Over the past few weeks, I’ve shown the How old is the shepherd? problem to both of my kids and then shown them the video from Robert Kaplinsky’s blog. Both were shocked at how many students don’t pay attention to what is happening in the problem. Connor even said, “I guess I’m not one of the 24.”
Here is my son, Connor, with his response to the problem:
Unfortunately, his first statement, “That’s stupid!” was not caught on video!
My daughter, Lura, with her response:
Last Saturday, after ambushing one of my daughter’s friends with the problem while she was visiting, Kim (my wife) became more curious about the problem, so I showed the video to her and shared some of the data on Kaplinsky’s blog. She was also shocked at the results. We had a brief conversation that went something like this:
Me: This is why we need to teach math content through patient problem solving and sense making!
Kim: Ok. (with a look that says, I know you’re passionate about this, and that it’s important. We’ll talk later. Go make a 3-act video and post it to your blog.)
It was left alone until this morning. It’s just me, but I like to think we would’ve talked sooner if I hadn’t been fighting a cold. She texted me and asked me to send her the Shepherd problem. I did, but only with the requirement that she share what she does with it.
Kim (and her co-teacher) gave the problem to each of their students and I just received the results:
- 3 out of 19 students made sense of the problem (15.8%)
- One student added 125 five times.
- One student reasoned that by the time you had 5 dogs and 125 sheep, you have to be in your fifties.
- One student divided 125 by 5.
- 6 students added 125 and 5 to get 130.
- 3 computed an operation with the two numbers incorrectly
- The other students guessed or showed no reasoning.
Now the good stuff:
- One student (an autistic child) shared his reasoning about the problem with his classmates:
“The shepherd has no-o-o-othing (said as a sheep might say it) to do with the sheep and the dogs.”
- Both teachers lost it!
Take aways from this:
- It’s best that we start teaching math content through problem solving early and consistently K-12 and beyond.
- Making sense of mathematics needs to be a priority for all students. (SMP 1)
- All students bring something of value to a classroom.
- Stories like the student who shared his reasoning sometimes get us through days that are not so much like this.
Below, you will find some of the students’ reasoning.
Thank you for sharing! I think my favorite response that you showed is the kid who wrote all the computations (division, multiplication, addition, subtraction) with 5 and 125. He/she crossed out all of them except for the division…makes me wonder if he/she wrote them down, computed in their mind, and then thought which answer was reasonable. Because, you know that in any math problem you HAVE to do one of those operations, so try them all. 🙂
Thank you for your comments. You bring up a good point about how students think about solving problems. Division does give the most “reasonable” answer as far as he age of a shepherd goes. As you know, thinking about how even that answer fits this context is really the big issue here. Thanks again! More to come.