Why we teach math differently

Robert Kaplinsky shared this on his website
http://robertkaplinsky.com/how-old-is-the-shepherd/

How do you think 32 eighth grade students would respond to this nonsensical question: “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?”* Take a guess as to what percentage of them would give a numerical answer and then watch the video below:

Of the 32 students I interviewed, 75% of them gave me numerical responses.  Going into this, I predicted it would be closer to 50%.  Here are some of my observations from the 32 students:

• 2 students calculated the answer to be 130 (125 + 5)
• 2 students calculated the answer to be 120 (125 – 5)
• 12 students calculated the answer to be 25 (125 ÷ 5)
• 0 students calculated the answer to be 625 (125 x 5)
• 4 students stated that they guessed their answer (90, 5, 42, and 50)
• 4 students tried to divide 125 by 5 but could not correctly implement the procedure

 

Three particularly interesting students included:

• The student who found the shepherd’s age by using the old “add the sheep and dogs and divide by two” trick and got 65.  You didn’t know about that trick?
• The student who got 120, then said that you don’t have enough information to figure out the shepherd’s age, then seemed to feel so uncomfortable with that conclusion that the student decided to guess 90 years old.
• The last student who explained that the reason for dividing was because it didn’t say “sum,” “difference,” or “product” in the problem

 

That’s why we teach them to understand the math  and not to just follow a procedure.