Misconceptions in Mathematics:

Presenter: Sunny Chin-Look (sunnylook@yahoo.com)• 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

The Origins of Misconceptions

3

Misconceptions Impede Learning

What does learning look like under CCSSM?

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. 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 did4 + 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 SCHOOL11

possible origin?

Array Model for Multiplication 12

710

2

50

100

350

14

500

17 × 52 = (10 × 50) + (10 × 2) +

(7 × 50) + (7 × 2) = 500 + 100 + 350 + 14 = 964

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 #2The 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

Nix the Tricks (eBook free download) nixthetricks.com/

Error Patterns in Computation (Sample Chapters) http://www.pearsonhighered.com/assets/hip/us/hip_us_pearsonhighered/samplechapter/0135009103.pdf

20