Detect, Correct, and Reflect:
Making the Most of
Math Mistakes
41st AMATYC Annual Conference
New Orleans, LA
November 21, 2015
Charlotte Skinner
Associate Professor of Mathematics
University of Cincinnati
Blue Ash College
[email protected]
Error Detection/Correction
Techniques
• Exam Revisions
• Spot-the-Mistake (STM) Exercises – in
class, on HW, test review, on exams
• Homework quizzes
• Bonus points for instructor mistakes
Template for Exam Revisions
Question Corrected
#
Solution
Problem
number
from exam
Mathematical
Notes
Problem
done
correctly,
showing
all work
Additional
Example
Confidence
Level
Mathematical
properties that
apply; helpful notes
Template for Exam Revisions
Complete a similar problem, provided
by the instructor
Question Corrected
#
Solution
Mathematical
Notes
Additional
Example
Confidence
Level
Indicate your confidence level with solving this type
of problem in the future using the scale 1-5 with
5 = Very confident and 1 = Not at all confident
Exam Revision Example
Q
Corrected Solution
Ex.
Mathematical Notes
Exam Revision Example
Additional Example
C
5
Exam Revisions - Student Samples
Exam Revisions - Student Samples
Exam Revisions - Student Samples
Variations
• Principle or Topic instead of Math Notes
e.g. simple harmonic motion of mass on a spring
• Student identifies a similar problem from
text or class notes, in place of instructorprovided example
Evolution
Improve quality of
test corrections
Student confusion
Created the
template
Model it for students
Spot-the-Mistake (STM) Model
Traditional
Spot-the-Mistake
Spot-the-Mistake (STM) Model
Traditional
Solve:
3x + y = 10

4 x − 2y = 0
Spot-the-Mistake
Spot-the-Mistake Examples
• Exam Review Assignment
The answer to every one of the following
problems is incorrect or incomplete.
a.) Describe the error that was made, and
b.) Re-do each problem correctly
1.) Evaluate: − 42
Wrong Answer: 16
2.) Express with positive exponents and
simplify: − x −2
Wrong Answer: x2
3.) Simplify: x3 + x3
Wrong Answer: x 6
4.) Simplify: x 4 ⋅ x5
Wrong Answer: x20
Exam Review Student Samples
Exam Review Student Samples
Exam Review Student Samples
Spot-the-Mistake Examples
• In class practice
There is an error in the solution to the
following problem. Identify the error and
correct it.
Rationalize the denominator: 2
3x
3 x 23 x
2
Wrong Solution:
⋅
= x
3x 3x
More In Class STM Practice
Detect and correct the error in the following:
Find the slope of the line through the points
(2, -3) and (-5, 1).
Incorrect solution:
Description of mistake:
Correct solution:
More In Class STM Practice
Detect and correct the errors:
3−1 = −3
𝑎𝑎−3
𝑏𝑏4
=
𝑏𝑏4
𝑎𝑎3
Spot-the-Mistake Examples
• Exam Problem – Student Sample
Exam Problem – Student Sample
Exam Problem – Student Sample
Advantages
Mistakes are learning opportunities
Students explain their thinking
Encourages communication about mathematics
Distinguish between faulty reasoning and simply
a different, but correct solution
• Focus on strategy, not just the correct answer
• Leads to deeper conceptual understanding
•
•
•
•
Advantages
• Target most common student mistakes
• Promote self-sufficiency – students develop the
habit of reviewing their own work for errors
• Variety
• Challenging
• Construct viable arguments and evaluate the
reasoning of others
• Benefits supported by research
Additional Strategies to Target
Error Correction
• Bonus points for detecting instructor
errors in class
• Homework Quizzes
Homework Quiz Sample
Next steps
• Determine whether an argument is reasonable
or not, and then correct if necessary
• Critique anonymous student work
– As a class
– Peer critique
Thank You!
[email protected]