships between force, velocity, and acceleration on the FVA test are similar to those relationships probed in several questions on the FCI (questions 4, 7, and 9) and FMCE (questions 1, 3, and 12). The FVA is relatively newer than the FCI and FMCE, so there is not as much comparison data available. Also, the FVA test has been primarily used at the developers’ institutions, so it has a lower level of research validation than the FMCE and FCI.

Test of Understanding of Graphs in Kinematics (TUG-K)

The pre/post multiple-choice questions on the Test of Understanding of Graphs in Kinematics (TUG-K) (Beichner 1994) focus on introductory college and high school students’ conceptual understanding of position, velocity, and acceleration versus time graphs. Questions ask students to find displacement, velocity, or acceleration from a given graph or select a graph corresponding to the one given or a textual description. The TUG-K has been validated for high school students, but the TUG-K2 variant was written specifically for high school students. The TUG-K questions were based on the objectives that came from banks of test questions, introductory textbooks, and informal interviews with instructors. Multiple-choice options were written based on the previously studied student difficulties with kinematics graphs. The TUG-K is similar in content and format to the FMCE, which contains 17 out of 47 questions about graphs of motion, including graphs of force versus time, velocity versus time, and acceleration versus time. Both the FMCE and TUGK have a strong research validation.

Recommendations for choosing a kinematics and forces assessment

Use the FCI if you want a broad understanding of what your students understand about kinematics and Newton’s laws, and lots of comparison data. Use the FMCE if you want a more thorough understanding of what your students understand about kinematics and Newton’s laws in one-dimension. Use the MBT in conjunction with the FCI to assess more formal parts of your course. Use the FVA if you want to know about your students’ understanding of the relationships between force, velocity, and acceleration vectors. Use the TUG-K if you want to thoroughly assess your students’ understanding of motion graphs.

Energy assessments 

Overview of energy assessments

There are two RBAIs that cover energy: the Energy and Momentum Conceptual Survey (EMCS) (Singh et al. 2003) and the Energy Concept Assessment (ECA) (Ding 2007). Research and development of energy RBAIs has been occurring since the early 2000s to develop these pre/post multiple-choice assessments for introductory classes at the university level.

Energy and Momentum Conceptual Survey (EMCS)

The Energy and Momentum Conceptual Survey (EMCS) was designed for use in standard first-semester introductory physics courses. It emphasizes energy and momentum in common contexts that your students are likely to have seen in their courses, e.g., carts on tracks, cart filling with rain, bouncing balls, etc. The multiple-choice questions on the EMCS were developed by planning the content and complexity to be tested, getting expert feedback then writing questions. Student responses to open-ended versions of the questions were collected and these responses along with findings from student interviews were used to create the multiple-choice options.

Energy Concept Assessment (ECA)

The Energy Concept Assessment (ECA) was designed specifically to assess conceptual understanding of students in the Matter & Interactions (M&I) mechanics course (Chabay and Sherwood 2007). This is a first-semester introductory physics course with a radical change in content and emphasis, focusing on the power of fundamental principles, on both the macroscopic and the microscopic levels. Because of this, only about half of the questions on the ECA align well with the topics in a standard introductory course. The other half of the questions are not emphasized or covered in a standard course, for example, relativistic energy including rest mass, quantized energy levels, and photon emission and absorption

Recommendation for choosing an energy assessment

The ECA contains questions about non-standard introductory course topics (discussed above) while the EMCS contains more standard questions about energy and momentum. Use whichever test more closely matches the content in your course. Both tests were rigorously developed, tested, and found to be reliable.

Rotation assessments

Overview of rotation assessments

There are two tests about rotation: Rotational and Rolling Motion Conceptual Survey (RRMCS) (Rimoldini et al. 2005) and the Rotational Kinematics Inventory (RKI) (Mashood et al. 2012, Mashood et al. 2012, Mashood et al. 2015). Research and development of rotational motion RBAIs has been occurring since the mid- 2000s. Both are multiple-choice conceptual tests that use some physics formalism, which means that the pre-test scores are likely not meaningful because students do not have enough background knowledge to understand the questions (Rimoldini et al. 2005).

Rotational and Rolling Motion Conceptual Survey (RRMCS)

The Rotational and Rolling Motion Conceptual Survey assesses students’ understanding of rotational kinematics and kinetic energy, moment of inertia, torque, and rolling motion. It is appropriate for introductory college students in both algebra-based and calculus-based courses. The RRMCS questions were developed using student ideas from demonstration-based interviews.

Rotational Kinematics Inventory (RKI)

The Rotational Kinematics Inventory has three parts: “Part 1: Particles” (Mashood et al. 2012) assesses students’ understanding of angular velocity and acceleration of a particle in various standard contexts (the hands of a clock, orbiting plants, swinging pendulum, etc.); “Part 2: Particle in rectilinear motion” (Mashood et al. 2012) assesses students’ understanding of the angular velocity and acceleration of a particle moving along a straight line where the origin is not located on that line; “Part 3: Rigid body about a fixed axis,” (Mashood et al. 2015) assesses students’ understanding of the rotational kinematics of rigid bodies like pulleys and Ferris wheels. Some of the RKI questions use vector calculus including the cross product. The RKI has been tested with high school students and upper-division college students. Parts of this assessment would also be appropriate for introductory college students. You can use all three parts of the RKI, or only the parts match the content you cover in your course. The RKI questions were developed by creating a map of content and complexity to be tested and a literature review. The RKI was developed in India.

Recommendations for choosing a rotation assessments

The RRMCS and RKI both cover rotational motion topics but with different emphases. The RRMCS focuses on rota- tional motion concepts commonly taught in introductory courses. The RKI covers these standard topics and also includes some non-standard topics, e.g., a particle in rectilinear motion, and higher-level math (vector calculus) that is more difficult than the content tested on the RRMCS. Both have a similar level of research validation.

Density

Density Survey (DS)

The Density Survey (DS) (Loverude et al. 2001) is a pre/post conceptual assessment of basic density concepts meant for high school and introductory college students. Most of the questions are standard multiple-choice questions, but there are two questions that require simple calculations. The questions on the DS were developed based on a survey of the literature and one-on-one interviews with several high school students. One question is from the Third International Mathematics and Science Study, and three are adapted from research on electric charge density. Use the density survey if you want to assess the change in your students’ understanding of density before and after covering it in your course.

Intermediate mechanics

Colorado Mechanics/Math Methods Instrument (CCMI)

The Colorado Mechanics/Math Methods Instrument (CCMI) (Caballero and Pollock 2013, Pollock et al. 2012)  is an open-ended assessment of topics and skills commonly taught in a first-semester intermediate classical mechanics course, including the ability to visualize a problem, correctly apply problem-solving methods, connect math to physics, and describe the limiting behavior. The CCMI covers both content and mathematical skills though the questions are largely conceptual, including reasoning, explanation, graphing, and sketching. The CCMI does not cover all content in intermediate classical mechanics, but rather a sample of important skills. There is an optional shorter pre-test and longer post-test. Both are graded using rubrics. The CCMI questions were developed based on a set of learning goals produced by faculty and observed student difficulty with these concepts. This is the only RBAI for intermediate classical mechanics.

Table 2. Intermediate level mechanics assessment.

Title Content Intended Population Research Validation Purpose 

Intermediate mechanics

Colorado Mechanics/Math Methods Instrument (CCMI)

Ordinary differential equations, Taylor series, potential energy, simple harmonic motion, Newton’s laws

Intermediate, upper-level

Silver

To gauge student learning in your first semester classical mechanics course in a way that traditional exams do not allow and compare your students’ skills to other.