Question 45 of the Spring 2003, Grade 11, Texas Assessment of Knowledge and Skills (TAKS), released Science test reads as follows:
45 If a force of 100 newtons was exerted on an
object and no work was done, the object must
A accelerated rapidly
B remained motionless
C decreased its velocity
D gained momentum
A formula chart on a beginning page of the test provides the formula
Work = force x distance W = Fd
Out of the 187214 students who took the test, the response frequencies for answers A, B, C, D, and no answer were, respectively, 22650, 115222, 21041, 27536, and 765.
All of the listed answers, A, B, C, and D, are incorrect. The Texas Education Agency made the mistakes of giving credit for the incorrect answer B and of not throwing out question 45. The TEA wrongly increased the scores of those 115222 students who chose answer B and, with respect to scaled scores that would result from throwing out question 45, wrongly decreased the scores of the remaining 71992 students. The remedy is to remove credit for answer B, throw out question 45, and rescale the test scores based on whatever valid test questions remain.
Plenty of simple examples show that answer B is incorrect.
The force due to Earth's gravity does no work on any object that only moves horizontally because the force is perpendicular to the motion. This includes cases in which the force due to Earth's gravity has a magnitude of 100 newtons. Since these cases include cases in which the objects do not remain motionless, answer B is incorrect.
For any object that moves in a circle at constant speed, the total force exerted on the object does no work on the object because, at any point on the circle, the object's motion (which is tangent to the circle) is perpendicular to the total force (which is centripetal). Examples, at least approximately, include an object being whirled at the end of a string above one's head and the Moon orbiting under the influence of Earth's gravity. Since any object that moves in a circle at constant speed does not remain motionless, including any object on which the total force has a magnitude of 100 newtons, answer B is incorrect. [Moreover, for an object whose mass is less than m = F/g = (100 N)/(9.8 m/s2) = 10.2 kg, the magnitude of the acceleration caused by a total force of 100 newtons is greater than that of the acceleration due to Earth's gravity, which could be considered as rapid acceleration.]
In the given formula, "force x distance" means force multiplied by the component of distance parallel to the force or, equivalently, distance multiplied by the component of force parallel to the distance. If force and distance are perpendicular, then the component is zero and no work is done even though both force and distance may be non-zero.
Failures to correct the scoring mistakes
informed the Texas Education Agency of the scoring mistakes on 3 June 2003. On 4 August 2003, the TEA issued the response TAKS Released Test Items
and issued, in "Additional Information Regarding Released Science Items", the statements
Item 45 asked students to use the formula for work, which is found on the
formula chart given to students during testing. This item was intended to
measure the IPC TEKS 4(A), which required students to calculate work. The
basic concept being tested---that physical work, which can be stored as energy,
requires movement in the direction of the applied force---is assessed properly for
the introductory-level student. While it is possible to have rapid centripetal
acceleration and still do no work, it is also possible to remain motionless and do
no work. For students at this level, circular motion is the exception to a general
rule that work is done only when there is motion. Therefore, this item has only
one correct answer and is appropriate for students tested at this level.
The TEA states that "However, upon review, these items were determined to be correct and no action was taken by the agency." This TEA statement refers to questions that include question 45. By "determined to be correct" the TEA means that answer B is correct. The TEA's claim that answer B is correct is false.
The TEA states that "The basic concept being tested--that physical work, which can be stored as energy, requires movement in the direction of the applied force--is assessed properly for the introductory-level student." This TEA statement is false. Answer B does not test whether "work ... requires movement in the direction of the applied force" (or whether "work requires movement" or whether "no work requires no movement in the direction of the applied force"). Question 45 was not "assessed properly"; credit was given for the incorrect answer B and, despite the fact that all of the listed answers are incorrect, the question was not thrown out.
The TEA states that "While it is possible to have rapid centripetal acceleration and still do no work, it is also possible to remain motionless and do no work." The first part of this TEA statement effectively admits that answer B is incorrect (since acceleration effectively implies both force and motion); the second part may be a TEA attempt to pretend that "is also possible to remain motionless" implies "must have remained motionless", an implication which the TEA knows is false.
The TEA states that "For students at this level, circular motion is the exception to a general rule that work is done only when there is motion." This TEA statement is false. Circular motion is not an exception to the rule "work is done only when there is motion." The TEA's attempt to dismiss circular motion as an "exception" appears to be an attempt to dismiss one class of simple examples that show that answer B is incorrect. Moreover, to dismiss circular motion at constant speed appears to conflict with the spirit of the "state-mandated curriculum" mentioned in an earlier (14 July 2003) letter to Dr. Loewe from then Associate Commissioner Smisko; this curriculum specifically mentions "satellite orbits", the simplest possible of which are circular orbits at constant speed.
The TEA states that "Therefore, this item has only one correct answer and is appropriate for students tested at this level." By "only one correct answer" the TEA means answer B. The TEA's claim that answer B is correct is false.
The TEA issued scores to all 11th-graders who took the test, including those who realized that answer B is incorrect and those who did not realize that answer B is incorrect. That answer B is incorrect is based on nothing more than basic knowledge of how work is related to force and distance, knowledge which was undoubtedly possessed by some students who took the test and which should readily have been possessed by many students who took the test.
The TEA's false claims are due to incompetence or dishonesty. Texans are ill-served by such incompetence or dishonesty.
The TEA has continued to propagate the scoring mistakes and false claims without correction.
On 15 July 2005, Mark Loewe
gave written and oral testimony to the State Board of Education
on the topic "TEA failed to correct TAKS mistakes". The SBOE has failed to acknowledge or to correct any of the TEA's scoring mistakes or false claims.
Question 45 has been discussed in Fort Worth Star-Telegram articles and letters to the editor:
"Physicist challenges 2 TAKS answers", Fort Worth Star-Telegram, 6 June 2003,
"Disputed TAKS answers correct, state agency says", Fort Worth Star-Telegram, 7 June 2003,
"Ambiguous questions", letter, Fort Worth Star-Telegram, 10 June 2003,
"Physics, testing and a frog", letter by Charles Reidl and letter by Mike Stepp, Fort Worth Star-Telegram, 14 June 2003,