Education research: overcoming initial problem-solving block

Arnold B. Arons (1997) from the University of Washington, Seattle, WA observes that an effect of firmly requiring use of a systematic problem-solving procedure is that

Most students at this early stage in their development refuse to put pencil to paper, or to analyze the verbal-to-symbol transitions that are essential, until they "see" the solution as a whole. Requiring that they institute the procedure propels them, willy nilly, into the problem, and the momentum thus acquired frequently carries them through to the solution. The increasing satisfaction gained from such experiences gradually makes them more willing to penetrate a new problem, with pencil and paper and inquiry, without waiting until the entire solution has been perceived. This is a very large step indeed in intellectual development and capacity for abstract logical reasoning.

Wilbert J. McKeachie, University of Michigan, Ann Arbor, MI, and Marilla Svinicki, University of Texas at Austin, TX (2006) have similar advice for the student:

If a question completely baffles you, start writing...anything you know that could possibly be relevant. This starts your memory functioning, and usually you'll soon find that you have some relevant ideas.

For Physics 8AB (university physics, calculus-based) at Cuesta College in San Luis Obispo, CA, students are graded not so much as for obtaining the correct answer, but for how successful they are in implementing a constructive, systematic approach towards a solution. As an incentive to get students to get started by applying pencil to paper, they are given "pity points" for not leaving the page blank (e.g., writing down equations, restating knowns, or even writing "I don't know" avoids the "z" rubric for no response). However, students are warned that they can "b---s--- their way out of an 'F,' but can't b---s--- their way to an 'A.'" A throughly methodical approach that shows understanding and mastery of the essential concepts, up to the point where purely algebraic elimination and back-substitution of unknowns would begin is worth a "t" rubric, which on the grade scale is just below the B-/C+ cutoff.

Physics 8AB problem rubric

• p = 15/15: Correct.
  
• r = 12/15: Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t = 9/15: Contains right ideas, but discussion is unclear/incomplete or contains major errors.
  
• v = 6/15: Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x = 3/15: Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 1.5/15: Irrelevant discussion/effectively blank.
  
• z = 0/15: Blank.

Astronomy 10 (introductory astronomy, general education requirement) has a similar grading scale, where the "y" rubric provides an incentive for students to at least start writing and hopefully get past an initial "brain-lock," and the "t" rubric is the B-/C+ cutoff for the "worst of the best answers" (or "best of the worst answers").

Astronomy 10 short-answer rubric

• p = 20/20: Correct.
  
• r = 16/20: Nearly correct, but includes minor math errors.
  
• t = 12/20: Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
  
• v = 8/20: Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  
• x = 4/20: Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20: Irrelevant discussion/effectively blank.
  
• z = 0/20: Blank.

Arnold B. Arons, Teaching Introductory Physics, John Wiley & Sons, Inc., New York, 1997, p. 39.

Wilbert J. McKeachie, Marilla Svinicki, McKeachie's Teaching Tips: Strategies, Research, and Theory for College and University Teachers (12th edition), Houghton Mifflin Company, Boston, 2006, p. 109.