Using ‘Good Wrong Answers’ to Achieve Math Confidence and Success Robin Schwartz

Using ‘Good Wrong Answers’ to Achieve Math Confidence and Success

• Robin Schwartz

• College of Mount Saint Vincent

• Math Confidence

• www.mathconfidence.com

Why ‘Good Wrong Answers’?

• GWA are designed with common mistakes and misunderstandings in mind

• The answer is there!!

Why ‘Good Wrong Answers’?

• Showing students ‘the right way’ can be complemented with GWA

• They are fun ;)

• The comparative is very instructive

Student Opinion

• Looking at ‘good wrong answers’ with a student allows him or her to see a mistake that is easy to make, and thus learn not to do so in the future. Without ‘good wrong answers’, the student might never learn to look out for these simple mistakes that look like they will work.

• Solomon Spigel, 15, homeschooler, Riverdale, New York

• student since 2002

Schools

• Bronx: Bronx Science

• Fordham Prep
• PS 81
• SAR Academy
• Horace Mann
• Fieldston
• MS/HS 141 Riverdale/Kingsbridge Academy
• Homeschoolers

• Westchester: Maria Regina

• New Rochelle High School

• Solomon Schechter
• Ursuline
• Our Lady of Victory
• Eastchester Middle School

Schools

• Manhattan: Hunter College High School

• Beacon High School

• Hunter Sciences High School

• HS for Math, Science and Engineering

• York Prep

• Trevor Day

• Wagner Middle School

• Eleanor Roosevelt HS

• The Lab School

• Manhattan East Middle School

• United Nations International School

The Hot Stove and the Oven Mitt Learning by Fire

(x+3)2 – (x+2)2 =

• A) 13

• B) 5

• C) 2x + 5

• D) 10x + 13

• E) 10x + 5

The Lonely Girl at the Dance

• The Middle Term

No More SAT Quantitative Comparisons

• A B

Quantitative Comparison

• A if A is always larger

• B if B is always larger

• C if A and B are always equal

• D if the relationship cannot be determined

QC Example

• A B

• 3

QC Example

• A B

• 3

Factoring

Factoring With “The Lonely Girl”

• “Two sets of parentheses”

• “Two plusses, two minuses or one of each?”

• A) (8x + 1) (10x + 1) EVEN

• B) (4x +1) (20x + 1) EVEN

• C) (2x + 1) (40x + 1) EVEN

• D) (16x + 1) (5x + 1)ODD!!

Factoring

Factoring Using “Evenness” vs. “Oddness”

• A) (4x + 4) (10x + 10) B) (4x + 8) (10x + 5)

• Even Even

• C) (4x + 20) (10x + 2) D) (8x + 5) (5x + 8)

• Even Odd

12 divided by…

QC Example

• A B

0 and 1

• What happens when you divide by 0?

• P/E Ratio

QC Example (no calculator)

• A

Quantitative Comparison

• A B

If you cancel x’s, beware The Math Police

Absolute Value Equality | x – 5 | = 3

• A) x = 8

• B) x = 8 or x = -8

• C) x = 2

• D) x = 2 or x = 8

• E) x = -2

• A) 2

• B) 16

• C) 0

• D) 48

What is the value of

• A)

• B)

• C) -9

• D) -6

More Exponents

Word Problem Percent

• A suit is on sale for $100 after a 20% discount. What was the original price?

• A) $120

• B) $125

• C) $80

• D) $500

Word Problem Average

• You drive uphill at 40mph and downhill at 60mph. What is your average speed (x)?

• A B

• x 50

Mathematics Builds Attention to Detail, Frustration Tolerance and Critical Thinking Skills

Student Opinions

• "It's helpful to look over the answers for a multiple choice test so you can learn from your mistakes and review what you already understand.  By doing this, you can only improve and score higher on your next exam."

• Josh Friedman,

• salutatorian, MS/HS 141

• freshman, Boston University

• student 2003-2005

Contact Information:

• Robin Schwartz

• www.mathconfidence.com

• [e-mail]