Today's class was a very humbling experience. One of the math problems we explored today was actually a problem created by Liisa's mom! And to my surprise, it had me stumped. Here's the problem in case you wanted to take a stab at it:
Seems simple right? It's your typical "guess how many jelly beans are in the jar" question that you see at raffles, except you're given enough pieces of information that you should be able to come up with the right answer.
Like always, I overcomplicated math and instantly resorted to tackling this question algebraically. However, my algebra skills failed me and I didn't get the right number (my final answer was a decimal so something definitely went wrong during the process)!
When Liisa asked one of my classmates to share her answer, I was shocked and almost jealous that I hadn't thought of the question that way. My classmate had simply drawn out a jar and split it up based on the information given. She solved this entire word problem with one single diagram. I was astonished at how simple this solution was.
Here's my quick replica of her solution: (please excuse my very quick handwriting!)
I find it so interesting how I am always resorting to solving things algebraically. This is probably because I've been told my entire life that algebra is always the end goal and is more "mathematical" than diagrams. Algebra is suppose to be the most efficient way to solve problems but in this case, it wasn't!
There is such a stigma around drawing diagrams and using visual aids in math. It's permitted, but you should be able to solve it algebraically. It is perceived as "higher level thinking". The common misconception is that people who need pictures and manipulatives aren't intelligent enough to solve it with just numbers. But, it's ironic because just as Paul Alves stated at the conference on Saturday, math originated from diagrams and pictures! The numbers and variables came after. In the beginning, math was represented pictorially!
I have a tendency to over-think problems like these and I make it so much harder than it has to be. This activity definitely opened my eyes and made me realize the value in solving problems visually. I am now beginning to challenge myself to use different methods of solving problems and not always using algebra. This is especially important when I start teaching because not all of the students will be strong at solving algebraically and some students will think more visually and I need to be prepared for that. I'm so "jelly" that I don't automatically process things this way, but I think with some more intentional practice, I can train myself to exert different strategies.
Now, for your weekly math joke: Why is the obtuse triangle always upset?
.
.
.
.
.
.
.
Because it's never right.
Cheers,
The Function(al) Teacher
Comments
Post a Comment