```Misconceptions in
Mathematics:
Presenter: Sunny Chin-Look
([email protected])
• K-12 Math Instructional Specialist at Alhambra Unified
• Member of CDE Curriculum Framework and Evaluation
Criteria Committee
• CSULA Teaching Credential Program
1
Misconceptions
alternative conceptions or
intuitive theories
Students’ erroneous,
illogical or misinformed
math understandings.
2
Misconceptions
Impede Learning
The Origins of Misconceptions
3
What does learning look like
under CCSSM?
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning
of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
4
Won’t Work
5
Hard Nuts to Crack
610 is not closer to 500 than 400.
6
4+5=7
“The problem I want to solve is 4 + 5, but I did
4 + 4, and then since 4 + 5 is one away from 4 + 4,
I had to take one away”
Vol. 20, No. 5 | teaching children mathematics
• December 2013/January 2014
7
possible origin?
Double Plus
or
Double Minus
8
48 – 19 = 27
“ I added 1 to 19 so I have to take away 1 from 48.
47 – 20 = 27”
9
possible origin?
28 + 15
“ Since I added 2 to 28, I need to minus 2 from 15.
30 + 13 = 43”
10
965 ÷ 16
Vol. 17, No. 7, March 2012 MATHEMATICS TEACHING IN THE MIDDLE SCHOOL
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possible origin?
10
50
2
7
500 350
100
14
17 × 52
= (10 × 50) + (10 × 2) +
(7 × 50) + (7 × 2)
= 500 + 100 + 350 + 14
= 964
Array Model for Multiplication
12
Raccoon Eyes
13
Error Location and Counterexample
• determine conceptual
reasoning.
• Confront student with
counterexamples to
their misconception.
14
Seating Chart
This is the seating chart for Mrs. Blake’s class. One student
sits at each desk.
= one desk
At the beginning of the year, 5/8 of the students were girls.
A new student was added to Mrs. Blake’s class, and now 3/5
of the students are girls. Is the new student a boy or girl?
15
Student #1
The fraction of the class for girls increased so the new student is a girl.
16
Student #2
The new student was a girl. I got 5/8 from the
girls and then I found a common
denominator. The 2 numbers from the girls
was 26/40 (after) and 25/40 (previously). This
means they got a new student because if you
– (minus sign) 26/40 – 25/40 = 1/40 which = a
new student. The boy technically lost a
student because they didn’t get a new
student.
17
Student #3
1. First, I changed both the fractions to the same denominator. I did this so
that I could compare to see if the total had 1 more student or 1 less.
2. After , I compared it and found out that there was one less girl. So, I
thought that the new student was a boy.
18
Student #4
1 1/24 of the new boy
19
Free Online Resources
 How Do I Get My Students Over Their Alternative
Conceptions for Learning?
http://apa.org/education/k12
 Student Thinking: Misconceptions in Mathematics
www.math.tamu.edu/~snite/MisMath.pdf
nixthetricks.com/
 Error Patterns in Computation (Sample Chapters)
http://www.pearsonhighered.com/assets/hip/us/hip_
us_pearsonhighered/samplechapter/0135009103.pdf
20
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