“Correction Reflections”
Often times when a student makes a mistake in a mathematics problem he/she
realizes, after the fact, that he/she made a careless error in computation. Other times, the
student may think he/she made a careless error but in reality he/she may have serious
misunderstandings regarding a particular concept. As a facilitator of learning, a very
effective way to assess a student’s understanding is by hearing his/her problem solving
process. Because of time constraints and because of the often times shy nature of
students, it becomes a daunting task to pull from each and every student his/her thinking
processes. An assessment tool that helps to accomplish the task is an error analysis
process called “ Correction Reflections “
Outline of an acceptable “Correction Reflection”
I.
“Correction Reflections” are composed of two different languages; Symbolic
(mathematical) language and Written/Verbal (English) language.
a. Symbolically: Students must show detailed new work for each missed
problem. Final new answer must be highlighted or circled.
b. Writing: Each revised problem must be supported by a written proof
statement. This statement must convince the instructor that the student has
reviewed, analyzed, and assessed his/her own errors in the problem
solving process. Proof of understanding is demonstrated by following
some or all of the following guidelines:
1. Using mathematics vocabulary state a rule, theorem, definition,
etc. (from your textbook) that applies to the error you made.
• Example: If you incorrectly place a negative sign in an
answer, after reworking the problem correctly you would
state the rule of signed numbers that would support your
correct answer.
• Your original work: -3 – (-2) = -5 is incorrect. Your
revision: -3 – (-2) =
-3 + 2 = -1 is correct. My proof of understanding
statement would be “I recall that the Definition of
Subtraction is addition of the opposite. Thus, the
subtraction sign changes to addition and –2 becomes it’s
opposite which is 2. Then,
–3 + 2 follows the rule for addition of unlike signed
numbers which states that you must subtract the two
numbers and assign the answer the same sign as the largest
number (in absolute value) in the sum.”
(Continued on p. 2)
P.2
2.
Never use the following as proof statements: (each is
followed by what goes on in your instructor’s head when
he/she reads such statements.)
• “I messed up because I put the wrong sign.” (DUH!)
• “I made a stupid mistake” (You will continue to make stupid
mistakes unless you do your correction reflections well)
• “I rushed.” (Obviously, you still are!!)
• “I ran out of time.” (Now, you have plenty of time to do this
correction reflection)
• “I don’t know what I did wrong.” (Why didn’t you ask
others or me, refer to the book, worksheets, other student’s
work, lab (6331) tutors, videotaped lectures, Internet tutorial
resources, or the president of the United States in order to
gain understanding.)
“Correction Reflections,” when done effectively, will dramatically increase your
understanding and future mathematics success as well as your overall problem solving
skills in life. If you choose not to use this powerful tool you will be penalized as
follows:
• Quiz grade of Zero if you did not achieve a perfect score and did not write your
correction reflections.
• 10% deduction in your Test Grade if you did not complete correction reflections for
all errors.
Hints:
• You can get help from anywhere or anyone in order to do correction reflections.
There is no excuse for continuing to not understand.
• The instructor will often work out the problem for students and give them the correct
answers. Thus, the importance of the written proof should be obvious. Simply
copying the instructor’s work or the correct answer does the student no service and
proves nothing to the instructor of a students understanding.
• More time spent on reading, studying, working problems, and reviewing prior to a
test or quiz is directly proportional to less work doing correction reflections.
When assessing “correction reflections,” the instructor is judge and the student is
attorney. The student must prove to the instructor, beyond a reasonable doubt, that
his/her understanding (client) is clear (innocent). Would an attorney ever plead that his
client is not guilty because he/she didn’t do it? Ask yourself this after each of your
corrections. “Did I represent my knowledge with my words sufficiently to prove my
understanding to my instructor?”