doing math vs. understanding math david “coach g” ginsburg david@ginsburgcoaching.com

Electrolysis

Doing Math vs. Understanding MathDavid Coach G Ginsburgdavid@ginsburgcoaching.com1How would you solve this problem? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price?

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2Would you use this approach? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price?

$124.00 x .35 = $43.40$124.00 - $43.40 = $80.60

david@ginsburgcoaching.com3This approach? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price?

100% - 35% = 65% $124.00 x .65 = $80.60

david@ginsburgcoaching.com4Or would you do something like this?A pair of shoes that cost $124 was on sale for 35% off. What is the sale price?

65% = 50% + 10% + 5%$124.00 x 50% = $62.00$124.00 x 10% = $12.40 $124.00 x 5% = $ 6.20 Sale price = $80.60

david@ginsburgcoaching.com5Is one approach better than others? Why?Procedural FluencyConceptual Understandingdavid@ginsburgcoaching.com6Procedural Fluency > AccuracyProcedural fluency is the ability to apply procedures accurately, efficiently, and flexibly

NCTM Position Paper

david@ginsburgcoaching.com7Approach #1: Efficient? Flexible?A pair of shoes that cost $124 was on sale for 35% off. What is the sale price?

$124.00 x .35 = $43.40$124.00 - $43.40 = $80.60

david@ginsburgcoaching.com8Approach #2: Efficient? Flexible? A pair of shoes that cost $124 was on sale for 35% off. What is the sale price?

100% - 35% = 65% $124.00 x .65 = $80.60

david@ginsburgcoaching.com9Approach #3: Efficient? Flexible?A pair of shoes that cost $124 was on sale for 35% off. What is the sale price?

65% = 50% + 10% + 5%$124.00 x 50% = $62.00$124.00 x 10% = $12.40 $124.00 x 5% = $ 6.20 Sale price = $80.60

david@ginsburgcoaching.com10Approach #1: Conceptual understanding?A pair of shoes that cost $124 was on sale for 35% off. What is the sale price?

$124.00 x .35 = $43.40$124.00 - $43.40 = $80.60

david@ginsburgcoaching.com11Approach #2: Conceptual understanding?A pair of shoes that cost $124 was on sale for 35% off. What is the sale price?

100% - 35% = 65% $124.00 x .65 = $80.60

david@ginsburgcoaching.com12Approach #3: Conceptual understanding?A pair of shoes that cost $124 was on sale for 35% off. What is the sale price?

65% = 50% + 10% + 5%$124.00 x 50% = $62.00$124.00 x 10% = $12.40 $124.00 x 5% = $ 6.20 Sale price = $80.60

david@ginsburgcoaching.com13Procedural Fluency and Conceptual Understanding5 Supporting Practices for Your Classroom

david@ginsburgcoaching.com141. A Purpose for Every Problemdavid@ginsburgcoaching.com

152. Pencils Down, Minds On

david@ginsburgcoaching.com163. Multiple Solution Strategiesdavid@ginsburgcoaching.com

174. Gradual Rapid Release of Responsibilitydavid@ginsburgcoaching.com

Work the crap out of every problem185. Assist Less, Assess Moredavid@ginsburgcoaching.com

19The Procedural Fluency and Conceptual Understanding ConnectionJoin me tomorrow for pencils down, minds on math!

12:30 - Room 303

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