Tag Archives: Mathematics

Innovative Thinking

Math has always been easy for me. Heck, I was top of my class in every grade except Grade 12. I had a feisty Calculus teacher that didn’t quite mesh with me. She was incredibly nice, intelligent and very very passionate, but she wasn’t very patient. And if there’s anything I’ve learned so far in my teaching program, it’s how patient we, as educators, HAVE to be. In any case, the traditional approach worked for me. I thrived in this setting. I could work on my own, or work collaboratively but all in all, math wasn’t very hard for me. I never dreaded the class, I never had a problem with learning new concepts, and please, like as if I had to study for my exams. Essentially, I’ve never had to think about the way I learned Math until now.

Like my previous post, the teaching program is all about innovation. Finding ways to engage, to hook, to make things fun but also balance it with deep understanding of the concept, of Math. One reason why this is extremely, extremely difficult for me to accomplish is the fact that I don’t even have a deep understanding of Math. My math teacher in my program is excellent. He’s passionate, he’s animated, he’s so incredibly intelligent. But the one thing that stands out when you meet him is how deep his understanding of math is. If his different math shirts don’t tell you right away, once he gets into a concept, his ability to explain it in 600 different ways, beginning with 200 different angles, using 150 different tools, makes it contact clear. M knows his stuff inside out, right side up. And as inspiring as this is, it makes me insecure and intimidated. How will I ever be able to find ways to explain different concepts when I only know one way. In fact, there are times when my peers have explained their understanding in an extremely different way and I’m left picking my jaw off the ground. Say wwhhhattt? Again, this is not a new idea. I’ve written before about my insecurities in regards to innovative thinking. However, as part of our assignment in which we look at blogs to help find inspiration or reflection, I found one that helped me with my anxiety.

http://ispeakmath.wordpress.com/2012/09/21/algebra-vocabulary-with-dry-erase-necklaces/

The blogger for this post essentially made up an activity to help her student better understand algebraic terms. She made dry-erase necklaces and made a little game for her students to not only learn the terms but be invested in learning the terms. Her blog spot is just a reflection of her own practices. Up to this point, I had somehow made myself believe that I needed to figure this innovative stuff on my own. I needed to come up with activities, find ways myself. I needed to be smarter, braver, more creative. I had not realized how much I had put on my own shoulders. I failed to realize that there were many many teachers that became innovative through the internet world. The blogger mentioned, adopted most of her activities from other educators. There were times where she was also lost. I guess that is what makes a teacher. Not the ability have light bulb moments and have all things miraculously come to place. But instead, finding bulbs that already lit and figuring how to use them in your class.

She found activities that were successful and adapted them for her own class. She herself was lost. It’s something I have to wrap my head around and start to accept. I’m not somehow weak just because I’m lost. It’s still very hard to accept help, or inspiration when up to this point, when it came to my education process, I never had to. I am relieved to know that I am allowed, or that I’m finally allowing myself, to seek inspiration, creatively, and innovation elsewhere. Perhaps along the way, I myself, will come across my own brand of innovation.

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Blogger space: Replicating.

As part of an ongoing assignment, I have to visit an assigned blogger’s website and search through his/her archives until I find something that calls to me organically. For this week, it was this website: http://christopherdanielson.wordpress.com/

The post that instantly called to me was titled: “How many tens?”

Here is one from the archives.

Nearly a year ago, Griffin was seven years old and I was doing some thinking about the number course I teach for future elementary teachers. I decided to see how Griffin was thinking about place value.

Me: How many tens are in 32?

Griffin (seven years old at the time): Three, and then two leftover.

Me: How do you know that?

G: Thirty—that’s three tens, and then the zero means no ones.

Me: How many tens in 268?

G: [long thoughtful pause] Twenty-six, and then there would be 8 left over.

Me: What would you say to someone who thought there were six tens in 268?

G: I’d say there are 20 more than that.

That’s my boy.

When I finished reading this post, for some reason I couldn’t move past it. I lingered on the last sentence and then ended up re-reading the whole thing again. And then re-reading it again. I couldn’t articulate what exactly I liked or disliked about it, only that it made me feel curious, puzzled even. I needed to leave the assignment for now because I wasn’t getting anywhere with it and go for dinner with my family. At dinner, I decided to ask the same questions to my niece. H is eight years old, hates homework but LOVES math. Granted, she hates actually doing math homework but loves to problem solve and verbally solve questions throughout the day. She enjoys asking me multiplication questions and is always willing to help solve math questions for me.

Me: How many tens are in 32?

H: Three tens.

Me: How do you know that?

H: Thirty—that’s three tens.

Me: How many tens in 268?

H: 6.

Me: You sure?

H: There’s only 6 in the tens’ place so only 6 tens.

Me: What does the 2 in 268 represent?

H: 2 hundred.

Me: What would you say to someone who thought there were six tens in 268?

H: I’d say they are right.

I would be lying if I said I wasn’t disappointed. I was down right concern. I then explained to her why the answer wasn’t 6. I actually had to take out a paper and pen and draw it for her so she could understand. In the end she did but it made me wonder if any of her other classmates would have correctly answered. After looking at her math homework that were assigned, it truly made me aware of how anal teachers have become in regards to getting the correct answer. Her classmates and her have not been taught what it means to have the 6 in the ten’ place only that it is. How many tens are there? In her eyes, I can see that there is no other answer other than 6 because with the way she’s been taught, how can there be another answer?

I suppose what the post brought to light for me is how neglecting the little details just because I may want a specific answer or because it appears clear to me can end up completely misleading the teaching. In this case, the need for the students to understand place value ended up becoming more important than them understanding the concept of the number being in the tens’ place.

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