Thursday, November 5, 2015

Yet again I am joining with Teach Second Grade team. The topic of this week was Squirrels and Acorns. My first reaction was to pass, but then I remembered an interesting problem that my daughter brought home from school. So here is my rave and rant about “squirreled away” problem of the month.Math for Fast Finishers: Squirrels and Acorns

A Squirrel Problem of the Month

I’ve seen many debates online on whether mathematically advanced children should go deeper into their math curriculum or further ahead. Our school is firmly in “go deeper” camp. It uses “problem of the month” approach to challenge fast finishers, and October problem of the month was Squirreling It Away. The goals for Problem of the Month program are to promote problem-solving and mathematical reasoning skills and apply these skills to “non-routine” problems. Problem of the months are available for free from Inside Mathematics website. Each problem has 5 levels, and Inside Mathematics has a convenient explanation on when an average math student should be able to tackle each level of the problem. So, if we look at the squirrel problem, here is what average second grader should be able to figure out reasonably easily:
Level A: Austin had a bag of 17 acorns. Eight squirrels came up to him. He gave each squirrel an acorn. Then five more squirrels came up to him and he gave away one acorn to each of them. How many more squirrels could he still feed? Show how you figured it out?
Here is a level that would could be a good challenge for advanced second graders and is marked as “appropriately difficult” for average fourth graders.
Level B: Austin likes to watch squirrels find and store acorns for the winter. Brown Squirrels can carry two acorns at a time. Gray Squirrels can carry three acorns at a time and Black Squirrels can carry five acorns at a time. There is a pile of 24 acorns. How many trips would a Brown Squirrel need to make to store all of the acorns in the pile? How many trips would a Gray Squirrel need to make to store all of the acorns in the pile? How many trips would a Black Squirrel need to make to store all of the acorns in the pile? If all three squirrels worked together to store the acorns how many trips would the squirrels need to make to store all of the acorns? Explain your solution.

So What’s the Problem with This Problem?

So here is how the problem of the month was implemented in my daughter’s school. The gifted 4th graders (there is a cluster of 4 of them in my daughter’s class) were given the full PDF with 5 levels and told to work together and show their work. Nobody has mentioned to them that level C is meant for 6th grade, level D is meant for 8th grade, and level E is high school material. Smarty eventually has mentioned to me that they are doing this problem of the month and it’s crazy hard, and I asked her to bring it home to take a look. They were stuck on level D:
The squirrels are rather smart. They realize that they can carry less than their maximum loads. How many different ways could the squirrels divide up the 24 acorns? Explain your solution.
Perhaps a math genius savant could figure out this problem without any help, but Smarty’s gifted cluster was lost. When I looked at an attempted solution from my daughter, I realized that she considered, for example, {1,1,1} data set to be a valid answer, because the group did not understand correctly what “divide up” means. Without any sort of coaching on problem-solving strategies (e.g. reducing the number of acorns and looking at the emerging patterns), this problem of the month simply became an exercise in “brute force approach” and busy work. One of the gifted students in her class specifically detests busy work and doesn’t deal well with frustration, so he started to act out and fool around instead of trying to figure out the solution. Not surprisingly, the group quickly became dysfunctional and the teacher pulled them back into regular tasks and reprimanded them for not turning in their work. In other words, exercise in problem solving became instead an exercise in frustration and perhaps even damaged these kids’ confidence in their abilities as problem solvers.

Could It Be Done Better?

I don’t want to blame the teacher. She has an almost impossible job of trying to get kids with significant learning delays to be where they need to be. She is also doing a terrific jobs integrating social studies into daily curriculum, and it’s the first year my daughter is enjoying social studies. I also give her points for at least trying to provide differentiated instruction in math. But I don’t think that she leverages our school incredible strength – a hard core of dedicated parent volunteers. Last year our third grade teacher had volunteers twice a week during math time. The class was divided into 4 groups of students with different needs for math instruction, and a teacher was working with one group at a time while volunteers supervised two other groups working independently and one group working on iPads. If we had the same format this year, then perhaps the teacher would actually be able to scaffold students in their problem solving techniques instead of leaving them to struggle with the problem designed for several grades higher completely on their own. As a minimum, I think she should have told them that this problem was meant to be for 8th graders. When I told my daughter, she was suddenly freshly inspired to work on it trying to prove that she can be as smart as an 8th grader. Alas, she didn’t want to listen to my hints, so off to brute force land she went. Let’s see if she returns with a solution!

Post-Publishing Thoughts

There was an interesting article shared in comments on this post about Productive Failure that made me look at the situation differently and think that perhaps the approach of not knowing how to solve the problem and not knowing the difficulty level is, in fact, good teaching approach for gifted students. I am still missing the eventual scaffolding to solution. Now Smarty got this problem as her math "independent study" work (my husband took her out of school for a week to visit family in Florida). I am hoping that my husband can nudge her to a solution - after all, he figured it out in his head in about 10 minutes when I explained him the challenge one morning.

Your Turn
Problem of the month challenges for mathematically advanced students

How would you challenge fast finishers in the classroom?

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2 comments:

JL said...

Have you read this article?
http://qz.com/535443/the-best-way-to-understand-math-is-learning-how-to-fail-productively/

If you want more scaffolding in problem-solving, look into Becoming a Problem Solving Genius by Zaccaro.

Whenever I wanted to motivate my students, I used to tell them that the problem was "college math" and amazingly, their enthusiasm and motivation increased. They really wanted to prove to themselves they could do it.

Ticia said...

Snicker, brute force land. Math is a hard one for me to figure out how to differentiate. I just switched Princess to a different math curriculum a few levels back (to bolster confidence), and so I'm working through how to best differentiate with my kids.