Monday 28 October 2013

Mission #3: Pieces of Eight

Misson #3 for Explore the MTBoS was to choose from a variety of collaborative websites. The possibilities were amazing, and I am hoping to find the time to go back to each and every site. The one that intrigued me the most right now, was the Collaborative Mathematics site. This intrigued me the most because Jason Ermer (@CollaboMath) (the creator of the site) had posted a comment on my blog post about my 1-100 Assignment (see the post entitled A Few of My Favourite Things) that I should show my students his Pieces of Eight Challenge. This challenged related very well to what we have been doing in class, which was looking at the 4 4s puzzle and then tackling the 1-100 Assignment.

The first thing that was really interesting was that a bunch of my students said, "Done!" I've got it!". They quickly found a solution that worked and were satisfied that the solved the "challenge".

Here is an example of student work giving me only one solution

It surprised me that for many of my students, their thinking ended with one solution. Most ignored the latter part of the challenge which asked them to think beyond one solution. It asked them to find another, and another, and then, figure out how many solutions there might be. There are many students I sent back to the drawing board.

Examples of students being asked to go back to the drawing board. Now I was getting more than one solution.
Some of my students came up with more than one solution, but once again, I asked them to continue to think about it - to look for patterns and relationships between some of the numbers they are finding that work - namely 8s, 88s, and 888s. A few of my keen students really started thinking about this. One of my students immediately got on board and was VERY motivated to exhaust all possibilities. I was very pleased with his thinking. Here is what he came up with, which we think is the final solution.

Another student kept trying. She would email me one solution then I would ask her if she could think of more and I got her thinking about looking for patterns. After a few back and forth tries, she emailed me a solution with all 14 possibilities worked out. I was so proud of her for persevering and for the excellent thinking that she showed.

Many of my other students are still working on it, and I am hopeful that they will come up with all the possible solutions.

The second thing that surpised me was that many of my students immediately asked me, "If I do this challenge, will I get any bonus marks?". You see, I showed them this challenge as an additional thinking task to try, it was not the focus of a lesson. I was shocked that my students were willing to do the challenge, but only if it counted for something. What have I (or we - the school system) done to students to make them think things are only worth doing if they are "worth" something. What about the love of learning? What about curiousity and intrigue? Are those not "worth" something? Where has the internal motivation to learn gone? It probably has something to do with the emphasis we put on grades and marks. My school is beginning go down the path of examining our assessment practices so that hopefully soon we can get rid of numerical grades. Perhaps this will make a difference. But, in the meantime, it is disheartening that many students have lost their internal drive to learn. Maybe I will just keep doing more of these challenges, and hopefully they will jump in and reignite their love of learning!


  1. Hi Carrie!

    I love reading about your students' experiences with "Pieces of Eight", as well as seeing some of their work. I especially like how you kept prompting them to explore the problem, even when they thought they were "finished". :)

    Like you, I also wonder about how numerical grades impact a student's enjoyment of learning. I agree with continuing to present problem solving experiences as a means of engaging them in fun, challenging, creative mathematics -- whether or not it is tied directly to "a grade".

    Maybe some other videos over at Collaborative Mathematics can help in that regard? For instance, "Challenge 03: Finger Counting" has been a hit with other students, and might be with yours, too!

    Thanks again to you and your students for participating! :)

    1. I will definitely check out some more of your challenges. I was really pleased with the impact that this had on some students. If I do it more often, I think more students will "get on board" and do challenges for the fun of it!

  2. Thanks for leading me to such a great resource.

    It is too bad that students are so grade focused. I've started doing more formative assessment in my classes, and I think this helps remove some of the grade stigma. Students have realized that if they do the work well, they will get useful feedback, which can help them improve and be prepared for when there is a grade.

  3. I agree. I am also doing more formative assessment. At the end of the day though, the students know they are going to get a percent grade. My school is starting to look at that way of marking and we are hoping to make some significant changes to this in the coming months.

  4. Pieces of 8 sounds really cool, and I think you did awesomely in motivating your students to rethink their answers again and again - I love problems that go on like that; with different solutions or routes there. I hope you find loads more from the sites in collaboration post!

    All the best