Math Fair Reflection

A brief synopsis:

The problem Sara M & I presented was called "The Sword of Knowledge" whereby a dragon with 3 heads & 3 tails had to be slayed by cutting off all its heads & tails. Using the sword of knowledge, with 1 swipe, you could either cut off 1 head, 2 heads, 1 tail, or 2 tails. Sounds simple enough. However, there was a catch. When cutting off certain heads & tails, as a consequence, some usually grew back, depending on what chops you took (they were listed in a table). The goal was to find a way to slay the dragon by following the given rules.

The mathematics:

Hmm, I actually had to think a little bit about this one. I never knew that finding the mathematics in a math problem could be tricky! Here's what I have come up with: the mathematics in the problem had to do with number concepts and operations. Solvers had to choose whether they wanted to chop either 1 or 2 heads or 1 or 2 tails at a time. Then they had to add/subtract the number of heads/tails that were removed/grew back in its place (if any). The mathematics also required students to use logic to come up with a strategy/the knowledge to beat the dragon. For example, the only time nothing grew back after a swipe of the sword was when 2 heads were cut off. Therefore, using logic, problem solvers would realize that you need to find a way to cut off all tails and be left with an even number of heads at the end so that 2 at a time can be chopped off without anything growing back! The mathematics also involved showcasing the necessary skills to draw mathematical information from the supplied charts/tables and often required an ability to use trial and error to spot patterns and find ways to overcome problems as they faced them.

How was it received?

When it was my turn to stay by our board and present the problem, I found that classmates were very determined to find the solution to our problem. Everyone seemed to love it, and nobody walked away undefeated. Although some people found the solution right away, there were many that were finding it tricky. However, nobody gave up. They all had the urge to keep trying and it felt great to know that it was interesting enough to keep people's attention and determination even when it got tough. I have heard a couple classmates say that it was one of their favorite problems to solve, so that makes me happy! :)

If given the chance, would I do anything differently?

Realistically, probably not! I loved the problem, the way we presented it, I loved the manipulatives we made, and how everyone really seemed to genuinely enjoy it. I am happy we made the manipulatives - the heads, tails, and sword - because classmates really liked doing the chopping motions and actually seeing what heads and tails were left after each chop. I think the visual element kept interest and made the task more enjoyable and solvable for everyone - versus just writing in charts on lined paper.  

As facilitator of the problem, I:

found out just how difficult it was to NOT give hints & suggestions to struggling problem solvers. Knowing the solution made it difficult to just stand there and let classmates figure out their mistakes themselves. It took some conscience effort to stand by and not say something when the problem was so close to being solved and watching them make just one last mistake. It was especially difficult to not give in when classmates straight up asked for help/solutions. It made me aware that it will be difficult as an educator to not give into pleading eyes when future students are struggling and asking for help - but I also understand the importance that I allow them to grow and become independent, active problem solvers on their own.

When solving problems, I learned:

that as a mathematical thinker, I am very persistent. I never want to give up when a problem interests me. I never like to feel "defeated" and will try and try again until I get it right. It brought back memories of completing mathematics homework while in grade school. When I would find something difficult I would not, no matter if it took me hours of just staring at the paper, give up. I would get so frustrated and I can still hear my mom saying "that's enough Amy, just take a break and start over fresh. Sometimes you just need a change of scenery and it'll come to you". I would never listen though, and somehow, in the end, I always figured it out. I never felt that determination in a long time, and all of a sudden, when completing the problems at the math fair, there it was again.. that deep desire to solve each problem that I attempted.

What I enjoyed the most:

I enjoyed the atmosphere of the math fair the most. I loved how interactive it was. The problems were presented in such appealing ways that they invited you in. The drive to solve the presented problems was much higher than if the problems were just written on paper. The interactive environment (working with others, working with manipulatives) made for such a peaceful and fun mathematics experience - without all the unnecessary pressure that normally accompanies math classrooms.

My challenge:

as mentioned earlier, was definitely keeping quiet as facilitator of the problem. I wanted so badly to chime in and offer hints as soon as classmates came to a block - however, I think I did a pretty good job at resisting that urge. I tried my best to let them work it out, and it was fun to see the different ways that people's minds work. Everyone had a different strategy and approached the problem differently, it was neat to see.

Would I consider doing a math fair with future students?

Of course! As I already mentioned, the interactive atmosphere of the math fair is so inviting. I loved it! I think children would find a math fair much more exciting than writing out and solving problems on worksheets. I think with such a fun environment, children would learn to let go of their mathematical insecurities and just have fun with it. I would definitely recommend having one to any teacher of mathematics!